combining disdrometer, microscopic photography, and cloud ...€¦ · types and their fall...
TRANSCRIPT
1
Combining Disdrometer Microscopic Photography and Cloud 1
Radar to Study Distributions of Hydrometeor Types Size and Fall 2
Velocity3
Xingcan Jia12 Yangang Liu2 Deping Ding3 Xincheng Ma3 Yichen Chen3 Bi 4
Kai3 Ping Tian3 Chunsong Lu4 Jiannong Quan15
1 Institute of Urban Meteorology Chinese Meteorological Administration Beijing 1000896
China 7
2 Brookhaven National Laboratory Upton NY 11973 US8
3 Beijing Weather Modification Office Beijing 100089 China9
4 Nanjing University of Information Science amp Technology Nanjing 210044 China10
11
Corresponding authors 12
Xingcan Jia xcjiaiumcn 13
Yangang Liu lygbnlgov 14
Deping Ding zytddpvipsinacom 15
Chunsong Lu clunuisteducn 16
17
Abstract Addressing solid precipitation poses additional challenges compared to warm 18
rain due to complex hydrometeor shapes involved including the dependence of fall 19
velocity on hydrometeor sizes hydrometeor size distributions and hydrometeor 20
classification This study is an extension of our previous work (Niu et al 2010) to 21
address these challenges by combining measurements from a PARSIVEL disdrometer 22
microscope photography and millimeter wavelength cloud radar The combined 23
BNL-211738-2019-JAAM
2
measurements are analyzed to classify the precipitation hydrometeor types examine 24
the dependence of fall velocity on hydrometeor sizes for different hydrometeor types 25
and determine the best distributions to describe the hydrometeor size distributions of 26
different hydrometeor types The results show (1) Hydrometeors can be classified to 27
four main types of raindrop graupel snowflake and mixed-phase according to the 28
dependence of terminal velocity on particle sizes corresponding microscope photos 29
and cloud radar observations (2) There are significant scatters in fall velocity for a given 30
hydrometer size velocities and the fall velocity spread for the solid hydrometeors 31
appear wider than that for raindrops across hydrometeor sizes with that for the 32
mixed-phase precipitation being largest suggesting that the effects of hydrometeor 33
shape on hydrometeor fall velocities (3) Hydrometeor size distributions for the four 34
types can all be well described by the Gamma or Weibull distribution Weibull (Gamma) 35
distribution performs better when skewness is less (larger) than 2 36
Key words hydrometeor fall velocity hydrometeor size distribution PARSIVEL 37
disdrometer microscope photography cloud radar 38
39
1 Introduction 40
Solid precipitation is important for weather and climate forecasting models since 41
predictions of precipitation amount location and duration depend greatly on how 42
precipitation particles are parameterized The last few decades have witnessed great 43
progress in both areas of parameterizing cold precipitation processes (Reisner et al 44
1998 Field et al 2007 Lin et al 2010 Agosta et al 2015) remote sensing (Tokay and 45
3
Short 1996 Souverijns et al 2017) and ground measurement (Chen et al 2011 46
Nurzyńska et al 2012 Ishizaka et al 2013 Huang et al 2017) of solid hydrometeors 47
Despite the great development solid precipitation measurement and parameterization 48
still suffer from large uncertainties and much work remains to be done Detailed solid 49
hydrometeor observations including size distribution fall velocity and shape of 50
hydrometeors are needed to improve microphysical parameterization in numerical 51
models and remote sensing 52
Hydrometeors properties (eg size concentration geometric shape and fall 53
velocity) are essential for further improving parameterizations of precipitation 54
processes and remote sensing (especially of polarized radar) In particular recent 55
developments in disdrometer and remote sensing techniques permit retrievals of more 56
hydrometeor size distribution (HSD) parameters and their vertical profiles over large 57
areas (Loumlffler-Mang and Blahak 2001 Matrosov 2007 Kneifel et al 2015) and 58
enhance our ability to monitor and investigate solid hydrometeor events and 59
microphysics At the same time more accurate assumptions regarding the spectral 60
shape of HSDs for different hydrometer types are needed which vary spatially and 61
temporally (Kikuchi et al 2013) Unfortunately our understanding of the hydrometeors 62
and direct measurements of solid precipitation is far from complete and more analyses 63
of in situ measurements are needed (Souverijns et al 2017) 64
Fall velocity is equally important and closely related to the HSD measurements 65
radar retrievals and parameterizations Fall velocity measurements of solid 66
hydrometeors can be traced to an empirical study by Locatelli and Hobbs (1974) which 67
4
is still utilized in microphysical parameterizations Later studies include those based on 68
fluid dynamics (Boumlhm 1989 Mitchell 1996 Khvorostyanov 2005 Heymsfield and 69
Westbrook 2010 Kubicek and Wang 2012) and using automated ground-based 70
disdrometers (Barthazy and Schefold 2006 Yuter et al 2006 Ishizaka et al 2013 Chen 71
et al 2011) 72
Most of these studies assume that the surrounding air is still rather than a 73
turbulent environment as in actual precipitating clouds Yuter et al (2006) obtained size 74
and fall velocity distributions within coexisting rain and wet snow (sleet) by using a 75
disdrometer but insufficient details of quantified results were provided The influence 76
of riming particle shape temperature and turbulence on the fallspeed of solid 77
precipitation in disdrometer measurements were further discussed (Barthazy and 78
Schefold 2006 Garrett and Yuter 2014 Geresdi et al 2014) However many factors 79
have influences on solid hydrometeor fall velocity and the complex effects have not 80
been yet adequately investigated 81
In a previous study (Niu et al 2010) we discussed the air density and other factors 82
(ie turbulence organized air motions break-up and measurement errors) that 83
potentially influence on distributions of raindrop sizes and fall velocities and called 84
attention to the turbulence induced the large velocity spread at given raindrop sizes 85
This work is a further extension of Niu et al (2010) to analyze measurements of size 86
and fall velocity distributions of solid hydrometeors collected during a recent field 87
experiment campaign conducted northeast of Beijing China to simultaneously 88
measure HSDs and fall velocities with a PARSIVEL disdrometer (see Section 2 for details) 89
5
This paper has two specific objectives (1) to distinguish and quantify hydrometeor 90
types and their fall velocities by combining disdrometer microscopic photography and 91
cloud radar observation (2) to characterize and compare the spectral shapes of HSDs 92
from different precipitation types 93
The rest of the paper is organized as follows Section 2 describes the experiment and 94
data Section 3 classifies hydrometeors and analyzes the size and fall velocity 95
distributions Section 4 examines the characters of HSDs and evaluates the distribution 96
function for describing HSDs The major findings are summarized in Section 5 97
2 Description of Experiment and Data 98
The observation site was on Haituo Mountain at a height of 1310 m located in 99
northwest of Beijing (40deg35primeN 115deg50primeE) China (Fig 1) The site is in the semiarid 100
temperate monsoon climate regime with mean winter precipitation amount for each 101
event is about 080 mm (2014-2015) (Ma et al 2017) All the observed events are stratiform 102
precipitation classified by the surface cloud radar China Weather Radar (Doppler radar) 103
and manual observations The entire radar reflectivity maximums are lower than 30 dBZ 104
which is chosen as the threshold reflectivity of convective precipitation (Zhang and Du 105
2000) 106
HSDs were measured with a PARSIVEL disdrometer and the measurement methods 107
are the same as employed in Niu et al (2010) Loumlffler-Mang and Joss (2000) and Tokay 108
et al (2014) provided detailed description of the PARSIVEL disdrometer The instrument 109
measures the maximum diameter of one-dimensional projection of the particle which is 110
smaller than or equal to the actual maximum diameter Snow particles are often not 111
6
horizontally symmetric and thus particle sizes for snow may underestimate actual maximum 112
particle diameter Battaglia et al (2010) pointed out that PARSIVELrsquos fall velocity 113
measurement may not be accurate for snowflakes due to the internally assumed relationship 114
between horizontal and vertical snow particle dimensions The uncertainty originates from 115
the shape-related factor which tends to depart more with increasing snowflake sizes and 116
can produce large errors When averaging over a large number of snowflakes the correction 117
factor is size dependent with a systematic tendency to underestimate the fall speed (but 118
never exceeding 20) The maximum error 20 of the empirical terminal velocities for 119
graupel and snowflake is used to estimate the instrument caused possible velocities such 120
as the dash lines in igure 2b In addition graupel is almost spherical hydrometeor and the 121
instrument error could not reach 20 The individual HSD sample interval was 10 seconds 122
The following criteria are used in choosing data for analysis (1) Particles smaller 123
than 025 mm are discarded (2) the total particle number of a HSD is over 10 counts 124
(every 10-sec sample) (Niu et al 2010) (3) precipitation lasted more than 30 minutes 125
are chosen (4) solid hydrometeor density is corrected with the equation ρs =126
017Dminus1 for solid hydrometeors (Boudala et al 2014) (5) Following Chen et al (2017) 127
raindrops outside +60 of the empirical terminal velocity of raindrop (Table 3) and -60 128
of empirical terminal velocity of densely rimed dendrites were excluded in the analysis 129
to minimize the effects of ldquomargin fallersrdquo winds and splashing Hydrometeors were 130
also collected with Formvar slides (76 cm long and 26 cm wide) which are exposed 131
outside for 5s to capture the hydrometeors with a sampling interval of 5 minutes The 132
Formvar samples were examined and photographed with a microscope-camera system 133
7
following the method described by Schaefer (1956) The two-dimensional photo of 134
hydrometeors allows a careful determination of the hydrometeor shape and size The 135
Formvar data were used to distinguish dominant hydrometeor types eg raindrop 136
graupel or snowflake The hydrometeor type with a percentage of occurrence gt60 is 137
used to represent the solid precipitation type for convenience of analysis 138
A Ka-band millimeter wavelength cloud radar (wavelength is 8 mm) was used to 139
probe the vertical structure of clouds by vertical scanning from 11202016 which can 140
be used to determine cloud properties at 1 min temporal and 30 m vertical resolution 141
A total of 11098 HSD samples were collected from 12 precipitation events (Table 1) 142
Four representative hydrometeor types from the precipitation events are identified 143
raindrop graupel snowflake and mixed-phase precipitation The identification of the 144
hydrometeor types is mainly based on hydrometeors velocity observations and Formvar 145
images which will be detailed in Section 4 Mixed-phased precipitation contains 146
raindrops graupels and snowflakes simultaneously and none is dominant over another 147
The duration sample number precipitation rate and dominant type of hydrometeor 148
are shown in Table 1 The precipitation rate is calculated from HSD using the method 149
presented in Boudala et al (2014) 150
3 Hydrometeor Classification and Size and Fall Velocity 151
Distributions 152
a General Feature 153
Fig 2 illustrates the observed mean number concentration as a function of the 154
maximum dimension and the fall velocity for the four types of hydrometeors 155
8
respectively Also shown as a reference are the seven solid curves representing 156
different types of hydrometeor terminal velocities obtained from the laboratory 157
measurements calibrated by coefficient 50
0
since the site altitude is 1310 m 158
average pressure is 868 hpa and the average temperature is -5 ordmC (Niu et al2010) 159
(equations are shown in Table 3) Here ρ is the actual air density and ρ0 is the 160
standard atmospheric density The updrafts downdrafts and turbulence often 161
accompany falling hydrometeors inducing deviations in the velocity and trajectory of 162
falling hydrometeors from those in still air (Donnadieu 1980) Hence in this field 163
observation fall velocities of hydrometeors distribute along the terminal velocity curves 164
with large spread for each given size Similar features have been previously reported in 165
some situ measurements of raindrop fall velocities (Niu et al 2010 Rasmussen et al 166
2012) 167
In the previous study we discussed the air density and potential influencing 168
factors (eg turbulence organized air motions break-up and measurement errors) for 169
raindrop (Niu et al 2010) For precipitation in winter the hydrometeor shape is vitally 170
important for fall velocity The hydrometeor shape influence on fall velocities physical 171
mechanisms and instrument error underlying the large spread in the measured fall 172
velocities of different types are discussed in detail in the next two sub-sections 173
b Effect of Hydrometeor Type on Fall Velocity 174
In Fig 2a the hydrometeor fall velocities agree with the typical raindrop terminal 175
velocity curve which is obviously larger than the terminal velocities of graupel and 176
9
snowflake at given maximum diameters From the fall velocity distribution we can infer 177
that these hydrometeors are mainly raindrops The microscope photos obtained on the 178
ground confirm this However unlike the raindrop size and velocity distribution in 179
summer in Figure 8a of Niu et al (2010) there are some small size hydrometeors 180
(05~35mm) at very low speeds (05~2 ms) distributing among the terminal velocity 181
curves for graupel and snowflake This result implies that beside liquid raindrops 182
(including small raindrops or droplets from drizzle) some small snowflakes also exist in 183
the measurement The microscope photos also support the finding that although 184
raindrops are dominant some small plane- and column- shaped snowflakes co-exist 185
Fig 2b shows the joint hydrometeor size and fall velocity distribution during the 186
graupel event The hydrometeors are mainly symmetrically distributed around the ideal 187
terminal velocity of graupel (Locatelli and Hobbs 1974) supported by the photo-based 188
hydrometeor classification On the other hand it is found that certain small droplets 189
with the maximum dimensions among 03 to 10 mm are distributed around the liquid 190
raindrop curve suggesting that there are some raindrops and droplets coexisting in the 191
graupel dominated precipitation It is recognized that graupels grow by snow crystals 192
collecting cloud droplets and small raindrops (Pruppacher and Klett 1998) high cloud 193
top more liquid water content and presence of small raindrops (as shown in 194
microscope photography) provide favorable conditions for graupel The microscope 195
photos also display that graupelsrsquo surfaces are lumpy because of riming super cooled 196
drops during growing 197
The fall velocities of hydrometeors in Fig 2c are much smaller than the terminal 198
10
velocities of raindrop and graupel but are close to the terminal velocity curves of snow 199
of hexagonal densely rimed dendrites aggregates of dendrites Synthesizing the size 200
data the hydrometeors can be inferred as snowflakes which are further confirmed by 201
surface microscope photos From the surface observation we found many 202
rimedunrimed or aggregated dendrites or hexagonal snowflakes Although riming and 203
aggregation microphysical processes have some influence on terminal velocity 204
(Barthazy and Schefold 2006 Garrett and Yuter 2014 Heymsfield and Westbrook 205
2010) but the influences are too small to distinguish only from observed fall velocity 206
since it is a combined result of many factors When maximum dimensions are among 207
03 to 10 mm there are some small hydrometeors with fall velocities larger than 208
snowflakes which maybe graupels raindrops and droplets 209
Fig 2d is the hydrometeor size and fall velocity distribution during a mixed-phased 210
precipitation The hydrometeor fall velocities exhibit the largest spread for example 211
the fall velocities for hydrometeors with maximum dimension equaling to 3 mm 212
change from 05 to 5 ms and do not distribute along any of the ideal terminal velocity 213
curves This result suggests that different hydrometeor types might coexist during the 214
same sampling time To substantiate supercooled raindrops graupels and different 215
kinds of snowflakes are observed from the surface microscope simultaneously Similar 216
changes in particle size and fall velocity distribution documented by the disdrometer as 217
the storm transitions from rain to mixed-phase to snow were found at Marshall Field 218
site (Rasmussen et al 2012) 219
11
c Other Influencing Factors 220
The different dependence on particle size of terminal velocities for different types 221
of hydrometeors can explain some systematic distribution of the PARSIVEL-measured 222
fall velocities but the large spreads in the measurement of the instant particle fall 223
velocities await further inspection 224
According to our previous work the fall velocity (V) of a hydrometeor measured by 225
the PARSIVEL can be regarded as a combination of the terminal velocity in still air (Vt) 226
and a component Vrsquo that results from all other potential influencing factors eg type 227
turbulence organized air motions break-up and measurement errors (Niu et al 228
2010) 229
119881 = 119881119905 + 119881 prime (1) 230
The large spread of the measurements at both sides of the terminal velocity curves 231
shown in figure 2 seems compatible with the notion of nearly random collections of 232
downdraft and updraft A wider spread for fall velocities implies a wider range of 233
variation in vertical motions when hydrometeors are liquid raindrops (Niu et al 2010) 234
Solid nonspherical hydrometeors are much more complex than liquid drops and the 235
large spread of velocities may be caused by several other factors First different types 236
of hydrometeors (columns bullets plates lump graupels and hexagonal snowflakes et 237
al) have different fall speeds It is long recognized that microphysical processes in cold 238
precipitation are more complex and consequently generate more types of solid 239
hydrometeors comparing to the generation of raindrops The averaged concentration 240
distributions of large number of samples shown in Figure 2 also represents the possible 241
12
distributions of hydrometeors If there is only one kind particle the high concentration 242
would along its ideal terminal velocity very well just like the raindrop possible 243
distribution (Niu et al 2010) The concentration of mixed precipitation in Fig 2d does 244
not along any singe ideal terminal velocity further improved there are more than one 245
kind of hydrometers Coexistence of different types of hydrometeors induces larger 246
spread of fall velocities Second different degrees of riming and aggregating may affect 247
the results Densely rimed particles fall faster than unrimed particles with the same 248
maximum dimension aggregated snowflakes generally fall faster than their component 249
crystals (Barthazy and Schefold 2006 Garrett and Yuter 2014 Locatelli and Hobbs 250
1974) Third solid hydrometeors more likely occur breakup aggregation collision and 251
coalescence processes because of the large range of speeds According to prior 252
research of raindrop breakup and coalescence would lead to the ldquohigher-than-terminal 253
velocityrdquo fall velocity for small drops but ldquolower-than-terminal velocityrdquo fall velocity for 254
large drops (Niu et al 2010 Montero-Martiacutenez et al 2009 Larsen et al 2014) Similar 255
results are expected for the fall velocity of solid hydrometeors Last but not the least 256
the disdrometer may suffer from instrumental errors due to the internally assumed 257
relationship between horizontal and vertical particle dimensions likely resulting in a 258
wider spreads of fall velocities for the graupel and snowflakes as compared to the 259
raindrop counterpart as discussed in Section 2 Although the instrument error is an 260
important factor that should be considered in velocity spread as shown in Fig2b the 261
instrument error could not cause that large velocity spread The possible distributions 262
of fall velocities are the combine effects of physical and instrument principle 263
13
Further support for the possible instrumental uncertainty is from the cloud radar 264
observations Fig 3 shows the cloud reflectivity and linear depolarization ratio (LDR) in 265
lower level (less than 08 km) for the graupel snowflake and mixed-phased 266
precipitations respectively The LDR is a valuable observable in identifying the 267
hydrometeor types (Oue et al 2015) As shown in Fig 3a the cloud top height of 268
graupel precipitation was up to 7km during 1900 to 2050 Beijng Time (BT) which was 269
highest among the three events The high cloud top implies stronger updraft and 270
turbulence which further induces a larger fall velocity spread The LDR value was the 271
smallest among the three events indicating that the hydrometeors were close to 272
spherical consistent to the surface observations The cloud top height of snowflake 273
precipitation was up to 35 km (Fig 3c) which was the lowest among the three types of 274
precipitations implying weakest updraft and turbulence Notably although the 275
snowflake types are more complex than those of graupels the velocity spread was not 276
as large as that of the graupel type likely because of the weakest updraft and 277
turbulence The LDR was relatively larger consistent with the surface snowflake 278
observations (Fig 3d) The cloud top height of mixed-phase precipitation was up to 45 279
km (Fig 3e) and the LDR in lower level was largest among the three types of 280
precipitations owing to coexistence of raindrops graupels and snowflakes (Fig 3f) 281
4 Hydrometeor Size Distributions 282
a Comparison of HSDs between Different Types 283
There were four representative types of precipitations during this field experiment 284
providing us a unique opportunity to examine the HSD differences between the four 285
14
types of hydrometeors The sample numbers mean maximum dimensions and number 286
concentrations for each kind of HSDs are given in Table 2 Figure 4 is the averaged 287
distribution of all measured HSDs of 4 kinds As shown in Figure 4 on average the 288
mixed-phased precipitation tends to have most small size hydrometeors with D lt 15 289
mm while snowflake precipitation has the least small hydrometeors among the four 290
types The snowflake precipitation has more large size hydrometeors ie 3 mm lt D lt 11 291
mm Graupel size distribution tends to have two peeks around 13 mm and 26 mm The 292
mean maximum dimension is largest for snowflake (126 mm) and smallest for the 293
mixed HSD due to many small particles Similar results were found in precipitation 294
occurring in the Cascade and Rocky Mountains (Yuter et al 2006) The PARSIVEL 295
disdrometer doesnrsquot provide reliable data for small drops lower than 05 mm and tends to 296
underestimate small drops so the relatively low concentrations of small drops likely resulted 297
from the instrumentrsquos shortcomings (Tokay et al 2013 and Chen et al 2017) 298
b Evaluation of Distribution Functions for Describing HSDs 299
Over the last few decades great efforts have been devoted to finding the 300
appropriate analytical functions for describing the HSD because of its wide applications 301
in many areas including remote sensing and parameterization of precipitation (Chen et 302
al 2017) The two distribution functions mostly used up to now are the Lognormal 303
(Feingold and Levin 1986 Rosenfeld and Ulbrich 2003) and the Gamma (Ulbrich 1983) 304
distributions The Gamma distribution has been proposed as a first order generalization 305
of the Exponential distribution when μ equals 0 (Table 4) Weibull distribution is 306
another function used to describe size distributions of raindrops and cloud droplets (Liu 307
15
and Liu 1994 Liu et al 1995) Nevertheless the question as to which functions are 308
more adequate to describe HSDs of solid hydrometeors have been rarely investigated 309
systematically and quantitatively Thus the objective of this section is to examine the 310
most adequate distribution function used to describe HSDs 311
Considering size distributions of raindrops cloud droplets and aerosol particles are 312
the end results of many (stochastic) complex processes Liu (1992 1993 1994 and 313
1995) proposed a statistical method based on the relationships between the skewness 314
(S) and kurtosis (K) derived from an ensemble of particle size distribution 315
measurements and from those commonly used size distribution functions Cugerone 316
and Michele (2017) also used a similar approach based on the S-K relationships to study 317
raindrop size distributions Unlike the conventional curve-fitting of individual size 318
distributions this approach applies to an ensemble of size distribution measurements 319
and identifies the most appropriate statistical distribution pattern Here we apply this 320
approach to investigate if the statistical pattern of the HSDs of four precipitation types 321
follows the Exponential Gaussian Gamma Weibull and Lognormal distributions (Table 322
4) and if there are any pattern differences between them Briefly S and K of a HSD are 323
calculated from the corresponding HSD with the following two equations 324
23
2
3
t
iii
t
iii
dDN
)(Dn)D(D
dDN
)(Dn)D(D
S
minus
minus
=
(2) 325
32
2
4
minus
minus
minus
=
dDN
)(Dn)D(D
dDN
)(Dn)D(D
K
t
iii
t
iii
(3) 326
16
where Di is the central diameter of the i-th bin ni is the number concentration of the 327
i-th bin and Nt is total number concentration Note that each individual HSD can be 328
used to obtain a pair of S and K which is shown as a dot in Figure 5 Also noteworthy is 329
that the SndashK relationships for the families of Gamma Weibull and Lognormal are 330
described by known analytical functions (Liu 1993 1994 and 1995 Cugerone and 331
Michele 2017) represented by theoretical curves in Figure 5 The Exponential and 332
Gaussian distributions are represented by single points on the S-K diagram (S=2 and K=6 333
for Exponential) and (S=0 and K=0 for Gaussian) respectively Thus by comparing the 334
measured S and K values (points) with the known theoretical curves one can determine 335
the most proper function used to describe HSDs 336
Figure 5 shows the scatter plots of observed SndashK pairs calculated from the HSD 337
measurements for raindrop graupel snowflake mixed-phase precipitations Also 338
shown as comparison are the theoretical curves corresponding to the analytical HSD 339
functions A few points are evident First despite some occasional departures most of 340
the points fall near the theoretical lines of Gamma and Weibull distributions suggesting 341
that the HSD patterns for all the four types of precipitations well follow the Gamma and 342
Weibull distributions statistically Second HSDs of raindrops and mixed hydrometeors 343
are better described by Gamma and Weibull distribution than graupels and snowflakes 344
Third the S and K do not cluster around points (2 6) and (0 0) suggesting that the 345
Gaussian and Exponential distribution are not appropriate for describing HSDs 346
especially Gaussian distribution 347
To further evaluate the overall performance of the different distribution functions 348
17
we employ the widely used technique of Taylor diagram (Taylor 2001) and ldquoRelative 349
Euclidean Distancerdquo (RED) (Wu et al 2012) as a supplement to the Taylor diagram The 350
Taylor diagram has been widely used to visualize the statistical differences between 351
model results and observations in evaluation of model performance against 352
measurements or other benchmarks (IPCC 2001) Correlation coefficient (r) standard 353
deviation (σ) and ldquocentered root-mean-square errorrdquo (RMSE hereafter) are used in 354
the Taylor diagram The RED is introduced to add the bias as well in a dimensionless 355
framework that allows for comparison between different physical quantities with 356
different units In this study we consider the S and K values derived from the 357
distribution functions as model results and evaluate them against those derived from 358
the HSD measurements Brieflythe expressions for calculating r and σ and RMSE are 359
shown below 360
119903 =1
119873sum (119872119899minus)(119874119899minus)119873119899=1
120590119872120590119900 (4) 361
119877119872119878119864 = 1
119873sum [(119872119899 minus ) minus (119874119899 minus )]2119873119899=1
12
(5) 362
120590119872 = [1
119873sum (119872119899 minus )119873119899=1 ]
12
(6) 363
1205900 = [1
119873sum (119874119899 minus )119873119899=1 ]
12
(7) 364
where M and O denote distribution function and observed variables The RED 365
expression is shown below 366
119877119864119863 = [(minus)
]2
+ [(120590119872minus120590119874)
120590119900]2
+ (1 minus 119903)212
( 8 ) 367
Equation (8) indicates that RED considers all the components of mean bias variations 368
and correlations in a dimensionless way the distribution function performance 369
degrades as RED increases from the perfect agreement with RED=0 370
18
In the Taylor diagrams shown in Fig 6 the cosine of azimuthal angle of each point 371
gives the r between the function-calculated and observed data The distance between 372
individual point and the reference point ldquoObsrdquo represents the RMSE normalized by the 373
amplitude of the observationally based variations As this distance approaches to zero 374
the function-calculated K and S approach to the observations Clearly the values of r 375
are around 097 for Gamma and Weibull r for Lognormal function is slightly smaller 376
(095) The normalized σ are much different for Lognormal Gamma and Weibull 377
distributions with averaged value being 057 0895 and 0785 respectively Therefore 378
the Lognormal distribution exhibits the worst performance for describing HSDs and 379
Gamma and Weibull distributions appear to perform much better (Fig 6a) 380
Noticing that S and K of Gamma and Weibull distributions are equal at the point of S 381
= 2 and K = 6 and have positive relationship (If S lt 2 then K lt 6 and if S gt 2 then k gt 6) In 382
this part we further separately examine the group of data with S lt 2 and K lt 6 (Fig 6b) 383
and compare its result with those of total data The averaged normalized σ are 103 and 384
109 and r are 091 and 090 for Weibull and Gamma distributions respectively 385
suggesting that Weibull distribution performs slightly better than Gamma distribution 386
for the four HSD types in the data group of S lt 2 and K lt 6 whereas the opposite is true 387
for all data This conclusion is further substantiated by comparison of RED values for the 388
four type of precipitation (Fig7) which shows that Lognormal has the largest RED 389
Gamma the smallest and Weibull in between for four types of precipitations in all data 390
whereas Weibull (Lognormal) has smallest (largest) RED values when S lt 2 and K lt 6 It 391
can be inferred for data group of S gt 2 and k gt 6 Gamma distribution performs better 392
19
Further comparison between different precipitation types shows these functions all 393
performs better for raindrop size distributions and mixed-phase than graupel and 394
snowflake size distributions The RED for snowflakes is largest among the four types 395
The performance of Gamma is better for describing solid HSDs of all data but Weibull 396
distribution is better when S lt 2 and K lt 6 397
5 Conclusion 398
The combined measurements collected during a field experiment conducted at the 399
Haituo Mountain site using PARSIVEL disdrometer millimeter wavelength cloud radar 400
and microscope photography are analyzed to classify the precipitation hydrometeor 401
types examine the dependence of fall velocity on hydrometeor size for different 402
hydrometeor types and determine the best distribution functions to describe the 403
hydrometeor size distributions of different types 404
Analysis of the PARSIVEL-measured fall velocities show that on average the 405
dependence of fall velocity on hydrometeor size largely follow their corresponding 406
terminal velocity curves for raindrops graupels and snowflakes respectively suggesting 407
that such measurements are useful to identify the hydrometeor types The associated 408
microscope photos and cloud radar observations support the classification of 409
hydrometeor types based on the PARSIVEL-observed fall velocities Furthermore there 410
are velocity spreads in fall velocity across hydrometeor sizes for all hydrometeors and 411
the spreads for the solid hydrometeors could cause by hydrometeor type turbulence or 412
updraftdowndraft and instrument measured principle The coexistence of various 413
types of hydrometeors likely induces additional spread of fall velocity for given 414
20
hydrometeor sizes such as mixed precipitation Meanwhile complex microphysical 415
processes in cold precipitation such as riming aggregation breakup and collision and 416
coalescence influence fall velocity which likely induce larger spread of fall velocity Last 417
but not the least the disdrometer may suffer from instrumental errors due to the 418
internally assumed relationship between horizontal and vertical particle dimensions 419
Comparison of the type-averaged hydrometeor size distributions shows that the 420
mixed precipitation has more small hydrometeors with D lt 15 mm than others 421
whereas the snowflake precipitation has the least number of small hydrometeors 422
among the four types On the contrary the snowflake precipitation has more large 423
hydrometeors with D between 3 mm and 11 mm 424
The commonly used size distribution functions (Gamma Weibull and Lognormal) 425
are further examined to determine the most adequate function to describe the size 426
distribution measurements for all the hydrometeor types by use of an approach based 427
on the relationship between skewness (S) and kurtosis (K) Taylor diagram and RED are 428
further introduced to assess the performance of different size distribution functions 429
against measurements It is shown that the HSDs for the four types can all be well 430
described statistically by the Gamma and Weibull distribution but Lognormal 431
Exponential and Gaussian are not fit to describe HSDs Gamma and Weibull distribution 432
describe raindrop and mixed-phase size distribution better than snowflake and graupel 433
size distribution and their performances are worst for snowflake It may due to graupel 434
and snowflake precipitation have more big particles When S less than 2 and K less than 435
6 Weibull distribution performs better than Gamma distribution to describe HSDs but 436
21
Gamma distribution performs better for total data 437
A few points are noteworthy First although this study demonstrates the great 438
potential of combining simultaneous disdrometer measurements of particle fall velocity 439
and size distributions microscopic photography and cloud radar to address the 440
challenges facing solid precipitation the data are limited More research is needed to 441
discern such effects on the results presented here Second as the observations show 442
that in addition to sizes there are many other factors (eg hydrometeor type 443
microphysical processes turbulence and measuring principle) that can potentially 444
influence particle fall velocity as well More comprehensive research is needed to 445
further discern and separate these factors Finally the combined use of S-K diagram 446
Taylor diagram and relative Euclidean distance appears to be a powerful tool for 447
identifying the best function used to describe the HSDs and quantify the differences 448
between different precipitation types More research is in order along this direction 449
Acknowledgements 450
This study is mainly supported by the Chinese National Science Foundation under Grant 451
No 41675138 and National Key RampD Program of China (2017YFC0209604) It is partly 452
supported by Beijing National Science Foundation (8172023) the US Department 453
Energys Atmospheric System Research (ASR) Program (Liu and Jia at BNL) Lu is 454
supported by the Natural Science Foundation of Jiangsu Province (BK20160041) The 455
observation data are archived at a specialized supercomputer at Beijing Meteorology 456
Information Center (ftp10224592) which are available from the corresponding 457
author upon request The authors also thank Beijing weather modification office for 458
their support during the field experiment 459
Reference 460
22
Agosta CC Fettweis XX Datta RR 2015 Evaluation of the CMIP5 models in the 461
aim of regional modelling of the Antarctic surface mass balance Cryosphere 9 2311ndash462
2321 httpdxdoiorg105194tc-9-2311-2015 463
Barthazy E and R Schefold 2006 Fall velocity of snowflakes of different riming degree 464
and crystal types Atmos Res 82(1) 391-398 httpsdoiorg101016jatmosres 465
200512009 466
Battaglia A Rustemeier E Tokay A et al 2010 PARSIVEL snow observations a critical 467
assessment J Atmos Oceanic Technol 27(2) 333-344 doi 1011752009jtecha13321 468
Boumlhm H P 1989 A General Equation for the Terminal Fall Speed of Solid Hydrometeors 469
J Atmos Sci 46(15) 2419-2427 httpsdoiorg1011751520-0469(1989)046 lt2419A 470
GEFTTgt20CO2 471
Boudala F S G A Isaac et al 2014 Comparisons of Snowfall Measurements in 472
Complex Terrain Made During the 2010 Winter Olympics in Vancouver Pure and 473
Applied Geophysics 171(1) 113-127 474
Chen B W Hu and J Pu 2011 Characteristics of the raindrop size distribution for 475
freezing precipitation observed in southern China J Geophys Res 116 D06201 476
doi1010292010JD015305 477
Chen B Z Hu L Liu and G Zhang (2017) Raindrop Size Distribution Measurements at 478
4500m on the Tibetan Plateau during TIPEX-III J Geophys Res 122 11092-11106 479
doiorg10100 22017JD027233 480
23
Cugerone K and C De Michele 2017 Investigating raindrop size distributions in the 481
(L-)skewness-(L-)kurtosis plane Quart J Roy Meteor Soc 143(704) 1303-1312 482
httpsdoiorg101002qj3005 483
Donnadieu G 1980 Comparison of results obtained with the VIDIAZ spectro 484
pluviometer and the JossndashWaldvogel rainfall disdrometer in a ldquorain of a thundery typerdquo 485
J Appl Meteor 19 593ndash597 486
Feingold G and Levin Z 1986 The lognormal fit to raindrop spectra from frontal 487
convective clouds in Israel J Clim Appl Meteorol 25 1346ndash1363 488
httpsdoiorg1011751520-0450(1986)025lt1346tlftrsgt20CO2 489
Field P R A J Heymsfield and A Bansemer 2007 Snow Size Distribution 490
Parameterization for Midlatitude and Tropical Ice Clouds J Atmos Sci 64(12) 491
4346-4365 httpsdoiorg1011752007JAS23441 492
Garrett T J and S E Yuter 2014 Observed influence of riming temperature and 493
turbulence on the fallspeed of solid precipitation Geophysical Research Letters 41(18) 494
6515ndash6522 495
Geresdi I N Sarkadi and G Thompson 2014 Effect of the accretion by water drops 496
on the melting of snowflakes Atmos Res 149 96-110 497
Gunn R and G D Kinzer 1949 The terminal velocity of fall for water drops in stagnant 498
air J Meteor 6 243-248 httpsdoiorg1011751520-0469(1949)006lt0243TTVOFFgt 499
20CO2 500
24
Heymsfield A J and C D Westbrook 2010 Advances in the Estimation of Ice Particle 501
Fall Speeds Using Laboratory and Field Measurements J Atmos Sci 67(8) 2469-2482 502
httpsdoiorg1011752010JAS33791 503
Huang G-J C Kleinkort V N Bringi and B M Notaroš 2017 Winter precipitation 504
particle size distribution measurement by Multi-Angle Snowflake Camera Atmos Res 505
198 81-96 506
Intergovernmental Panel on Climate Change (IPCC) 2001 Climate Change 2001 The 507
Scientific Basis Contribution of Working Group I to the Third Assessment Report of the 508
Intergovernmental Panel on Climate Change edited by J T Houghton et al 881 pp 509
Cambridge Univ Press New York 510
Ishizaka M H Motoyoshi S Nakai T Shiina T Kumakura and K-i Muramoto 2013 A 511
New Method for Identifying the Main Type of Solid Hydrometeors Contributing to 512
Snowfall from Measured Size-Fall Speed Relationship Journal of the Meteorological 513
Society of Japan Ser II 91(6) 747-762 httpsdoiorg102151jmsj2013-602 514
Khvorostyanov V 2005 Fall Velocities of Hydrometeors in the Atmosphere 515
Refinements to a Continuous Analytical Power Law J Atmos Sci 62 4343-4357 516
httpsdoiorg101175JAS36221 517
Kikuchi K T Kameda K Higuchi and A Yamashita 2013 A global classification of 518
snow crystals ice crystals and solid precipitation based on observations from middle 519
latitudes to polar regions Atmos Res 132-133 460-472 520
Kneifel S A von Lerber J Tiira D Moisseev P Kollias and J Leinonen 2015 521
Observed relations between snowfall microphysics and triple-frequency radar 522
25
measurements J Geophys Res Atmos 120(12) 6034-6055 523
httpsdoi1010022015JD023156 524
Kubicek A and P K Wang 2012 A numerical study of the flow fields around a typical 525
conical graupel falling at various inclination angles Atmos Res 118 15ndash26 526
httpsdoi101016jatmosres201206001 527
Larsen M L A B Kostinski and A R Jameson (2014) Further evidence for 528
superterminal raindrops Geophys Res Lett 41(19) 6914-6918 529
Lee JE SH Jung H M Park S Kwon P L Lin and G W Lee 2015 Classification of 530
Precipitation Types Using Fall Velocity Diameter Relationships from 2D-Video 531
Distrometer Measurements Advances in Atmospheric Sciences (09) 532
Lin Y L J Donner and B A Colle 2010 Parameterization of riming intensity and its 533
impact on ice fall speed using arm data Mon Weather Rev 139(3) 1036ndash1047 534
httpsdoi1011752010MWR32991 535
Liu Y G 1992 Skewness and kurtosis of measured raindrop size distributions Atmos 536
Environ 26A 2713-2716 httpsdoiorg1010160960-1686(92)90005-6 537
Liu Y G 1993 Statistical theory of the Marshall-Parmer distribution of raindrops 538
Atmos Environ 27A 15-19 httpsdoiorg1010160960-1686(93)90066-8 539
Liu Y G and F Liu 1994 On the description of aerosol particle size distribution Atmos 540
Res 31(1-3) 187-198 httpsdoiorg1010160169-8095(94)90043-4 541
Liu Y G L You W Yang F Liu 1995 On the size distribution of cloud droplets Atmos 542
Res 35 (2-4) 201-216 httpsdoiorg1010160169-8095(94)00019-A 543
Locatelli J D and P V Hobbs 1974 Fall speeds and masses of solid precipitation 544
26
particles J Geophys Res 79(15) 2185-2197 httpsdoi101029JC079i015p02185 545
Loumlffler-Mang M and J Joss 2000 An optical disdrometer for measuring size and 546
velocity of hydrometeors J Atmos Oceanic Technol 17 130-139 547
httpsdoiorg1011751520-0426(2000)017lt0130AODFMSgt20CO2 548
Loumlffler-Mang M and U Blahak 2001 Estimation of the Equivalent Radar Reflectivity 549
Factor from Measured Snow Size Spectra J Clim Appl Meteorol 40(4) 843-849 550
httpsdoiorg1011751520-0450(2001)040lt0843EOTERRgt20CO2 551
Matrosov S Y 2007 Modeling Backscatter Properties of Snowfall at Millimeter 552
Wavelengths J Atmos Sci 64(5) 1727-1736 httpsdoiorg101175JAS39041 553
Mitchell D L 1996 Use of mass- and area-dimensional power laws for determining 554
precipitation particle terminal velocities J Atmos Sci 53 1710-1723 555
httpsdoiorg1011751520-0469(1996)053lt1710UOMAADgt20CO2 556
Montero-Martiacutenez G A B Kostinski R A Shaw and F Garciacutea-Garciacutea 2009 Do all 557
raindrops fall at terminal speed Geophys Res Lett 36 L11818 558
httpsdoiorg1010292008GL037111 559
Niu S X Jia J Sang X Liu C Lu and Y Liu 2010 Distributions of raindrop sizes and 560
fall velocities in a semiarid plateau climate Convective vs stratiform rains J Appl 561
Meteorol Climatol 49 632ndash645 httpsdoi1011752009JAMC22081 562
Nurzyńska K M Kubo and K-i Muramoto 2012 Texture operator for snow particle 563
classification into snowflake and graupel Atmos Res 118 121-132 564
Oue M M R Kumjian Y Lu J Verlinde K Aydin and E E Clothiaux 2015 Linear 565
27
Depolarization Ratios of columnar ice crystals in a deep precipitating system over the 566
Arctic observed by Zenith-Pointing Ka-Band Doppler radar J Clim Appl Meteorol 567
54(5) 1060-1068 httpsdoiorg101175JAMC-D-15-00121 568
Pruppacher H R and J D Klett 1998 Microphysics of clouds and precipitation Kluwer 569
Academic 954 pp 570
Rasmussen R B Baker et al 2012 How well are we measuring snow the 571
NOAAFAANCAR winter precipitation test bed Bull Amer Meteor Soc 93(6) 811-829 572
httpsdoiorg101175BAMS-D-11-000521 573
Reisner J R M Rasmussen and R T Bruintjes 1998 Explicit forecasting of 574
supercooled liquid water in winter storms using the MM5 mesoscale model Q J R 575
Meteorol Soc 124 1071ndash1107 httpsdoi101256smsqj54803 576
Rosenfeld D and Ulbrich C W 2003 Cloud microphysical properties processes and 577
rainfall estimation opportunities Meteorol Monogr 30 237-237 578
httpsdoiorg101175 0065-9401(2003)030lt0237cmppargt20CO2 579
Schaefer V J 1956 The preparation of snow crystal replicas-VI Weatherwsie 9 580
132-135 581
Souverijns N A Gossart S Lhermitte I V Gorodetskaya S Kneifel M Maahn F L 582
Bliven and N P M van Lipzig (2017) Estimating radar reflectivity - Snowfall rate 583
relationships and their uncertainties over Antarctica by combining disdrometer and 584
radar observations Atmos Res 196 211-223 585
Taylor K E 2001 Summarizing multiple aspects of model performance in a single 586
diagram J Geophys Res 106 7183ndash7192 httpsdoi1010292000JD900719 587
28
Tokay A and D A Short 1996 Evidence from tropical raindrop spectra of the origin of 588
rain from stratiform versus convective clouds J Appl Meteor 35 355ndash371 589
Tokay A and D Atlas 1999 Rainfall microphysics and radar properties analysis 590
methods for drop size spectra J Appl Meteor 37 912-923 591
httpsdoiorg1011751520-0450(1998)037lt0912RMARPAgt20CO2 592
Tokay A D B Wolff et al 2014 Evaluation of the New version of the laser-optical 593
disdrometer OTT Parsivel2 J Atmos Oceanic Technol 31(6) 1276-1288 594
httpsdoiorg101175JTECH-D-13-001741 595
Ulbrich C W 1983 Natural variations in the analytical form of the raindrop size 596
distribution J Appl Meteor 5 1764-1775 597
Wen G H Xiao H Yang Y Bi and W Xu 2017 Characteristics of summer and winter 598
precipitation over northern China Atmos Res 197 390-406 599
Wu W Y Liu and A K Betts 2012 Observationally based evaluation of NWP 600
reanalyses in modeling cloud properties over the Southern Great Plains J Geophys 601
Res 117 D12202 httpsdoi1010292011JD016971 602
Yuter S E D E Kingsmill L B Nance and M Loumlffler-Mang 2006 Observations of 603
precipitation size and fall velocity characteristics within coexisting rain and wet snow J 604
Appl Meteor Climatol 45 1450ndash1464 doi httpsdoiorg101175JAM24061 605
Zhang P C and B Y Du 2000 Radar Meteorology China Meteorological Press 511pp 606
(in Chinese) 607
608
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
2
measurements are analyzed to classify the precipitation hydrometeor types examine 24
the dependence of fall velocity on hydrometeor sizes for different hydrometeor types 25
and determine the best distributions to describe the hydrometeor size distributions of 26
different hydrometeor types The results show (1) Hydrometeors can be classified to 27
four main types of raindrop graupel snowflake and mixed-phase according to the 28
dependence of terminal velocity on particle sizes corresponding microscope photos 29
and cloud radar observations (2) There are significant scatters in fall velocity for a given 30
hydrometer size velocities and the fall velocity spread for the solid hydrometeors 31
appear wider than that for raindrops across hydrometeor sizes with that for the 32
mixed-phase precipitation being largest suggesting that the effects of hydrometeor 33
shape on hydrometeor fall velocities (3) Hydrometeor size distributions for the four 34
types can all be well described by the Gamma or Weibull distribution Weibull (Gamma) 35
distribution performs better when skewness is less (larger) than 2 36
Key words hydrometeor fall velocity hydrometeor size distribution PARSIVEL 37
disdrometer microscope photography cloud radar 38
39
1 Introduction 40
Solid precipitation is important for weather and climate forecasting models since 41
predictions of precipitation amount location and duration depend greatly on how 42
precipitation particles are parameterized The last few decades have witnessed great 43
progress in both areas of parameterizing cold precipitation processes (Reisner et al 44
1998 Field et al 2007 Lin et al 2010 Agosta et al 2015) remote sensing (Tokay and 45
3
Short 1996 Souverijns et al 2017) and ground measurement (Chen et al 2011 46
Nurzyńska et al 2012 Ishizaka et al 2013 Huang et al 2017) of solid hydrometeors 47
Despite the great development solid precipitation measurement and parameterization 48
still suffer from large uncertainties and much work remains to be done Detailed solid 49
hydrometeor observations including size distribution fall velocity and shape of 50
hydrometeors are needed to improve microphysical parameterization in numerical 51
models and remote sensing 52
Hydrometeors properties (eg size concentration geometric shape and fall 53
velocity) are essential for further improving parameterizations of precipitation 54
processes and remote sensing (especially of polarized radar) In particular recent 55
developments in disdrometer and remote sensing techniques permit retrievals of more 56
hydrometeor size distribution (HSD) parameters and their vertical profiles over large 57
areas (Loumlffler-Mang and Blahak 2001 Matrosov 2007 Kneifel et al 2015) and 58
enhance our ability to monitor and investigate solid hydrometeor events and 59
microphysics At the same time more accurate assumptions regarding the spectral 60
shape of HSDs for different hydrometer types are needed which vary spatially and 61
temporally (Kikuchi et al 2013) Unfortunately our understanding of the hydrometeors 62
and direct measurements of solid precipitation is far from complete and more analyses 63
of in situ measurements are needed (Souverijns et al 2017) 64
Fall velocity is equally important and closely related to the HSD measurements 65
radar retrievals and parameterizations Fall velocity measurements of solid 66
hydrometeors can be traced to an empirical study by Locatelli and Hobbs (1974) which 67
4
is still utilized in microphysical parameterizations Later studies include those based on 68
fluid dynamics (Boumlhm 1989 Mitchell 1996 Khvorostyanov 2005 Heymsfield and 69
Westbrook 2010 Kubicek and Wang 2012) and using automated ground-based 70
disdrometers (Barthazy and Schefold 2006 Yuter et al 2006 Ishizaka et al 2013 Chen 71
et al 2011) 72
Most of these studies assume that the surrounding air is still rather than a 73
turbulent environment as in actual precipitating clouds Yuter et al (2006) obtained size 74
and fall velocity distributions within coexisting rain and wet snow (sleet) by using a 75
disdrometer but insufficient details of quantified results were provided The influence 76
of riming particle shape temperature and turbulence on the fallspeed of solid 77
precipitation in disdrometer measurements were further discussed (Barthazy and 78
Schefold 2006 Garrett and Yuter 2014 Geresdi et al 2014) However many factors 79
have influences on solid hydrometeor fall velocity and the complex effects have not 80
been yet adequately investigated 81
In a previous study (Niu et al 2010) we discussed the air density and other factors 82
(ie turbulence organized air motions break-up and measurement errors) that 83
potentially influence on distributions of raindrop sizes and fall velocities and called 84
attention to the turbulence induced the large velocity spread at given raindrop sizes 85
This work is a further extension of Niu et al (2010) to analyze measurements of size 86
and fall velocity distributions of solid hydrometeors collected during a recent field 87
experiment campaign conducted northeast of Beijing China to simultaneously 88
measure HSDs and fall velocities with a PARSIVEL disdrometer (see Section 2 for details) 89
5
This paper has two specific objectives (1) to distinguish and quantify hydrometeor 90
types and their fall velocities by combining disdrometer microscopic photography and 91
cloud radar observation (2) to characterize and compare the spectral shapes of HSDs 92
from different precipitation types 93
The rest of the paper is organized as follows Section 2 describes the experiment and 94
data Section 3 classifies hydrometeors and analyzes the size and fall velocity 95
distributions Section 4 examines the characters of HSDs and evaluates the distribution 96
function for describing HSDs The major findings are summarized in Section 5 97
2 Description of Experiment and Data 98
The observation site was on Haituo Mountain at a height of 1310 m located in 99
northwest of Beijing (40deg35primeN 115deg50primeE) China (Fig 1) The site is in the semiarid 100
temperate monsoon climate regime with mean winter precipitation amount for each 101
event is about 080 mm (2014-2015) (Ma et al 2017) All the observed events are stratiform 102
precipitation classified by the surface cloud radar China Weather Radar (Doppler radar) 103
and manual observations The entire radar reflectivity maximums are lower than 30 dBZ 104
which is chosen as the threshold reflectivity of convective precipitation (Zhang and Du 105
2000) 106
HSDs were measured with a PARSIVEL disdrometer and the measurement methods 107
are the same as employed in Niu et al (2010) Loumlffler-Mang and Joss (2000) and Tokay 108
et al (2014) provided detailed description of the PARSIVEL disdrometer The instrument 109
measures the maximum diameter of one-dimensional projection of the particle which is 110
smaller than or equal to the actual maximum diameter Snow particles are often not 111
6
horizontally symmetric and thus particle sizes for snow may underestimate actual maximum 112
particle diameter Battaglia et al (2010) pointed out that PARSIVELrsquos fall velocity 113
measurement may not be accurate for snowflakes due to the internally assumed relationship 114
between horizontal and vertical snow particle dimensions The uncertainty originates from 115
the shape-related factor which tends to depart more with increasing snowflake sizes and 116
can produce large errors When averaging over a large number of snowflakes the correction 117
factor is size dependent with a systematic tendency to underestimate the fall speed (but 118
never exceeding 20) The maximum error 20 of the empirical terminal velocities for 119
graupel and snowflake is used to estimate the instrument caused possible velocities such 120
as the dash lines in igure 2b In addition graupel is almost spherical hydrometeor and the 121
instrument error could not reach 20 The individual HSD sample interval was 10 seconds 122
The following criteria are used in choosing data for analysis (1) Particles smaller 123
than 025 mm are discarded (2) the total particle number of a HSD is over 10 counts 124
(every 10-sec sample) (Niu et al 2010) (3) precipitation lasted more than 30 minutes 125
are chosen (4) solid hydrometeor density is corrected with the equation ρs =126
017Dminus1 for solid hydrometeors (Boudala et al 2014) (5) Following Chen et al (2017) 127
raindrops outside +60 of the empirical terminal velocity of raindrop (Table 3) and -60 128
of empirical terminal velocity of densely rimed dendrites were excluded in the analysis 129
to minimize the effects of ldquomargin fallersrdquo winds and splashing Hydrometeors were 130
also collected with Formvar slides (76 cm long and 26 cm wide) which are exposed 131
outside for 5s to capture the hydrometeors with a sampling interval of 5 minutes The 132
Formvar samples were examined and photographed with a microscope-camera system 133
7
following the method described by Schaefer (1956) The two-dimensional photo of 134
hydrometeors allows a careful determination of the hydrometeor shape and size The 135
Formvar data were used to distinguish dominant hydrometeor types eg raindrop 136
graupel or snowflake The hydrometeor type with a percentage of occurrence gt60 is 137
used to represent the solid precipitation type for convenience of analysis 138
A Ka-band millimeter wavelength cloud radar (wavelength is 8 mm) was used to 139
probe the vertical structure of clouds by vertical scanning from 11202016 which can 140
be used to determine cloud properties at 1 min temporal and 30 m vertical resolution 141
A total of 11098 HSD samples were collected from 12 precipitation events (Table 1) 142
Four representative hydrometeor types from the precipitation events are identified 143
raindrop graupel snowflake and mixed-phase precipitation The identification of the 144
hydrometeor types is mainly based on hydrometeors velocity observations and Formvar 145
images which will be detailed in Section 4 Mixed-phased precipitation contains 146
raindrops graupels and snowflakes simultaneously and none is dominant over another 147
The duration sample number precipitation rate and dominant type of hydrometeor 148
are shown in Table 1 The precipitation rate is calculated from HSD using the method 149
presented in Boudala et al (2014) 150
3 Hydrometeor Classification and Size and Fall Velocity 151
Distributions 152
a General Feature 153
Fig 2 illustrates the observed mean number concentration as a function of the 154
maximum dimension and the fall velocity for the four types of hydrometeors 155
8
respectively Also shown as a reference are the seven solid curves representing 156
different types of hydrometeor terminal velocities obtained from the laboratory 157
measurements calibrated by coefficient 50
0
since the site altitude is 1310 m 158
average pressure is 868 hpa and the average temperature is -5 ordmC (Niu et al2010) 159
(equations are shown in Table 3) Here ρ is the actual air density and ρ0 is the 160
standard atmospheric density The updrafts downdrafts and turbulence often 161
accompany falling hydrometeors inducing deviations in the velocity and trajectory of 162
falling hydrometeors from those in still air (Donnadieu 1980) Hence in this field 163
observation fall velocities of hydrometeors distribute along the terminal velocity curves 164
with large spread for each given size Similar features have been previously reported in 165
some situ measurements of raindrop fall velocities (Niu et al 2010 Rasmussen et al 166
2012) 167
In the previous study we discussed the air density and potential influencing 168
factors (eg turbulence organized air motions break-up and measurement errors) for 169
raindrop (Niu et al 2010) For precipitation in winter the hydrometeor shape is vitally 170
important for fall velocity The hydrometeor shape influence on fall velocities physical 171
mechanisms and instrument error underlying the large spread in the measured fall 172
velocities of different types are discussed in detail in the next two sub-sections 173
b Effect of Hydrometeor Type on Fall Velocity 174
In Fig 2a the hydrometeor fall velocities agree with the typical raindrop terminal 175
velocity curve which is obviously larger than the terminal velocities of graupel and 176
9
snowflake at given maximum diameters From the fall velocity distribution we can infer 177
that these hydrometeors are mainly raindrops The microscope photos obtained on the 178
ground confirm this However unlike the raindrop size and velocity distribution in 179
summer in Figure 8a of Niu et al (2010) there are some small size hydrometeors 180
(05~35mm) at very low speeds (05~2 ms) distributing among the terminal velocity 181
curves for graupel and snowflake This result implies that beside liquid raindrops 182
(including small raindrops or droplets from drizzle) some small snowflakes also exist in 183
the measurement The microscope photos also support the finding that although 184
raindrops are dominant some small plane- and column- shaped snowflakes co-exist 185
Fig 2b shows the joint hydrometeor size and fall velocity distribution during the 186
graupel event The hydrometeors are mainly symmetrically distributed around the ideal 187
terminal velocity of graupel (Locatelli and Hobbs 1974) supported by the photo-based 188
hydrometeor classification On the other hand it is found that certain small droplets 189
with the maximum dimensions among 03 to 10 mm are distributed around the liquid 190
raindrop curve suggesting that there are some raindrops and droplets coexisting in the 191
graupel dominated precipitation It is recognized that graupels grow by snow crystals 192
collecting cloud droplets and small raindrops (Pruppacher and Klett 1998) high cloud 193
top more liquid water content and presence of small raindrops (as shown in 194
microscope photography) provide favorable conditions for graupel The microscope 195
photos also display that graupelsrsquo surfaces are lumpy because of riming super cooled 196
drops during growing 197
The fall velocities of hydrometeors in Fig 2c are much smaller than the terminal 198
10
velocities of raindrop and graupel but are close to the terminal velocity curves of snow 199
of hexagonal densely rimed dendrites aggregates of dendrites Synthesizing the size 200
data the hydrometeors can be inferred as snowflakes which are further confirmed by 201
surface microscope photos From the surface observation we found many 202
rimedunrimed or aggregated dendrites or hexagonal snowflakes Although riming and 203
aggregation microphysical processes have some influence on terminal velocity 204
(Barthazy and Schefold 2006 Garrett and Yuter 2014 Heymsfield and Westbrook 205
2010) but the influences are too small to distinguish only from observed fall velocity 206
since it is a combined result of many factors When maximum dimensions are among 207
03 to 10 mm there are some small hydrometeors with fall velocities larger than 208
snowflakes which maybe graupels raindrops and droplets 209
Fig 2d is the hydrometeor size and fall velocity distribution during a mixed-phased 210
precipitation The hydrometeor fall velocities exhibit the largest spread for example 211
the fall velocities for hydrometeors with maximum dimension equaling to 3 mm 212
change from 05 to 5 ms and do not distribute along any of the ideal terminal velocity 213
curves This result suggests that different hydrometeor types might coexist during the 214
same sampling time To substantiate supercooled raindrops graupels and different 215
kinds of snowflakes are observed from the surface microscope simultaneously Similar 216
changes in particle size and fall velocity distribution documented by the disdrometer as 217
the storm transitions from rain to mixed-phase to snow were found at Marshall Field 218
site (Rasmussen et al 2012) 219
11
c Other Influencing Factors 220
The different dependence on particle size of terminal velocities for different types 221
of hydrometeors can explain some systematic distribution of the PARSIVEL-measured 222
fall velocities but the large spreads in the measurement of the instant particle fall 223
velocities await further inspection 224
According to our previous work the fall velocity (V) of a hydrometeor measured by 225
the PARSIVEL can be regarded as a combination of the terminal velocity in still air (Vt) 226
and a component Vrsquo that results from all other potential influencing factors eg type 227
turbulence organized air motions break-up and measurement errors (Niu et al 228
2010) 229
119881 = 119881119905 + 119881 prime (1) 230
The large spread of the measurements at both sides of the terminal velocity curves 231
shown in figure 2 seems compatible with the notion of nearly random collections of 232
downdraft and updraft A wider spread for fall velocities implies a wider range of 233
variation in vertical motions when hydrometeors are liquid raindrops (Niu et al 2010) 234
Solid nonspherical hydrometeors are much more complex than liquid drops and the 235
large spread of velocities may be caused by several other factors First different types 236
of hydrometeors (columns bullets plates lump graupels and hexagonal snowflakes et 237
al) have different fall speeds It is long recognized that microphysical processes in cold 238
precipitation are more complex and consequently generate more types of solid 239
hydrometeors comparing to the generation of raindrops The averaged concentration 240
distributions of large number of samples shown in Figure 2 also represents the possible 241
12
distributions of hydrometeors If there is only one kind particle the high concentration 242
would along its ideal terminal velocity very well just like the raindrop possible 243
distribution (Niu et al 2010) The concentration of mixed precipitation in Fig 2d does 244
not along any singe ideal terminal velocity further improved there are more than one 245
kind of hydrometers Coexistence of different types of hydrometeors induces larger 246
spread of fall velocities Second different degrees of riming and aggregating may affect 247
the results Densely rimed particles fall faster than unrimed particles with the same 248
maximum dimension aggregated snowflakes generally fall faster than their component 249
crystals (Barthazy and Schefold 2006 Garrett and Yuter 2014 Locatelli and Hobbs 250
1974) Third solid hydrometeors more likely occur breakup aggregation collision and 251
coalescence processes because of the large range of speeds According to prior 252
research of raindrop breakup and coalescence would lead to the ldquohigher-than-terminal 253
velocityrdquo fall velocity for small drops but ldquolower-than-terminal velocityrdquo fall velocity for 254
large drops (Niu et al 2010 Montero-Martiacutenez et al 2009 Larsen et al 2014) Similar 255
results are expected for the fall velocity of solid hydrometeors Last but not the least 256
the disdrometer may suffer from instrumental errors due to the internally assumed 257
relationship between horizontal and vertical particle dimensions likely resulting in a 258
wider spreads of fall velocities for the graupel and snowflakes as compared to the 259
raindrop counterpart as discussed in Section 2 Although the instrument error is an 260
important factor that should be considered in velocity spread as shown in Fig2b the 261
instrument error could not cause that large velocity spread The possible distributions 262
of fall velocities are the combine effects of physical and instrument principle 263
13
Further support for the possible instrumental uncertainty is from the cloud radar 264
observations Fig 3 shows the cloud reflectivity and linear depolarization ratio (LDR) in 265
lower level (less than 08 km) for the graupel snowflake and mixed-phased 266
precipitations respectively The LDR is a valuable observable in identifying the 267
hydrometeor types (Oue et al 2015) As shown in Fig 3a the cloud top height of 268
graupel precipitation was up to 7km during 1900 to 2050 Beijng Time (BT) which was 269
highest among the three events The high cloud top implies stronger updraft and 270
turbulence which further induces a larger fall velocity spread The LDR value was the 271
smallest among the three events indicating that the hydrometeors were close to 272
spherical consistent to the surface observations The cloud top height of snowflake 273
precipitation was up to 35 km (Fig 3c) which was the lowest among the three types of 274
precipitations implying weakest updraft and turbulence Notably although the 275
snowflake types are more complex than those of graupels the velocity spread was not 276
as large as that of the graupel type likely because of the weakest updraft and 277
turbulence The LDR was relatively larger consistent with the surface snowflake 278
observations (Fig 3d) The cloud top height of mixed-phase precipitation was up to 45 279
km (Fig 3e) and the LDR in lower level was largest among the three types of 280
precipitations owing to coexistence of raindrops graupels and snowflakes (Fig 3f) 281
4 Hydrometeor Size Distributions 282
a Comparison of HSDs between Different Types 283
There were four representative types of precipitations during this field experiment 284
providing us a unique opportunity to examine the HSD differences between the four 285
14
types of hydrometeors The sample numbers mean maximum dimensions and number 286
concentrations for each kind of HSDs are given in Table 2 Figure 4 is the averaged 287
distribution of all measured HSDs of 4 kinds As shown in Figure 4 on average the 288
mixed-phased precipitation tends to have most small size hydrometeors with D lt 15 289
mm while snowflake precipitation has the least small hydrometeors among the four 290
types The snowflake precipitation has more large size hydrometeors ie 3 mm lt D lt 11 291
mm Graupel size distribution tends to have two peeks around 13 mm and 26 mm The 292
mean maximum dimension is largest for snowflake (126 mm) and smallest for the 293
mixed HSD due to many small particles Similar results were found in precipitation 294
occurring in the Cascade and Rocky Mountains (Yuter et al 2006) The PARSIVEL 295
disdrometer doesnrsquot provide reliable data for small drops lower than 05 mm and tends to 296
underestimate small drops so the relatively low concentrations of small drops likely resulted 297
from the instrumentrsquos shortcomings (Tokay et al 2013 and Chen et al 2017) 298
b Evaluation of Distribution Functions for Describing HSDs 299
Over the last few decades great efforts have been devoted to finding the 300
appropriate analytical functions for describing the HSD because of its wide applications 301
in many areas including remote sensing and parameterization of precipitation (Chen et 302
al 2017) The two distribution functions mostly used up to now are the Lognormal 303
(Feingold and Levin 1986 Rosenfeld and Ulbrich 2003) and the Gamma (Ulbrich 1983) 304
distributions The Gamma distribution has been proposed as a first order generalization 305
of the Exponential distribution when μ equals 0 (Table 4) Weibull distribution is 306
another function used to describe size distributions of raindrops and cloud droplets (Liu 307
15
and Liu 1994 Liu et al 1995) Nevertheless the question as to which functions are 308
more adequate to describe HSDs of solid hydrometeors have been rarely investigated 309
systematically and quantitatively Thus the objective of this section is to examine the 310
most adequate distribution function used to describe HSDs 311
Considering size distributions of raindrops cloud droplets and aerosol particles are 312
the end results of many (stochastic) complex processes Liu (1992 1993 1994 and 313
1995) proposed a statistical method based on the relationships between the skewness 314
(S) and kurtosis (K) derived from an ensemble of particle size distribution 315
measurements and from those commonly used size distribution functions Cugerone 316
and Michele (2017) also used a similar approach based on the S-K relationships to study 317
raindrop size distributions Unlike the conventional curve-fitting of individual size 318
distributions this approach applies to an ensemble of size distribution measurements 319
and identifies the most appropriate statistical distribution pattern Here we apply this 320
approach to investigate if the statistical pattern of the HSDs of four precipitation types 321
follows the Exponential Gaussian Gamma Weibull and Lognormal distributions (Table 322
4) and if there are any pattern differences between them Briefly S and K of a HSD are 323
calculated from the corresponding HSD with the following two equations 324
23
2
3
t
iii
t
iii
dDN
)(Dn)D(D
dDN
)(Dn)D(D
S
minus
minus
=
(2) 325
32
2
4
minus
minus
minus
=
dDN
)(Dn)D(D
dDN
)(Dn)D(D
K
t
iii
t
iii
(3) 326
16
where Di is the central diameter of the i-th bin ni is the number concentration of the 327
i-th bin and Nt is total number concentration Note that each individual HSD can be 328
used to obtain a pair of S and K which is shown as a dot in Figure 5 Also noteworthy is 329
that the SndashK relationships for the families of Gamma Weibull and Lognormal are 330
described by known analytical functions (Liu 1993 1994 and 1995 Cugerone and 331
Michele 2017) represented by theoretical curves in Figure 5 The Exponential and 332
Gaussian distributions are represented by single points on the S-K diagram (S=2 and K=6 333
for Exponential) and (S=0 and K=0 for Gaussian) respectively Thus by comparing the 334
measured S and K values (points) with the known theoretical curves one can determine 335
the most proper function used to describe HSDs 336
Figure 5 shows the scatter plots of observed SndashK pairs calculated from the HSD 337
measurements for raindrop graupel snowflake mixed-phase precipitations Also 338
shown as comparison are the theoretical curves corresponding to the analytical HSD 339
functions A few points are evident First despite some occasional departures most of 340
the points fall near the theoretical lines of Gamma and Weibull distributions suggesting 341
that the HSD patterns for all the four types of precipitations well follow the Gamma and 342
Weibull distributions statistically Second HSDs of raindrops and mixed hydrometeors 343
are better described by Gamma and Weibull distribution than graupels and snowflakes 344
Third the S and K do not cluster around points (2 6) and (0 0) suggesting that the 345
Gaussian and Exponential distribution are not appropriate for describing HSDs 346
especially Gaussian distribution 347
To further evaluate the overall performance of the different distribution functions 348
17
we employ the widely used technique of Taylor diagram (Taylor 2001) and ldquoRelative 349
Euclidean Distancerdquo (RED) (Wu et al 2012) as a supplement to the Taylor diagram The 350
Taylor diagram has been widely used to visualize the statistical differences between 351
model results and observations in evaluation of model performance against 352
measurements or other benchmarks (IPCC 2001) Correlation coefficient (r) standard 353
deviation (σ) and ldquocentered root-mean-square errorrdquo (RMSE hereafter) are used in 354
the Taylor diagram The RED is introduced to add the bias as well in a dimensionless 355
framework that allows for comparison between different physical quantities with 356
different units In this study we consider the S and K values derived from the 357
distribution functions as model results and evaluate them against those derived from 358
the HSD measurements Brieflythe expressions for calculating r and σ and RMSE are 359
shown below 360
119903 =1
119873sum (119872119899minus)(119874119899minus)119873119899=1
120590119872120590119900 (4) 361
119877119872119878119864 = 1
119873sum [(119872119899 minus ) minus (119874119899 minus )]2119873119899=1
12
(5) 362
120590119872 = [1
119873sum (119872119899 minus )119873119899=1 ]
12
(6) 363
1205900 = [1
119873sum (119874119899 minus )119873119899=1 ]
12
(7) 364
where M and O denote distribution function and observed variables The RED 365
expression is shown below 366
119877119864119863 = [(minus)
]2
+ [(120590119872minus120590119874)
120590119900]2
+ (1 minus 119903)212
( 8 ) 367
Equation (8) indicates that RED considers all the components of mean bias variations 368
and correlations in a dimensionless way the distribution function performance 369
degrades as RED increases from the perfect agreement with RED=0 370
18
In the Taylor diagrams shown in Fig 6 the cosine of azimuthal angle of each point 371
gives the r between the function-calculated and observed data The distance between 372
individual point and the reference point ldquoObsrdquo represents the RMSE normalized by the 373
amplitude of the observationally based variations As this distance approaches to zero 374
the function-calculated K and S approach to the observations Clearly the values of r 375
are around 097 for Gamma and Weibull r for Lognormal function is slightly smaller 376
(095) The normalized σ are much different for Lognormal Gamma and Weibull 377
distributions with averaged value being 057 0895 and 0785 respectively Therefore 378
the Lognormal distribution exhibits the worst performance for describing HSDs and 379
Gamma and Weibull distributions appear to perform much better (Fig 6a) 380
Noticing that S and K of Gamma and Weibull distributions are equal at the point of S 381
= 2 and K = 6 and have positive relationship (If S lt 2 then K lt 6 and if S gt 2 then k gt 6) In 382
this part we further separately examine the group of data with S lt 2 and K lt 6 (Fig 6b) 383
and compare its result with those of total data The averaged normalized σ are 103 and 384
109 and r are 091 and 090 for Weibull and Gamma distributions respectively 385
suggesting that Weibull distribution performs slightly better than Gamma distribution 386
for the four HSD types in the data group of S lt 2 and K lt 6 whereas the opposite is true 387
for all data This conclusion is further substantiated by comparison of RED values for the 388
four type of precipitation (Fig7) which shows that Lognormal has the largest RED 389
Gamma the smallest and Weibull in between for four types of precipitations in all data 390
whereas Weibull (Lognormal) has smallest (largest) RED values when S lt 2 and K lt 6 It 391
can be inferred for data group of S gt 2 and k gt 6 Gamma distribution performs better 392
19
Further comparison between different precipitation types shows these functions all 393
performs better for raindrop size distributions and mixed-phase than graupel and 394
snowflake size distributions The RED for snowflakes is largest among the four types 395
The performance of Gamma is better for describing solid HSDs of all data but Weibull 396
distribution is better when S lt 2 and K lt 6 397
5 Conclusion 398
The combined measurements collected during a field experiment conducted at the 399
Haituo Mountain site using PARSIVEL disdrometer millimeter wavelength cloud radar 400
and microscope photography are analyzed to classify the precipitation hydrometeor 401
types examine the dependence of fall velocity on hydrometeor size for different 402
hydrometeor types and determine the best distribution functions to describe the 403
hydrometeor size distributions of different types 404
Analysis of the PARSIVEL-measured fall velocities show that on average the 405
dependence of fall velocity on hydrometeor size largely follow their corresponding 406
terminal velocity curves for raindrops graupels and snowflakes respectively suggesting 407
that such measurements are useful to identify the hydrometeor types The associated 408
microscope photos and cloud radar observations support the classification of 409
hydrometeor types based on the PARSIVEL-observed fall velocities Furthermore there 410
are velocity spreads in fall velocity across hydrometeor sizes for all hydrometeors and 411
the spreads for the solid hydrometeors could cause by hydrometeor type turbulence or 412
updraftdowndraft and instrument measured principle The coexistence of various 413
types of hydrometeors likely induces additional spread of fall velocity for given 414
20
hydrometeor sizes such as mixed precipitation Meanwhile complex microphysical 415
processes in cold precipitation such as riming aggregation breakup and collision and 416
coalescence influence fall velocity which likely induce larger spread of fall velocity Last 417
but not the least the disdrometer may suffer from instrumental errors due to the 418
internally assumed relationship between horizontal and vertical particle dimensions 419
Comparison of the type-averaged hydrometeor size distributions shows that the 420
mixed precipitation has more small hydrometeors with D lt 15 mm than others 421
whereas the snowflake precipitation has the least number of small hydrometeors 422
among the four types On the contrary the snowflake precipitation has more large 423
hydrometeors with D between 3 mm and 11 mm 424
The commonly used size distribution functions (Gamma Weibull and Lognormal) 425
are further examined to determine the most adequate function to describe the size 426
distribution measurements for all the hydrometeor types by use of an approach based 427
on the relationship between skewness (S) and kurtosis (K) Taylor diagram and RED are 428
further introduced to assess the performance of different size distribution functions 429
against measurements It is shown that the HSDs for the four types can all be well 430
described statistically by the Gamma and Weibull distribution but Lognormal 431
Exponential and Gaussian are not fit to describe HSDs Gamma and Weibull distribution 432
describe raindrop and mixed-phase size distribution better than snowflake and graupel 433
size distribution and their performances are worst for snowflake It may due to graupel 434
and snowflake precipitation have more big particles When S less than 2 and K less than 435
6 Weibull distribution performs better than Gamma distribution to describe HSDs but 436
21
Gamma distribution performs better for total data 437
A few points are noteworthy First although this study demonstrates the great 438
potential of combining simultaneous disdrometer measurements of particle fall velocity 439
and size distributions microscopic photography and cloud radar to address the 440
challenges facing solid precipitation the data are limited More research is needed to 441
discern such effects on the results presented here Second as the observations show 442
that in addition to sizes there are many other factors (eg hydrometeor type 443
microphysical processes turbulence and measuring principle) that can potentially 444
influence particle fall velocity as well More comprehensive research is needed to 445
further discern and separate these factors Finally the combined use of S-K diagram 446
Taylor diagram and relative Euclidean distance appears to be a powerful tool for 447
identifying the best function used to describe the HSDs and quantify the differences 448
between different precipitation types More research is in order along this direction 449
Acknowledgements 450
This study is mainly supported by the Chinese National Science Foundation under Grant 451
No 41675138 and National Key RampD Program of China (2017YFC0209604) It is partly 452
supported by Beijing National Science Foundation (8172023) the US Department 453
Energys Atmospheric System Research (ASR) Program (Liu and Jia at BNL) Lu is 454
supported by the Natural Science Foundation of Jiangsu Province (BK20160041) The 455
observation data are archived at a specialized supercomputer at Beijing Meteorology 456
Information Center (ftp10224592) which are available from the corresponding 457
author upon request The authors also thank Beijing weather modification office for 458
their support during the field experiment 459
Reference 460
22
Agosta CC Fettweis XX Datta RR 2015 Evaluation of the CMIP5 models in the 461
aim of regional modelling of the Antarctic surface mass balance Cryosphere 9 2311ndash462
2321 httpdxdoiorg105194tc-9-2311-2015 463
Barthazy E and R Schefold 2006 Fall velocity of snowflakes of different riming degree 464
and crystal types Atmos Res 82(1) 391-398 httpsdoiorg101016jatmosres 465
200512009 466
Battaglia A Rustemeier E Tokay A et al 2010 PARSIVEL snow observations a critical 467
assessment J Atmos Oceanic Technol 27(2) 333-344 doi 1011752009jtecha13321 468
Boumlhm H P 1989 A General Equation for the Terminal Fall Speed of Solid Hydrometeors 469
J Atmos Sci 46(15) 2419-2427 httpsdoiorg1011751520-0469(1989)046 lt2419A 470
GEFTTgt20CO2 471
Boudala F S G A Isaac et al 2014 Comparisons of Snowfall Measurements in 472
Complex Terrain Made During the 2010 Winter Olympics in Vancouver Pure and 473
Applied Geophysics 171(1) 113-127 474
Chen B W Hu and J Pu 2011 Characteristics of the raindrop size distribution for 475
freezing precipitation observed in southern China J Geophys Res 116 D06201 476
doi1010292010JD015305 477
Chen B Z Hu L Liu and G Zhang (2017) Raindrop Size Distribution Measurements at 478
4500m on the Tibetan Plateau during TIPEX-III J Geophys Res 122 11092-11106 479
doiorg10100 22017JD027233 480
23
Cugerone K and C De Michele 2017 Investigating raindrop size distributions in the 481
(L-)skewness-(L-)kurtosis plane Quart J Roy Meteor Soc 143(704) 1303-1312 482
httpsdoiorg101002qj3005 483
Donnadieu G 1980 Comparison of results obtained with the VIDIAZ spectro 484
pluviometer and the JossndashWaldvogel rainfall disdrometer in a ldquorain of a thundery typerdquo 485
J Appl Meteor 19 593ndash597 486
Feingold G and Levin Z 1986 The lognormal fit to raindrop spectra from frontal 487
convective clouds in Israel J Clim Appl Meteorol 25 1346ndash1363 488
httpsdoiorg1011751520-0450(1986)025lt1346tlftrsgt20CO2 489
Field P R A J Heymsfield and A Bansemer 2007 Snow Size Distribution 490
Parameterization for Midlatitude and Tropical Ice Clouds J Atmos Sci 64(12) 491
4346-4365 httpsdoiorg1011752007JAS23441 492
Garrett T J and S E Yuter 2014 Observed influence of riming temperature and 493
turbulence on the fallspeed of solid precipitation Geophysical Research Letters 41(18) 494
6515ndash6522 495
Geresdi I N Sarkadi and G Thompson 2014 Effect of the accretion by water drops 496
on the melting of snowflakes Atmos Res 149 96-110 497
Gunn R and G D Kinzer 1949 The terminal velocity of fall for water drops in stagnant 498
air J Meteor 6 243-248 httpsdoiorg1011751520-0469(1949)006lt0243TTVOFFgt 499
20CO2 500
24
Heymsfield A J and C D Westbrook 2010 Advances in the Estimation of Ice Particle 501
Fall Speeds Using Laboratory and Field Measurements J Atmos Sci 67(8) 2469-2482 502
httpsdoiorg1011752010JAS33791 503
Huang G-J C Kleinkort V N Bringi and B M Notaroš 2017 Winter precipitation 504
particle size distribution measurement by Multi-Angle Snowflake Camera Atmos Res 505
198 81-96 506
Intergovernmental Panel on Climate Change (IPCC) 2001 Climate Change 2001 The 507
Scientific Basis Contribution of Working Group I to the Third Assessment Report of the 508
Intergovernmental Panel on Climate Change edited by J T Houghton et al 881 pp 509
Cambridge Univ Press New York 510
Ishizaka M H Motoyoshi S Nakai T Shiina T Kumakura and K-i Muramoto 2013 A 511
New Method for Identifying the Main Type of Solid Hydrometeors Contributing to 512
Snowfall from Measured Size-Fall Speed Relationship Journal of the Meteorological 513
Society of Japan Ser II 91(6) 747-762 httpsdoiorg102151jmsj2013-602 514
Khvorostyanov V 2005 Fall Velocities of Hydrometeors in the Atmosphere 515
Refinements to a Continuous Analytical Power Law J Atmos Sci 62 4343-4357 516
httpsdoiorg101175JAS36221 517
Kikuchi K T Kameda K Higuchi and A Yamashita 2013 A global classification of 518
snow crystals ice crystals and solid precipitation based on observations from middle 519
latitudes to polar regions Atmos Res 132-133 460-472 520
Kneifel S A von Lerber J Tiira D Moisseev P Kollias and J Leinonen 2015 521
Observed relations between snowfall microphysics and triple-frequency radar 522
25
measurements J Geophys Res Atmos 120(12) 6034-6055 523
httpsdoi1010022015JD023156 524
Kubicek A and P K Wang 2012 A numerical study of the flow fields around a typical 525
conical graupel falling at various inclination angles Atmos Res 118 15ndash26 526
httpsdoi101016jatmosres201206001 527
Larsen M L A B Kostinski and A R Jameson (2014) Further evidence for 528
superterminal raindrops Geophys Res Lett 41(19) 6914-6918 529
Lee JE SH Jung H M Park S Kwon P L Lin and G W Lee 2015 Classification of 530
Precipitation Types Using Fall Velocity Diameter Relationships from 2D-Video 531
Distrometer Measurements Advances in Atmospheric Sciences (09) 532
Lin Y L J Donner and B A Colle 2010 Parameterization of riming intensity and its 533
impact on ice fall speed using arm data Mon Weather Rev 139(3) 1036ndash1047 534
httpsdoi1011752010MWR32991 535
Liu Y G 1992 Skewness and kurtosis of measured raindrop size distributions Atmos 536
Environ 26A 2713-2716 httpsdoiorg1010160960-1686(92)90005-6 537
Liu Y G 1993 Statistical theory of the Marshall-Parmer distribution of raindrops 538
Atmos Environ 27A 15-19 httpsdoiorg1010160960-1686(93)90066-8 539
Liu Y G and F Liu 1994 On the description of aerosol particle size distribution Atmos 540
Res 31(1-3) 187-198 httpsdoiorg1010160169-8095(94)90043-4 541
Liu Y G L You W Yang F Liu 1995 On the size distribution of cloud droplets Atmos 542
Res 35 (2-4) 201-216 httpsdoiorg1010160169-8095(94)00019-A 543
Locatelli J D and P V Hobbs 1974 Fall speeds and masses of solid precipitation 544
26
particles J Geophys Res 79(15) 2185-2197 httpsdoi101029JC079i015p02185 545
Loumlffler-Mang M and J Joss 2000 An optical disdrometer for measuring size and 546
velocity of hydrometeors J Atmos Oceanic Technol 17 130-139 547
httpsdoiorg1011751520-0426(2000)017lt0130AODFMSgt20CO2 548
Loumlffler-Mang M and U Blahak 2001 Estimation of the Equivalent Radar Reflectivity 549
Factor from Measured Snow Size Spectra J Clim Appl Meteorol 40(4) 843-849 550
httpsdoiorg1011751520-0450(2001)040lt0843EOTERRgt20CO2 551
Matrosov S Y 2007 Modeling Backscatter Properties of Snowfall at Millimeter 552
Wavelengths J Atmos Sci 64(5) 1727-1736 httpsdoiorg101175JAS39041 553
Mitchell D L 1996 Use of mass- and area-dimensional power laws for determining 554
precipitation particle terminal velocities J Atmos Sci 53 1710-1723 555
httpsdoiorg1011751520-0469(1996)053lt1710UOMAADgt20CO2 556
Montero-Martiacutenez G A B Kostinski R A Shaw and F Garciacutea-Garciacutea 2009 Do all 557
raindrops fall at terminal speed Geophys Res Lett 36 L11818 558
httpsdoiorg1010292008GL037111 559
Niu S X Jia J Sang X Liu C Lu and Y Liu 2010 Distributions of raindrop sizes and 560
fall velocities in a semiarid plateau climate Convective vs stratiform rains J Appl 561
Meteorol Climatol 49 632ndash645 httpsdoi1011752009JAMC22081 562
Nurzyńska K M Kubo and K-i Muramoto 2012 Texture operator for snow particle 563
classification into snowflake and graupel Atmos Res 118 121-132 564
Oue M M R Kumjian Y Lu J Verlinde K Aydin and E E Clothiaux 2015 Linear 565
27
Depolarization Ratios of columnar ice crystals in a deep precipitating system over the 566
Arctic observed by Zenith-Pointing Ka-Band Doppler radar J Clim Appl Meteorol 567
54(5) 1060-1068 httpsdoiorg101175JAMC-D-15-00121 568
Pruppacher H R and J D Klett 1998 Microphysics of clouds and precipitation Kluwer 569
Academic 954 pp 570
Rasmussen R B Baker et al 2012 How well are we measuring snow the 571
NOAAFAANCAR winter precipitation test bed Bull Amer Meteor Soc 93(6) 811-829 572
httpsdoiorg101175BAMS-D-11-000521 573
Reisner J R M Rasmussen and R T Bruintjes 1998 Explicit forecasting of 574
supercooled liquid water in winter storms using the MM5 mesoscale model Q J R 575
Meteorol Soc 124 1071ndash1107 httpsdoi101256smsqj54803 576
Rosenfeld D and Ulbrich C W 2003 Cloud microphysical properties processes and 577
rainfall estimation opportunities Meteorol Monogr 30 237-237 578
httpsdoiorg101175 0065-9401(2003)030lt0237cmppargt20CO2 579
Schaefer V J 1956 The preparation of snow crystal replicas-VI Weatherwsie 9 580
132-135 581
Souverijns N A Gossart S Lhermitte I V Gorodetskaya S Kneifel M Maahn F L 582
Bliven and N P M van Lipzig (2017) Estimating radar reflectivity - Snowfall rate 583
relationships and their uncertainties over Antarctica by combining disdrometer and 584
radar observations Atmos Res 196 211-223 585
Taylor K E 2001 Summarizing multiple aspects of model performance in a single 586
diagram J Geophys Res 106 7183ndash7192 httpsdoi1010292000JD900719 587
28
Tokay A and D A Short 1996 Evidence from tropical raindrop spectra of the origin of 588
rain from stratiform versus convective clouds J Appl Meteor 35 355ndash371 589
Tokay A and D Atlas 1999 Rainfall microphysics and radar properties analysis 590
methods for drop size spectra J Appl Meteor 37 912-923 591
httpsdoiorg1011751520-0450(1998)037lt0912RMARPAgt20CO2 592
Tokay A D B Wolff et al 2014 Evaluation of the New version of the laser-optical 593
disdrometer OTT Parsivel2 J Atmos Oceanic Technol 31(6) 1276-1288 594
httpsdoiorg101175JTECH-D-13-001741 595
Ulbrich C W 1983 Natural variations in the analytical form of the raindrop size 596
distribution J Appl Meteor 5 1764-1775 597
Wen G H Xiao H Yang Y Bi and W Xu 2017 Characteristics of summer and winter 598
precipitation over northern China Atmos Res 197 390-406 599
Wu W Y Liu and A K Betts 2012 Observationally based evaluation of NWP 600
reanalyses in modeling cloud properties over the Southern Great Plains J Geophys 601
Res 117 D12202 httpsdoi1010292011JD016971 602
Yuter S E D E Kingsmill L B Nance and M Loumlffler-Mang 2006 Observations of 603
precipitation size and fall velocity characteristics within coexisting rain and wet snow J 604
Appl Meteor Climatol 45 1450ndash1464 doi httpsdoiorg101175JAM24061 605
Zhang P C and B Y Du 2000 Radar Meteorology China Meteorological Press 511pp 606
(in Chinese) 607
608
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
3
Short 1996 Souverijns et al 2017) and ground measurement (Chen et al 2011 46
Nurzyńska et al 2012 Ishizaka et al 2013 Huang et al 2017) of solid hydrometeors 47
Despite the great development solid precipitation measurement and parameterization 48
still suffer from large uncertainties and much work remains to be done Detailed solid 49
hydrometeor observations including size distribution fall velocity and shape of 50
hydrometeors are needed to improve microphysical parameterization in numerical 51
models and remote sensing 52
Hydrometeors properties (eg size concentration geometric shape and fall 53
velocity) are essential for further improving parameterizations of precipitation 54
processes and remote sensing (especially of polarized radar) In particular recent 55
developments in disdrometer and remote sensing techniques permit retrievals of more 56
hydrometeor size distribution (HSD) parameters and their vertical profiles over large 57
areas (Loumlffler-Mang and Blahak 2001 Matrosov 2007 Kneifel et al 2015) and 58
enhance our ability to monitor and investigate solid hydrometeor events and 59
microphysics At the same time more accurate assumptions regarding the spectral 60
shape of HSDs for different hydrometer types are needed which vary spatially and 61
temporally (Kikuchi et al 2013) Unfortunately our understanding of the hydrometeors 62
and direct measurements of solid precipitation is far from complete and more analyses 63
of in situ measurements are needed (Souverijns et al 2017) 64
Fall velocity is equally important and closely related to the HSD measurements 65
radar retrievals and parameterizations Fall velocity measurements of solid 66
hydrometeors can be traced to an empirical study by Locatelli and Hobbs (1974) which 67
4
is still utilized in microphysical parameterizations Later studies include those based on 68
fluid dynamics (Boumlhm 1989 Mitchell 1996 Khvorostyanov 2005 Heymsfield and 69
Westbrook 2010 Kubicek and Wang 2012) and using automated ground-based 70
disdrometers (Barthazy and Schefold 2006 Yuter et al 2006 Ishizaka et al 2013 Chen 71
et al 2011) 72
Most of these studies assume that the surrounding air is still rather than a 73
turbulent environment as in actual precipitating clouds Yuter et al (2006) obtained size 74
and fall velocity distributions within coexisting rain and wet snow (sleet) by using a 75
disdrometer but insufficient details of quantified results were provided The influence 76
of riming particle shape temperature and turbulence on the fallspeed of solid 77
precipitation in disdrometer measurements were further discussed (Barthazy and 78
Schefold 2006 Garrett and Yuter 2014 Geresdi et al 2014) However many factors 79
have influences on solid hydrometeor fall velocity and the complex effects have not 80
been yet adequately investigated 81
In a previous study (Niu et al 2010) we discussed the air density and other factors 82
(ie turbulence organized air motions break-up and measurement errors) that 83
potentially influence on distributions of raindrop sizes and fall velocities and called 84
attention to the turbulence induced the large velocity spread at given raindrop sizes 85
This work is a further extension of Niu et al (2010) to analyze measurements of size 86
and fall velocity distributions of solid hydrometeors collected during a recent field 87
experiment campaign conducted northeast of Beijing China to simultaneously 88
measure HSDs and fall velocities with a PARSIVEL disdrometer (see Section 2 for details) 89
5
This paper has two specific objectives (1) to distinguish and quantify hydrometeor 90
types and their fall velocities by combining disdrometer microscopic photography and 91
cloud radar observation (2) to characterize and compare the spectral shapes of HSDs 92
from different precipitation types 93
The rest of the paper is organized as follows Section 2 describes the experiment and 94
data Section 3 classifies hydrometeors and analyzes the size and fall velocity 95
distributions Section 4 examines the characters of HSDs and evaluates the distribution 96
function for describing HSDs The major findings are summarized in Section 5 97
2 Description of Experiment and Data 98
The observation site was on Haituo Mountain at a height of 1310 m located in 99
northwest of Beijing (40deg35primeN 115deg50primeE) China (Fig 1) The site is in the semiarid 100
temperate monsoon climate regime with mean winter precipitation amount for each 101
event is about 080 mm (2014-2015) (Ma et al 2017) All the observed events are stratiform 102
precipitation classified by the surface cloud radar China Weather Radar (Doppler radar) 103
and manual observations The entire radar reflectivity maximums are lower than 30 dBZ 104
which is chosen as the threshold reflectivity of convective precipitation (Zhang and Du 105
2000) 106
HSDs were measured with a PARSIVEL disdrometer and the measurement methods 107
are the same as employed in Niu et al (2010) Loumlffler-Mang and Joss (2000) and Tokay 108
et al (2014) provided detailed description of the PARSIVEL disdrometer The instrument 109
measures the maximum diameter of one-dimensional projection of the particle which is 110
smaller than or equal to the actual maximum diameter Snow particles are often not 111
6
horizontally symmetric and thus particle sizes for snow may underestimate actual maximum 112
particle diameter Battaglia et al (2010) pointed out that PARSIVELrsquos fall velocity 113
measurement may not be accurate for snowflakes due to the internally assumed relationship 114
between horizontal and vertical snow particle dimensions The uncertainty originates from 115
the shape-related factor which tends to depart more with increasing snowflake sizes and 116
can produce large errors When averaging over a large number of snowflakes the correction 117
factor is size dependent with a systematic tendency to underestimate the fall speed (but 118
never exceeding 20) The maximum error 20 of the empirical terminal velocities for 119
graupel and snowflake is used to estimate the instrument caused possible velocities such 120
as the dash lines in igure 2b In addition graupel is almost spherical hydrometeor and the 121
instrument error could not reach 20 The individual HSD sample interval was 10 seconds 122
The following criteria are used in choosing data for analysis (1) Particles smaller 123
than 025 mm are discarded (2) the total particle number of a HSD is over 10 counts 124
(every 10-sec sample) (Niu et al 2010) (3) precipitation lasted more than 30 minutes 125
are chosen (4) solid hydrometeor density is corrected with the equation ρs =126
017Dminus1 for solid hydrometeors (Boudala et al 2014) (5) Following Chen et al (2017) 127
raindrops outside +60 of the empirical terminal velocity of raindrop (Table 3) and -60 128
of empirical terminal velocity of densely rimed dendrites were excluded in the analysis 129
to minimize the effects of ldquomargin fallersrdquo winds and splashing Hydrometeors were 130
also collected with Formvar slides (76 cm long and 26 cm wide) which are exposed 131
outside for 5s to capture the hydrometeors with a sampling interval of 5 minutes The 132
Formvar samples were examined and photographed with a microscope-camera system 133
7
following the method described by Schaefer (1956) The two-dimensional photo of 134
hydrometeors allows a careful determination of the hydrometeor shape and size The 135
Formvar data were used to distinguish dominant hydrometeor types eg raindrop 136
graupel or snowflake The hydrometeor type with a percentage of occurrence gt60 is 137
used to represent the solid precipitation type for convenience of analysis 138
A Ka-band millimeter wavelength cloud radar (wavelength is 8 mm) was used to 139
probe the vertical structure of clouds by vertical scanning from 11202016 which can 140
be used to determine cloud properties at 1 min temporal and 30 m vertical resolution 141
A total of 11098 HSD samples were collected from 12 precipitation events (Table 1) 142
Four representative hydrometeor types from the precipitation events are identified 143
raindrop graupel snowflake and mixed-phase precipitation The identification of the 144
hydrometeor types is mainly based on hydrometeors velocity observations and Formvar 145
images which will be detailed in Section 4 Mixed-phased precipitation contains 146
raindrops graupels and snowflakes simultaneously and none is dominant over another 147
The duration sample number precipitation rate and dominant type of hydrometeor 148
are shown in Table 1 The precipitation rate is calculated from HSD using the method 149
presented in Boudala et al (2014) 150
3 Hydrometeor Classification and Size and Fall Velocity 151
Distributions 152
a General Feature 153
Fig 2 illustrates the observed mean number concentration as a function of the 154
maximum dimension and the fall velocity for the four types of hydrometeors 155
8
respectively Also shown as a reference are the seven solid curves representing 156
different types of hydrometeor terminal velocities obtained from the laboratory 157
measurements calibrated by coefficient 50
0
since the site altitude is 1310 m 158
average pressure is 868 hpa and the average temperature is -5 ordmC (Niu et al2010) 159
(equations are shown in Table 3) Here ρ is the actual air density and ρ0 is the 160
standard atmospheric density The updrafts downdrafts and turbulence often 161
accompany falling hydrometeors inducing deviations in the velocity and trajectory of 162
falling hydrometeors from those in still air (Donnadieu 1980) Hence in this field 163
observation fall velocities of hydrometeors distribute along the terminal velocity curves 164
with large spread for each given size Similar features have been previously reported in 165
some situ measurements of raindrop fall velocities (Niu et al 2010 Rasmussen et al 166
2012) 167
In the previous study we discussed the air density and potential influencing 168
factors (eg turbulence organized air motions break-up and measurement errors) for 169
raindrop (Niu et al 2010) For precipitation in winter the hydrometeor shape is vitally 170
important for fall velocity The hydrometeor shape influence on fall velocities physical 171
mechanisms and instrument error underlying the large spread in the measured fall 172
velocities of different types are discussed in detail in the next two sub-sections 173
b Effect of Hydrometeor Type on Fall Velocity 174
In Fig 2a the hydrometeor fall velocities agree with the typical raindrop terminal 175
velocity curve which is obviously larger than the terminal velocities of graupel and 176
9
snowflake at given maximum diameters From the fall velocity distribution we can infer 177
that these hydrometeors are mainly raindrops The microscope photos obtained on the 178
ground confirm this However unlike the raindrop size and velocity distribution in 179
summer in Figure 8a of Niu et al (2010) there are some small size hydrometeors 180
(05~35mm) at very low speeds (05~2 ms) distributing among the terminal velocity 181
curves for graupel and snowflake This result implies that beside liquid raindrops 182
(including small raindrops or droplets from drizzle) some small snowflakes also exist in 183
the measurement The microscope photos also support the finding that although 184
raindrops are dominant some small plane- and column- shaped snowflakes co-exist 185
Fig 2b shows the joint hydrometeor size and fall velocity distribution during the 186
graupel event The hydrometeors are mainly symmetrically distributed around the ideal 187
terminal velocity of graupel (Locatelli and Hobbs 1974) supported by the photo-based 188
hydrometeor classification On the other hand it is found that certain small droplets 189
with the maximum dimensions among 03 to 10 mm are distributed around the liquid 190
raindrop curve suggesting that there are some raindrops and droplets coexisting in the 191
graupel dominated precipitation It is recognized that graupels grow by snow crystals 192
collecting cloud droplets and small raindrops (Pruppacher and Klett 1998) high cloud 193
top more liquid water content and presence of small raindrops (as shown in 194
microscope photography) provide favorable conditions for graupel The microscope 195
photos also display that graupelsrsquo surfaces are lumpy because of riming super cooled 196
drops during growing 197
The fall velocities of hydrometeors in Fig 2c are much smaller than the terminal 198
10
velocities of raindrop and graupel but are close to the terminal velocity curves of snow 199
of hexagonal densely rimed dendrites aggregates of dendrites Synthesizing the size 200
data the hydrometeors can be inferred as snowflakes which are further confirmed by 201
surface microscope photos From the surface observation we found many 202
rimedunrimed or aggregated dendrites or hexagonal snowflakes Although riming and 203
aggregation microphysical processes have some influence on terminal velocity 204
(Barthazy and Schefold 2006 Garrett and Yuter 2014 Heymsfield and Westbrook 205
2010) but the influences are too small to distinguish only from observed fall velocity 206
since it is a combined result of many factors When maximum dimensions are among 207
03 to 10 mm there are some small hydrometeors with fall velocities larger than 208
snowflakes which maybe graupels raindrops and droplets 209
Fig 2d is the hydrometeor size and fall velocity distribution during a mixed-phased 210
precipitation The hydrometeor fall velocities exhibit the largest spread for example 211
the fall velocities for hydrometeors with maximum dimension equaling to 3 mm 212
change from 05 to 5 ms and do not distribute along any of the ideal terminal velocity 213
curves This result suggests that different hydrometeor types might coexist during the 214
same sampling time To substantiate supercooled raindrops graupels and different 215
kinds of snowflakes are observed from the surface microscope simultaneously Similar 216
changes in particle size and fall velocity distribution documented by the disdrometer as 217
the storm transitions from rain to mixed-phase to snow were found at Marshall Field 218
site (Rasmussen et al 2012) 219
11
c Other Influencing Factors 220
The different dependence on particle size of terminal velocities for different types 221
of hydrometeors can explain some systematic distribution of the PARSIVEL-measured 222
fall velocities but the large spreads in the measurement of the instant particle fall 223
velocities await further inspection 224
According to our previous work the fall velocity (V) of a hydrometeor measured by 225
the PARSIVEL can be regarded as a combination of the terminal velocity in still air (Vt) 226
and a component Vrsquo that results from all other potential influencing factors eg type 227
turbulence organized air motions break-up and measurement errors (Niu et al 228
2010) 229
119881 = 119881119905 + 119881 prime (1) 230
The large spread of the measurements at both sides of the terminal velocity curves 231
shown in figure 2 seems compatible with the notion of nearly random collections of 232
downdraft and updraft A wider spread for fall velocities implies a wider range of 233
variation in vertical motions when hydrometeors are liquid raindrops (Niu et al 2010) 234
Solid nonspherical hydrometeors are much more complex than liquid drops and the 235
large spread of velocities may be caused by several other factors First different types 236
of hydrometeors (columns bullets plates lump graupels and hexagonal snowflakes et 237
al) have different fall speeds It is long recognized that microphysical processes in cold 238
precipitation are more complex and consequently generate more types of solid 239
hydrometeors comparing to the generation of raindrops The averaged concentration 240
distributions of large number of samples shown in Figure 2 also represents the possible 241
12
distributions of hydrometeors If there is only one kind particle the high concentration 242
would along its ideal terminal velocity very well just like the raindrop possible 243
distribution (Niu et al 2010) The concentration of mixed precipitation in Fig 2d does 244
not along any singe ideal terminal velocity further improved there are more than one 245
kind of hydrometers Coexistence of different types of hydrometeors induces larger 246
spread of fall velocities Second different degrees of riming and aggregating may affect 247
the results Densely rimed particles fall faster than unrimed particles with the same 248
maximum dimension aggregated snowflakes generally fall faster than their component 249
crystals (Barthazy and Schefold 2006 Garrett and Yuter 2014 Locatelli and Hobbs 250
1974) Third solid hydrometeors more likely occur breakup aggregation collision and 251
coalescence processes because of the large range of speeds According to prior 252
research of raindrop breakup and coalescence would lead to the ldquohigher-than-terminal 253
velocityrdquo fall velocity for small drops but ldquolower-than-terminal velocityrdquo fall velocity for 254
large drops (Niu et al 2010 Montero-Martiacutenez et al 2009 Larsen et al 2014) Similar 255
results are expected for the fall velocity of solid hydrometeors Last but not the least 256
the disdrometer may suffer from instrumental errors due to the internally assumed 257
relationship between horizontal and vertical particle dimensions likely resulting in a 258
wider spreads of fall velocities for the graupel and snowflakes as compared to the 259
raindrop counterpart as discussed in Section 2 Although the instrument error is an 260
important factor that should be considered in velocity spread as shown in Fig2b the 261
instrument error could not cause that large velocity spread The possible distributions 262
of fall velocities are the combine effects of physical and instrument principle 263
13
Further support for the possible instrumental uncertainty is from the cloud radar 264
observations Fig 3 shows the cloud reflectivity and linear depolarization ratio (LDR) in 265
lower level (less than 08 km) for the graupel snowflake and mixed-phased 266
precipitations respectively The LDR is a valuable observable in identifying the 267
hydrometeor types (Oue et al 2015) As shown in Fig 3a the cloud top height of 268
graupel precipitation was up to 7km during 1900 to 2050 Beijng Time (BT) which was 269
highest among the three events The high cloud top implies stronger updraft and 270
turbulence which further induces a larger fall velocity spread The LDR value was the 271
smallest among the three events indicating that the hydrometeors were close to 272
spherical consistent to the surface observations The cloud top height of snowflake 273
precipitation was up to 35 km (Fig 3c) which was the lowest among the three types of 274
precipitations implying weakest updraft and turbulence Notably although the 275
snowflake types are more complex than those of graupels the velocity spread was not 276
as large as that of the graupel type likely because of the weakest updraft and 277
turbulence The LDR was relatively larger consistent with the surface snowflake 278
observations (Fig 3d) The cloud top height of mixed-phase precipitation was up to 45 279
km (Fig 3e) and the LDR in lower level was largest among the three types of 280
precipitations owing to coexistence of raindrops graupels and snowflakes (Fig 3f) 281
4 Hydrometeor Size Distributions 282
a Comparison of HSDs between Different Types 283
There were four representative types of precipitations during this field experiment 284
providing us a unique opportunity to examine the HSD differences between the four 285
14
types of hydrometeors The sample numbers mean maximum dimensions and number 286
concentrations for each kind of HSDs are given in Table 2 Figure 4 is the averaged 287
distribution of all measured HSDs of 4 kinds As shown in Figure 4 on average the 288
mixed-phased precipitation tends to have most small size hydrometeors with D lt 15 289
mm while snowflake precipitation has the least small hydrometeors among the four 290
types The snowflake precipitation has more large size hydrometeors ie 3 mm lt D lt 11 291
mm Graupel size distribution tends to have two peeks around 13 mm and 26 mm The 292
mean maximum dimension is largest for snowflake (126 mm) and smallest for the 293
mixed HSD due to many small particles Similar results were found in precipitation 294
occurring in the Cascade and Rocky Mountains (Yuter et al 2006) The PARSIVEL 295
disdrometer doesnrsquot provide reliable data for small drops lower than 05 mm and tends to 296
underestimate small drops so the relatively low concentrations of small drops likely resulted 297
from the instrumentrsquos shortcomings (Tokay et al 2013 and Chen et al 2017) 298
b Evaluation of Distribution Functions for Describing HSDs 299
Over the last few decades great efforts have been devoted to finding the 300
appropriate analytical functions for describing the HSD because of its wide applications 301
in many areas including remote sensing and parameterization of precipitation (Chen et 302
al 2017) The two distribution functions mostly used up to now are the Lognormal 303
(Feingold and Levin 1986 Rosenfeld and Ulbrich 2003) and the Gamma (Ulbrich 1983) 304
distributions The Gamma distribution has been proposed as a first order generalization 305
of the Exponential distribution when μ equals 0 (Table 4) Weibull distribution is 306
another function used to describe size distributions of raindrops and cloud droplets (Liu 307
15
and Liu 1994 Liu et al 1995) Nevertheless the question as to which functions are 308
more adequate to describe HSDs of solid hydrometeors have been rarely investigated 309
systematically and quantitatively Thus the objective of this section is to examine the 310
most adequate distribution function used to describe HSDs 311
Considering size distributions of raindrops cloud droplets and aerosol particles are 312
the end results of many (stochastic) complex processes Liu (1992 1993 1994 and 313
1995) proposed a statistical method based on the relationships between the skewness 314
(S) and kurtosis (K) derived from an ensemble of particle size distribution 315
measurements and from those commonly used size distribution functions Cugerone 316
and Michele (2017) also used a similar approach based on the S-K relationships to study 317
raindrop size distributions Unlike the conventional curve-fitting of individual size 318
distributions this approach applies to an ensemble of size distribution measurements 319
and identifies the most appropriate statistical distribution pattern Here we apply this 320
approach to investigate if the statistical pattern of the HSDs of four precipitation types 321
follows the Exponential Gaussian Gamma Weibull and Lognormal distributions (Table 322
4) and if there are any pattern differences between them Briefly S and K of a HSD are 323
calculated from the corresponding HSD with the following two equations 324
23
2
3
t
iii
t
iii
dDN
)(Dn)D(D
dDN
)(Dn)D(D
S
minus
minus
=
(2) 325
32
2
4
minus
minus
minus
=
dDN
)(Dn)D(D
dDN
)(Dn)D(D
K
t
iii
t
iii
(3) 326
16
where Di is the central diameter of the i-th bin ni is the number concentration of the 327
i-th bin and Nt is total number concentration Note that each individual HSD can be 328
used to obtain a pair of S and K which is shown as a dot in Figure 5 Also noteworthy is 329
that the SndashK relationships for the families of Gamma Weibull and Lognormal are 330
described by known analytical functions (Liu 1993 1994 and 1995 Cugerone and 331
Michele 2017) represented by theoretical curves in Figure 5 The Exponential and 332
Gaussian distributions are represented by single points on the S-K diagram (S=2 and K=6 333
for Exponential) and (S=0 and K=0 for Gaussian) respectively Thus by comparing the 334
measured S and K values (points) with the known theoretical curves one can determine 335
the most proper function used to describe HSDs 336
Figure 5 shows the scatter plots of observed SndashK pairs calculated from the HSD 337
measurements for raindrop graupel snowflake mixed-phase precipitations Also 338
shown as comparison are the theoretical curves corresponding to the analytical HSD 339
functions A few points are evident First despite some occasional departures most of 340
the points fall near the theoretical lines of Gamma and Weibull distributions suggesting 341
that the HSD patterns for all the four types of precipitations well follow the Gamma and 342
Weibull distributions statistically Second HSDs of raindrops and mixed hydrometeors 343
are better described by Gamma and Weibull distribution than graupels and snowflakes 344
Third the S and K do not cluster around points (2 6) and (0 0) suggesting that the 345
Gaussian and Exponential distribution are not appropriate for describing HSDs 346
especially Gaussian distribution 347
To further evaluate the overall performance of the different distribution functions 348
17
we employ the widely used technique of Taylor diagram (Taylor 2001) and ldquoRelative 349
Euclidean Distancerdquo (RED) (Wu et al 2012) as a supplement to the Taylor diagram The 350
Taylor diagram has been widely used to visualize the statistical differences between 351
model results and observations in evaluation of model performance against 352
measurements or other benchmarks (IPCC 2001) Correlation coefficient (r) standard 353
deviation (σ) and ldquocentered root-mean-square errorrdquo (RMSE hereafter) are used in 354
the Taylor diagram The RED is introduced to add the bias as well in a dimensionless 355
framework that allows for comparison between different physical quantities with 356
different units In this study we consider the S and K values derived from the 357
distribution functions as model results and evaluate them against those derived from 358
the HSD measurements Brieflythe expressions for calculating r and σ and RMSE are 359
shown below 360
119903 =1
119873sum (119872119899minus)(119874119899minus)119873119899=1
120590119872120590119900 (4) 361
119877119872119878119864 = 1
119873sum [(119872119899 minus ) minus (119874119899 minus )]2119873119899=1
12
(5) 362
120590119872 = [1
119873sum (119872119899 minus )119873119899=1 ]
12
(6) 363
1205900 = [1
119873sum (119874119899 minus )119873119899=1 ]
12
(7) 364
where M and O denote distribution function and observed variables The RED 365
expression is shown below 366
119877119864119863 = [(minus)
]2
+ [(120590119872minus120590119874)
120590119900]2
+ (1 minus 119903)212
( 8 ) 367
Equation (8) indicates that RED considers all the components of mean bias variations 368
and correlations in a dimensionless way the distribution function performance 369
degrades as RED increases from the perfect agreement with RED=0 370
18
In the Taylor diagrams shown in Fig 6 the cosine of azimuthal angle of each point 371
gives the r between the function-calculated and observed data The distance between 372
individual point and the reference point ldquoObsrdquo represents the RMSE normalized by the 373
amplitude of the observationally based variations As this distance approaches to zero 374
the function-calculated K and S approach to the observations Clearly the values of r 375
are around 097 for Gamma and Weibull r for Lognormal function is slightly smaller 376
(095) The normalized σ are much different for Lognormal Gamma and Weibull 377
distributions with averaged value being 057 0895 and 0785 respectively Therefore 378
the Lognormal distribution exhibits the worst performance for describing HSDs and 379
Gamma and Weibull distributions appear to perform much better (Fig 6a) 380
Noticing that S and K of Gamma and Weibull distributions are equal at the point of S 381
= 2 and K = 6 and have positive relationship (If S lt 2 then K lt 6 and if S gt 2 then k gt 6) In 382
this part we further separately examine the group of data with S lt 2 and K lt 6 (Fig 6b) 383
and compare its result with those of total data The averaged normalized σ are 103 and 384
109 and r are 091 and 090 for Weibull and Gamma distributions respectively 385
suggesting that Weibull distribution performs slightly better than Gamma distribution 386
for the four HSD types in the data group of S lt 2 and K lt 6 whereas the opposite is true 387
for all data This conclusion is further substantiated by comparison of RED values for the 388
four type of precipitation (Fig7) which shows that Lognormal has the largest RED 389
Gamma the smallest and Weibull in between for four types of precipitations in all data 390
whereas Weibull (Lognormal) has smallest (largest) RED values when S lt 2 and K lt 6 It 391
can be inferred for data group of S gt 2 and k gt 6 Gamma distribution performs better 392
19
Further comparison between different precipitation types shows these functions all 393
performs better for raindrop size distributions and mixed-phase than graupel and 394
snowflake size distributions The RED for snowflakes is largest among the four types 395
The performance of Gamma is better for describing solid HSDs of all data but Weibull 396
distribution is better when S lt 2 and K lt 6 397
5 Conclusion 398
The combined measurements collected during a field experiment conducted at the 399
Haituo Mountain site using PARSIVEL disdrometer millimeter wavelength cloud radar 400
and microscope photography are analyzed to classify the precipitation hydrometeor 401
types examine the dependence of fall velocity on hydrometeor size for different 402
hydrometeor types and determine the best distribution functions to describe the 403
hydrometeor size distributions of different types 404
Analysis of the PARSIVEL-measured fall velocities show that on average the 405
dependence of fall velocity on hydrometeor size largely follow their corresponding 406
terminal velocity curves for raindrops graupels and snowflakes respectively suggesting 407
that such measurements are useful to identify the hydrometeor types The associated 408
microscope photos and cloud radar observations support the classification of 409
hydrometeor types based on the PARSIVEL-observed fall velocities Furthermore there 410
are velocity spreads in fall velocity across hydrometeor sizes for all hydrometeors and 411
the spreads for the solid hydrometeors could cause by hydrometeor type turbulence or 412
updraftdowndraft and instrument measured principle The coexistence of various 413
types of hydrometeors likely induces additional spread of fall velocity for given 414
20
hydrometeor sizes such as mixed precipitation Meanwhile complex microphysical 415
processes in cold precipitation such as riming aggregation breakup and collision and 416
coalescence influence fall velocity which likely induce larger spread of fall velocity Last 417
but not the least the disdrometer may suffer from instrumental errors due to the 418
internally assumed relationship between horizontal and vertical particle dimensions 419
Comparison of the type-averaged hydrometeor size distributions shows that the 420
mixed precipitation has more small hydrometeors with D lt 15 mm than others 421
whereas the snowflake precipitation has the least number of small hydrometeors 422
among the four types On the contrary the snowflake precipitation has more large 423
hydrometeors with D between 3 mm and 11 mm 424
The commonly used size distribution functions (Gamma Weibull and Lognormal) 425
are further examined to determine the most adequate function to describe the size 426
distribution measurements for all the hydrometeor types by use of an approach based 427
on the relationship between skewness (S) and kurtosis (K) Taylor diagram and RED are 428
further introduced to assess the performance of different size distribution functions 429
against measurements It is shown that the HSDs for the four types can all be well 430
described statistically by the Gamma and Weibull distribution but Lognormal 431
Exponential and Gaussian are not fit to describe HSDs Gamma and Weibull distribution 432
describe raindrop and mixed-phase size distribution better than snowflake and graupel 433
size distribution and their performances are worst for snowflake It may due to graupel 434
and snowflake precipitation have more big particles When S less than 2 and K less than 435
6 Weibull distribution performs better than Gamma distribution to describe HSDs but 436
21
Gamma distribution performs better for total data 437
A few points are noteworthy First although this study demonstrates the great 438
potential of combining simultaneous disdrometer measurements of particle fall velocity 439
and size distributions microscopic photography and cloud radar to address the 440
challenges facing solid precipitation the data are limited More research is needed to 441
discern such effects on the results presented here Second as the observations show 442
that in addition to sizes there are many other factors (eg hydrometeor type 443
microphysical processes turbulence and measuring principle) that can potentially 444
influence particle fall velocity as well More comprehensive research is needed to 445
further discern and separate these factors Finally the combined use of S-K diagram 446
Taylor diagram and relative Euclidean distance appears to be a powerful tool for 447
identifying the best function used to describe the HSDs and quantify the differences 448
between different precipitation types More research is in order along this direction 449
Acknowledgements 450
This study is mainly supported by the Chinese National Science Foundation under Grant 451
No 41675138 and National Key RampD Program of China (2017YFC0209604) It is partly 452
supported by Beijing National Science Foundation (8172023) the US Department 453
Energys Atmospheric System Research (ASR) Program (Liu and Jia at BNL) Lu is 454
supported by the Natural Science Foundation of Jiangsu Province (BK20160041) The 455
observation data are archived at a specialized supercomputer at Beijing Meteorology 456
Information Center (ftp10224592) which are available from the corresponding 457
author upon request The authors also thank Beijing weather modification office for 458
their support during the field experiment 459
Reference 460
22
Agosta CC Fettweis XX Datta RR 2015 Evaluation of the CMIP5 models in the 461
aim of regional modelling of the Antarctic surface mass balance Cryosphere 9 2311ndash462
2321 httpdxdoiorg105194tc-9-2311-2015 463
Barthazy E and R Schefold 2006 Fall velocity of snowflakes of different riming degree 464
and crystal types Atmos Res 82(1) 391-398 httpsdoiorg101016jatmosres 465
200512009 466
Battaglia A Rustemeier E Tokay A et al 2010 PARSIVEL snow observations a critical 467
assessment J Atmos Oceanic Technol 27(2) 333-344 doi 1011752009jtecha13321 468
Boumlhm H P 1989 A General Equation for the Terminal Fall Speed of Solid Hydrometeors 469
J Atmos Sci 46(15) 2419-2427 httpsdoiorg1011751520-0469(1989)046 lt2419A 470
GEFTTgt20CO2 471
Boudala F S G A Isaac et al 2014 Comparisons of Snowfall Measurements in 472
Complex Terrain Made During the 2010 Winter Olympics in Vancouver Pure and 473
Applied Geophysics 171(1) 113-127 474
Chen B W Hu and J Pu 2011 Characteristics of the raindrop size distribution for 475
freezing precipitation observed in southern China J Geophys Res 116 D06201 476
doi1010292010JD015305 477
Chen B Z Hu L Liu and G Zhang (2017) Raindrop Size Distribution Measurements at 478
4500m on the Tibetan Plateau during TIPEX-III J Geophys Res 122 11092-11106 479
doiorg10100 22017JD027233 480
23
Cugerone K and C De Michele 2017 Investigating raindrop size distributions in the 481
(L-)skewness-(L-)kurtosis plane Quart J Roy Meteor Soc 143(704) 1303-1312 482
httpsdoiorg101002qj3005 483
Donnadieu G 1980 Comparison of results obtained with the VIDIAZ spectro 484
pluviometer and the JossndashWaldvogel rainfall disdrometer in a ldquorain of a thundery typerdquo 485
J Appl Meteor 19 593ndash597 486
Feingold G and Levin Z 1986 The lognormal fit to raindrop spectra from frontal 487
convective clouds in Israel J Clim Appl Meteorol 25 1346ndash1363 488
httpsdoiorg1011751520-0450(1986)025lt1346tlftrsgt20CO2 489
Field P R A J Heymsfield and A Bansemer 2007 Snow Size Distribution 490
Parameterization for Midlatitude and Tropical Ice Clouds J Atmos Sci 64(12) 491
4346-4365 httpsdoiorg1011752007JAS23441 492
Garrett T J and S E Yuter 2014 Observed influence of riming temperature and 493
turbulence on the fallspeed of solid precipitation Geophysical Research Letters 41(18) 494
6515ndash6522 495
Geresdi I N Sarkadi and G Thompson 2014 Effect of the accretion by water drops 496
on the melting of snowflakes Atmos Res 149 96-110 497
Gunn R and G D Kinzer 1949 The terminal velocity of fall for water drops in stagnant 498
air J Meteor 6 243-248 httpsdoiorg1011751520-0469(1949)006lt0243TTVOFFgt 499
20CO2 500
24
Heymsfield A J and C D Westbrook 2010 Advances in the Estimation of Ice Particle 501
Fall Speeds Using Laboratory and Field Measurements J Atmos Sci 67(8) 2469-2482 502
httpsdoiorg1011752010JAS33791 503
Huang G-J C Kleinkort V N Bringi and B M Notaroš 2017 Winter precipitation 504
particle size distribution measurement by Multi-Angle Snowflake Camera Atmos Res 505
198 81-96 506
Intergovernmental Panel on Climate Change (IPCC) 2001 Climate Change 2001 The 507
Scientific Basis Contribution of Working Group I to the Third Assessment Report of the 508
Intergovernmental Panel on Climate Change edited by J T Houghton et al 881 pp 509
Cambridge Univ Press New York 510
Ishizaka M H Motoyoshi S Nakai T Shiina T Kumakura and K-i Muramoto 2013 A 511
New Method for Identifying the Main Type of Solid Hydrometeors Contributing to 512
Snowfall from Measured Size-Fall Speed Relationship Journal of the Meteorological 513
Society of Japan Ser II 91(6) 747-762 httpsdoiorg102151jmsj2013-602 514
Khvorostyanov V 2005 Fall Velocities of Hydrometeors in the Atmosphere 515
Refinements to a Continuous Analytical Power Law J Atmos Sci 62 4343-4357 516
httpsdoiorg101175JAS36221 517
Kikuchi K T Kameda K Higuchi and A Yamashita 2013 A global classification of 518
snow crystals ice crystals and solid precipitation based on observations from middle 519
latitudes to polar regions Atmos Res 132-133 460-472 520
Kneifel S A von Lerber J Tiira D Moisseev P Kollias and J Leinonen 2015 521
Observed relations between snowfall microphysics and triple-frequency radar 522
25
measurements J Geophys Res Atmos 120(12) 6034-6055 523
httpsdoi1010022015JD023156 524
Kubicek A and P K Wang 2012 A numerical study of the flow fields around a typical 525
conical graupel falling at various inclination angles Atmos Res 118 15ndash26 526
httpsdoi101016jatmosres201206001 527
Larsen M L A B Kostinski and A R Jameson (2014) Further evidence for 528
superterminal raindrops Geophys Res Lett 41(19) 6914-6918 529
Lee JE SH Jung H M Park S Kwon P L Lin and G W Lee 2015 Classification of 530
Precipitation Types Using Fall Velocity Diameter Relationships from 2D-Video 531
Distrometer Measurements Advances in Atmospheric Sciences (09) 532
Lin Y L J Donner and B A Colle 2010 Parameterization of riming intensity and its 533
impact on ice fall speed using arm data Mon Weather Rev 139(3) 1036ndash1047 534
httpsdoi1011752010MWR32991 535
Liu Y G 1992 Skewness and kurtosis of measured raindrop size distributions Atmos 536
Environ 26A 2713-2716 httpsdoiorg1010160960-1686(92)90005-6 537
Liu Y G 1993 Statistical theory of the Marshall-Parmer distribution of raindrops 538
Atmos Environ 27A 15-19 httpsdoiorg1010160960-1686(93)90066-8 539
Liu Y G and F Liu 1994 On the description of aerosol particle size distribution Atmos 540
Res 31(1-3) 187-198 httpsdoiorg1010160169-8095(94)90043-4 541
Liu Y G L You W Yang F Liu 1995 On the size distribution of cloud droplets Atmos 542
Res 35 (2-4) 201-216 httpsdoiorg1010160169-8095(94)00019-A 543
Locatelli J D and P V Hobbs 1974 Fall speeds and masses of solid precipitation 544
26
particles J Geophys Res 79(15) 2185-2197 httpsdoi101029JC079i015p02185 545
Loumlffler-Mang M and J Joss 2000 An optical disdrometer for measuring size and 546
velocity of hydrometeors J Atmos Oceanic Technol 17 130-139 547
httpsdoiorg1011751520-0426(2000)017lt0130AODFMSgt20CO2 548
Loumlffler-Mang M and U Blahak 2001 Estimation of the Equivalent Radar Reflectivity 549
Factor from Measured Snow Size Spectra J Clim Appl Meteorol 40(4) 843-849 550
httpsdoiorg1011751520-0450(2001)040lt0843EOTERRgt20CO2 551
Matrosov S Y 2007 Modeling Backscatter Properties of Snowfall at Millimeter 552
Wavelengths J Atmos Sci 64(5) 1727-1736 httpsdoiorg101175JAS39041 553
Mitchell D L 1996 Use of mass- and area-dimensional power laws for determining 554
precipitation particle terminal velocities J Atmos Sci 53 1710-1723 555
httpsdoiorg1011751520-0469(1996)053lt1710UOMAADgt20CO2 556
Montero-Martiacutenez G A B Kostinski R A Shaw and F Garciacutea-Garciacutea 2009 Do all 557
raindrops fall at terminal speed Geophys Res Lett 36 L11818 558
httpsdoiorg1010292008GL037111 559
Niu S X Jia J Sang X Liu C Lu and Y Liu 2010 Distributions of raindrop sizes and 560
fall velocities in a semiarid plateau climate Convective vs stratiform rains J Appl 561
Meteorol Climatol 49 632ndash645 httpsdoi1011752009JAMC22081 562
Nurzyńska K M Kubo and K-i Muramoto 2012 Texture operator for snow particle 563
classification into snowflake and graupel Atmos Res 118 121-132 564
Oue M M R Kumjian Y Lu J Verlinde K Aydin and E E Clothiaux 2015 Linear 565
27
Depolarization Ratios of columnar ice crystals in a deep precipitating system over the 566
Arctic observed by Zenith-Pointing Ka-Band Doppler radar J Clim Appl Meteorol 567
54(5) 1060-1068 httpsdoiorg101175JAMC-D-15-00121 568
Pruppacher H R and J D Klett 1998 Microphysics of clouds and precipitation Kluwer 569
Academic 954 pp 570
Rasmussen R B Baker et al 2012 How well are we measuring snow the 571
NOAAFAANCAR winter precipitation test bed Bull Amer Meteor Soc 93(6) 811-829 572
httpsdoiorg101175BAMS-D-11-000521 573
Reisner J R M Rasmussen and R T Bruintjes 1998 Explicit forecasting of 574
supercooled liquid water in winter storms using the MM5 mesoscale model Q J R 575
Meteorol Soc 124 1071ndash1107 httpsdoi101256smsqj54803 576
Rosenfeld D and Ulbrich C W 2003 Cloud microphysical properties processes and 577
rainfall estimation opportunities Meteorol Monogr 30 237-237 578
httpsdoiorg101175 0065-9401(2003)030lt0237cmppargt20CO2 579
Schaefer V J 1956 The preparation of snow crystal replicas-VI Weatherwsie 9 580
132-135 581
Souverijns N A Gossart S Lhermitte I V Gorodetskaya S Kneifel M Maahn F L 582
Bliven and N P M van Lipzig (2017) Estimating radar reflectivity - Snowfall rate 583
relationships and their uncertainties over Antarctica by combining disdrometer and 584
radar observations Atmos Res 196 211-223 585
Taylor K E 2001 Summarizing multiple aspects of model performance in a single 586
diagram J Geophys Res 106 7183ndash7192 httpsdoi1010292000JD900719 587
28
Tokay A and D A Short 1996 Evidence from tropical raindrop spectra of the origin of 588
rain from stratiform versus convective clouds J Appl Meteor 35 355ndash371 589
Tokay A and D Atlas 1999 Rainfall microphysics and radar properties analysis 590
methods for drop size spectra J Appl Meteor 37 912-923 591
httpsdoiorg1011751520-0450(1998)037lt0912RMARPAgt20CO2 592
Tokay A D B Wolff et al 2014 Evaluation of the New version of the laser-optical 593
disdrometer OTT Parsivel2 J Atmos Oceanic Technol 31(6) 1276-1288 594
httpsdoiorg101175JTECH-D-13-001741 595
Ulbrich C W 1983 Natural variations in the analytical form of the raindrop size 596
distribution J Appl Meteor 5 1764-1775 597
Wen G H Xiao H Yang Y Bi and W Xu 2017 Characteristics of summer and winter 598
precipitation over northern China Atmos Res 197 390-406 599
Wu W Y Liu and A K Betts 2012 Observationally based evaluation of NWP 600
reanalyses in modeling cloud properties over the Southern Great Plains J Geophys 601
Res 117 D12202 httpsdoi1010292011JD016971 602
Yuter S E D E Kingsmill L B Nance and M Loumlffler-Mang 2006 Observations of 603
precipitation size and fall velocity characteristics within coexisting rain and wet snow J 604
Appl Meteor Climatol 45 1450ndash1464 doi httpsdoiorg101175JAM24061 605
Zhang P C and B Y Du 2000 Radar Meteorology China Meteorological Press 511pp 606
(in Chinese) 607
608
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
4
is still utilized in microphysical parameterizations Later studies include those based on 68
fluid dynamics (Boumlhm 1989 Mitchell 1996 Khvorostyanov 2005 Heymsfield and 69
Westbrook 2010 Kubicek and Wang 2012) and using automated ground-based 70
disdrometers (Barthazy and Schefold 2006 Yuter et al 2006 Ishizaka et al 2013 Chen 71
et al 2011) 72
Most of these studies assume that the surrounding air is still rather than a 73
turbulent environment as in actual precipitating clouds Yuter et al (2006) obtained size 74
and fall velocity distributions within coexisting rain and wet snow (sleet) by using a 75
disdrometer but insufficient details of quantified results were provided The influence 76
of riming particle shape temperature and turbulence on the fallspeed of solid 77
precipitation in disdrometer measurements were further discussed (Barthazy and 78
Schefold 2006 Garrett and Yuter 2014 Geresdi et al 2014) However many factors 79
have influences on solid hydrometeor fall velocity and the complex effects have not 80
been yet adequately investigated 81
In a previous study (Niu et al 2010) we discussed the air density and other factors 82
(ie turbulence organized air motions break-up and measurement errors) that 83
potentially influence on distributions of raindrop sizes and fall velocities and called 84
attention to the turbulence induced the large velocity spread at given raindrop sizes 85
This work is a further extension of Niu et al (2010) to analyze measurements of size 86
and fall velocity distributions of solid hydrometeors collected during a recent field 87
experiment campaign conducted northeast of Beijing China to simultaneously 88
measure HSDs and fall velocities with a PARSIVEL disdrometer (see Section 2 for details) 89
5
This paper has two specific objectives (1) to distinguish and quantify hydrometeor 90
types and their fall velocities by combining disdrometer microscopic photography and 91
cloud radar observation (2) to characterize and compare the spectral shapes of HSDs 92
from different precipitation types 93
The rest of the paper is organized as follows Section 2 describes the experiment and 94
data Section 3 classifies hydrometeors and analyzes the size and fall velocity 95
distributions Section 4 examines the characters of HSDs and evaluates the distribution 96
function for describing HSDs The major findings are summarized in Section 5 97
2 Description of Experiment and Data 98
The observation site was on Haituo Mountain at a height of 1310 m located in 99
northwest of Beijing (40deg35primeN 115deg50primeE) China (Fig 1) The site is in the semiarid 100
temperate monsoon climate regime with mean winter precipitation amount for each 101
event is about 080 mm (2014-2015) (Ma et al 2017) All the observed events are stratiform 102
precipitation classified by the surface cloud radar China Weather Radar (Doppler radar) 103
and manual observations The entire radar reflectivity maximums are lower than 30 dBZ 104
which is chosen as the threshold reflectivity of convective precipitation (Zhang and Du 105
2000) 106
HSDs were measured with a PARSIVEL disdrometer and the measurement methods 107
are the same as employed in Niu et al (2010) Loumlffler-Mang and Joss (2000) and Tokay 108
et al (2014) provided detailed description of the PARSIVEL disdrometer The instrument 109
measures the maximum diameter of one-dimensional projection of the particle which is 110
smaller than or equal to the actual maximum diameter Snow particles are often not 111
6
horizontally symmetric and thus particle sizes for snow may underestimate actual maximum 112
particle diameter Battaglia et al (2010) pointed out that PARSIVELrsquos fall velocity 113
measurement may not be accurate for snowflakes due to the internally assumed relationship 114
between horizontal and vertical snow particle dimensions The uncertainty originates from 115
the shape-related factor which tends to depart more with increasing snowflake sizes and 116
can produce large errors When averaging over a large number of snowflakes the correction 117
factor is size dependent with a systematic tendency to underestimate the fall speed (but 118
never exceeding 20) The maximum error 20 of the empirical terminal velocities for 119
graupel and snowflake is used to estimate the instrument caused possible velocities such 120
as the dash lines in igure 2b In addition graupel is almost spherical hydrometeor and the 121
instrument error could not reach 20 The individual HSD sample interval was 10 seconds 122
The following criteria are used in choosing data for analysis (1) Particles smaller 123
than 025 mm are discarded (2) the total particle number of a HSD is over 10 counts 124
(every 10-sec sample) (Niu et al 2010) (3) precipitation lasted more than 30 minutes 125
are chosen (4) solid hydrometeor density is corrected with the equation ρs =126
017Dminus1 for solid hydrometeors (Boudala et al 2014) (5) Following Chen et al (2017) 127
raindrops outside +60 of the empirical terminal velocity of raindrop (Table 3) and -60 128
of empirical terminal velocity of densely rimed dendrites were excluded in the analysis 129
to minimize the effects of ldquomargin fallersrdquo winds and splashing Hydrometeors were 130
also collected with Formvar slides (76 cm long and 26 cm wide) which are exposed 131
outside for 5s to capture the hydrometeors with a sampling interval of 5 minutes The 132
Formvar samples were examined and photographed with a microscope-camera system 133
7
following the method described by Schaefer (1956) The two-dimensional photo of 134
hydrometeors allows a careful determination of the hydrometeor shape and size The 135
Formvar data were used to distinguish dominant hydrometeor types eg raindrop 136
graupel or snowflake The hydrometeor type with a percentage of occurrence gt60 is 137
used to represent the solid precipitation type for convenience of analysis 138
A Ka-band millimeter wavelength cloud radar (wavelength is 8 mm) was used to 139
probe the vertical structure of clouds by vertical scanning from 11202016 which can 140
be used to determine cloud properties at 1 min temporal and 30 m vertical resolution 141
A total of 11098 HSD samples were collected from 12 precipitation events (Table 1) 142
Four representative hydrometeor types from the precipitation events are identified 143
raindrop graupel snowflake and mixed-phase precipitation The identification of the 144
hydrometeor types is mainly based on hydrometeors velocity observations and Formvar 145
images which will be detailed in Section 4 Mixed-phased precipitation contains 146
raindrops graupels and snowflakes simultaneously and none is dominant over another 147
The duration sample number precipitation rate and dominant type of hydrometeor 148
are shown in Table 1 The precipitation rate is calculated from HSD using the method 149
presented in Boudala et al (2014) 150
3 Hydrometeor Classification and Size and Fall Velocity 151
Distributions 152
a General Feature 153
Fig 2 illustrates the observed mean number concentration as a function of the 154
maximum dimension and the fall velocity for the four types of hydrometeors 155
8
respectively Also shown as a reference are the seven solid curves representing 156
different types of hydrometeor terminal velocities obtained from the laboratory 157
measurements calibrated by coefficient 50
0
since the site altitude is 1310 m 158
average pressure is 868 hpa and the average temperature is -5 ordmC (Niu et al2010) 159
(equations are shown in Table 3) Here ρ is the actual air density and ρ0 is the 160
standard atmospheric density The updrafts downdrafts and turbulence often 161
accompany falling hydrometeors inducing deviations in the velocity and trajectory of 162
falling hydrometeors from those in still air (Donnadieu 1980) Hence in this field 163
observation fall velocities of hydrometeors distribute along the terminal velocity curves 164
with large spread for each given size Similar features have been previously reported in 165
some situ measurements of raindrop fall velocities (Niu et al 2010 Rasmussen et al 166
2012) 167
In the previous study we discussed the air density and potential influencing 168
factors (eg turbulence organized air motions break-up and measurement errors) for 169
raindrop (Niu et al 2010) For precipitation in winter the hydrometeor shape is vitally 170
important for fall velocity The hydrometeor shape influence on fall velocities physical 171
mechanisms and instrument error underlying the large spread in the measured fall 172
velocities of different types are discussed in detail in the next two sub-sections 173
b Effect of Hydrometeor Type on Fall Velocity 174
In Fig 2a the hydrometeor fall velocities agree with the typical raindrop terminal 175
velocity curve which is obviously larger than the terminal velocities of graupel and 176
9
snowflake at given maximum diameters From the fall velocity distribution we can infer 177
that these hydrometeors are mainly raindrops The microscope photos obtained on the 178
ground confirm this However unlike the raindrop size and velocity distribution in 179
summer in Figure 8a of Niu et al (2010) there are some small size hydrometeors 180
(05~35mm) at very low speeds (05~2 ms) distributing among the terminal velocity 181
curves for graupel and snowflake This result implies that beside liquid raindrops 182
(including small raindrops or droplets from drizzle) some small snowflakes also exist in 183
the measurement The microscope photos also support the finding that although 184
raindrops are dominant some small plane- and column- shaped snowflakes co-exist 185
Fig 2b shows the joint hydrometeor size and fall velocity distribution during the 186
graupel event The hydrometeors are mainly symmetrically distributed around the ideal 187
terminal velocity of graupel (Locatelli and Hobbs 1974) supported by the photo-based 188
hydrometeor classification On the other hand it is found that certain small droplets 189
with the maximum dimensions among 03 to 10 mm are distributed around the liquid 190
raindrop curve suggesting that there are some raindrops and droplets coexisting in the 191
graupel dominated precipitation It is recognized that graupels grow by snow crystals 192
collecting cloud droplets and small raindrops (Pruppacher and Klett 1998) high cloud 193
top more liquid water content and presence of small raindrops (as shown in 194
microscope photography) provide favorable conditions for graupel The microscope 195
photos also display that graupelsrsquo surfaces are lumpy because of riming super cooled 196
drops during growing 197
The fall velocities of hydrometeors in Fig 2c are much smaller than the terminal 198
10
velocities of raindrop and graupel but are close to the terminal velocity curves of snow 199
of hexagonal densely rimed dendrites aggregates of dendrites Synthesizing the size 200
data the hydrometeors can be inferred as snowflakes which are further confirmed by 201
surface microscope photos From the surface observation we found many 202
rimedunrimed or aggregated dendrites or hexagonal snowflakes Although riming and 203
aggregation microphysical processes have some influence on terminal velocity 204
(Barthazy and Schefold 2006 Garrett and Yuter 2014 Heymsfield and Westbrook 205
2010) but the influences are too small to distinguish only from observed fall velocity 206
since it is a combined result of many factors When maximum dimensions are among 207
03 to 10 mm there are some small hydrometeors with fall velocities larger than 208
snowflakes which maybe graupels raindrops and droplets 209
Fig 2d is the hydrometeor size and fall velocity distribution during a mixed-phased 210
precipitation The hydrometeor fall velocities exhibit the largest spread for example 211
the fall velocities for hydrometeors with maximum dimension equaling to 3 mm 212
change from 05 to 5 ms and do not distribute along any of the ideal terminal velocity 213
curves This result suggests that different hydrometeor types might coexist during the 214
same sampling time To substantiate supercooled raindrops graupels and different 215
kinds of snowflakes are observed from the surface microscope simultaneously Similar 216
changes in particle size and fall velocity distribution documented by the disdrometer as 217
the storm transitions from rain to mixed-phase to snow were found at Marshall Field 218
site (Rasmussen et al 2012) 219
11
c Other Influencing Factors 220
The different dependence on particle size of terminal velocities for different types 221
of hydrometeors can explain some systematic distribution of the PARSIVEL-measured 222
fall velocities but the large spreads in the measurement of the instant particle fall 223
velocities await further inspection 224
According to our previous work the fall velocity (V) of a hydrometeor measured by 225
the PARSIVEL can be regarded as a combination of the terminal velocity in still air (Vt) 226
and a component Vrsquo that results from all other potential influencing factors eg type 227
turbulence organized air motions break-up and measurement errors (Niu et al 228
2010) 229
119881 = 119881119905 + 119881 prime (1) 230
The large spread of the measurements at both sides of the terminal velocity curves 231
shown in figure 2 seems compatible with the notion of nearly random collections of 232
downdraft and updraft A wider spread for fall velocities implies a wider range of 233
variation in vertical motions when hydrometeors are liquid raindrops (Niu et al 2010) 234
Solid nonspherical hydrometeors are much more complex than liquid drops and the 235
large spread of velocities may be caused by several other factors First different types 236
of hydrometeors (columns bullets plates lump graupels and hexagonal snowflakes et 237
al) have different fall speeds It is long recognized that microphysical processes in cold 238
precipitation are more complex and consequently generate more types of solid 239
hydrometeors comparing to the generation of raindrops The averaged concentration 240
distributions of large number of samples shown in Figure 2 also represents the possible 241
12
distributions of hydrometeors If there is only one kind particle the high concentration 242
would along its ideal terminal velocity very well just like the raindrop possible 243
distribution (Niu et al 2010) The concentration of mixed precipitation in Fig 2d does 244
not along any singe ideal terminal velocity further improved there are more than one 245
kind of hydrometers Coexistence of different types of hydrometeors induces larger 246
spread of fall velocities Second different degrees of riming and aggregating may affect 247
the results Densely rimed particles fall faster than unrimed particles with the same 248
maximum dimension aggregated snowflakes generally fall faster than their component 249
crystals (Barthazy and Schefold 2006 Garrett and Yuter 2014 Locatelli and Hobbs 250
1974) Third solid hydrometeors more likely occur breakup aggregation collision and 251
coalescence processes because of the large range of speeds According to prior 252
research of raindrop breakup and coalescence would lead to the ldquohigher-than-terminal 253
velocityrdquo fall velocity for small drops but ldquolower-than-terminal velocityrdquo fall velocity for 254
large drops (Niu et al 2010 Montero-Martiacutenez et al 2009 Larsen et al 2014) Similar 255
results are expected for the fall velocity of solid hydrometeors Last but not the least 256
the disdrometer may suffer from instrumental errors due to the internally assumed 257
relationship between horizontal and vertical particle dimensions likely resulting in a 258
wider spreads of fall velocities for the graupel and snowflakes as compared to the 259
raindrop counterpart as discussed in Section 2 Although the instrument error is an 260
important factor that should be considered in velocity spread as shown in Fig2b the 261
instrument error could not cause that large velocity spread The possible distributions 262
of fall velocities are the combine effects of physical and instrument principle 263
13
Further support for the possible instrumental uncertainty is from the cloud radar 264
observations Fig 3 shows the cloud reflectivity and linear depolarization ratio (LDR) in 265
lower level (less than 08 km) for the graupel snowflake and mixed-phased 266
precipitations respectively The LDR is a valuable observable in identifying the 267
hydrometeor types (Oue et al 2015) As shown in Fig 3a the cloud top height of 268
graupel precipitation was up to 7km during 1900 to 2050 Beijng Time (BT) which was 269
highest among the three events The high cloud top implies stronger updraft and 270
turbulence which further induces a larger fall velocity spread The LDR value was the 271
smallest among the three events indicating that the hydrometeors were close to 272
spherical consistent to the surface observations The cloud top height of snowflake 273
precipitation was up to 35 km (Fig 3c) which was the lowest among the three types of 274
precipitations implying weakest updraft and turbulence Notably although the 275
snowflake types are more complex than those of graupels the velocity spread was not 276
as large as that of the graupel type likely because of the weakest updraft and 277
turbulence The LDR was relatively larger consistent with the surface snowflake 278
observations (Fig 3d) The cloud top height of mixed-phase precipitation was up to 45 279
km (Fig 3e) and the LDR in lower level was largest among the three types of 280
precipitations owing to coexistence of raindrops graupels and snowflakes (Fig 3f) 281
4 Hydrometeor Size Distributions 282
a Comparison of HSDs between Different Types 283
There were four representative types of precipitations during this field experiment 284
providing us a unique opportunity to examine the HSD differences between the four 285
14
types of hydrometeors The sample numbers mean maximum dimensions and number 286
concentrations for each kind of HSDs are given in Table 2 Figure 4 is the averaged 287
distribution of all measured HSDs of 4 kinds As shown in Figure 4 on average the 288
mixed-phased precipitation tends to have most small size hydrometeors with D lt 15 289
mm while snowflake precipitation has the least small hydrometeors among the four 290
types The snowflake precipitation has more large size hydrometeors ie 3 mm lt D lt 11 291
mm Graupel size distribution tends to have two peeks around 13 mm and 26 mm The 292
mean maximum dimension is largest for snowflake (126 mm) and smallest for the 293
mixed HSD due to many small particles Similar results were found in precipitation 294
occurring in the Cascade and Rocky Mountains (Yuter et al 2006) The PARSIVEL 295
disdrometer doesnrsquot provide reliable data for small drops lower than 05 mm and tends to 296
underestimate small drops so the relatively low concentrations of small drops likely resulted 297
from the instrumentrsquos shortcomings (Tokay et al 2013 and Chen et al 2017) 298
b Evaluation of Distribution Functions for Describing HSDs 299
Over the last few decades great efforts have been devoted to finding the 300
appropriate analytical functions for describing the HSD because of its wide applications 301
in many areas including remote sensing and parameterization of precipitation (Chen et 302
al 2017) The two distribution functions mostly used up to now are the Lognormal 303
(Feingold and Levin 1986 Rosenfeld and Ulbrich 2003) and the Gamma (Ulbrich 1983) 304
distributions The Gamma distribution has been proposed as a first order generalization 305
of the Exponential distribution when μ equals 0 (Table 4) Weibull distribution is 306
another function used to describe size distributions of raindrops and cloud droplets (Liu 307
15
and Liu 1994 Liu et al 1995) Nevertheless the question as to which functions are 308
more adequate to describe HSDs of solid hydrometeors have been rarely investigated 309
systematically and quantitatively Thus the objective of this section is to examine the 310
most adequate distribution function used to describe HSDs 311
Considering size distributions of raindrops cloud droplets and aerosol particles are 312
the end results of many (stochastic) complex processes Liu (1992 1993 1994 and 313
1995) proposed a statistical method based on the relationships between the skewness 314
(S) and kurtosis (K) derived from an ensemble of particle size distribution 315
measurements and from those commonly used size distribution functions Cugerone 316
and Michele (2017) also used a similar approach based on the S-K relationships to study 317
raindrop size distributions Unlike the conventional curve-fitting of individual size 318
distributions this approach applies to an ensemble of size distribution measurements 319
and identifies the most appropriate statistical distribution pattern Here we apply this 320
approach to investigate if the statistical pattern of the HSDs of four precipitation types 321
follows the Exponential Gaussian Gamma Weibull and Lognormal distributions (Table 322
4) and if there are any pattern differences between them Briefly S and K of a HSD are 323
calculated from the corresponding HSD with the following two equations 324
23
2
3
t
iii
t
iii
dDN
)(Dn)D(D
dDN
)(Dn)D(D
S
minus
minus
=
(2) 325
32
2
4
minus
minus
minus
=
dDN
)(Dn)D(D
dDN
)(Dn)D(D
K
t
iii
t
iii
(3) 326
16
where Di is the central diameter of the i-th bin ni is the number concentration of the 327
i-th bin and Nt is total number concentration Note that each individual HSD can be 328
used to obtain a pair of S and K which is shown as a dot in Figure 5 Also noteworthy is 329
that the SndashK relationships for the families of Gamma Weibull and Lognormal are 330
described by known analytical functions (Liu 1993 1994 and 1995 Cugerone and 331
Michele 2017) represented by theoretical curves in Figure 5 The Exponential and 332
Gaussian distributions are represented by single points on the S-K diagram (S=2 and K=6 333
for Exponential) and (S=0 and K=0 for Gaussian) respectively Thus by comparing the 334
measured S and K values (points) with the known theoretical curves one can determine 335
the most proper function used to describe HSDs 336
Figure 5 shows the scatter plots of observed SndashK pairs calculated from the HSD 337
measurements for raindrop graupel snowflake mixed-phase precipitations Also 338
shown as comparison are the theoretical curves corresponding to the analytical HSD 339
functions A few points are evident First despite some occasional departures most of 340
the points fall near the theoretical lines of Gamma and Weibull distributions suggesting 341
that the HSD patterns for all the four types of precipitations well follow the Gamma and 342
Weibull distributions statistically Second HSDs of raindrops and mixed hydrometeors 343
are better described by Gamma and Weibull distribution than graupels and snowflakes 344
Third the S and K do not cluster around points (2 6) and (0 0) suggesting that the 345
Gaussian and Exponential distribution are not appropriate for describing HSDs 346
especially Gaussian distribution 347
To further evaluate the overall performance of the different distribution functions 348
17
we employ the widely used technique of Taylor diagram (Taylor 2001) and ldquoRelative 349
Euclidean Distancerdquo (RED) (Wu et al 2012) as a supplement to the Taylor diagram The 350
Taylor diagram has been widely used to visualize the statistical differences between 351
model results and observations in evaluation of model performance against 352
measurements or other benchmarks (IPCC 2001) Correlation coefficient (r) standard 353
deviation (σ) and ldquocentered root-mean-square errorrdquo (RMSE hereafter) are used in 354
the Taylor diagram The RED is introduced to add the bias as well in a dimensionless 355
framework that allows for comparison between different physical quantities with 356
different units In this study we consider the S and K values derived from the 357
distribution functions as model results and evaluate them against those derived from 358
the HSD measurements Brieflythe expressions for calculating r and σ and RMSE are 359
shown below 360
119903 =1
119873sum (119872119899minus)(119874119899minus)119873119899=1
120590119872120590119900 (4) 361
119877119872119878119864 = 1
119873sum [(119872119899 minus ) minus (119874119899 minus )]2119873119899=1
12
(5) 362
120590119872 = [1
119873sum (119872119899 minus )119873119899=1 ]
12
(6) 363
1205900 = [1
119873sum (119874119899 minus )119873119899=1 ]
12
(7) 364
where M and O denote distribution function and observed variables The RED 365
expression is shown below 366
119877119864119863 = [(minus)
]2
+ [(120590119872minus120590119874)
120590119900]2
+ (1 minus 119903)212
( 8 ) 367
Equation (8) indicates that RED considers all the components of mean bias variations 368
and correlations in a dimensionless way the distribution function performance 369
degrades as RED increases from the perfect agreement with RED=0 370
18
In the Taylor diagrams shown in Fig 6 the cosine of azimuthal angle of each point 371
gives the r between the function-calculated and observed data The distance between 372
individual point and the reference point ldquoObsrdquo represents the RMSE normalized by the 373
amplitude of the observationally based variations As this distance approaches to zero 374
the function-calculated K and S approach to the observations Clearly the values of r 375
are around 097 for Gamma and Weibull r for Lognormal function is slightly smaller 376
(095) The normalized σ are much different for Lognormal Gamma and Weibull 377
distributions with averaged value being 057 0895 and 0785 respectively Therefore 378
the Lognormal distribution exhibits the worst performance for describing HSDs and 379
Gamma and Weibull distributions appear to perform much better (Fig 6a) 380
Noticing that S and K of Gamma and Weibull distributions are equal at the point of S 381
= 2 and K = 6 and have positive relationship (If S lt 2 then K lt 6 and if S gt 2 then k gt 6) In 382
this part we further separately examine the group of data with S lt 2 and K lt 6 (Fig 6b) 383
and compare its result with those of total data The averaged normalized σ are 103 and 384
109 and r are 091 and 090 for Weibull and Gamma distributions respectively 385
suggesting that Weibull distribution performs slightly better than Gamma distribution 386
for the four HSD types in the data group of S lt 2 and K lt 6 whereas the opposite is true 387
for all data This conclusion is further substantiated by comparison of RED values for the 388
four type of precipitation (Fig7) which shows that Lognormal has the largest RED 389
Gamma the smallest and Weibull in between for four types of precipitations in all data 390
whereas Weibull (Lognormal) has smallest (largest) RED values when S lt 2 and K lt 6 It 391
can be inferred for data group of S gt 2 and k gt 6 Gamma distribution performs better 392
19
Further comparison between different precipitation types shows these functions all 393
performs better for raindrop size distributions and mixed-phase than graupel and 394
snowflake size distributions The RED for snowflakes is largest among the four types 395
The performance of Gamma is better for describing solid HSDs of all data but Weibull 396
distribution is better when S lt 2 and K lt 6 397
5 Conclusion 398
The combined measurements collected during a field experiment conducted at the 399
Haituo Mountain site using PARSIVEL disdrometer millimeter wavelength cloud radar 400
and microscope photography are analyzed to classify the precipitation hydrometeor 401
types examine the dependence of fall velocity on hydrometeor size for different 402
hydrometeor types and determine the best distribution functions to describe the 403
hydrometeor size distributions of different types 404
Analysis of the PARSIVEL-measured fall velocities show that on average the 405
dependence of fall velocity on hydrometeor size largely follow their corresponding 406
terminal velocity curves for raindrops graupels and snowflakes respectively suggesting 407
that such measurements are useful to identify the hydrometeor types The associated 408
microscope photos and cloud radar observations support the classification of 409
hydrometeor types based on the PARSIVEL-observed fall velocities Furthermore there 410
are velocity spreads in fall velocity across hydrometeor sizes for all hydrometeors and 411
the spreads for the solid hydrometeors could cause by hydrometeor type turbulence or 412
updraftdowndraft and instrument measured principle The coexistence of various 413
types of hydrometeors likely induces additional spread of fall velocity for given 414
20
hydrometeor sizes such as mixed precipitation Meanwhile complex microphysical 415
processes in cold precipitation such as riming aggregation breakup and collision and 416
coalescence influence fall velocity which likely induce larger spread of fall velocity Last 417
but not the least the disdrometer may suffer from instrumental errors due to the 418
internally assumed relationship between horizontal and vertical particle dimensions 419
Comparison of the type-averaged hydrometeor size distributions shows that the 420
mixed precipitation has more small hydrometeors with D lt 15 mm than others 421
whereas the snowflake precipitation has the least number of small hydrometeors 422
among the four types On the contrary the snowflake precipitation has more large 423
hydrometeors with D between 3 mm and 11 mm 424
The commonly used size distribution functions (Gamma Weibull and Lognormal) 425
are further examined to determine the most adequate function to describe the size 426
distribution measurements for all the hydrometeor types by use of an approach based 427
on the relationship between skewness (S) and kurtosis (K) Taylor diagram and RED are 428
further introduced to assess the performance of different size distribution functions 429
against measurements It is shown that the HSDs for the four types can all be well 430
described statistically by the Gamma and Weibull distribution but Lognormal 431
Exponential and Gaussian are not fit to describe HSDs Gamma and Weibull distribution 432
describe raindrop and mixed-phase size distribution better than snowflake and graupel 433
size distribution and their performances are worst for snowflake It may due to graupel 434
and snowflake precipitation have more big particles When S less than 2 and K less than 435
6 Weibull distribution performs better than Gamma distribution to describe HSDs but 436
21
Gamma distribution performs better for total data 437
A few points are noteworthy First although this study demonstrates the great 438
potential of combining simultaneous disdrometer measurements of particle fall velocity 439
and size distributions microscopic photography and cloud radar to address the 440
challenges facing solid precipitation the data are limited More research is needed to 441
discern such effects on the results presented here Second as the observations show 442
that in addition to sizes there are many other factors (eg hydrometeor type 443
microphysical processes turbulence and measuring principle) that can potentially 444
influence particle fall velocity as well More comprehensive research is needed to 445
further discern and separate these factors Finally the combined use of S-K diagram 446
Taylor diagram and relative Euclidean distance appears to be a powerful tool for 447
identifying the best function used to describe the HSDs and quantify the differences 448
between different precipitation types More research is in order along this direction 449
Acknowledgements 450
This study is mainly supported by the Chinese National Science Foundation under Grant 451
No 41675138 and National Key RampD Program of China (2017YFC0209604) It is partly 452
supported by Beijing National Science Foundation (8172023) the US Department 453
Energys Atmospheric System Research (ASR) Program (Liu and Jia at BNL) Lu is 454
supported by the Natural Science Foundation of Jiangsu Province (BK20160041) The 455
observation data are archived at a specialized supercomputer at Beijing Meteorology 456
Information Center (ftp10224592) which are available from the corresponding 457
author upon request The authors also thank Beijing weather modification office for 458
their support during the field experiment 459
Reference 460
22
Agosta CC Fettweis XX Datta RR 2015 Evaluation of the CMIP5 models in the 461
aim of regional modelling of the Antarctic surface mass balance Cryosphere 9 2311ndash462
2321 httpdxdoiorg105194tc-9-2311-2015 463
Barthazy E and R Schefold 2006 Fall velocity of snowflakes of different riming degree 464
and crystal types Atmos Res 82(1) 391-398 httpsdoiorg101016jatmosres 465
200512009 466
Battaglia A Rustemeier E Tokay A et al 2010 PARSIVEL snow observations a critical 467
assessment J Atmos Oceanic Technol 27(2) 333-344 doi 1011752009jtecha13321 468
Boumlhm H P 1989 A General Equation for the Terminal Fall Speed of Solid Hydrometeors 469
J Atmos Sci 46(15) 2419-2427 httpsdoiorg1011751520-0469(1989)046 lt2419A 470
GEFTTgt20CO2 471
Boudala F S G A Isaac et al 2014 Comparisons of Snowfall Measurements in 472
Complex Terrain Made During the 2010 Winter Olympics in Vancouver Pure and 473
Applied Geophysics 171(1) 113-127 474
Chen B W Hu and J Pu 2011 Characteristics of the raindrop size distribution for 475
freezing precipitation observed in southern China J Geophys Res 116 D06201 476
doi1010292010JD015305 477
Chen B Z Hu L Liu and G Zhang (2017) Raindrop Size Distribution Measurements at 478
4500m on the Tibetan Plateau during TIPEX-III J Geophys Res 122 11092-11106 479
doiorg10100 22017JD027233 480
23
Cugerone K and C De Michele 2017 Investigating raindrop size distributions in the 481
(L-)skewness-(L-)kurtosis plane Quart J Roy Meteor Soc 143(704) 1303-1312 482
httpsdoiorg101002qj3005 483
Donnadieu G 1980 Comparison of results obtained with the VIDIAZ spectro 484
pluviometer and the JossndashWaldvogel rainfall disdrometer in a ldquorain of a thundery typerdquo 485
J Appl Meteor 19 593ndash597 486
Feingold G and Levin Z 1986 The lognormal fit to raindrop spectra from frontal 487
convective clouds in Israel J Clim Appl Meteorol 25 1346ndash1363 488
httpsdoiorg1011751520-0450(1986)025lt1346tlftrsgt20CO2 489
Field P R A J Heymsfield and A Bansemer 2007 Snow Size Distribution 490
Parameterization for Midlatitude and Tropical Ice Clouds J Atmos Sci 64(12) 491
4346-4365 httpsdoiorg1011752007JAS23441 492
Garrett T J and S E Yuter 2014 Observed influence of riming temperature and 493
turbulence on the fallspeed of solid precipitation Geophysical Research Letters 41(18) 494
6515ndash6522 495
Geresdi I N Sarkadi and G Thompson 2014 Effect of the accretion by water drops 496
on the melting of snowflakes Atmos Res 149 96-110 497
Gunn R and G D Kinzer 1949 The terminal velocity of fall for water drops in stagnant 498
air J Meteor 6 243-248 httpsdoiorg1011751520-0469(1949)006lt0243TTVOFFgt 499
20CO2 500
24
Heymsfield A J and C D Westbrook 2010 Advances in the Estimation of Ice Particle 501
Fall Speeds Using Laboratory and Field Measurements J Atmos Sci 67(8) 2469-2482 502
httpsdoiorg1011752010JAS33791 503
Huang G-J C Kleinkort V N Bringi and B M Notaroš 2017 Winter precipitation 504
particle size distribution measurement by Multi-Angle Snowflake Camera Atmos Res 505
198 81-96 506
Intergovernmental Panel on Climate Change (IPCC) 2001 Climate Change 2001 The 507
Scientific Basis Contribution of Working Group I to the Third Assessment Report of the 508
Intergovernmental Panel on Climate Change edited by J T Houghton et al 881 pp 509
Cambridge Univ Press New York 510
Ishizaka M H Motoyoshi S Nakai T Shiina T Kumakura and K-i Muramoto 2013 A 511
New Method for Identifying the Main Type of Solid Hydrometeors Contributing to 512
Snowfall from Measured Size-Fall Speed Relationship Journal of the Meteorological 513
Society of Japan Ser II 91(6) 747-762 httpsdoiorg102151jmsj2013-602 514
Khvorostyanov V 2005 Fall Velocities of Hydrometeors in the Atmosphere 515
Refinements to a Continuous Analytical Power Law J Atmos Sci 62 4343-4357 516
httpsdoiorg101175JAS36221 517
Kikuchi K T Kameda K Higuchi and A Yamashita 2013 A global classification of 518
snow crystals ice crystals and solid precipitation based on observations from middle 519
latitudes to polar regions Atmos Res 132-133 460-472 520
Kneifel S A von Lerber J Tiira D Moisseev P Kollias and J Leinonen 2015 521
Observed relations between snowfall microphysics and triple-frequency radar 522
25
measurements J Geophys Res Atmos 120(12) 6034-6055 523
httpsdoi1010022015JD023156 524
Kubicek A and P K Wang 2012 A numerical study of the flow fields around a typical 525
conical graupel falling at various inclination angles Atmos Res 118 15ndash26 526
httpsdoi101016jatmosres201206001 527
Larsen M L A B Kostinski and A R Jameson (2014) Further evidence for 528
superterminal raindrops Geophys Res Lett 41(19) 6914-6918 529
Lee JE SH Jung H M Park S Kwon P L Lin and G W Lee 2015 Classification of 530
Precipitation Types Using Fall Velocity Diameter Relationships from 2D-Video 531
Distrometer Measurements Advances in Atmospheric Sciences (09) 532
Lin Y L J Donner and B A Colle 2010 Parameterization of riming intensity and its 533
impact on ice fall speed using arm data Mon Weather Rev 139(3) 1036ndash1047 534
httpsdoi1011752010MWR32991 535
Liu Y G 1992 Skewness and kurtosis of measured raindrop size distributions Atmos 536
Environ 26A 2713-2716 httpsdoiorg1010160960-1686(92)90005-6 537
Liu Y G 1993 Statistical theory of the Marshall-Parmer distribution of raindrops 538
Atmos Environ 27A 15-19 httpsdoiorg1010160960-1686(93)90066-8 539
Liu Y G and F Liu 1994 On the description of aerosol particle size distribution Atmos 540
Res 31(1-3) 187-198 httpsdoiorg1010160169-8095(94)90043-4 541
Liu Y G L You W Yang F Liu 1995 On the size distribution of cloud droplets Atmos 542
Res 35 (2-4) 201-216 httpsdoiorg1010160169-8095(94)00019-A 543
Locatelli J D and P V Hobbs 1974 Fall speeds and masses of solid precipitation 544
26
particles J Geophys Res 79(15) 2185-2197 httpsdoi101029JC079i015p02185 545
Loumlffler-Mang M and J Joss 2000 An optical disdrometer for measuring size and 546
velocity of hydrometeors J Atmos Oceanic Technol 17 130-139 547
httpsdoiorg1011751520-0426(2000)017lt0130AODFMSgt20CO2 548
Loumlffler-Mang M and U Blahak 2001 Estimation of the Equivalent Radar Reflectivity 549
Factor from Measured Snow Size Spectra J Clim Appl Meteorol 40(4) 843-849 550
httpsdoiorg1011751520-0450(2001)040lt0843EOTERRgt20CO2 551
Matrosov S Y 2007 Modeling Backscatter Properties of Snowfall at Millimeter 552
Wavelengths J Atmos Sci 64(5) 1727-1736 httpsdoiorg101175JAS39041 553
Mitchell D L 1996 Use of mass- and area-dimensional power laws for determining 554
precipitation particle terminal velocities J Atmos Sci 53 1710-1723 555
httpsdoiorg1011751520-0469(1996)053lt1710UOMAADgt20CO2 556
Montero-Martiacutenez G A B Kostinski R A Shaw and F Garciacutea-Garciacutea 2009 Do all 557
raindrops fall at terminal speed Geophys Res Lett 36 L11818 558
httpsdoiorg1010292008GL037111 559
Niu S X Jia J Sang X Liu C Lu and Y Liu 2010 Distributions of raindrop sizes and 560
fall velocities in a semiarid plateau climate Convective vs stratiform rains J Appl 561
Meteorol Climatol 49 632ndash645 httpsdoi1011752009JAMC22081 562
Nurzyńska K M Kubo and K-i Muramoto 2012 Texture operator for snow particle 563
classification into snowflake and graupel Atmos Res 118 121-132 564
Oue M M R Kumjian Y Lu J Verlinde K Aydin and E E Clothiaux 2015 Linear 565
27
Depolarization Ratios of columnar ice crystals in a deep precipitating system over the 566
Arctic observed by Zenith-Pointing Ka-Band Doppler radar J Clim Appl Meteorol 567
54(5) 1060-1068 httpsdoiorg101175JAMC-D-15-00121 568
Pruppacher H R and J D Klett 1998 Microphysics of clouds and precipitation Kluwer 569
Academic 954 pp 570
Rasmussen R B Baker et al 2012 How well are we measuring snow the 571
NOAAFAANCAR winter precipitation test bed Bull Amer Meteor Soc 93(6) 811-829 572
httpsdoiorg101175BAMS-D-11-000521 573
Reisner J R M Rasmussen and R T Bruintjes 1998 Explicit forecasting of 574
supercooled liquid water in winter storms using the MM5 mesoscale model Q J R 575
Meteorol Soc 124 1071ndash1107 httpsdoi101256smsqj54803 576
Rosenfeld D and Ulbrich C W 2003 Cloud microphysical properties processes and 577
rainfall estimation opportunities Meteorol Monogr 30 237-237 578
httpsdoiorg101175 0065-9401(2003)030lt0237cmppargt20CO2 579
Schaefer V J 1956 The preparation of snow crystal replicas-VI Weatherwsie 9 580
132-135 581
Souverijns N A Gossart S Lhermitte I V Gorodetskaya S Kneifel M Maahn F L 582
Bliven and N P M van Lipzig (2017) Estimating radar reflectivity - Snowfall rate 583
relationships and their uncertainties over Antarctica by combining disdrometer and 584
radar observations Atmos Res 196 211-223 585
Taylor K E 2001 Summarizing multiple aspects of model performance in a single 586
diagram J Geophys Res 106 7183ndash7192 httpsdoi1010292000JD900719 587
28
Tokay A and D A Short 1996 Evidence from tropical raindrop spectra of the origin of 588
rain from stratiform versus convective clouds J Appl Meteor 35 355ndash371 589
Tokay A and D Atlas 1999 Rainfall microphysics and radar properties analysis 590
methods for drop size spectra J Appl Meteor 37 912-923 591
httpsdoiorg1011751520-0450(1998)037lt0912RMARPAgt20CO2 592
Tokay A D B Wolff et al 2014 Evaluation of the New version of the laser-optical 593
disdrometer OTT Parsivel2 J Atmos Oceanic Technol 31(6) 1276-1288 594
httpsdoiorg101175JTECH-D-13-001741 595
Ulbrich C W 1983 Natural variations in the analytical form of the raindrop size 596
distribution J Appl Meteor 5 1764-1775 597
Wen G H Xiao H Yang Y Bi and W Xu 2017 Characteristics of summer and winter 598
precipitation over northern China Atmos Res 197 390-406 599
Wu W Y Liu and A K Betts 2012 Observationally based evaluation of NWP 600
reanalyses in modeling cloud properties over the Southern Great Plains J Geophys 601
Res 117 D12202 httpsdoi1010292011JD016971 602
Yuter S E D E Kingsmill L B Nance and M Loumlffler-Mang 2006 Observations of 603
precipitation size and fall velocity characteristics within coexisting rain and wet snow J 604
Appl Meteor Climatol 45 1450ndash1464 doi httpsdoiorg101175JAM24061 605
Zhang P C and B Y Du 2000 Radar Meteorology China Meteorological Press 511pp 606
(in Chinese) 607
608
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
5
This paper has two specific objectives (1) to distinguish and quantify hydrometeor 90
types and their fall velocities by combining disdrometer microscopic photography and 91
cloud radar observation (2) to characterize and compare the spectral shapes of HSDs 92
from different precipitation types 93
The rest of the paper is organized as follows Section 2 describes the experiment and 94
data Section 3 classifies hydrometeors and analyzes the size and fall velocity 95
distributions Section 4 examines the characters of HSDs and evaluates the distribution 96
function for describing HSDs The major findings are summarized in Section 5 97
2 Description of Experiment and Data 98
The observation site was on Haituo Mountain at a height of 1310 m located in 99
northwest of Beijing (40deg35primeN 115deg50primeE) China (Fig 1) The site is in the semiarid 100
temperate monsoon climate regime with mean winter precipitation amount for each 101
event is about 080 mm (2014-2015) (Ma et al 2017) All the observed events are stratiform 102
precipitation classified by the surface cloud radar China Weather Radar (Doppler radar) 103
and manual observations The entire radar reflectivity maximums are lower than 30 dBZ 104
which is chosen as the threshold reflectivity of convective precipitation (Zhang and Du 105
2000) 106
HSDs were measured with a PARSIVEL disdrometer and the measurement methods 107
are the same as employed in Niu et al (2010) Loumlffler-Mang and Joss (2000) and Tokay 108
et al (2014) provided detailed description of the PARSIVEL disdrometer The instrument 109
measures the maximum diameter of one-dimensional projection of the particle which is 110
smaller than or equal to the actual maximum diameter Snow particles are often not 111
6
horizontally symmetric and thus particle sizes for snow may underestimate actual maximum 112
particle diameter Battaglia et al (2010) pointed out that PARSIVELrsquos fall velocity 113
measurement may not be accurate for snowflakes due to the internally assumed relationship 114
between horizontal and vertical snow particle dimensions The uncertainty originates from 115
the shape-related factor which tends to depart more with increasing snowflake sizes and 116
can produce large errors When averaging over a large number of snowflakes the correction 117
factor is size dependent with a systematic tendency to underestimate the fall speed (but 118
never exceeding 20) The maximum error 20 of the empirical terminal velocities for 119
graupel and snowflake is used to estimate the instrument caused possible velocities such 120
as the dash lines in igure 2b In addition graupel is almost spherical hydrometeor and the 121
instrument error could not reach 20 The individual HSD sample interval was 10 seconds 122
The following criteria are used in choosing data for analysis (1) Particles smaller 123
than 025 mm are discarded (2) the total particle number of a HSD is over 10 counts 124
(every 10-sec sample) (Niu et al 2010) (3) precipitation lasted more than 30 minutes 125
are chosen (4) solid hydrometeor density is corrected with the equation ρs =126
017Dminus1 for solid hydrometeors (Boudala et al 2014) (5) Following Chen et al (2017) 127
raindrops outside +60 of the empirical terminal velocity of raindrop (Table 3) and -60 128
of empirical terminal velocity of densely rimed dendrites were excluded in the analysis 129
to minimize the effects of ldquomargin fallersrdquo winds and splashing Hydrometeors were 130
also collected with Formvar slides (76 cm long and 26 cm wide) which are exposed 131
outside for 5s to capture the hydrometeors with a sampling interval of 5 minutes The 132
Formvar samples were examined and photographed with a microscope-camera system 133
7
following the method described by Schaefer (1956) The two-dimensional photo of 134
hydrometeors allows a careful determination of the hydrometeor shape and size The 135
Formvar data were used to distinguish dominant hydrometeor types eg raindrop 136
graupel or snowflake The hydrometeor type with a percentage of occurrence gt60 is 137
used to represent the solid precipitation type for convenience of analysis 138
A Ka-band millimeter wavelength cloud radar (wavelength is 8 mm) was used to 139
probe the vertical structure of clouds by vertical scanning from 11202016 which can 140
be used to determine cloud properties at 1 min temporal and 30 m vertical resolution 141
A total of 11098 HSD samples were collected from 12 precipitation events (Table 1) 142
Four representative hydrometeor types from the precipitation events are identified 143
raindrop graupel snowflake and mixed-phase precipitation The identification of the 144
hydrometeor types is mainly based on hydrometeors velocity observations and Formvar 145
images which will be detailed in Section 4 Mixed-phased precipitation contains 146
raindrops graupels and snowflakes simultaneously and none is dominant over another 147
The duration sample number precipitation rate and dominant type of hydrometeor 148
are shown in Table 1 The precipitation rate is calculated from HSD using the method 149
presented in Boudala et al (2014) 150
3 Hydrometeor Classification and Size and Fall Velocity 151
Distributions 152
a General Feature 153
Fig 2 illustrates the observed mean number concentration as a function of the 154
maximum dimension and the fall velocity for the four types of hydrometeors 155
8
respectively Also shown as a reference are the seven solid curves representing 156
different types of hydrometeor terminal velocities obtained from the laboratory 157
measurements calibrated by coefficient 50
0
since the site altitude is 1310 m 158
average pressure is 868 hpa and the average temperature is -5 ordmC (Niu et al2010) 159
(equations are shown in Table 3) Here ρ is the actual air density and ρ0 is the 160
standard atmospheric density The updrafts downdrafts and turbulence often 161
accompany falling hydrometeors inducing deviations in the velocity and trajectory of 162
falling hydrometeors from those in still air (Donnadieu 1980) Hence in this field 163
observation fall velocities of hydrometeors distribute along the terminal velocity curves 164
with large spread for each given size Similar features have been previously reported in 165
some situ measurements of raindrop fall velocities (Niu et al 2010 Rasmussen et al 166
2012) 167
In the previous study we discussed the air density and potential influencing 168
factors (eg turbulence organized air motions break-up and measurement errors) for 169
raindrop (Niu et al 2010) For precipitation in winter the hydrometeor shape is vitally 170
important for fall velocity The hydrometeor shape influence on fall velocities physical 171
mechanisms and instrument error underlying the large spread in the measured fall 172
velocities of different types are discussed in detail in the next two sub-sections 173
b Effect of Hydrometeor Type on Fall Velocity 174
In Fig 2a the hydrometeor fall velocities agree with the typical raindrop terminal 175
velocity curve which is obviously larger than the terminal velocities of graupel and 176
9
snowflake at given maximum diameters From the fall velocity distribution we can infer 177
that these hydrometeors are mainly raindrops The microscope photos obtained on the 178
ground confirm this However unlike the raindrop size and velocity distribution in 179
summer in Figure 8a of Niu et al (2010) there are some small size hydrometeors 180
(05~35mm) at very low speeds (05~2 ms) distributing among the terminal velocity 181
curves for graupel and snowflake This result implies that beside liquid raindrops 182
(including small raindrops or droplets from drizzle) some small snowflakes also exist in 183
the measurement The microscope photos also support the finding that although 184
raindrops are dominant some small plane- and column- shaped snowflakes co-exist 185
Fig 2b shows the joint hydrometeor size and fall velocity distribution during the 186
graupel event The hydrometeors are mainly symmetrically distributed around the ideal 187
terminal velocity of graupel (Locatelli and Hobbs 1974) supported by the photo-based 188
hydrometeor classification On the other hand it is found that certain small droplets 189
with the maximum dimensions among 03 to 10 mm are distributed around the liquid 190
raindrop curve suggesting that there are some raindrops and droplets coexisting in the 191
graupel dominated precipitation It is recognized that graupels grow by snow crystals 192
collecting cloud droplets and small raindrops (Pruppacher and Klett 1998) high cloud 193
top more liquid water content and presence of small raindrops (as shown in 194
microscope photography) provide favorable conditions for graupel The microscope 195
photos also display that graupelsrsquo surfaces are lumpy because of riming super cooled 196
drops during growing 197
The fall velocities of hydrometeors in Fig 2c are much smaller than the terminal 198
10
velocities of raindrop and graupel but are close to the terminal velocity curves of snow 199
of hexagonal densely rimed dendrites aggregates of dendrites Synthesizing the size 200
data the hydrometeors can be inferred as snowflakes which are further confirmed by 201
surface microscope photos From the surface observation we found many 202
rimedunrimed or aggregated dendrites or hexagonal snowflakes Although riming and 203
aggregation microphysical processes have some influence on terminal velocity 204
(Barthazy and Schefold 2006 Garrett and Yuter 2014 Heymsfield and Westbrook 205
2010) but the influences are too small to distinguish only from observed fall velocity 206
since it is a combined result of many factors When maximum dimensions are among 207
03 to 10 mm there are some small hydrometeors with fall velocities larger than 208
snowflakes which maybe graupels raindrops and droplets 209
Fig 2d is the hydrometeor size and fall velocity distribution during a mixed-phased 210
precipitation The hydrometeor fall velocities exhibit the largest spread for example 211
the fall velocities for hydrometeors with maximum dimension equaling to 3 mm 212
change from 05 to 5 ms and do not distribute along any of the ideal terminal velocity 213
curves This result suggests that different hydrometeor types might coexist during the 214
same sampling time To substantiate supercooled raindrops graupels and different 215
kinds of snowflakes are observed from the surface microscope simultaneously Similar 216
changes in particle size and fall velocity distribution documented by the disdrometer as 217
the storm transitions from rain to mixed-phase to snow were found at Marshall Field 218
site (Rasmussen et al 2012) 219
11
c Other Influencing Factors 220
The different dependence on particle size of terminal velocities for different types 221
of hydrometeors can explain some systematic distribution of the PARSIVEL-measured 222
fall velocities but the large spreads in the measurement of the instant particle fall 223
velocities await further inspection 224
According to our previous work the fall velocity (V) of a hydrometeor measured by 225
the PARSIVEL can be regarded as a combination of the terminal velocity in still air (Vt) 226
and a component Vrsquo that results from all other potential influencing factors eg type 227
turbulence organized air motions break-up and measurement errors (Niu et al 228
2010) 229
119881 = 119881119905 + 119881 prime (1) 230
The large spread of the measurements at both sides of the terminal velocity curves 231
shown in figure 2 seems compatible with the notion of nearly random collections of 232
downdraft and updraft A wider spread for fall velocities implies a wider range of 233
variation in vertical motions when hydrometeors are liquid raindrops (Niu et al 2010) 234
Solid nonspherical hydrometeors are much more complex than liquid drops and the 235
large spread of velocities may be caused by several other factors First different types 236
of hydrometeors (columns bullets plates lump graupels and hexagonal snowflakes et 237
al) have different fall speeds It is long recognized that microphysical processes in cold 238
precipitation are more complex and consequently generate more types of solid 239
hydrometeors comparing to the generation of raindrops The averaged concentration 240
distributions of large number of samples shown in Figure 2 also represents the possible 241
12
distributions of hydrometeors If there is only one kind particle the high concentration 242
would along its ideal terminal velocity very well just like the raindrop possible 243
distribution (Niu et al 2010) The concentration of mixed precipitation in Fig 2d does 244
not along any singe ideal terminal velocity further improved there are more than one 245
kind of hydrometers Coexistence of different types of hydrometeors induces larger 246
spread of fall velocities Second different degrees of riming and aggregating may affect 247
the results Densely rimed particles fall faster than unrimed particles with the same 248
maximum dimension aggregated snowflakes generally fall faster than their component 249
crystals (Barthazy and Schefold 2006 Garrett and Yuter 2014 Locatelli and Hobbs 250
1974) Third solid hydrometeors more likely occur breakup aggregation collision and 251
coalescence processes because of the large range of speeds According to prior 252
research of raindrop breakup and coalescence would lead to the ldquohigher-than-terminal 253
velocityrdquo fall velocity for small drops but ldquolower-than-terminal velocityrdquo fall velocity for 254
large drops (Niu et al 2010 Montero-Martiacutenez et al 2009 Larsen et al 2014) Similar 255
results are expected for the fall velocity of solid hydrometeors Last but not the least 256
the disdrometer may suffer from instrumental errors due to the internally assumed 257
relationship between horizontal and vertical particle dimensions likely resulting in a 258
wider spreads of fall velocities for the graupel and snowflakes as compared to the 259
raindrop counterpart as discussed in Section 2 Although the instrument error is an 260
important factor that should be considered in velocity spread as shown in Fig2b the 261
instrument error could not cause that large velocity spread The possible distributions 262
of fall velocities are the combine effects of physical and instrument principle 263
13
Further support for the possible instrumental uncertainty is from the cloud radar 264
observations Fig 3 shows the cloud reflectivity and linear depolarization ratio (LDR) in 265
lower level (less than 08 km) for the graupel snowflake and mixed-phased 266
precipitations respectively The LDR is a valuable observable in identifying the 267
hydrometeor types (Oue et al 2015) As shown in Fig 3a the cloud top height of 268
graupel precipitation was up to 7km during 1900 to 2050 Beijng Time (BT) which was 269
highest among the three events The high cloud top implies stronger updraft and 270
turbulence which further induces a larger fall velocity spread The LDR value was the 271
smallest among the three events indicating that the hydrometeors were close to 272
spherical consistent to the surface observations The cloud top height of snowflake 273
precipitation was up to 35 km (Fig 3c) which was the lowest among the three types of 274
precipitations implying weakest updraft and turbulence Notably although the 275
snowflake types are more complex than those of graupels the velocity spread was not 276
as large as that of the graupel type likely because of the weakest updraft and 277
turbulence The LDR was relatively larger consistent with the surface snowflake 278
observations (Fig 3d) The cloud top height of mixed-phase precipitation was up to 45 279
km (Fig 3e) and the LDR in lower level was largest among the three types of 280
precipitations owing to coexistence of raindrops graupels and snowflakes (Fig 3f) 281
4 Hydrometeor Size Distributions 282
a Comparison of HSDs between Different Types 283
There were four representative types of precipitations during this field experiment 284
providing us a unique opportunity to examine the HSD differences between the four 285
14
types of hydrometeors The sample numbers mean maximum dimensions and number 286
concentrations for each kind of HSDs are given in Table 2 Figure 4 is the averaged 287
distribution of all measured HSDs of 4 kinds As shown in Figure 4 on average the 288
mixed-phased precipitation tends to have most small size hydrometeors with D lt 15 289
mm while snowflake precipitation has the least small hydrometeors among the four 290
types The snowflake precipitation has more large size hydrometeors ie 3 mm lt D lt 11 291
mm Graupel size distribution tends to have two peeks around 13 mm and 26 mm The 292
mean maximum dimension is largest for snowflake (126 mm) and smallest for the 293
mixed HSD due to many small particles Similar results were found in precipitation 294
occurring in the Cascade and Rocky Mountains (Yuter et al 2006) The PARSIVEL 295
disdrometer doesnrsquot provide reliable data for small drops lower than 05 mm and tends to 296
underestimate small drops so the relatively low concentrations of small drops likely resulted 297
from the instrumentrsquos shortcomings (Tokay et al 2013 and Chen et al 2017) 298
b Evaluation of Distribution Functions for Describing HSDs 299
Over the last few decades great efforts have been devoted to finding the 300
appropriate analytical functions for describing the HSD because of its wide applications 301
in many areas including remote sensing and parameterization of precipitation (Chen et 302
al 2017) The two distribution functions mostly used up to now are the Lognormal 303
(Feingold and Levin 1986 Rosenfeld and Ulbrich 2003) and the Gamma (Ulbrich 1983) 304
distributions The Gamma distribution has been proposed as a first order generalization 305
of the Exponential distribution when μ equals 0 (Table 4) Weibull distribution is 306
another function used to describe size distributions of raindrops and cloud droplets (Liu 307
15
and Liu 1994 Liu et al 1995) Nevertheless the question as to which functions are 308
more adequate to describe HSDs of solid hydrometeors have been rarely investigated 309
systematically and quantitatively Thus the objective of this section is to examine the 310
most adequate distribution function used to describe HSDs 311
Considering size distributions of raindrops cloud droplets and aerosol particles are 312
the end results of many (stochastic) complex processes Liu (1992 1993 1994 and 313
1995) proposed a statistical method based on the relationships between the skewness 314
(S) and kurtosis (K) derived from an ensemble of particle size distribution 315
measurements and from those commonly used size distribution functions Cugerone 316
and Michele (2017) also used a similar approach based on the S-K relationships to study 317
raindrop size distributions Unlike the conventional curve-fitting of individual size 318
distributions this approach applies to an ensemble of size distribution measurements 319
and identifies the most appropriate statistical distribution pattern Here we apply this 320
approach to investigate if the statistical pattern of the HSDs of four precipitation types 321
follows the Exponential Gaussian Gamma Weibull and Lognormal distributions (Table 322
4) and if there are any pattern differences between them Briefly S and K of a HSD are 323
calculated from the corresponding HSD with the following two equations 324
23
2
3
t
iii
t
iii
dDN
)(Dn)D(D
dDN
)(Dn)D(D
S
minus
minus
=
(2) 325
32
2
4
minus
minus
minus
=
dDN
)(Dn)D(D
dDN
)(Dn)D(D
K
t
iii
t
iii
(3) 326
16
where Di is the central diameter of the i-th bin ni is the number concentration of the 327
i-th bin and Nt is total number concentration Note that each individual HSD can be 328
used to obtain a pair of S and K which is shown as a dot in Figure 5 Also noteworthy is 329
that the SndashK relationships for the families of Gamma Weibull and Lognormal are 330
described by known analytical functions (Liu 1993 1994 and 1995 Cugerone and 331
Michele 2017) represented by theoretical curves in Figure 5 The Exponential and 332
Gaussian distributions are represented by single points on the S-K diagram (S=2 and K=6 333
for Exponential) and (S=0 and K=0 for Gaussian) respectively Thus by comparing the 334
measured S and K values (points) with the known theoretical curves one can determine 335
the most proper function used to describe HSDs 336
Figure 5 shows the scatter plots of observed SndashK pairs calculated from the HSD 337
measurements for raindrop graupel snowflake mixed-phase precipitations Also 338
shown as comparison are the theoretical curves corresponding to the analytical HSD 339
functions A few points are evident First despite some occasional departures most of 340
the points fall near the theoretical lines of Gamma and Weibull distributions suggesting 341
that the HSD patterns for all the four types of precipitations well follow the Gamma and 342
Weibull distributions statistically Second HSDs of raindrops and mixed hydrometeors 343
are better described by Gamma and Weibull distribution than graupels and snowflakes 344
Third the S and K do not cluster around points (2 6) and (0 0) suggesting that the 345
Gaussian and Exponential distribution are not appropriate for describing HSDs 346
especially Gaussian distribution 347
To further evaluate the overall performance of the different distribution functions 348
17
we employ the widely used technique of Taylor diagram (Taylor 2001) and ldquoRelative 349
Euclidean Distancerdquo (RED) (Wu et al 2012) as a supplement to the Taylor diagram The 350
Taylor diagram has been widely used to visualize the statistical differences between 351
model results and observations in evaluation of model performance against 352
measurements or other benchmarks (IPCC 2001) Correlation coefficient (r) standard 353
deviation (σ) and ldquocentered root-mean-square errorrdquo (RMSE hereafter) are used in 354
the Taylor diagram The RED is introduced to add the bias as well in a dimensionless 355
framework that allows for comparison between different physical quantities with 356
different units In this study we consider the S and K values derived from the 357
distribution functions as model results and evaluate them against those derived from 358
the HSD measurements Brieflythe expressions for calculating r and σ and RMSE are 359
shown below 360
119903 =1
119873sum (119872119899minus)(119874119899minus)119873119899=1
120590119872120590119900 (4) 361
119877119872119878119864 = 1
119873sum [(119872119899 minus ) minus (119874119899 minus )]2119873119899=1
12
(5) 362
120590119872 = [1
119873sum (119872119899 minus )119873119899=1 ]
12
(6) 363
1205900 = [1
119873sum (119874119899 minus )119873119899=1 ]
12
(7) 364
where M and O denote distribution function and observed variables The RED 365
expression is shown below 366
119877119864119863 = [(minus)
]2
+ [(120590119872minus120590119874)
120590119900]2
+ (1 minus 119903)212
( 8 ) 367
Equation (8) indicates that RED considers all the components of mean bias variations 368
and correlations in a dimensionless way the distribution function performance 369
degrades as RED increases from the perfect agreement with RED=0 370
18
In the Taylor diagrams shown in Fig 6 the cosine of azimuthal angle of each point 371
gives the r between the function-calculated and observed data The distance between 372
individual point and the reference point ldquoObsrdquo represents the RMSE normalized by the 373
amplitude of the observationally based variations As this distance approaches to zero 374
the function-calculated K and S approach to the observations Clearly the values of r 375
are around 097 for Gamma and Weibull r for Lognormal function is slightly smaller 376
(095) The normalized σ are much different for Lognormal Gamma and Weibull 377
distributions with averaged value being 057 0895 and 0785 respectively Therefore 378
the Lognormal distribution exhibits the worst performance for describing HSDs and 379
Gamma and Weibull distributions appear to perform much better (Fig 6a) 380
Noticing that S and K of Gamma and Weibull distributions are equal at the point of S 381
= 2 and K = 6 and have positive relationship (If S lt 2 then K lt 6 and if S gt 2 then k gt 6) In 382
this part we further separately examine the group of data with S lt 2 and K lt 6 (Fig 6b) 383
and compare its result with those of total data The averaged normalized σ are 103 and 384
109 and r are 091 and 090 for Weibull and Gamma distributions respectively 385
suggesting that Weibull distribution performs slightly better than Gamma distribution 386
for the four HSD types in the data group of S lt 2 and K lt 6 whereas the opposite is true 387
for all data This conclusion is further substantiated by comparison of RED values for the 388
four type of precipitation (Fig7) which shows that Lognormal has the largest RED 389
Gamma the smallest and Weibull in between for four types of precipitations in all data 390
whereas Weibull (Lognormal) has smallest (largest) RED values when S lt 2 and K lt 6 It 391
can be inferred for data group of S gt 2 and k gt 6 Gamma distribution performs better 392
19
Further comparison between different precipitation types shows these functions all 393
performs better for raindrop size distributions and mixed-phase than graupel and 394
snowflake size distributions The RED for snowflakes is largest among the four types 395
The performance of Gamma is better for describing solid HSDs of all data but Weibull 396
distribution is better when S lt 2 and K lt 6 397
5 Conclusion 398
The combined measurements collected during a field experiment conducted at the 399
Haituo Mountain site using PARSIVEL disdrometer millimeter wavelength cloud radar 400
and microscope photography are analyzed to classify the precipitation hydrometeor 401
types examine the dependence of fall velocity on hydrometeor size for different 402
hydrometeor types and determine the best distribution functions to describe the 403
hydrometeor size distributions of different types 404
Analysis of the PARSIVEL-measured fall velocities show that on average the 405
dependence of fall velocity on hydrometeor size largely follow their corresponding 406
terminal velocity curves for raindrops graupels and snowflakes respectively suggesting 407
that such measurements are useful to identify the hydrometeor types The associated 408
microscope photos and cloud radar observations support the classification of 409
hydrometeor types based on the PARSIVEL-observed fall velocities Furthermore there 410
are velocity spreads in fall velocity across hydrometeor sizes for all hydrometeors and 411
the spreads for the solid hydrometeors could cause by hydrometeor type turbulence or 412
updraftdowndraft and instrument measured principle The coexistence of various 413
types of hydrometeors likely induces additional spread of fall velocity for given 414
20
hydrometeor sizes such as mixed precipitation Meanwhile complex microphysical 415
processes in cold precipitation such as riming aggregation breakup and collision and 416
coalescence influence fall velocity which likely induce larger spread of fall velocity Last 417
but not the least the disdrometer may suffer from instrumental errors due to the 418
internally assumed relationship between horizontal and vertical particle dimensions 419
Comparison of the type-averaged hydrometeor size distributions shows that the 420
mixed precipitation has more small hydrometeors with D lt 15 mm than others 421
whereas the snowflake precipitation has the least number of small hydrometeors 422
among the four types On the contrary the snowflake precipitation has more large 423
hydrometeors with D between 3 mm and 11 mm 424
The commonly used size distribution functions (Gamma Weibull and Lognormal) 425
are further examined to determine the most adequate function to describe the size 426
distribution measurements for all the hydrometeor types by use of an approach based 427
on the relationship between skewness (S) and kurtosis (K) Taylor diagram and RED are 428
further introduced to assess the performance of different size distribution functions 429
against measurements It is shown that the HSDs for the four types can all be well 430
described statistically by the Gamma and Weibull distribution but Lognormal 431
Exponential and Gaussian are not fit to describe HSDs Gamma and Weibull distribution 432
describe raindrop and mixed-phase size distribution better than snowflake and graupel 433
size distribution and their performances are worst for snowflake It may due to graupel 434
and snowflake precipitation have more big particles When S less than 2 and K less than 435
6 Weibull distribution performs better than Gamma distribution to describe HSDs but 436
21
Gamma distribution performs better for total data 437
A few points are noteworthy First although this study demonstrates the great 438
potential of combining simultaneous disdrometer measurements of particle fall velocity 439
and size distributions microscopic photography and cloud radar to address the 440
challenges facing solid precipitation the data are limited More research is needed to 441
discern such effects on the results presented here Second as the observations show 442
that in addition to sizes there are many other factors (eg hydrometeor type 443
microphysical processes turbulence and measuring principle) that can potentially 444
influence particle fall velocity as well More comprehensive research is needed to 445
further discern and separate these factors Finally the combined use of S-K diagram 446
Taylor diagram and relative Euclidean distance appears to be a powerful tool for 447
identifying the best function used to describe the HSDs and quantify the differences 448
between different precipitation types More research is in order along this direction 449
Acknowledgements 450
This study is mainly supported by the Chinese National Science Foundation under Grant 451
No 41675138 and National Key RampD Program of China (2017YFC0209604) It is partly 452
supported by Beijing National Science Foundation (8172023) the US Department 453
Energys Atmospheric System Research (ASR) Program (Liu and Jia at BNL) Lu is 454
supported by the Natural Science Foundation of Jiangsu Province (BK20160041) The 455
observation data are archived at a specialized supercomputer at Beijing Meteorology 456
Information Center (ftp10224592) which are available from the corresponding 457
author upon request The authors also thank Beijing weather modification office for 458
their support during the field experiment 459
Reference 460
22
Agosta CC Fettweis XX Datta RR 2015 Evaluation of the CMIP5 models in the 461
aim of regional modelling of the Antarctic surface mass balance Cryosphere 9 2311ndash462
2321 httpdxdoiorg105194tc-9-2311-2015 463
Barthazy E and R Schefold 2006 Fall velocity of snowflakes of different riming degree 464
and crystal types Atmos Res 82(1) 391-398 httpsdoiorg101016jatmosres 465
200512009 466
Battaglia A Rustemeier E Tokay A et al 2010 PARSIVEL snow observations a critical 467
assessment J Atmos Oceanic Technol 27(2) 333-344 doi 1011752009jtecha13321 468
Boumlhm H P 1989 A General Equation for the Terminal Fall Speed of Solid Hydrometeors 469
J Atmos Sci 46(15) 2419-2427 httpsdoiorg1011751520-0469(1989)046 lt2419A 470
GEFTTgt20CO2 471
Boudala F S G A Isaac et al 2014 Comparisons of Snowfall Measurements in 472
Complex Terrain Made During the 2010 Winter Olympics in Vancouver Pure and 473
Applied Geophysics 171(1) 113-127 474
Chen B W Hu and J Pu 2011 Characteristics of the raindrop size distribution for 475
freezing precipitation observed in southern China J Geophys Res 116 D06201 476
doi1010292010JD015305 477
Chen B Z Hu L Liu and G Zhang (2017) Raindrop Size Distribution Measurements at 478
4500m on the Tibetan Plateau during TIPEX-III J Geophys Res 122 11092-11106 479
doiorg10100 22017JD027233 480
23
Cugerone K and C De Michele 2017 Investigating raindrop size distributions in the 481
(L-)skewness-(L-)kurtosis plane Quart J Roy Meteor Soc 143(704) 1303-1312 482
httpsdoiorg101002qj3005 483
Donnadieu G 1980 Comparison of results obtained with the VIDIAZ spectro 484
pluviometer and the JossndashWaldvogel rainfall disdrometer in a ldquorain of a thundery typerdquo 485
J Appl Meteor 19 593ndash597 486
Feingold G and Levin Z 1986 The lognormal fit to raindrop spectra from frontal 487
convective clouds in Israel J Clim Appl Meteorol 25 1346ndash1363 488
httpsdoiorg1011751520-0450(1986)025lt1346tlftrsgt20CO2 489
Field P R A J Heymsfield and A Bansemer 2007 Snow Size Distribution 490
Parameterization for Midlatitude and Tropical Ice Clouds J Atmos Sci 64(12) 491
4346-4365 httpsdoiorg1011752007JAS23441 492
Garrett T J and S E Yuter 2014 Observed influence of riming temperature and 493
turbulence on the fallspeed of solid precipitation Geophysical Research Letters 41(18) 494
6515ndash6522 495
Geresdi I N Sarkadi and G Thompson 2014 Effect of the accretion by water drops 496
on the melting of snowflakes Atmos Res 149 96-110 497
Gunn R and G D Kinzer 1949 The terminal velocity of fall for water drops in stagnant 498
air J Meteor 6 243-248 httpsdoiorg1011751520-0469(1949)006lt0243TTVOFFgt 499
20CO2 500
24
Heymsfield A J and C D Westbrook 2010 Advances in the Estimation of Ice Particle 501
Fall Speeds Using Laboratory and Field Measurements J Atmos Sci 67(8) 2469-2482 502
httpsdoiorg1011752010JAS33791 503
Huang G-J C Kleinkort V N Bringi and B M Notaroš 2017 Winter precipitation 504
particle size distribution measurement by Multi-Angle Snowflake Camera Atmos Res 505
198 81-96 506
Intergovernmental Panel on Climate Change (IPCC) 2001 Climate Change 2001 The 507
Scientific Basis Contribution of Working Group I to the Third Assessment Report of the 508
Intergovernmental Panel on Climate Change edited by J T Houghton et al 881 pp 509
Cambridge Univ Press New York 510
Ishizaka M H Motoyoshi S Nakai T Shiina T Kumakura and K-i Muramoto 2013 A 511
New Method for Identifying the Main Type of Solid Hydrometeors Contributing to 512
Snowfall from Measured Size-Fall Speed Relationship Journal of the Meteorological 513
Society of Japan Ser II 91(6) 747-762 httpsdoiorg102151jmsj2013-602 514
Khvorostyanov V 2005 Fall Velocities of Hydrometeors in the Atmosphere 515
Refinements to a Continuous Analytical Power Law J Atmos Sci 62 4343-4357 516
httpsdoiorg101175JAS36221 517
Kikuchi K T Kameda K Higuchi and A Yamashita 2013 A global classification of 518
snow crystals ice crystals and solid precipitation based on observations from middle 519
latitudes to polar regions Atmos Res 132-133 460-472 520
Kneifel S A von Lerber J Tiira D Moisseev P Kollias and J Leinonen 2015 521
Observed relations between snowfall microphysics and triple-frequency radar 522
25
measurements J Geophys Res Atmos 120(12) 6034-6055 523
httpsdoi1010022015JD023156 524
Kubicek A and P K Wang 2012 A numerical study of the flow fields around a typical 525
conical graupel falling at various inclination angles Atmos Res 118 15ndash26 526
httpsdoi101016jatmosres201206001 527
Larsen M L A B Kostinski and A R Jameson (2014) Further evidence for 528
superterminal raindrops Geophys Res Lett 41(19) 6914-6918 529
Lee JE SH Jung H M Park S Kwon P L Lin and G W Lee 2015 Classification of 530
Precipitation Types Using Fall Velocity Diameter Relationships from 2D-Video 531
Distrometer Measurements Advances in Atmospheric Sciences (09) 532
Lin Y L J Donner and B A Colle 2010 Parameterization of riming intensity and its 533
impact on ice fall speed using arm data Mon Weather Rev 139(3) 1036ndash1047 534
httpsdoi1011752010MWR32991 535
Liu Y G 1992 Skewness and kurtosis of measured raindrop size distributions Atmos 536
Environ 26A 2713-2716 httpsdoiorg1010160960-1686(92)90005-6 537
Liu Y G 1993 Statistical theory of the Marshall-Parmer distribution of raindrops 538
Atmos Environ 27A 15-19 httpsdoiorg1010160960-1686(93)90066-8 539
Liu Y G and F Liu 1994 On the description of aerosol particle size distribution Atmos 540
Res 31(1-3) 187-198 httpsdoiorg1010160169-8095(94)90043-4 541
Liu Y G L You W Yang F Liu 1995 On the size distribution of cloud droplets Atmos 542
Res 35 (2-4) 201-216 httpsdoiorg1010160169-8095(94)00019-A 543
Locatelli J D and P V Hobbs 1974 Fall speeds and masses of solid precipitation 544
26
particles J Geophys Res 79(15) 2185-2197 httpsdoi101029JC079i015p02185 545
Loumlffler-Mang M and J Joss 2000 An optical disdrometer for measuring size and 546
velocity of hydrometeors J Atmos Oceanic Technol 17 130-139 547
httpsdoiorg1011751520-0426(2000)017lt0130AODFMSgt20CO2 548
Loumlffler-Mang M and U Blahak 2001 Estimation of the Equivalent Radar Reflectivity 549
Factor from Measured Snow Size Spectra J Clim Appl Meteorol 40(4) 843-849 550
httpsdoiorg1011751520-0450(2001)040lt0843EOTERRgt20CO2 551
Matrosov S Y 2007 Modeling Backscatter Properties of Snowfall at Millimeter 552
Wavelengths J Atmos Sci 64(5) 1727-1736 httpsdoiorg101175JAS39041 553
Mitchell D L 1996 Use of mass- and area-dimensional power laws for determining 554
precipitation particle terminal velocities J Atmos Sci 53 1710-1723 555
httpsdoiorg1011751520-0469(1996)053lt1710UOMAADgt20CO2 556
Montero-Martiacutenez G A B Kostinski R A Shaw and F Garciacutea-Garciacutea 2009 Do all 557
raindrops fall at terminal speed Geophys Res Lett 36 L11818 558
httpsdoiorg1010292008GL037111 559
Niu S X Jia J Sang X Liu C Lu and Y Liu 2010 Distributions of raindrop sizes and 560
fall velocities in a semiarid plateau climate Convective vs stratiform rains J Appl 561
Meteorol Climatol 49 632ndash645 httpsdoi1011752009JAMC22081 562
Nurzyńska K M Kubo and K-i Muramoto 2012 Texture operator for snow particle 563
classification into snowflake and graupel Atmos Res 118 121-132 564
Oue M M R Kumjian Y Lu J Verlinde K Aydin and E E Clothiaux 2015 Linear 565
27
Depolarization Ratios of columnar ice crystals in a deep precipitating system over the 566
Arctic observed by Zenith-Pointing Ka-Band Doppler radar J Clim Appl Meteorol 567
54(5) 1060-1068 httpsdoiorg101175JAMC-D-15-00121 568
Pruppacher H R and J D Klett 1998 Microphysics of clouds and precipitation Kluwer 569
Academic 954 pp 570
Rasmussen R B Baker et al 2012 How well are we measuring snow the 571
NOAAFAANCAR winter precipitation test bed Bull Amer Meteor Soc 93(6) 811-829 572
httpsdoiorg101175BAMS-D-11-000521 573
Reisner J R M Rasmussen and R T Bruintjes 1998 Explicit forecasting of 574
supercooled liquid water in winter storms using the MM5 mesoscale model Q J R 575
Meteorol Soc 124 1071ndash1107 httpsdoi101256smsqj54803 576
Rosenfeld D and Ulbrich C W 2003 Cloud microphysical properties processes and 577
rainfall estimation opportunities Meteorol Monogr 30 237-237 578
httpsdoiorg101175 0065-9401(2003)030lt0237cmppargt20CO2 579
Schaefer V J 1956 The preparation of snow crystal replicas-VI Weatherwsie 9 580
132-135 581
Souverijns N A Gossart S Lhermitte I V Gorodetskaya S Kneifel M Maahn F L 582
Bliven and N P M van Lipzig (2017) Estimating radar reflectivity - Snowfall rate 583
relationships and their uncertainties over Antarctica by combining disdrometer and 584
radar observations Atmos Res 196 211-223 585
Taylor K E 2001 Summarizing multiple aspects of model performance in a single 586
diagram J Geophys Res 106 7183ndash7192 httpsdoi1010292000JD900719 587
28
Tokay A and D A Short 1996 Evidence from tropical raindrop spectra of the origin of 588
rain from stratiform versus convective clouds J Appl Meteor 35 355ndash371 589
Tokay A and D Atlas 1999 Rainfall microphysics and radar properties analysis 590
methods for drop size spectra J Appl Meteor 37 912-923 591
httpsdoiorg1011751520-0450(1998)037lt0912RMARPAgt20CO2 592
Tokay A D B Wolff et al 2014 Evaluation of the New version of the laser-optical 593
disdrometer OTT Parsivel2 J Atmos Oceanic Technol 31(6) 1276-1288 594
httpsdoiorg101175JTECH-D-13-001741 595
Ulbrich C W 1983 Natural variations in the analytical form of the raindrop size 596
distribution J Appl Meteor 5 1764-1775 597
Wen G H Xiao H Yang Y Bi and W Xu 2017 Characteristics of summer and winter 598
precipitation over northern China Atmos Res 197 390-406 599
Wu W Y Liu and A K Betts 2012 Observationally based evaluation of NWP 600
reanalyses in modeling cloud properties over the Southern Great Plains J Geophys 601
Res 117 D12202 httpsdoi1010292011JD016971 602
Yuter S E D E Kingsmill L B Nance and M Loumlffler-Mang 2006 Observations of 603
precipitation size and fall velocity characteristics within coexisting rain and wet snow J 604
Appl Meteor Climatol 45 1450ndash1464 doi httpsdoiorg101175JAM24061 605
Zhang P C and B Y Du 2000 Radar Meteorology China Meteorological Press 511pp 606
(in Chinese) 607
608
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
6
horizontally symmetric and thus particle sizes for snow may underestimate actual maximum 112
particle diameter Battaglia et al (2010) pointed out that PARSIVELrsquos fall velocity 113
measurement may not be accurate for snowflakes due to the internally assumed relationship 114
between horizontal and vertical snow particle dimensions The uncertainty originates from 115
the shape-related factor which tends to depart more with increasing snowflake sizes and 116
can produce large errors When averaging over a large number of snowflakes the correction 117
factor is size dependent with a systematic tendency to underestimate the fall speed (but 118
never exceeding 20) The maximum error 20 of the empirical terminal velocities for 119
graupel and snowflake is used to estimate the instrument caused possible velocities such 120
as the dash lines in igure 2b In addition graupel is almost spherical hydrometeor and the 121
instrument error could not reach 20 The individual HSD sample interval was 10 seconds 122
The following criteria are used in choosing data for analysis (1) Particles smaller 123
than 025 mm are discarded (2) the total particle number of a HSD is over 10 counts 124
(every 10-sec sample) (Niu et al 2010) (3) precipitation lasted more than 30 minutes 125
are chosen (4) solid hydrometeor density is corrected with the equation ρs =126
017Dminus1 for solid hydrometeors (Boudala et al 2014) (5) Following Chen et al (2017) 127
raindrops outside +60 of the empirical terminal velocity of raindrop (Table 3) and -60 128
of empirical terminal velocity of densely rimed dendrites were excluded in the analysis 129
to minimize the effects of ldquomargin fallersrdquo winds and splashing Hydrometeors were 130
also collected with Formvar slides (76 cm long and 26 cm wide) which are exposed 131
outside for 5s to capture the hydrometeors with a sampling interval of 5 minutes The 132
Formvar samples were examined and photographed with a microscope-camera system 133
7
following the method described by Schaefer (1956) The two-dimensional photo of 134
hydrometeors allows a careful determination of the hydrometeor shape and size The 135
Formvar data were used to distinguish dominant hydrometeor types eg raindrop 136
graupel or snowflake The hydrometeor type with a percentage of occurrence gt60 is 137
used to represent the solid precipitation type for convenience of analysis 138
A Ka-band millimeter wavelength cloud radar (wavelength is 8 mm) was used to 139
probe the vertical structure of clouds by vertical scanning from 11202016 which can 140
be used to determine cloud properties at 1 min temporal and 30 m vertical resolution 141
A total of 11098 HSD samples were collected from 12 precipitation events (Table 1) 142
Four representative hydrometeor types from the precipitation events are identified 143
raindrop graupel snowflake and mixed-phase precipitation The identification of the 144
hydrometeor types is mainly based on hydrometeors velocity observations and Formvar 145
images which will be detailed in Section 4 Mixed-phased precipitation contains 146
raindrops graupels and snowflakes simultaneously and none is dominant over another 147
The duration sample number precipitation rate and dominant type of hydrometeor 148
are shown in Table 1 The precipitation rate is calculated from HSD using the method 149
presented in Boudala et al (2014) 150
3 Hydrometeor Classification and Size and Fall Velocity 151
Distributions 152
a General Feature 153
Fig 2 illustrates the observed mean number concentration as a function of the 154
maximum dimension and the fall velocity for the four types of hydrometeors 155
8
respectively Also shown as a reference are the seven solid curves representing 156
different types of hydrometeor terminal velocities obtained from the laboratory 157
measurements calibrated by coefficient 50
0
since the site altitude is 1310 m 158
average pressure is 868 hpa and the average temperature is -5 ordmC (Niu et al2010) 159
(equations are shown in Table 3) Here ρ is the actual air density and ρ0 is the 160
standard atmospheric density The updrafts downdrafts and turbulence often 161
accompany falling hydrometeors inducing deviations in the velocity and trajectory of 162
falling hydrometeors from those in still air (Donnadieu 1980) Hence in this field 163
observation fall velocities of hydrometeors distribute along the terminal velocity curves 164
with large spread for each given size Similar features have been previously reported in 165
some situ measurements of raindrop fall velocities (Niu et al 2010 Rasmussen et al 166
2012) 167
In the previous study we discussed the air density and potential influencing 168
factors (eg turbulence organized air motions break-up and measurement errors) for 169
raindrop (Niu et al 2010) For precipitation in winter the hydrometeor shape is vitally 170
important for fall velocity The hydrometeor shape influence on fall velocities physical 171
mechanisms and instrument error underlying the large spread in the measured fall 172
velocities of different types are discussed in detail in the next two sub-sections 173
b Effect of Hydrometeor Type on Fall Velocity 174
In Fig 2a the hydrometeor fall velocities agree with the typical raindrop terminal 175
velocity curve which is obviously larger than the terminal velocities of graupel and 176
9
snowflake at given maximum diameters From the fall velocity distribution we can infer 177
that these hydrometeors are mainly raindrops The microscope photos obtained on the 178
ground confirm this However unlike the raindrop size and velocity distribution in 179
summer in Figure 8a of Niu et al (2010) there are some small size hydrometeors 180
(05~35mm) at very low speeds (05~2 ms) distributing among the terminal velocity 181
curves for graupel and snowflake This result implies that beside liquid raindrops 182
(including small raindrops or droplets from drizzle) some small snowflakes also exist in 183
the measurement The microscope photos also support the finding that although 184
raindrops are dominant some small plane- and column- shaped snowflakes co-exist 185
Fig 2b shows the joint hydrometeor size and fall velocity distribution during the 186
graupel event The hydrometeors are mainly symmetrically distributed around the ideal 187
terminal velocity of graupel (Locatelli and Hobbs 1974) supported by the photo-based 188
hydrometeor classification On the other hand it is found that certain small droplets 189
with the maximum dimensions among 03 to 10 mm are distributed around the liquid 190
raindrop curve suggesting that there are some raindrops and droplets coexisting in the 191
graupel dominated precipitation It is recognized that graupels grow by snow crystals 192
collecting cloud droplets and small raindrops (Pruppacher and Klett 1998) high cloud 193
top more liquid water content and presence of small raindrops (as shown in 194
microscope photography) provide favorable conditions for graupel The microscope 195
photos also display that graupelsrsquo surfaces are lumpy because of riming super cooled 196
drops during growing 197
The fall velocities of hydrometeors in Fig 2c are much smaller than the terminal 198
10
velocities of raindrop and graupel but are close to the terminal velocity curves of snow 199
of hexagonal densely rimed dendrites aggregates of dendrites Synthesizing the size 200
data the hydrometeors can be inferred as snowflakes which are further confirmed by 201
surface microscope photos From the surface observation we found many 202
rimedunrimed or aggregated dendrites or hexagonal snowflakes Although riming and 203
aggregation microphysical processes have some influence on terminal velocity 204
(Barthazy and Schefold 2006 Garrett and Yuter 2014 Heymsfield and Westbrook 205
2010) but the influences are too small to distinguish only from observed fall velocity 206
since it is a combined result of many factors When maximum dimensions are among 207
03 to 10 mm there are some small hydrometeors with fall velocities larger than 208
snowflakes which maybe graupels raindrops and droplets 209
Fig 2d is the hydrometeor size and fall velocity distribution during a mixed-phased 210
precipitation The hydrometeor fall velocities exhibit the largest spread for example 211
the fall velocities for hydrometeors with maximum dimension equaling to 3 mm 212
change from 05 to 5 ms and do not distribute along any of the ideal terminal velocity 213
curves This result suggests that different hydrometeor types might coexist during the 214
same sampling time To substantiate supercooled raindrops graupels and different 215
kinds of snowflakes are observed from the surface microscope simultaneously Similar 216
changes in particle size and fall velocity distribution documented by the disdrometer as 217
the storm transitions from rain to mixed-phase to snow were found at Marshall Field 218
site (Rasmussen et al 2012) 219
11
c Other Influencing Factors 220
The different dependence on particle size of terminal velocities for different types 221
of hydrometeors can explain some systematic distribution of the PARSIVEL-measured 222
fall velocities but the large spreads in the measurement of the instant particle fall 223
velocities await further inspection 224
According to our previous work the fall velocity (V) of a hydrometeor measured by 225
the PARSIVEL can be regarded as a combination of the terminal velocity in still air (Vt) 226
and a component Vrsquo that results from all other potential influencing factors eg type 227
turbulence organized air motions break-up and measurement errors (Niu et al 228
2010) 229
119881 = 119881119905 + 119881 prime (1) 230
The large spread of the measurements at both sides of the terminal velocity curves 231
shown in figure 2 seems compatible with the notion of nearly random collections of 232
downdraft and updraft A wider spread for fall velocities implies a wider range of 233
variation in vertical motions when hydrometeors are liquid raindrops (Niu et al 2010) 234
Solid nonspherical hydrometeors are much more complex than liquid drops and the 235
large spread of velocities may be caused by several other factors First different types 236
of hydrometeors (columns bullets plates lump graupels and hexagonal snowflakes et 237
al) have different fall speeds It is long recognized that microphysical processes in cold 238
precipitation are more complex and consequently generate more types of solid 239
hydrometeors comparing to the generation of raindrops The averaged concentration 240
distributions of large number of samples shown in Figure 2 also represents the possible 241
12
distributions of hydrometeors If there is only one kind particle the high concentration 242
would along its ideal terminal velocity very well just like the raindrop possible 243
distribution (Niu et al 2010) The concentration of mixed precipitation in Fig 2d does 244
not along any singe ideal terminal velocity further improved there are more than one 245
kind of hydrometers Coexistence of different types of hydrometeors induces larger 246
spread of fall velocities Second different degrees of riming and aggregating may affect 247
the results Densely rimed particles fall faster than unrimed particles with the same 248
maximum dimension aggregated snowflakes generally fall faster than their component 249
crystals (Barthazy and Schefold 2006 Garrett and Yuter 2014 Locatelli and Hobbs 250
1974) Third solid hydrometeors more likely occur breakup aggregation collision and 251
coalescence processes because of the large range of speeds According to prior 252
research of raindrop breakup and coalescence would lead to the ldquohigher-than-terminal 253
velocityrdquo fall velocity for small drops but ldquolower-than-terminal velocityrdquo fall velocity for 254
large drops (Niu et al 2010 Montero-Martiacutenez et al 2009 Larsen et al 2014) Similar 255
results are expected for the fall velocity of solid hydrometeors Last but not the least 256
the disdrometer may suffer from instrumental errors due to the internally assumed 257
relationship between horizontal and vertical particle dimensions likely resulting in a 258
wider spreads of fall velocities for the graupel and snowflakes as compared to the 259
raindrop counterpart as discussed in Section 2 Although the instrument error is an 260
important factor that should be considered in velocity spread as shown in Fig2b the 261
instrument error could not cause that large velocity spread The possible distributions 262
of fall velocities are the combine effects of physical and instrument principle 263
13
Further support for the possible instrumental uncertainty is from the cloud radar 264
observations Fig 3 shows the cloud reflectivity and linear depolarization ratio (LDR) in 265
lower level (less than 08 km) for the graupel snowflake and mixed-phased 266
precipitations respectively The LDR is a valuable observable in identifying the 267
hydrometeor types (Oue et al 2015) As shown in Fig 3a the cloud top height of 268
graupel precipitation was up to 7km during 1900 to 2050 Beijng Time (BT) which was 269
highest among the three events The high cloud top implies stronger updraft and 270
turbulence which further induces a larger fall velocity spread The LDR value was the 271
smallest among the three events indicating that the hydrometeors were close to 272
spherical consistent to the surface observations The cloud top height of snowflake 273
precipitation was up to 35 km (Fig 3c) which was the lowest among the three types of 274
precipitations implying weakest updraft and turbulence Notably although the 275
snowflake types are more complex than those of graupels the velocity spread was not 276
as large as that of the graupel type likely because of the weakest updraft and 277
turbulence The LDR was relatively larger consistent with the surface snowflake 278
observations (Fig 3d) The cloud top height of mixed-phase precipitation was up to 45 279
km (Fig 3e) and the LDR in lower level was largest among the three types of 280
precipitations owing to coexistence of raindrops graupels and snowflakes (Fig 3f) 281
4 Hydrometeor Size Distributions 282
a Comparison of HSDs between Different Types 283
There were four representative types of precipitations during this field experiment 284
providing us a unique opportunity to examine the HSD differences between the four 285
14
types of hydrometeors The sample numbers mean maximum dimensions and number 286
concentrations for each kind of HSDs are given in Table 2 Figure 4 is the averaged 287
distribution of all measured HSDs of 4 kinds As shown in Figure 4 on average the 288
mixed-phased precipitation tends to have most small size hydrometeors with D lt 15 289
mm while snowflake precipitation has the least small hydrometeors among the four 290
types The snowflake precipitation has more large size hydrometeors ie 3 mm lt D lt 11 291
mm Graupel size distribution tends to have two peeks around 13 mm and 26 mm The 292
mean maximum dimension is largest for snowflake (126 mm) and smallest for the 293
mixed HSD due to many small particles Similar results were found in precipitation 294
occurring in the Cascade and Rocky Mountains (Yuter et al 2006) The PARSIVEL 295
disdrometer doesnrsquot provide reliable data for small drops lower than 05 mm and tends to 296
underestimate small drops so the relatively low concentrations of small drops likely resulted 297
from the instrumentrsquos shortcomings (Tokay et al 2013 and Chen et al 2017) 298
b Evaluation of Distribution Functions for Describing HSDs 299
Over the last few decades great efforts have been devoted to finding the 300
appropriate analytical functions for describing the HSD because of its wide applications 301
in many areas including remote sensing and parameterization of precipitation (Chen et 302
al 2017) The two distribution functions mostly used up to now are the Lognormal 303
(Feingold and Levin 1986 Rosenfeld and Ulbrich 2003) and the Gamma (Ulbrich 1983) 304
distributions The Gamma distribution has been proposed as a first order generalization 305
of the Exponential distribution when μ equals 0 (Table 4) Weibull distribution is 306
another function used to describe size distributions of raindrops and cloud droplets (Liu 307
15
and Liu 1994 Liu et al 1995) Nevertheless the question as to which functions are 308
more adequate to describe HSDs of solid hydrometeors have been rarely investigated 309
systematically and quantitatively Thus the objective of this section is to examine the 310
most adequate distribution function used to describe HSDs 311
Considering size distributions of raindrops cloud droplets and aerosol particles are 312
the end results of many (stochastic) complex processes Liu (1992 1993 1994 and 313
1995) proposed a statistical method based on the relationships between the skewness 314
(S) and kurtosis (K) derived from an ensemble of particle size distribution 315
measurements and from those commonly used size distribution functions Cugerone 316
and Michele (2017) also used a similar approach based on the S-K relationships to study 317
raindrop size distributions Unlike the conventional curve-fitting of individual size 318
distributions this approach applies to an ensemble of size distribution measurements 319
and identifies the most appropriate statistical distribution pattern Here we apply this 320
approach to investigate if the statistical pattern of the HSDs of four precipitation types 321
follows the Exponential Gaussian Gamma Weibull and Lognormal distributions (Table 322
4) and if there are any pattern differences between them Briefly S and K of a HSD are 323
calculated from the corresponding HSD with the following two equations 324
23
2
3
t
iii
t
iii
dDN
)(Dn)D(D
dDN
)(Dn)D(D
S
minus
minus
=
(2) 325
32
2
4
minus
minus
minus
=
dDN
)(Dn)D(D
dDN
)(Dn)D(D
K
t
iii
t
iii
(3) 326
16
where Di is the central diameter of the i-th bin ni is the number concentration of the 327
i-th bin and Nt is total number concentration Note that each individual HSD can be 328
used to obtain a pair of S and K which is shown as a dot in Figure 5 Also noteworthy is 329
that the SndashK relationships for the families of Gamma Weibull and Lognormal are 330
described by known analytical functions (Liu 1993 1994 and 1995 Cugerone and 331
Michele 2017) represented by theoretical curves in Figure 5 The Exponential and 332
Gaussian distributions are represented by single points on the S-K diagram (S=2 and K=6 333
for Exponential) and (S=0 and K=0 for Gaussian) respectively Thus by comparing the 334
measured S and K values (points) with the known theoretical curves one can determine 335
the most proper function used to describe HSDs 336
Figure 5 shows the scatter plots of observed SndashK pairs calculated from the HSD 337
measurements for raindrop graupel snowflake mixed-phase precipitations Also 338
shown as comparison are the theoretical curves corresponding to the analytical HSD 339
functions A few points are evident First despite some occasional departures most of 340
the points fall near the theoretical lines of Gamma and Weibull distributions suggesting 341
that the HSD patterns for all the four types of precipitations well follow the Gamma and 342
Weibull distributions statistically Second HSDs of raindrops and mixed hydrometeors 343
are better described by Gamma and Weibull distribution than graupels and snowflakes 344
Third the S and K do not cluster around points (2 6) and (0 0) suggesting that the 345
Gaussian and Exponential distribution are not appropriate for describing HSDs 346
especially Gaussian distribution 347
To further evaluate the overall performance of the different distribution functions 348
17
we employ the widely used technique of Taylor diagram (Taylor 2001) and ldquoRelative 349
Euclidean Distancerdquo (RED) (Wu et al 2012) as a supplement to the Taylor diagram The 350
Taylor diagram has been widely used to visualize the statistical differences between 351
model results and observations in evaluation of model performance against 352
measurements or other benchmarks (IPCC 2001) Correlation coefficient (r) standard 353
deviation (σ) and ldquocentered root-mean-square errorrdquo (RMSE hereafter) are used in 354
the Taylor diagram The RED is introduced to add the bias as well in a dimensionless 355
framework that allows for comparison between different physical quantities with 356
different units In this study we consider the S and K values derived from the 357
distribution functions as model results and evaluate them against those derived from 358
the HSD measurements Brieflythe expressions for calculating r and σ and RMSE are 359
shown below 360
119903 =1
119873sum (119872119899minus)(119874119899minus)119873119899=1
120590119872120590119900 (4) 361
119877119872119878119864 = 1
119873sum [(119872119899 minus ) minus (119874119899 minus )]2119873119899=1
12
(5) 362
120590119872 = [1
119873sum (119872119899 minus )119873119899=1 ]
12
(6) 363
1205900 = [1
119873sum (119874119899 minus )119873119899=1 ]
12
(7) 364
where M and O denote distribution function and observed variables The RED 365
expression is shown below 366
119877119864119863 = [(minus)
]2
+ [(120590119872minus120590119874)
120590119900]2
+ (1 minus 119903)212
( 8 ) 367
Equation (8) indicates that RED considers all the components of mean bias variations 368
and correlations in a dimensionless way the distribution function performance 369
degrades as RED increases from the perfect agreement with RED=0 370
18
In the Taylor diagrams shown in Fig 6 the cosine of azimuthal angle of each point 371
gives the r between the function-calculated and observed data The distance between 372
individual point and the reference point ldquoObsrdquo represents the RMSE normalized by the 373
amplitude of the observationally based variations As this distance approaches to zero 374
the function-calculated K and S approach to the observations Clearly the values of r 375
are around 097 for Gamma and Weibull r for Lognormal function is slightly smaller 376
(095) The normalized σ are much different for Lognormal Gamma and Weibull 377
distributions with averaged value being 057 0895 and 0785 respectively Therefore 378
the Lognormal distribution exhibits the worst performance for describing HSDs and 379
Gamma and Weibull distributions appear to perform much better (Fig 6a) 380
Noticing that S and K of Gamma and Weibull distributions are equal at the point of S 381
= 2 and K = 6 and have positive relationship (If S lt 2 then K lt 6 and if S gt 2 then k gt 6) In 382
this part we further separately examine the group of data with S lt 2 and K lt 6 (Fig 6b) 383
and compare its result with those of total data The averaged normalized σ are 103 and 384
109 and r are 091 and 090 for Weibull and Gamma distributions respectively 385
suggesting that Weibull distribution performs slightly better than Gamma distribution 386
for the four HSD types in the data group of S lt 2 and K lt 6 whereas the opposite is true 387
for all data This conclusion is further substantiated by comparison of RED values for the 388
four type of precipitation (Fig7) which shows that Lognormal has the largest RED 389
Gamma the smallest and Weibull in between for four types of precipitations in all data 390
whereas Weibull (Lognormal) has smallest (largest) RED values when S lt 2 and K lt 6 It 391
can be inferred for data group of S gt 2 and k gt 6 Gamma distribution performs better 392
19
Further comparison between different precipitation types shows these functions all 393
performs better for raindrop size distributions and mixed-phase than graupel and 394
snowflake size distributions The RED for snowflakes is largest among the four types 395
The performance of Gamma is better for describing solid HSDs of all data but Weibull 396
distribution is better when S lt 2 and K lt 6 397
5 Conclusion 398
The combined measurements collected during a field experiment conducted at the 399
Haituo Mountain site using PARSIVEL disdrometer millimeter wavelength cloud radar 400
and microscope photography are analyzed to classify the precipitation hydrometeor 401
types examine the dependence of fall velocity on hydrometeor size for different 402
hydrometeor types and determine the best distribution functions to describe the 403
hydrometeor size distributions of different types 404
Analysis of the PARSIVEL-measured fall velocities show that on average the 405
dependence of fall velocity on hydrometeor size largely follow their corresponding 406
terminal velocity curves for raindrops graupels and snowflakes respectively suggesting 407
that such measurements are useful to identify the hydrometeor types The associated 408
microscope photos and cloud radar observations support the classification of 409
hydrometeor types based on the PARSIVEL-observed fall velocities Furthermore there 410
are velocity spreads in fall velocity across hydrometeor sizes for all hydrometeors and 411
the spreads for the solid hydrometeors could cause by hydrometeor type turbulence or 412
updraftdowndraft and instrument measured principle The coexistence of various 413
types of hydrometeors likely induces additional spread of fall velocity for given 414
20
hydrometeor sizes such as mixed precipitation Meanwhile complex microphysical 415
processes in cold precipitation such as riming aggregation breakup and collision and 416
coalescence influence fall velocity which likely induce larger spread of fall velocity Last 417
but not the least the disdrometer may suffer from instrumental errors due to the 418
internally assumed relationship between horizontal and vertical particle dimensions 419
Comparison of the type-averaged hydrometeor size distributions shows that the 420
mixed precipitation has more small hydrometeors with D lt 15 mm than others 421
whereas the snowflake precipitation has the least number of small hydrometeors 422
among the four types On the contrary the snowflake precipitation has more large 423
hydrometeors with D between 3 mm and 11 mm 424
The commonly used size distribution functions (Gamma Weibull and Lognormal) 425
are further examined to determine the most adequate function to describe the size 426
distribution measurements for all the hydrometeor types by use of an approach based 427
on the relationship between skewness (S) and kurtosis (K) Taylor diagram and RED are 428
further introduced to assess the performance of different size distribution functions 429
against measurements It is shown that the HSDs for the four types can all be well 430
described statistically by the Gamma and Weibull distribution but Lognormal 431
Exponential and Gaussian are not fit to describe HSDs Gamma and Weibull distribution 432
describe raindrop and mixed-phase size distribution better than snowflake and graupel 433
size distribution and their performances are worst for snowflake It may due to graupel 434
and snowflake precipitation have more big particles When S less than 2 and K less than 435
6 Weibull distribution performs better than Gamma distribution to describe HSDs but 436
21
Gamma distribution performs better for total data 437
A few points are noteworthy First although this study demonstrates the great 438
potential of combining simultaneous disdrometer measurements of particle fall velocity 439
and size distributions microscopic photography and cloud radar to address the 440
challenges facing solid precipitation the data are limited More research is needed to 441
discern such effects on the results presented here Second as the observations show 442
that in addition to sizes there are many other factors (eg hydrometeor type 443
microphysical processes turbulence and measuring principle) that can potentially 444
influence particle fall velocity as well More comprehensive research is needed to 445
further discern and separate these factors Finally the combined use of S-K diagram 446
Taylor diagram and relative Euclidean distance appears to be a powerful tool for 447
identifying the best function used to describe the HSDs and quantify the differences 448
between different precipitation types More research is in order along this direction 449
Acknowledgements 450
This study is mainly supported by the Chinese National Science Foundation under Grant 451
No 41675138 and National Key RampD Program of China (2017YFC0209604) It is partly 452
supported by Beijing National Science Foundation (8172023) the US Department 453
Energys Atmospheric System Research (ASR) Program (Liu and Jia at BNL) Lu is 454
supported by the Natural Science Foundation of Jiangsu Province (BK20160041) The 455
observation data are archived at a specialized supercomputer at Beijing Meteorology 456
Information Center (ftp10224592) which are available from the corresponding 457
author upon request The authors also thank Beijing weather modification office for 458
their support during the field experiment 459
Reference 460
22
Agosta CC Fettweis XX Datta RR 2015 Evaluation of the CMIP5 models in the 461
aim of regional modelling of the Antarctic surface mass balance Cryosphere 9 2311ndash462
2321 httpdxdoiorg105194tc-9-2311-2015 463
Barthazy E and R Schefold 2006 Fall velocity of snowflakes of different riming degree 464
and crystal types Atmos Res 82(1) 391-398 httpsdoiorg101016jatmosres 465
200512009 466
Battaglia A Rustemeier E Tokay A et al 2010 PARSIVEL snow observations a critical 467
assessment J Atmos Oceanic Technol 27(2) 333-344 doi 1011752009jtecha13321 468
Boumlhm H P 1989 A General Equation for the Terminal Fall Speed of Solid Hydrometeors 469
J Atmos Sci 46(15) 2419-2427 httpsdoiorg1011751520-0469(1989)046 lt2419A 470
GEFTTgt20CO2 471
Boudala F S G A Isaac et al 2014 Comparisons of Snowfall Measurements in 472
Complex Terrain Made During the 2010 Winter Olympics in Vancouver Pure and 473
Applied Geophysics 171(1) 113-127 474
Chen B W Hu and J Pu 2011 Characteristics of the raindrop size distribution for 475
freezing precipitation observed in southern China J Geophys Res 116 D06201 476
doi1010292010JD015305 477
Chen B Z Hu L Liu and G Zhang (2017) Raindrop Size Distribution Measurements at 478
4500m on the Tibetan Plateau during TIPEX-III J Geophys Res 122 11092-11106 479
doiorg10100 22017JD027233 480
23
Cugerone K and C De Michele 2017 Investigating raindrop size distributions in the 481
(L-)skewness-(L-)kurtosis plane Quart J Roy Meteor Soc 143(704) 1303-1312 482
httpsdoiorg101002qj3005 483
Donnadieu G 1980 Comparison of results obtained with the VIDIAZ spectro 484
pluviometer and the JossndashWaldvogel rainfall disdrometer in a ldquorain of a thundery typerdquo 485
J Appl Meteor 19 593ndash597 486
Feingold G and Levin Z 1986 The lognormal fit to raindrop spectra from frontal 487
convective clouds in Israel J Clim Appl Meteorol 25 1346ndash1363 488
httpsdoiorg1011751520-0450(1986)025lt1346tlftrsgt20CO2 489
Field P R A J Heymsfield and A Bansemer 2007 Snow Size Distribution 490
Parameterization for Midlatitude and Tropical Ice Clouds J Atmos Sci 64(12) 491
4346-4365 httpsdoiorg1011752007JAS23441 492
Garrett T J and S E Yuter 2014 Observed influence of riming temperature and 493
turbulence on the fallspeed of solid precipitation Geophysical Research Letters 41(18) 494
6515ndash6522 495
Geresdi I N Sarkadi and G Thompson 2014 Effect of the accretion by water drops 496
on the melting of snowflakes Atmos Res 149 96-110 497
Gunn R and G D Kinzer 1949 The terminal velocity of fall for water drops in stagnant 498
air J Meteor 6 243-248 httpsdoiorg1011751520-0469(1949)006lt0243TTVOFFgt 499
20CO2 500
24
Heymsfield A J and C D Westbrook 2010 Advances in the Estimation of Ice Particle 501
Fall Speeds Using Laboratory and Field Measurements J Atmos Sci 67(8) 2469-2482 502
httpsdoiorg1011752010JAS33791 503
Huang G-J C Kleinkort V N Bringi and B M Notaroš 2017 Winter precipitation 504
particle size distribution measurement by Multi-Angle Snowflake Camera Atmos Res 505
198 81-96 506
Intergovernmental Panel on Climate Change (IPCC) 2001 Climate Change 2001 The 507
Scientific Basis Contribution of Working Group I to the Third Assessment Report of the 508
Intergovernmental Panel on Climate Change edited by J T Houghton et al 881 pp 509
Cambridge Univ Press New York 510
Ishizaka M H Motoyoshi S Nakai T Shiina T Kumakura and K-i Muramoto 2013 A 511
New Method for Identifying the Main Type of Solid Hydrometeors Contributing to 512
Snowfall from Measured Size-Fall Speed Relationship Journal of the Meteorological 513
Society of Japan Ser II 91(6) 747-762 httpsdoiorg102151jmsj2013-602 514
Khvorostyanov V 2005 Fall Velocities of Hydrometeors in the Atmosphere 515
Refinements to a Continuous Analytical Power Law J Atmos Sci 62 4343-4357 516
httpsdoiorg101175JAS36221 517
Kikuchi K T Kameda K Higuchi and A Yamashita 2013 A global classification of 518
snow crystals ice crystals and solid precipitation based on observations from middle 519
latitudes to polar regions Atmos Res 132-133 460-472 520
Kneifel S A von Lerber J Tiira D Moisseev P Kollias and J Leinonen 2015 521
Observed relations between snowfall microphysics and triple-frequency radar 522
25
measurements J Geophys Res Atmos 120(12) 6034-6055 523
httpsdoi1010022015JD023156 524
Kubicek A and P K Wang 2012 A numerical study of the flow fields around a typical 525
conical graupel falling at various inclination angles Atmos Res 118 15ndash26 526
httpsdoi101016jatmosres201206001 527
Larsen M L A B Kostinski and A R Jameson (2014) Further evidence for 528
superterminal raindrops Geophys Res Lett 41(19) 6914-6918 529
Lee JE SH Jung H M Park S Kwon P L Lin and G W Lee 2015 Classification of 530
Precipitation Types Using Fall Velocity Diameter Relationships from 2D-Video 531
Distrometer Measurements Advances in Atmospheric Sciences (09) 532
Lin Y L J Donner and B A Colle 2010 Parameterization of riming intensity and its 533
impact on ice fall speed using arm data Mon Weather Rev 139(3) 1036ndash1047 534
httpsdoi1011752010MWR32991 535
Liu Y G 1992 Skewness and kurtosis of measured raindrop size distributions Atmos 536
Environ 26A 2713-2716 httpsdoiorg1010160960-1686(92)90005-6 537
Liu Y G 1993 Statistical theory of the Marshall-Parmer distribution of raindrops 538
Atmos Environ 27A 15-19 httpsdoiorg1010160960-1686(93)90066-8 539
Liu Y G and F Liu 1994 On the description of aerosol particle size distribution Atmos 540
Res 31(1-3) 187-198 httpsdoiorg1010160169-8095(94)90043-4 541
Liu Y G L You W Yang F Liu 1995 On the size distribution of cloud droplets Atmos 542
Res 35 (2-4) 201-216 httpsdoiorg1010160169-8095(94)00019-A 543
Locatelli J D and P V Hobbs 1974 Fall speeds and masses of solid precipitation 544
26
particles J Geophys Res 79(15) 2185-2197 httpsdoi101029JC079i015p02185 545
Loumlffler-Mang M and J Joss 2000 An optical disdrometer for measuring size and 546
velocity of hydrometeors J Atmos Oceanic Technol 17 130-139 547
httpsdoiorg1011751520-0426(2000)017lt0130AODFMSgt20CO2 548
Loumlffler-Mang M and U Blahak 2001 Estimation of the Equivalent Radar Reflectivity 549
Factor from Measured Snow Size Spectra J Clim Appl Meteorol 40(4) 843-849 550
httpsdoiorg1011751520-0450(2001)040lt0843EOTERRgt20CO2 551
Matrosov S Y 2007 Modeling Backscatter Properties of Snowfall at Millimeter 552
Wavelengths J Atmos Sci 64(5) 1727-1736 httpsdoiorg101175JAS39041 553
Mitchell D L 1996 Use of mass- and area-dimensional power laws for determining 554
precipitation particle terminal velocities J Atmos Sci 53 1710-1723 555
httpsdoiorg1011751520-0469(1996)053lt1710UOMAADgt20CO2 556
Montero-Martiacutenez G A B Kostinski R A Shaw and F Garciacutea-Garciacutea 2009 Do all 557
raindrops fall at terminal speed Geophys Res Lett 36 L11818 558
httpsdoiorg1010292008GL037111 559
Niu S X Jia J Sang X Liu C Lu and Y Liu 2010 Distributions of raindrop sizes and 560
fall velocities in a semiarid plateau climate Convective vs stratiform rains J Appl 561
Meteorol Climatol 49 632ndash645 httpsdoi1011752009JAMC22081 562
Nurzyńska K M Kubo and K-i Muramoto 2012 Texture operator for snow particle 563
classification into snowflake and graupel Atmos Res 118 121-132 564
Oue M M R Kumjian Y Lu J Verlinde K Aydin and E E Clothiaux 2015 Linear 565
27
Depolarization Ratios of columnar ice crystals in a deep precipitating system over the 566
Arctic observed by Zenith-Pointing Ka-Band Doppler radar J Clim Appl Meteorol 567
54(5) 1060-1068 httpsdoiorg101175JAMC-D-15-00121 568
Pruppacher H R and J D Klett 1998 Microphysics of clouds and precipitation Kluwer 569
Academic 954 pp 570
Rasmussen R B Baker et al 2012 How well are we measuring snow the 571
NOAAFAANCAR winter precipitation test bed Bull Amer Meteor Soc 93(6) 811-829 572
httpsdoiorg101175BAMS-D-11-000521 573
Reisner J R M Rasmussen and R T Bruintjes 1998 Explicit forecasting of 574
supercooled liquid water in winter storms using the MM5 mesoscale model Q J R 575
Meteorol Soc 124 1071ndash1107 httpsdoi101256smsqj54803 576
Rosenfeld D and Ulbrich C W 2003 Cloud microphysical properties processes and 577
rainfall estimation opportunities Meteorol Monogr 30 237-237 578
httpsdoiorg101175 0065-9401(2003)030lt0237cmppargt20CO2 579
Schaefer V J 1956 The preparation of snow crystal replicas-VI Weatherwsie 9 580
132-135 581
Souverijns N A Gossart S Lhermitte I V Gorodetskaya S Kneifel M Maahn F L 582
Bliven and N P M van Lipzig (2017) Estimating radar reflectivity - Snowfall rate 583
relationships and their uncertainties over Antarctica by combining disdrometer and 584
radar observations Atmos Res 196 211-223 585
Taylor K E 2001 Summarizing multiple aspects of model performance in a single 586
diagram J Geophys Res 106 7183ndash7192 httpsdoi1010292000JD900719 587
28
Tokay A and D A Short 1996 Evidence from tropical raindrop spectra of the origin of 588
rain from stratiform versus convective clouds J Appl Meteor 35 355ndash371 589
Tokay A and D Atlas 1999 Rainfall microphysics and radar properties analysis 590
methods for drop size spectra J Appl Meteor 37 912-923 591
httpsdoiorg1011751520-0450(1998)037lt0912RMARPAgt20CO2 592
Tokay A D B Wolff et al 2014 Evaluation of the New version of the laser-optical 593
disdrometer OTT Parsivel2 J Atmos Oceanic Technol 31(6) 1276-1288 594
httpsdoiorg101175JTECH-D-13-001741 595
Ulbrich C W 1983 Natural variations in the analytical form of the raindrop size 596
distribution J Appl Meteor 5 1764-1775 597
Wen G H Xiao H Yang Y Bi and W Xu 2017 Characteristics of summer and winter 598
precipitation over northern China Atmos Res 197 390-406 599
Wu W Y Liu and A K Betts 2012 Observationally based evaluation of NWP 600
reanalyses in modeling cloud properties over the Southern Great Plains J Geophys 601
Res 117 D12202 httpsdoi1010292011JD016971 602
Yuter S E D E Kingsmill L B Nance and M Loumlffler-Mang 2006 Observations of 603
precipitation size and fall velocity characteristics within coexisting rain and wet snow J 604
Appl Meteor Climatol 45 1450ndash1464 doi httpsdoiorg101175JAM24061 605
Zhang P C and B Y Du 2000 Radar Meteorology China Meteorological Press 511pp 606
(in Chinese) 607
608
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
7
following the method described by Schaefer (1956) The two-dimensional photo of 134
hydrometeors allows a careful determination of the hydrometeor shape and size The 135
Formvar data were used to distinguish dominant hydrometeor types eg raindrop 136
graupel or snowflake The hydrometeor type with a percentage of occurrence gt60 is 137
used to represent the solid precipitation type for convenience of analysis 138
A Ka-band millimeter wavelength cloud radar (wavelength is 8 mm) was used to 139
probe the vertical structure of clouds by vertical scanning from 11202016 which can 140
be used to determine cloud properties at 1 min temporal and 30 m vertical resolution 141
A total of 11098 HSD samples were collected from 12 precipitation events (Table 1) 142
Four representative hydrometeor types from the precipitation events are identified 143
raindrop graupel snowflake and mixed-phase precipitation The identification of the 144
hydrometeor types is mainly based on hydrometeors velocity observations and Formvar 145
images which will be detailed in Section 4 Mixed-phased precipitation contains 146
raindrops graupels and snowflakes simultaneously and none is dominant over another 147
The duration sample number precipitation rate and dominant type of hydrometeor 148
are shown in Table 1 The precipitation rate is calculated from HSD using the method 149
presented in Boudala et al (2014) 150
3 Hydrometeor Classification and Size and Fall Velocity 151
Distributions 152
a General Feature 153
Fig 2 illustrates the observed mean number concentration as a function of the 154
maximum dimension and the fall velocity for the four types of hydrometeors 155
8
respectively Also shown as a reference are the seven solid curves representing 156
different types of hydrometeor terminal velocities obtained from the laboratory 157
measurements calibrated by coefficient 50
0
since the site altitude is 1310 m 158
average pressure is 868 hpa and the average temperature is -5 ordmC (Niu et al2010) 159
(equations are shown in Table 3) Here ρ is the actual air density and ρ0 is the 160
standard atmospheric density The updrafts downdrafts and turbulence often 161
accompany falling hydrometeors inducing deviations in the velocity and trajectory of 162
falling hydrometeors from those in still air (Donnadieu 1980) Hence in this field 163
observation fall velocities of hydrometeors distribute along the terminal velocity curves 164
with large spread for each given size Similar features have been previously reported in 165
some situ measurements of raindrop fall velocities (Niu et al 2010 Rasmussen et al 166
2012) 167
In the previous study we discussed the air density and potential influencing 168
factors (eg turbulence organized air motions break-up and measurement errors) for 169
raindrop (Niu et al 2010) For precipitation in winter the hydrometeor shape is vitally 170
important for fall velocity The hydrometeor shape influence on fall velocities physical 171
mechanisms and instrument error underlying the large spread in the measured fall 172
velocities of different types are discussed in detail in the next two sub-sections 173
b Effect of Hydrometeor Type on Fall Velocity 174
In Fig 2a the hydrometeor fall velocities agree with the typical raindrop terminal 175
velocity curve which is obviously larger than the terminal velocities of graupel and 176
9
snowflake at given maximum diameters From the fall velocity distribution we can infer 177
that these hydrometeors are mainly raindrops The microscope photos obtained on the 178
ground confirm this However unlike the raindrop size and velocity distribution in 179
summer in Figure 8a of Niu et al (2010) there are some small size hydrometeors 180
(05~35mm) at very low speeds (05~2 ms) distributing among the terminal velocity 181
curves for graupel and snowflake This result implies that beside liquid raindrops 182
(including small raindrops or droplets from drizzle) some small snowflakes also exist in 183
the measurement The microscope photos also support the finding that although 184
raindrops are dominant some small plane- and column- shaped snowflakes co-exist 185
Fig 2b shows the joint hydrometeor size and fall velocity distribution during the 186
graupel event The hydrometeors are mainly symmetrically distributed around the ideal 187
terminal velocity of graupel (Locatelli and Hobbs 1974) supported by the photo-based 188
hydrometeor classification On the other hand it is found that certain small droplets 189
with the maximum dimensions among 03 to 10 mm are distributed around the liquid 190
raindrop curve suggesting that there are some raindrops and droplets coexisting in the 191
graupel dominated precipitation It is recognized that graupels grow by snow crystals 192
collecting cloud droplets and small raindrops (Pruppacher and Klett 1998) high cloud 193
top more liquid water content and presence of small raindrops (as shown in 194
microscope photography) provide favorable conditions for graupel The microscope 195
photos also display that graupelsrsquo surfaces are lumpy because of riming super cooled 196
drops during growing 197
The fall velocities of hydrometeors in Fig 2c are much smaller than the terminal 198
10
velocities of raindrop and graupel but are close to the terminal velocity curves of snow 199
of hexagonal densely rimed dendrites aggregates of dendrites Synthesizing the size 200
data the hydrometeors can be inferred as snowflakes which are further confirmed by 201
surface microscope photos From the surface observation we found many 202
rimedunrimed or aggregated dendrites or hexagonal snowflakes Although riming and 203
aggregation microphysical processes have some influence on terminal velocity 204
(Barthazy and Schefold 2006 Garrett and Yuter 2014 Heymsfield and Westbrook 205
2010) but the influences are too small to distinguish only from observed fall velocity 206
since it is a combined result of many factors When maximum dimensions are among 207
03 to 10 mm there are some small hydrometeors with fall velocities larger than 208
snowflakes which maybe graupels raindrops and droplets 209
Fig 2d is the hydrometeor size and fall velocity distribution during a mixed-phased 210
precipitation The hydrometeor fall velocities exhibit the largest spread for example 211
the fall velocities for hydrometeors with maximum dimension equaling to 3 mm 212
change from 05 to 5 ms and do not distribute along any of the ideal terminal velocity 213
curves This result suggests that different hydrometeor types might coexist during the 214
same sampling time To substantiate supercooled raindrops graupels and different 215
kinds of snowflakes are observed from the surface microscope simultaneously Similar 216
changes in particle size and fall velocity distribution documented by the disdrometer as 217
the storm transitions from rain to mixed-phase to snow were found at Marshall Field 218
site (Rasmussen et al 2012) 219
11
c Other Influencing Factors 220
The different dependence on particle size of terminal velocities for different types 221
of hydrometeors can explain some systematic distribution of the PARSIVEL-measured 222
fall velocities but the large spreads in the measurement of the instant particle fall 223
velocities await further inspection 224
According to our previous work the fall velocity (V) of a hydrometeor measured by 225
the PARSIVEL can be regarded as a combination of the terminal velocity in still air (Vt) 226
and a component Vrsquo that results from all other potential influencing factors eg type 227
turbulence organized air motions break-up and measurement errors (Niu et al 228
2010) 229
119881 = 119881119905 + 119881 prime (1) 230
The large spread of the measurements at both sides of the terminal velocity curves 231
shown in figure 2 seems compatible with the notion of nearly random collections of 232
downdraft and updraft A wider spread for fall velocities implies a wider range of 233
variation in vertical motions when hydrometeors are liquid raindrops (Niu et al 2010) 234
Solid nonspherical hydrometeors are much more complex than liquid drops and the 235
large spread of velocities may be caused by several other factors First different types 236
of hydrometeors (columns bullets plates lump graupels and hexagonal snowflakes et 237
al) have different fall speeds It is long recognized that microphysical processes in cold 238
precipitation are more complex and consequently generate more types of solid 239
hydrometeors comparing to the generation of raindrops The averaged concentration 240
distributions of large number of samples shown in Figure 2 also represents the possible 241
12
distributions of hydrometeors If there is only one kind particle the high concentration 242
would along its ideal terminal velocity very well just like the raindrop possible 243
distribution (Niu et al 2010) The concentration of mixed precipitation in Fig 2d does 244
not along any singe ideal terminal velocity further improved there are more than one 245
kind of hydrometers Coexistence of different types of hydrometeors induces larger 246
spread of fall velocities Second different degrees of riming and aggregating may affect 247
the results Densely rimed particles fall faster than unrimed particles with the same 248
maximum dimension aggregated snowflakes generally fall faster than their component 249
crystals (Barthazy and Schefold 2006 Garrett and Yuter 2014 Locatelli and Hobbs 250
1974) Third solid hydrometeors more likely occur breakup aggregation collision and 251
coalescence processes because of the large range of speeds According to prior 252
research of raindrop breakup and coalescence would lead to the ldquohigher-than-terminal 253
velocityrdquo fall velocity for small drops but ldquolower-than-terminal velocityrdquo fall velocity for 254
large drops (Niu et al 2010 Montero-Martiacutenez et al 2009 Larsen et al 2014) Similar 255
results are expected for the fall velocity of solid hydrometeors Last but not the least 256
the disdrometer may suffer from instrumental errors due to the internally assumed 257
relationship between horizontal and vertical particle dimensions likely resulting in a 258
wider spreads of fall velocities for the graupel and snowflakes as compared to the 259
raindrop counterpart as discussed in Section 2 Although the instrument error is an 260
important factor that should be considered in velocity spread as shown in Fig2b the 261
instrument error could not cause that large velocity spread The possible distributions 262
of fall velocities are the combine effects of physical and instrument principle 263
13
Further support for the possible instrumental uncertainty is from the cloud radar 264
observations Fig 3 shows the cloud reflectivity and linear depolarization ratio (LDR) in 265
lower level (less than 08 km) for the graupel snowflake and mixed-phased 266
precipitations respectively The LDR is a valuable observable in identifying the 267
hydrometeor types (Oue et al 2015) As shown in Fig 3a the cloud top height of 268
graupel precipitation was up to 7km during 1900 to 2050 Beijng Time (BT) which was 269
highest among the three events The high cloud top implies stronger updraft and 270
turbulence which further induces a larger fall velocity spread The LDR value was the 271
smallest among the three events indicating that the hydrometeors were close to 272
spherical consistent to the surface observations The cloud top height of snowflake 273
precipitation was up to 35 km (Fig 3c) which was the lowest among the three types of 274
precipitations implying weakest updraft and turbulence Notably although the 275
snowflake types are more complex than those of graupels the velocity spread was not 276
as large as that of the graupel type likely because of the weakest updraft and 277
turbulence The LDR was relatively larger consistent with the surface snowflake 278
observations (Fig 3d) The cloud top height of mixed-phase precipitation was up to 45 279
km (Fig 3e) and the LDR in lower level was largest among the three types of 280
precipitations owing to coexistence of raindrops graupels and snowflakes (Fig 3f) 281
4 Hydrometeor Size Distributions 282
a Comparison of HSDs between Different Types 283
There were four representative types of precipitations during this field experiment 284
providing us a unique opportunity to examine the HSD differences between the four 285
14
types of hydrometeors The sample numbers mean maximum dimensions and number 286
concentrations for each kind of HSDs are given in Table 2 Figure 4 is the averaged 287
distribution of all measured HSDs of 4 kinds As shown in Figure 4 on average the 288
mixed-phased precipitation tends to have most small size hydrometeors with D lt 15 289
mm while snowflake precipitation has the least small hydrometeors among the four 290
types The snowflake precipitation has more large size hydrometeors ie 3 mm lt D lt 11 291
mm Graupel size distribution tends to have two peeks around 13 mm and 26 mm The 292
mean maximum dimension is largest for snowflake (126 mm) and smallest for the 293
mixed HSD due to many small particles Similar results were found in precipitation 294
occurring in the Cascade and Rocky Mountains (Yuter et al 2006) The PARSIVEL 295
disdrometer doesnrsquot provide reliable data for small drops lower than 05 mm and tends to 296
underestimate small drops so the relatively low concentrations of small drops likely resulted 297
from the instrumentrsquos shortcomings (Tokay et al 2013 and Chen et al 2017) 298
b Evaluation of Distribution Functions for Describing HSDs 299
Over the last few decades great efforts have been devoted to finding the 300
appropriate analytical functions for describing the HSD because of its wide applications 301
in many areas including remote sensing and parameterization of precipitation (Chen et 302
al 2017) The two distribution functions mostly used up to now are the Lognormal 303
(Feingold and Levin 1986 Rosenfeld and Ulbrich 2003) and the Gamma (Ulbrich 1983) 304
distributions The Gamma distribution has been proposed as a first order generalization 305
of the Exponential distribution when μ equals 0 (Table 4) Weibull distribution is 306
another function used to describe size distributions of raindrops and cloud droplets (Liu 307
15
and Liu 1994 Liu et al 1995) Nevertheless the question as to which functions are 308
more adequate to describe HSDs of solid hydrometeors have been rarely investigated 309
systematically and quantitatively Thus the objective of this section is to examine the 310
most adequate distribution function used to describe HSDs 311
Considering size distributions of raindrops cloud droplets and aerosol particles are 312
the end results of many (stochastic) complex processes Liu (1992 1993 1994 and 313
1995) proposed a statistical method based on the relationships between the skewness 314
(S) and kurtosis (K) derived from an ensemble of particle size distribution 315
measurements and from those commonly used size distribution functions Cugerone 316
and Michele (2017) also used a similar approach based on the S-K relationships to study 317
raindrop size distributions Unlike the conventional curve-fitting of individual size 318
distributions this approach applies to an ensemble of size distribution measurements 319
and identifies the most appropriate statistical distribution pattern Here we apply this 320
approach to investigate if the statistical pattern of the HSDs of four precipitation types 321
follows the Exponential Gaussian Gamma Weibull and Lognormal distributions (Table 322
4) and if there are any pattern differences between them Briefly S and K of a HSD are 323
calculated from the corresponding HSD with the following two equations 324
23
2
3
t
iii
t
iii
dDN
)(Dn)D(D
dDN
)(Dn)D(D
S
minus
minus
=
(2) 325
32
2
4
minus
minus
minus
=
dDN
)(Dn)D(D
dDN
)(Dn)D(D
K
t
iii
t
iii
(3) 326
16
where Di is the central diameter of the i-th bin ni is the number concentration of the 327
i-th bin and Nt is total number concentration Note that each individual HSD can be 328
used to obtain a pair of S and K which is shown as a dot in Figure 5 Also noteworthy is 329
that the SndashK relationships for the families of Gamma Weibull and Lognormal are 330
described by known analytical functions (Liu 1993 1994 and 1995 Cugerone and 331
Michele 2017) represented by theoretical curves in Figure 5 The Exponential and 332
Gaussian distributions are represented by single points on the S-K diagram (S=2 and K=6 333
for Exponential) and (S=0 and K=0 for Gaussian) respectively Thus by comparing the 334
measured S and K values (points) with the known theoretical curves one can determine 335
the most proper function used to describe HSDs 336
Figure 5 shows the scatter plots of observed SndashK pairs calculated from the HSD 337
measurements for raindrop graupel snowflake mixed-phase precipitations Also 338
shown as comparison are the theoretical curves corresponding to the analytical HSD 339
functions A few points are evident First despite some occasional departures most of 340
the points fall near the theoretical lines of Gamma and Weibull distributions suggesting 341
that the HSD patterns for all the four types of precipitations well follow the Gamma and 342
Weibull distributions statistically Second HSDs of raindrops and mixed hydrometeors 343
are better described by Gamma and Weibull distribution than graupels and snowflakes 344
Third the S and K do not cluster around points (2 6) and (0 0) suggesting that the 345
Gaussian and Exponential distribution are not appropriate for describing HSDs 346
especially Gaussian distribution 347
To further evaluate the overall performance of the different distribution functions 348
17
we employ the widely used technique of Taylor diagram (Taylor 2001) and ldquoRelative 349
Euclidean Distancerdquo (RED) (Wu et al 2012) as a supplement to the Taylor diagram The 350
Taylor diagram has been widely used to visualize the statistical differences between 351
model results and observations in evaluation of model performance against 352
measurements or other benchmarks (IPCC 2001) Correlation coefficient (r) standard 353
deviation (σ) and ldquocentered root-mean-square errorrdquo (RMSE hereafter) are used in 354
the Taylor diagram The RED is introduced to add the bias as well in a dimensionless 355
framework that allows for comparison between different physical quantities with 356
different units In this study we consider the S and K values derived from the 357
distribution functions as model results and evaluate them against those derived from 358
the HSD measurements Brieflythe expressions for calculating r and σ and RMSE are 359
shown below 360
119903 =1
119873sum (119872119899minus)(119874119899minus)119873119899=1
120590119872120590119900 (4) 361
119877119872119878119864 = 1
119873sum [(119872119899 minus ) minus (119874119899 minus )]2119873119899=1
12
(5) 362
120590119872 = [1
119873sum (119872119899 minus )119873119899=1 ]
12
(6) 363
1205900 = [1
119873sum (119874119899 minus )119873119899=1 ]
12
(7) 364
where M and O denote distribution function and observed variables The RED 365
expression is shown below 366
119877119864119863 = [(minus)
]2
+ [(120590119872minus120590119874)
120590119900]2
+ (1 minus 119903)212
( 8 ) 367
Equation (8) indicates that RED considers all the components of mean bias variations 368
and correlations in a dimensionless way the distribution function performance 369
degrades as RED increases from the perfect agreement with RED=0 370
18
In the Taylor diagrams shown in Fig 6 the cosine of azimuthal angle of each point 371
gives the r between the function-calculated and observed data The distance between 372
individual point and the reference point ldquoObsrdquo represents the RMSE normalized by the 373
amplitude of the observationally based variations As this distance approaches to zero 374
the function-calculated K and S approach to the observations Clearly the values of r 375
are around 097 for Gamma and Weibull r for Lognormal function is slightly smaller 376
(095) The normalized σ are much different for Lognormal Gamma and Weibull 377
distributions with averaged value being 057 0895 and 0785 respectively Therefore 378
the Lognormal distribution exhibits the worst performance for describing HSDs and 379
Gamma and Weibull distributions appear to perform much better (Fig 6a) 380
Noticing that S and K of Gamma and Weibull distributions are equal at the point of S 381
= 2 and K = 6 and have positive relationship (If S lt 2 then K lt 6 and if S gt 2 then k gt 6) In 382
this part we further separately examine the group of data with S lt 2 and K lt 6 (Fig 6b) 383
and compare its result with those of total data The averaged normalized σ are 103 and 384
109 and r are 091 and 090 for Weibull and Gamma distributions respectively 385
suggesting that Weibull distribution performs slightly better than Gamma distribution 386
for the four HSD types in the data group of S lt 2 and K lt 6 whereas the opposite is true 387
for all data This conclusion is further substantiated by comparison of RED values for the 388
four type of precipitation (Fig7) which shows that Lognormal has the largest RED 389
Gamma the smallest and Weibull in between for four types of precipitations in all data 390
whereas Weibull (Lognormal) has smallest (largest) RED values when S lt 2 and K lt 6 It 391
can be inferred for data group of S gt 2 and k gt 6 Gamma distribution performs better 392
19
Further comparison between different precipitation types shows these functions all 393
performs better for raindrop size distributions and mixed-phase than graupel and 394
snowflake size distributions The RED for snowflakes is largest among the four types 395
The performance of Gamma is better for describing solid HSDs of all data but Weibull 396
distribution is better when S lt 2 and K lt 6 397
5 Conclusion 398
The combined measurements collected during a field experiment conducted at the 399
Haituo Mountain site using PARSIVEL disdrometer millimeter wavelength cloud radar 400
and microscope photography are analyzed to classify the precipitation hydrometeor 401
types examine the dependence of fall velocity on hydrometeor size for different 402
hydrometeor types and determine the best distribution functions to describe the 403
hydrometeor size distributions of different types 404
Analysis of the PARSIVEL-measured fall velocities show that on average the 405
dependence of fall velocity on hydrometeor size largely follow their corresponding 406
terminal velocity curves for raindrops graupels and snowflakes respectively suggesting 407
that such measurements are useful to identify the hydrometeor types The associated 408
microscope photos and cloud radar observations support the classification of 409
hydrometeor types based on the PARSIVEL-observed fall velocities Furthermore there 410
are velocity spreads in fall velocity across hydrometeor sizes for all hydrometeors and 411
the spreads for the solid hydrometeors could cause by hydrometeor type turbulence or 412
updraftdowndraft and instrument measured principle The coexistence of various 413
types of hydrometeors likely induces additional spread of fall velocity for given 414
20
hydrometeor sizes such as mixed precipitation Meanwhile complex microphysical 415
processes in cold precipitation such as riming aggregation breakup and collision and 416
coalescence influence fall velocity which likely induce larger spread of fall velocity Last 417
but not the least the disdrometer may suffer from instrumental errors due to the 418
internally assumed relationship between horizontal and vertical particle dimensions 419
Comparison of the type-averaged hydrometeor size distributions shows that the 420
mixed precipitation has more small hydrometeors with D lt 15 mm than others 421
whereas the snowflake precipitation has the least number of small hydrometeors 422
among the four types On the contrary the snowflake precipitation has more large 423
hydrometeors with D between 3 mm and 11 mm 424
The commonly used size distribution functions (Gamma Weibull and Lognormal) 425
are further examined to determine the most adequate function to describe the size 426
distribution measurements for all the hydrometeor types by use of an approach based 427
on the relationship between skewness (S) and kurtosis (K) Taylor diagram and RED are 428
further introduced to assess the performance of different size distribution functions 429
against measurements It is shown that the HSDs for the four types can all be well 430
described statistically by the Gamma and Weibull distribution but Lognormal 431
Exponential and Gaussian are not fit to describe HSDs Gamma and Weibull distribution 432
describe raindrop and mixed-phase size distribution better than snowflake and graupel 433
size distribution and their performances are worst for snowflake It may due to graupel 434
and snowflake precipitation have more big particles When S less than 2 and K less than 435
6 Weibull distribution performs better than Gamma distribution to describe HSDs but 436
21
Gamma distribution performs better for total data 437
A few points are noteworthy First although this study demonstrates the great 438
potential of combining simultaneous disdrometer measurements of particle fall velocity 439
and size distributions microscopic photography and cloud radar to address the 440
challenges facing solid precipitation the data are limited More research is needed to 441
discern such effects on the results presented here Second as the observations show 442
that in addition to sizes there are many other factors (eg hydrometeor type 443
microphysical processes turbulence and measuring principle) that can potentially 444
influence particle fall velocity as well More comprehensive research is needed to 445
further discern and separate these factors Finally the combined use of S-K diagram 446
Taylor diagram and relative Euclidean distance appears to be a powerful tool for 447
identifying the best function used to describe the HSDs and quantify the differences 448
between different precipitation types More research is in order along this direction 449
Acknowledgements 450
This study is mainly supported by the Chinese National Science Foundation under Grant 451
No 41675138 and National Key RampD Program of China (2017YFC0209604) It is partly 452
supported by Beijing National Science Foundation (8172023) the US Department 453
Energys Atmospheric System Research (ASR) Program (Liu and Jia at BNL) Lu is 454
supported by the Natural Science Foundation of Jiangsu Province (BK20160041) The 455
observation data are archived at a specialized supercomputer at Beijing Meteorology 456
Information Center (ftp10224592) which are available from the corresponding 457
author upon request The authors also thank Beijing weather modification office for 458
their support during the field experiment 459
Reference 460
22
Agosta CC Fettweis XX Datta RR 2015 Evaluation of the CMIP5 models in the 461
aim of regional modelling of the Antarctic surface mass balance Cryosphere 9 2311ndash462
2321 httpdxdoiorg105194tc-9-2311-2015 463
Barthazy E and R Schefold 2006 Fall velocity of snowflakes of different riming degree 464
and crystal types Atmos Res 82(1) 391-398 httpsdoiorg101016jatmosres 465
200512009 466
Battaglia A Rustemeier E Tokay A et al 2010 PARSIVEL snow observations a critical 467
assessment J Atmos Oceanic Technol 27(2) 333-344 doi 1011752009jtecha13321 468
Boumlhm H P 1989 A General Equation for the Terminal Fall Speed of Solid Hydrometeors 469
J Atmos Sci 46(15) 2419-2427 httpsdoiorg1011751520-0469(1989)046 lt2419A 470
GEFTTgt20CO2 471
Boudala F S G A Isaac et al 2014 Comparisons of Snowfall Measurements in 472
Complex Terrain Made During the 2010 Winter Olympics in Vancouver Pure and 473
Applied Geophysics 171(1) 113-127 474
Chen B W Hu and J Pu 2011 Characteristics of the raindrop size distribution for 475
freezing precipitation observed in southern China J Geophys Res 116 D06201 476
doi1010292010JD015305 477
Chen B Z Hu L Liu and G Zhang (2017) Raindrop Size Distribution Measurements at 478
4500m on the Tibetan Plateau during TIPEX-III J Geophys Res 122 11092-11106 479
doiorg10100 22017JD027233 480
23
Cugerone K and C De Michele 2017 Investigating raindrop size distributions in the 481
(L-)skewness-(L-)kurtosis plane Quart J Roy Meteor Soc 143(704) 1303-1312 482
httpsdoiorg101002qj3005 483
Donnadieu G 1980 Comparison of results obtained with the VIDIAZ spectro 484
pluviometer and the JossndashWaldvogel rainfall disdrometer in a ldquorain of a thundery typerdquo 485
J Appl Meteor 19 593ndash597 486
Feingold G and Levin Z 1986 The lognormal fit to raindrop spectra from frontal 487
convective clouds in Israel J Clim Appl Meteorol 25 1346ndash1363 488
httpsdoiorg1011751520-0450(1986)025lt1346tlftrsgt20CO2 489
Field P R A J Heymsfield and A Bansemer 2007 Snow Size Distribution 490
Parameterization for Midlatitude and Tropical Ice Clouds J Atmos Sci 64(12) 491
4346-4365 httpsdoiorg1011752007JAS23441 492
Garrett T J and S E Yuter 2014 Observed influence of riming temperature and 493
turbulence on the fallspeed of solid precipitation Geophysical Research Letters 41(18) 494
6515ndash6522 495
Geresdi I N Sarkadi and G Thompson 2014 Effect of the accretion by water drops 496
on the melting of snowflakes Atmos Res 149 96-110 497
Gunn R and G D Kinzer 1949 The terminal velocity of fall for water drops in stagnant 498
air J Meteor 6 243-248 httpsdoiorg1011751520-0469(1949)006lt0243TTVOFFgt 499
20CO2 500
24
Heymsfield A J and C D Westbrook 2010 Advances in the Estimation of Ice Particle 501
Fall Speeds Using Laboratory and Field Measurements J Atmos Sci 67(8) 2469-2482 502
httpsdoiorg1011752010JAS33791 503
Huang G-J C Kleinkort V N Bringi and B M Notaroš 2017 Winter precipitation 504
particle size distribution measurement by Multi-Angle Snowflake Camera Atmos Res 505
198 81-96 506
Intergovernmental Panel on Climate Change (IPCC) 2001 Climate Change 2001 The 507
Scientific Basis Contribution of Working Group I to the Third Assessment Report of the 508
Intergovernmental Panel on Climate Change edited by J T Houghton et al 881 pp 509
Cambridge Univ Press New York 510
Ishizaka M H Motoyoshi S Nakai T Shiina T Kumakura and K-i Muramoto 2013 A 511
New Method for Identifying the Main Type of Solid Hydrometeors Contributing to 512
Snowfall from Measured Size-Fall Speed Relationship Journal of the Meteorological 513
Society of Japan Ser II 91(6) 747-762 httpsdoiorg102151jmsj2013-602 514
Khvorostyanov V 2005 Fall Velocities of Hydrometeors in the Atmosphere 515
Refinements to a Continuous Analytical Power Law J Atmos Sci 62 4343-4357 516
httpsdoiorg101175JAS36221 517
Kikuchi K T Kameda K Higuchi and A Yamashita 2013 A global classification of 518
snow crystals ice crystals and solid precipitation based on observations from middle 519
latitudes to polar regions Atmos Res 132-133 460-472 520
Kneifel S A von Lerber J Tiira D Moisseev P Kollias and J Leinonen 2015 521
Observed relations between snowfall microphysics and triple-frequency radar 522
25
measurements J Geophys Res Atmos 120(12) 6034-6055 523
httpsdoi1010022015JD023156 524
Kubicek A and P K Wang 2012 A numerical study of the flow fields around a typical 525
conical graupel falling at various inclination angles Atmos Res 118 15ndash26 526
httpsdoi101016jatmosres201206001 527
Larsen M L A B Kostinski and A R Jameson (2014) Further evidence for 528
superterminal raindrops Geophys Res Lett 41(19) 6914-6918 529
Lee JE SH Jung H M Park S Kwon P L Lin and G W Lee 2015 Classification of 530
Precipitation Types Using Fall Velocity Diameter Relationships from 2D-Video 531
Distrometer Measurements Advances in Atmospheric Sciences (09) 532
Lin Y L J Donner and B A Colle 2010 Parameterization of riming intensity and its 533
impact on ice fall speed using arm data Mon Weather Rev 139(3) 1036ndash1047 534
httpsdoi1011752010MWR32991 535
Liu Y G 1992 Skewness and kurtosis of measured raindrop size distributions Atmos 536
Environ 26A 2713-2716 httpsdoiorg1010160960-1686(92)90005-6 537
Liu Y G 1993 Statistical theory of the Marshall-Parmer distribution of raindrops 538
Atmos Environ 27A 15-19 httpsdoiorg1010160960-1686(93)90066-8 539
Liu Y G and F Liu 1994 On the description of aerosol particle size distribution Atmos 540
Res 31(1-3) 187-198 httpsdoiorg1010160169-8095(94)90043-4 541
Liu Y G L You W Yang F Liu 1995 On the size distribution of cloud droplets Atmos 542
Res 35 (2-4) 201-216 httpsdoiorg1010160169-8095(94)00019-A 543
Locatelli J D and P V Hobbs 1974 Fall speeds and masses of solid precipitation 544
26
particles J Geophys Res 79(15) 2185-2197 httpsdoi101029JC079i015p02185 545
Loumlffler-Mang M and J Joss 2000 An optical disdrometer for measuring size and 546
velocity of hydrometeors J Atmos Oceanic Technol 17 130-139 547
httpsdoiorg1011751520-0426(2000)017lt0130AODFMSgt20CO2 548
Loumlffler-Mang M and U Blahak 2001 Estimation of the Equivalent Radar Reflectivity 549
Factor from Measured Snow Size Spectra J Clim Appl Meteorol 40(4) 843-849 550
httpsdoiorg1011751520-0450(2001)040lt0843EOTERRgt20CO2 551
Matrosov S Y 2007 Modeling Backscatter Properties of Snowfall at Millimeter 552
Wavelengths J Atmos Sci 64(5) 1727-1736 httpsdoiorg101175JAS39041 553
Mitchell D L 1996 Use of mass- and area-dimensional power laws for determining 554
precipitation particle terminal velocities J Atmos Sci 53 1710-1723 555
httpsdoiorg1011751520-0469(1996)053lt1710UOMAADgt20CO2 556
Montero-Martiacutenez G A B Kostinski R A Shaw and F Garciacutea-Garciacutea 2009 Do all 557
raindrops fall at terminal speed Geophys Res Lett 36 L11818 558
httpsdoiorg1010292008GL037111 559
Niu S X Jia J Sang X Liu C Lu and Y Liu 2010 Distributions of raindrop sizes and 560
fall velocities in a semiarid plateau climate Convective vs stratiform rains J Appl 561
Meteorol Climatol 49 632ndash645 httpsdoi1011752009JAMC22081 562
Nurzyńska K M Kubo and K-i Muramoto 2012 Texture operator for snow particle 563
classification into snowflake and graupel Atmos Res 118 121-132 564
Oue M M R Kumjian Y Lu J Verlinde K Aydin and E E Clothiaux 2015 Linear 565
27
Depolarization Ratios of columnar ice crystals in a deep precipitating system over the 566
Arctic observed by Zenith-Pointing Ka-Band Doppler radar J Clim Appl Meteorol 567
54(5) 1060-1068 httpsdoiorg101175JAMC-D-15-00121 568
Pruppacher H R and J D Klett 1998 Microphysics of clouds and precipitation Kluwer 569
Academic 954 pp 570
Rasmussen R B Baker et al 2012 How well are we measuring snow the 571
NOAAFAANCAR winter precipitation test bed Bull Amer Meteor Soc 93(6) 811-829 572
httpsdoiorg101175BAMS-D-11-000521 573
Reisner J R M Rasmussen and R T Bruintjes 1998 Explicit forecasting of 574
supercooled liquid water in winter storms using the MM5 mesoscale model Q J R 575
Meteorol Soc 124 1071ndash1107 httpsdoi101256smsqj54803 576
Rosenfeld D and Ulbrich C W 2003 Cloud microphysical properties processes and 577
rainfall estimation opportunities Meteorol Monogr 30 237-237 578
httpsdoiorg101175 0065-9401(2003)030lt0237cmppargt20CO2 579
Schaefer V J 1956 The preparation of snow crystal replicas-VI Weatherwsie 9 580
132-135 581
Souverijns N A Gossart S Lhermitte I V Gorodetskaya S Kneifel M Maahn F L 582
Bliven and N P M van Lipzig (2017) Estimating radar reflectivity - Snowfall rate 583
relationships and their uncertainties over Antarctica by combining disdrometer and 584
radar observations Atmos Res 196 211-223 585
Taylor K E 2001 Summarizing multiple aspects of model performance in a single 586
diagram J Geophys Res 106 7183ndash7192 httpsdoi1010292000JD900719 587
28
Tokay A and D A Short 1996 Evidence from tropical raindrop spectra of the origin of 588
rain from stratiform versus convective clouds J Appl Meteor 35 355ndash371 589
Tokay A and D Atlas 1999 Rainfall microphysics and radar properties analysis 590
methods for drop size spectra J Appl Meteor 37 912-923 591
httpsdoiorg1011751520-0450(1998)037lt0912RMARPAgt20CO2 592
Tokay A D B Wolff et al 2014 Evaluation of the New version of the laser-optical 593
disdrometer OTT Parsivel2 J Atmos Oceanic Technol 31(6) 1276-1288 594
httpsdoiorg101175JTECH-D-13-001741 595
Ulbrich C W 1983 Natural variations in the analytical form of the raindrop size 596
distribution J Appl Meteor 5 1764-1775 597
Wen G H Xiao H Yang Y Bi and W Xu 2017 Characteristics of summer and winter 598
precipitation over northern China Atmos Res 197 390-406 599
Wu W Y Liu and A K Betts 2012 Observationally based evaluation of NWP 600
reanalyses in modeling cloud properties over the Southern Great Plains J Geophys 601
Res 117 D12202 httpsdoi1010292011JD016971 602
Yuter S E D E Kingsmill L B Nance and M Loumlffler-Mang 2006 Observations of 603
precipitation size and fall velocity characteristics within coexisting rain and wet snow J 604
Appl Meteor Climatol 45 1450ndash1464 doi httpsdoiorg101175JAM24061 605
Zhang P C and B Y Du 2000 Radar Meteorology China Meteorological Press 511pp 606
(in Chinese) 607
608
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
8
respectively Also shown as a reference are the seven solid curves representing 156
different types of hydrometeor terminal velocities obtained from the laboratory 157
measurements calibrated by coefficient 50
0
since the site altitude is 1310 m 158
average pressure is 868 hpa and the average temperature is -5 ordmC (Niu et al2010) 159
(equations are shown in Table 3) Here ρ is the actual air density and ρ0 is the 160
standard atmospheric density The updrafts downdrafts and turbulence often 161
accompany falling hydrometeors inducing deviations in the velocity and trajectory of 162
falling hydrometeors from those in still air (Donnadieu 1980) Hence in this field 163
observation fall velocities of hydrometeors distribute along the terminal velocity curves 164
with large spread for each given size Similar features have been previously reported in 165
some situ measurements of raindrop fall velocities (Niu et al 2010 Rasmussen et al 166
2012) 167
In the previous study we discussed the air density and potential influencing 168
factors (eg turbulence organized air motions break-up and measurement errors) for 169
raindrop (Niu et al 2010) For precipitation in winter the hydrometeor shape is vitally 170
important for fall velocity The hydrometeor shape influence on fall velocities physical 171
mechanisms and instrument error underlying the large spread in the measured fall 172
velocities of different types are discussed in detail in the next two sub-sections 173
b Effect of Hydrometeor Type on Fall Velocity 174
In Fig 2a the hydrometeor fall velocities agree with the typical raindrop terminal 175
velocity curve which is obviously larger than the terminal velocities of graupel and 176
9
snowflake at given maximum diameters From the fall velocity distribution we can infer 177
that these hydrometeors are mainly raindrops The microscope photos obtained on the 178
ground confirm this However unlike the raindrop size and velocity distribution in 179
summer in Figure 8a of Niu et al (2010) there are some small size hydrometeors 180
(05~35mm) at very low speeds (05~2 ms) distributing among the terminal velocity 181
curves for graupel and snowflake This result implies that beside liquid raindrops 182
(including small raindrops or droplets from drizzle) some small snowflakes also exist in 183
the measurement The microscope photos also support the finding that although 184
raindrops are dominant some small plane- and column- shaped snowflakes co-exist 185
Fig 2b shows the joint hydrometeor size and fall velocity distribution during the 186
graupel event The hydrometeors are mainly symmetrically distributed around the ideal 187
terminal velocity of graupel (Locatelli and Hobbs 1974) supported by the photo-based 188
hydrometeor classification On the other hand it is found that certain small droplets 189
with the maximum dimensions among 03 to 10 mm are distributed around the liquid 190
raindrop curve suggesting that there are some raindrops and droplets coexisting in the 191
graupel dominated precipitation It is recognized that graupels grow by snow crystals 192
collecting cloud droplets and small raindrops (Pruppacher and Klett 1998) high cloud 193
top more liquid water content and presence of small raindrops (as shown in 194
microscope photography) provide favorable conditions for graupel The microscope 195
photos also display that graupelsrsquo surfaces are lumpy because of riming super cooled 196
drops during growing 197
The fall velocities of hydrometeors in Fig 2c are much smaller than the terminal 198
10
velocities of raindrop and graupel but are close to the terminal velocity curves of snow 199
of hexagonal densely rimed dendrites aggregates of dendrites Synthesizing the size 200
data the hydrometeors can be inferred as snowflakes which are further confirmed by 201
surface microscope photos From the surface observation we found many 202
rimedunrimed or aggregated dendrites or hexagonal snowflakes Although riming and 203
aggregation microphysical processes have some influence on terminal velocity 204
(Barthazy and Schefold 2006 Garrett and Yuter 2014 Heymsfield and Westbrook 205
2010) but the influences are too small to distinguish only from observed fall velocity 206
since it is a combined result of many factors When maximum dimensions are among 207
03 to 10 mm there are some small hydrometeors with fall velocities larger than 208
snowflakes which maybe graupels raindrops and droplets 209
Fig 2d is the hydrometeor size and fall velocity distribution during a mixed-phased 210
precipitation The hydrometeor fall velocities exhibit the largest spread for example 211
the fall velocities for hydrometeors with maximum dimension equaling to 3 mm 212
change from 05 to 5 ms and do not distribute along any of the ideal terminal velocity 213
curves This result suggests that different hydrometeor types might coexist during the 214
same sampling time To substantiate supercooled raindrops graupels and different 215
kinds of snowflakes are observed from the surface microscope simultaneously Similar 216
changes in particle size and fall velocity distribution documented by the disdrometer as 217
the storm transitions from rain to mixed-phase to snow were found at Marshall Field 218
site (Rasmussen et al 2012) 219
11
c Other Influencing Factors 220
The different dependence on particle size of terminal velocities for different types 221
of hydrometeors can explain some systematic distribution of the PARSIVEL-measured 222
fall velocities but the large spreads in the measurement of the instant particle fall 223
velocities await further inspection 224
According to our previous work the fall velocity (V) of a hydrometeor measured by 225
the PARSIVEL can be regarded as a combination of the terminal velocity in still air (Vt) 226
and a component Vrsquo that results from all other potential influencing factors eg type 227
turbulence organized air motions break-up and measurement errors (Niu et al 228
2010) 229
119881 = 119881119905 + 119881 prime (1) 230
The large spread of the measurements at both sides of the terminal velocity curves 231
shown in figure 2 seems compatible with the notion of nearly random collections of 232
downdraft and updraft A wider spread for fall velocities implies a wider range of 233
variation in vertical motions when hydrometeors are liquid raindrops (Niu et al 2010) 234
Solid nonspherical hydrometeors are much more complex than liquid drops and the 235
large spread of velocities may be caused by several other factors First different types 236
of hydrometeors (columns bullets plates lump graupels and hexagonal snowflakes et 237
al) have different fall speeds It is long recognized that microphysical processes in cold 238
precipitation are more complex and consequently generate more types of solid 239
hydrometeors comparing to the generation of raindrops The averaged concentration 240
distributions of large number of samples shown in Figure 2 also represents the possible 241
12
distributions of hydrometeors If there is only one kind particle the high concentration 242
would along its ideal terminal velocity very well just like the raindrop possible 243
distribution (Niu et al 2010) The concentration of mixed precipitation in Fig 2d does 244
not along any singe ideal terminal velocity further improved there are more than one 245
kind of hydrometers Coexistence of different types of hydrometeors induces larger 246
spread of fall velocities Second different degrees of riming and aggregating may affect 247
the results Densely rimed particles fall faster than unrimed particles with the same 248
maximum dimension aggregated snowflakes generally fall faster than their component 249
crystals (Barthazy and Schefold 2006 Garrett and Yuter 2014 Locatelli and Hobbs 250
1974) Third solid hydrometeors more likely occur breakup aggregation collision and 251
coalescence processes because of the large range of speeds According to prior 252
research of raindrop breakup and coalescence would lead to the ldquohigher-than-terminal 253
velocityrdquo fall velocity for small drops but ldquolower-than-terminal velocityrdquo fall velocity for 254
large drops (Niu et al 2010 Montero-Martiacutenez et al 2009 Larsen et al 2014) Similar 255
results are expected for the fall velocity of solid hydrometeors Last but not the least 256
the disdrometer may suffer from instrumental errors due to the internally assumed 257
relationship between horizontal and vertical particle dimensions likely resulting in a 258
wider spreads of fall velocities for the graupel and snowflakes as compared to the 259
raindrop counterpart as discussed in Section 2 Although the instrument error is an 260
important factor that should be considered in velocity spread as shown in Fig2b the 261
instrument error could not cause that large velocity spread The possible distributions 262
of fall velocities are the combine effects of physical and instrument principle 263
13
Further support for the possible instrumental uncertainty is from the cloud radar 264
observations Fig 3 shows the cloud reflectivity and linear depolarization ratio (LDR) in 265
lower level (less than 08 km) for the graupel snowflake and mixed-phased 266
precipitations respectively The LDR is a valuable observable in identifying the 267
hydrometeor types (Oue et al 2015) As shown in Fig 3a the cloud top height of 268
graupel precipitation was up to 7km during 1900 to 2050 Beijng Time (BT) which was 269
highest among the three events The high cloud top implies stronger updraft and 270
turbulence which further induces a larger fall velocity spread The LDR value was the 271
smallest among the three events indicating that the hydrometeors were close to 272
spherical consistent to the surface observations The cloud top height of snowflake 273
precipitation was up to 35 km (Fig 3c) which was the lowest among the three types of 274
precipitations implying weakest updraft and turbulence Notably although the 275
snowflake types are more complex than those of graupels the velocity spread was not 276
as large as that of the graupel type likely because of the weakest updraft and 277
turbulence The LDR was relatively larger consistent with the surface snowflake 278
observations (Fig 3d) The cloud top height of mixed-phase precipitation was up to 45 279
km (Fig 3e) and the LDR in lower level was largest among the three types of 280
precipitations owing to coexistence of raindrops graupels and snowflakes (Fig 3f) 281
4 Hydrometeor Size Distributions 282
a Comparison of HSDs between Different Types 283
There were four representative types of precipitations during this field experiment 284
providing us a unique opportunity to examine the HSD differences between the four 285
14
types of hydrometeors The sample numbers mean maximum dimensions and number 286
concentrations for each kind of HSDs are given in Table 2 Figure 4 is the averaged 287
distribution of all measured HSDs of 4 kinds As shown in Figure 4 on average the 288
mixed-phased precipitation tends to have most small size hydrometeors with D lt 15 289
mm while snowflake precipitation has the least small hydrometeors among the four 290
types The snowflake precipitation has more large size hydrometeors ie 3 mm lt D lt 11 291
mm Graupel size distribution tends to have two peeks around 13 mm and 26 mm The 292
mean maximum dimension is largest for snowflake (126 mm) and smallest for the 293
mixed HSD due to many small particles Similar results were found in precipitation 294
occurring in the Cascade and Rocky Mountains (Yuter et al 2006) The PARSIVEL 295
disdrometer doesnrsquot provide reliable data for small drops lower than 05 mm and tends to 296
underestimate small drops so the relatively low concentrations of small drops likely resulted 297
from the instrumentrsquos shortcomings (Tokay et al 2013 and Chen et al 2017) 298
b Evaluation of Distribution Functions for Describing HSDs 299
Over the last few decades great efforts have been devoted to finding the 300
appropriate analytical functions for describing the HSD because of its wide applications 301
in many areas including remote sensing and parameterization of precipitation (Chen et 302
al 2017) The two distribution functions mostly used up to now are the Lognormal 303
(Feingold and Levin 1986 Rosenfeld and Ulbrich 2003) and the Gamma (Ulbrich 1983) 304
distributions The Gamma distribution has been proposed as a first order generalization 305
of the Exponential distribution when μ equals 0 (Table 4) Weibull distribution is 306
another function used to describe size distributions of raindrops and cloud droplets (Liu 307
15
and Liu 1994 Liu et al 1995) Nevertheless the question as to which functions are 308
more adequate to describe HSDs of solid hydrometeors have been rarely investigated 309
systematically and quantitatively Thus the objective of this section is to examine the 310
most adequate distribution function used to describe HSDs 311
Considering size distributions of raindrops cloud droplets and aerosol particles are 312
the end results of many (stochastic) complex processes Liu (1992 1993 1994 and 313
1995) proposed a statistical method based on the relationships between the skewness 314
(S) and kurtosis (K) derived from an ensemble of particle size distribution 315
measurements and from those commonly used size distribution functions Cugerone 316
and Michele (2017) also used a similar approach based on the S-K relationships to study 317
raindrop size distributions Unlike the conventional curve-fitting of individual size 318
distributions this approach applies to an ensemble of size distribution measurements 319
and identifies the most appropriate statistical distribution pattern Here we apply this 320
approach to investigate if the statistical pattern of the HSDs of four precipitation types 321
follows the Exponential Gaussian Gamma Weibull and Lognormal distributions (Table 322
4) and if there are any pattern differences between them Briefly S and K of a HSD are 323
calculated from the corresponding HSD with the following two equations 324
23
2
3
t
iii
t
iii
dDN
)(Dn)D(D
dDN
)(Dn)D(D
S
minus
minus
=
(2) 325
32
2
4
minus
minus
minus
=
dDN
)(Dn)D(D
dDN
)(Dn)D(D
K
t
iii
t
iii
(3) 326
16
where Di is the central diameter of the i-th bin ni is the number concentration of the 327
i-th bin and Nt is total number concentration Note that each individual HSD can be 328
used to obtain a pair of S and K which is shown as a dot in Figure 5 Also noteworthy is 329
that the SndashK relationships for the families of Gamma Weibull and Lognormal are 330
described by known analytical functions (Liu 1993 1994 and 1995 Cugerone and 331
Michele 2017) represented by theoretical curves in Figure 5 The Exponential and 332
Gaussian distributions are represented by single points on the S-K diagram (S=2 and K=6 333
for Exponential) and (S=0 and K=0 for Gaussian) respectively Thus by comparing the 334
measured S and K values (points) with the known theoretical curves one can determine 335
the most proper function used to describe HSDs 336
Figure 5 shows the scatter plots of observed SndashK pairs calculated from the HSD 337
measurements for raindrop graupel snowflake mixed-phase precipitations Also 338
shown as comparison are the theoretical curves corresponding to the analytical HSD 339
functions A few points are evident First despite some occasional departures most of 340
the points fall near the theoretical lines of Gamma and Weibull distributions suggesting 341
that the HSD patterns for all the four types of precipitations well follow the Gamma and 342
Weibull distributions statistically Second HSDs of raindrops and mixed hydrometeors 343
are better described by Gamma and Weibull distribution than graupels and snowflakes 344
Third the S and K do not cluster around points (2 6) and (0 0) suggesting that the 345
Gaussian and Exponential distribution are not appropriate for describing HSDs 346
especially Gaussian distribution 347
To further evaluate the overall performance of the different distribution functions 348
17
we employ the widely used technique of Taylor diagram (Taylor 2001) and ldquoRelative 349
Euclidean Distancerdquo (RED) (Wu et al 2012) as a supplement to the Taylor diagram The 350
Taylor diagram has been widely used to visualize the statistical differences between 351
model results and observations in evaluation of model performance against 352
measurements or other benchmarks (IPCC 2001) Correlation coefficient (r) standard 353
deviation (σ) and ldquocentered root-mean-square errorrdquo (RMSE hereafter) are used in 354
the Taylor diagram The RED is introduced to add the bias as well in a dimensionless 355
framework that allows for comparison between different physical quantities with 356
different units In this study we consider the S and K values derived from the 357
distribution functions as model results and evaluate them against those derived from 358
the HSD measurements Brieflythe expressions for calculating r and σ and RMSE are 359
shown below 360
119903 =1
119873sum (119872119899minus)(119874119899minus)119873119899=1
120590119872120590119900 (4) 361
119877119872119878119864 = 1
119873sum [(119872119899 minus ) minus (119874119899 minus )]2119873119899=1
12
(5) 362
120590119872 = [1
119873sum (119872119899 minus )119873119899=1 ]
12
(6) 363
1205900 = [1
119873sum (119874119899 minus )119873119899=1 ]
12
(7) 364
where M and O denote distribution function and observed variables The RED 365
expression is shown below 366
119877119864119863 = [(minus)
]2
+ [(120590119872minus120590119874)
120590119900]2
+ (1 minus 119903)212
( 8 ) 367
Equation (8) indicates that RED considers all the components of mean bias variations 368
and correlations in a dimensionless way the distribution function performance 369
degrades as RED increases from the perfect agreement with RED=0 370
18
In the Taylor diagrams shown in Fig 6 the cosine of azimuthal angle of each point 371
gives the r between the function-calculated and observed data The distance between 372
individual point and the reference point ldquoObsrdquo represents the RMSE normalized by the 373
amplitude of the observationally based variations As this distance approaches to zero 374
the function-calculated K and S approach to the observations Clearly the values of r 375
are around 097 for Gamma and Weibull r for Lognormal function is slightly smaller 376
(095) The normalized σ are much different for Lognormal Gamma and Weibull 377
distributions with averaged value being 057 0895 and 0785 respectively Therefore 378
the Lognormal distribution exhibits the worst performance for describing HSDs and 379
Gamma and Weibull distributions appear to perform much better (Fig 6a) 380
Noticing that S and K of Gamma and Weibull distributions are equal at the point of S 381
= 2 and K = 6 and have positive relationship (If S lt 2 then K lt 6 and if S gt 2 then k gt 6) In 382
this part we further separately examine the group of data with S lt 2 and K lt 6 (Fig 6b) 383
and compare its result with those of total data The averaged normalized σ are 103 and 384
109 and r are 091 and 090 for Weibull and Gamma distributions respectively 385
suggesting that Weibull distribution performs slightly better than Gamma distribution 386
for the four HSD types in the data group of S lt 2 and K lt 6 whereas the opposite is true 387
for all data This conclusion is further substantiated by comparison of RED values for the 388
four type of precipitation (Fig7) which shows that Lognormal has the largest RED 389
Gamma the smallest and Weibull in between for four types of precipitations in all data 390
whereas Weibull (Lognormal) has smallest (largest) RED values when S lt 2 and K lt 6 It 391
can be inferred for data group of S gt 2 and k gt 6 Gamma distribution performs better 392
19
Further comparison between different precipitation types shows these functions all 393
performs better for raindrop size distributions and mixed-phase than graupel and 394
snowflake size distributions The RED for snowflakes is largest among the four types 395
The performance of Gamma is better for describing solid HSDs of all data but Weibull 396
distribution is better when S lt 2 and K lt 6 397
5 Conclusion 398
The combined measurements collected during a field experiment conducted at the 399
Haituo Mountain site using PARSIVEL disdrometer millimeter wavelength cloud radar 400
and microscope photography are analyzed to classify the precipitation hydrometeor 401
types examine the dependence of fall velocity on hydrometeor size for different 402
hydrometeor types and determine the best distribution functions to describe the 403
hydrometeor size distributions of different types 404
Analysis of the PARSIVEL-measured fall velocities show that on average the 405
dependence of fall velocity on hydrometeor size largely follow their corresponding 406
terminal velocity curves for raindrops graupels and snowflakes respectively suggesting 407
that such measurements are useful to identify the hydrometeor types The associated 408
microscope photos and cloud radar observations support the classification of 409
hydrometeor types based on the PARSIVEL-observed fall velocities Furthermore there 410
are velocity spreads in fall velocity across hydrometeor sizes for all hydrometeors and 411
the spreads for the solid hydrometeors could cause by hydrometeor type turbulence or 412
updraftdowndraft and instrument measured principle The coexistence of various 413
types of hydrometeors likely induces additional spread of fall velocity for given 414
20
hydrometeor sizes such as mixed precipitation Meanwhile complex microphysical 415
processes in cold precipitation such as riming aggregation breakup and collision and 416
coalescence influence fall velocity which likely induce larger spread of fall velocity Last 417
but not the least the disdrometer may suffer from instrumental errors due to the 418
internally assumed relationship between horizontal and vertical particle dimensions 419
Comparison of the type-averaged hydrometeor size distributions shows that the 420
mixed precipitation has more small hydrometeors with D lt 15 mm than others 421
whereas the snowflake precipitation has the least number of small hydrometeors 422
among the four types On the contrary the snowflake precipitation has more large 423
hydrometeors with D between 3 mm and 11 mm 424
The commonly used size distribution functions (Gamma Weibull and Lognormal) 425
are further examined to determine the most adequate function to describe the size 426
distribution measurements for all the hydrometeor types by use of an approach based 427
on the relationship between skewness (S) and kurtosis (K) Taylor diagram and RED are 428
further introduced to assess the performance of different size distribution functions 429
against measurements It is shown that the HSDs for the four types can all be well 430
described statistically by the Gamma and Weibull distribution but Lognormal 431
Exponential and Gaussian are not fit to describe HSDs Gamma and Weibull distribution 432
describe raindrop and mixed-phase size distribution better than snowflake and graupel 433
size distribution and their performances are worst for snowflake It may due to graupel 434
and snowflake precipitation have more big particles When S less than 2 and K less than 435
6 Weibull distribution performs better than Gamma distribution to describe HSDs but 436
21
Gamma distribution performs better for total data 437
A few points are noteworthy First although this study demonstrates the great 438
potential of combining simultaneous disdrometer measurements of particle fall velocity 439
and size distributions microscopic photography and cloud radar to address the 440
challenges facing solid precipitation the data are limited More research is needed to 441
discern such effects on the results presented here Second as the observations show 442
that in addition to sizes there are many other factors (eg hydrometeor type 443
microphysical processes turbulence and measuring principle) that can potentially 444
influence particle fall velocity as well More comprehensive research is needed to 445
further discern and separate these factors Finally the combined use of S-K diagram 446
Taylor diagram and relative Euclidean distance appears to be a powerful tool for 447
identifying the best function used to describe the HSDs and quantify the differences 448
between different precipitation types More research is in order along this direction 449
Acknowledgements 450
This study is mainly supported by the Chinese National Science Foundation under Grant 451
No 41675138 and National Key RampD Program of China (2017YFC0209604) It is partly 452
supported by Beijing National Science Foundation (8172023) the US Department 453
Energys Atmospheric System Research (ASR) Program (Liu and Jia at BNL) Lu is 454
supported by the Natural Science Foundation of Jiangsu Province (BK20160041) The 455
observation data are archived at a specialized supercomputer at Beijing Meteorology 456
Information Center (ftp10224592) which are available from the corresponding 457
author upon request The authors also thank Beijing weather modification office for 458
their support during the field experiment 459
Reference 460
22
Agosta CC Fettweis XX Datta RR 2015 Evaluation of the CMIP5 models in the 461
aim of regional modelling of the Antarctic surface mass balance Cryosphere 9 2311ndash462
2321 httpdxdoiorg105194tc-9-2311-2015 463
Barthazy E and R Schefold 2006 Fall velocity of snowflakes of different riming degree 464
and crystal types Atmos Res 82(1) 391-398 httpsdoiorg101016jatmosres 465
200512009 466
Battaglia A Rustemeier E Tokay A et al 2010 PARSIVEL snow observations a critical 467
assessment J Atmos Oceanic Technol 27(2) 333-344 doi 1011752009jtecha13321 468
Boumlhm H P 1989 A General Equation for the Terminal Fall Speed of Solid Hydrometeors 469
J Atmos Sci 46(15) 2419-2427 httpsdoiorg1011751520-0469(1989)046 lt2419A 470
GEFTTgt20CO2 471
Boudala F S G A Isaac et al 2014 Comparisons of Snowfall Measurements in 472
Complex Terrain Made During the 2010 Winter Olympics in Vancouver Pure and 473
Applied Geophysics 171(1) 113-127 474
Chen B W Hu and J Pu 2011 Characteristics of the raindrop size distribution for 475
freezing precipitation observed in southern China J Geophys Res 116 D06201 476
doi1010292010JD015305 477
Chen B Z Hu L Liu and G Zhang (2017) Raindrop Size Distribution Measurements at 478
4500m on the Tibetan Plateau during TIPEX-III J Geophys Res 122 11092-11106 479
doiorg10100 22017JD027233 480
23
Cugerone K and C De Michele 2017 Investigating raindrop size distributions in the 481
(L-)skewness-(L-)kurtosis plane Quart J Roy Meteor Soc 143(704) 1303-1312 482
httpsdoiorg101002qj3005 483
Donnadieu G 1980 Comparison of results obtained with the VIDIAZ spectro 484
pluviometer and the JossndashWaldvogel rainfall disdrometer in a ldquorain of a thundery typerdquo 485
J Appl Meteor 19 593ndash597 486
Feingold G and Levin Z 1986 The lognormal fit to raindrop spectra from frontal 487
convective clouds in Israel J Clim Appl Meteorol 25 1346ndash1363 488
httpsdoiorg1011751520-0450(1986)025lt1346tlftrsgt20CO2 489
Field P R A J Heymsfield and A Bansemer 2007 Snow Size Distribution 490
Parameterization for Midlatitude and Tropical Ice Clouds J Atmos Sci 64(12) 491
4346-4365 httpsdoiorg1011752007JAS23441 492
Garrett T J and S E Yuter 2014 Observed influence of riming temperature and 493
turbulence on the fallspeed of solid precipitation Geophysical Research Letters 41(18) 494
6515ndash6522 495
Geresdi I N Sarkadi and G Thompson 2014 Effect of the accretion by water drops 496
on the melting of snowflakes Atmos Res 149 96-110 497
Gunn R and G D Kinzer 1949 The terminal velocity of fall for water drops in stagnant 498
air J Meteor 6 243-248 httpsdoiorg1011751520-0469(1949)006lt0243TTVOFFgt 499
20CO2 500
24
Heymsfield A J and C D Westbrook 2010 Advances in the Estimation of Ice Particle 501
Fall Speeds Using Laboratory and Field Measurements J Atmos Sci 67(8) 2469-2482 502
httpsdoiorg1011752010JAS33791 503
Huang G-J C Kleinkort V N Bringi and B M Notaroš 2017 Winter precipitation 504
particle size distribution measurement by Multi-Angle Snowflake Camera Atmos Res 505
198 81-96 506
Intergovernmental Panel on Climate Change (IPCC) 2001 Climate Change 2001 The 507
Scientific Basis Contribution of Working Group I to the Third Assessment Report of the 508
Intergovernmental Panel on Climate Change edited by J T Houghton et al 881 pp 509
Cambridge Univ Press New York 510
Ishizaka M H Motoyoshi S Nakai T Shiina T Kumakura and K-i Muramoto 2013 A 511
New Method for Identifying the Main Type of Solid Hydrometeors Contributing to 512
Snowfall from Measured Size-Fall Speed Relationship Journal of the Meteorological 513
Society of Japan Ser II 91(6) 747-762 httpsdoiorg102151jmsj2013-602 514
Khvorostyanov V 2005 Fall Velocities of Hydrometeors in the Atmosphere 515
Refinements to a Continuous Analytical Power Law J Atmos Sci 62 4343-4357 516
httpsdoiorg101175JAS36221 517
Kikuchi K T Kameda K Higuchi and A Yamashita 2013 A global classification of 518
snow crystals ice crystals and solid precipitation based on observations from middle 519
latitudes to polar regions Atmos Res 132-133 460-472 520
Kneifel S A von Lerber J Tiira D Moisseev P Kollias and J Leinonen 2015 521
Observed relations between snowfall microphysics and triple-frequency radar 522
25
measurements J Geophys Res Atmos 120(12) 6034-6055 523
httpsdoi1010022015JD023156 524
Kubicek A and P K Wang 2012 A numerical study of the flow fields around a typical 525
conical graupel falling at various inclination angles Atmos Res 118 15ndash26 526
httpsdoi101016jatmosres201206001 527
Larsen M L A B Kostinski and A R Jameson (2014) Further evidence for 528
superterminal raindrops Geophys Res Lett 41(19) 6914-6918 529
Lee JE SH Jung H M Park S Kwon P L Lin and G W Lee 2015 Classification of 530
Precipitation Types Using Fall Velocity Diameter Relationships from 2D-Video 531
Distrometer Measurements Advances in Atmospheric Sciences (09) 532
Lin Y L J Donner and B A Colle 2010 Parameterization of riming intensity and its 533
impact on ice fall speed using arm data Mon Weather Rev 139(3) 1036ndash1047 534
httpsdoi1011752010MWR32991 535
Liu Y G 1992 Skewness and kurtosis of measured raindrop size distributions Atmos 536
Environ 26A 2713-2716 httpsdoiorg1010160960-1686(92)90005-6 537
Liu Y G 1993 Statistical theory of the Marshall-Parmer distribution of raindrops 538
Atmos Environ 27A 15-19 httpsdoiorg1010160960-1686(93)90066-8 539
Liu Y G and F Liu 1994 On the description of aerosol particle size distribution Atmos 540
Res 31(1-3) 187-198 httpsdoiorg1010160169-8095(94)90043-4 541
Liu Y G L You W Yang F Liu 1995 On the size distribution of cloud droplets Atmos 542
Res 35 (2-4) 201-216 httpsdoiorg1010160169-8095(94)00019-A 543
Locatelli J D and P V Hobbs 1974 Fall speeds and masses of solid precipitation 544
26
particles J Geophys Res 79(15) 2185-2197 httpsdoi101029JC079i015p02185 545
Loumlffler-Mang M and J Joss 2000 An optical disdrometer for measuring size and 546
velocity of hydrometeors J Atmos Oceanic Technol 17 130-139 547
httpsdoiorg1011751520-0426(2000)017lt0130AODFMSgt20CO2 548
Loumlffler-Mang M and U Blahak 2001 Estimation of the Equivalent Radar Reflectivity 549
Factor from Measured Snow Size Spectra J Clim Appl Meteorol 40(4) 843-849 550
httpsdoiorg1011751520-0450(2001)040lt0843EOTERRgt20CO2 551
Matrosov S Y 2007 Modeling Backscatter Properties of Snowfall at Millimeter 552
Wavelengths J Atmos Sci 64(5) 1727-1736 httpsdoiorg101175JAS39041 553
Mitchell D L 1996 Use of mass- and area-dimensional power laws for determining 554
precipitation particle terminal velocities J Atmos Sci 53 1710-1723 555
httpsdoiorg1011751520-0469(1996)053lt1710UOMAADgt20CO2 556
Montero-Martiacutenez G A B Kostinski R A Shaw and F Garciacutea-Garciacutea 2009 Do all 557
raindrops fall at terminal speed Geophys Res Lett 36 L11818 558
httpsdoiorg1010292008GL037111 559
Niu S X Jia J Sang X Liu C Lu and Y Liu 2010 Distributions of raindrop sizes and 560
fall velocities in a semiarid plateau climate Convective vs stratiform rains J Appl 561
Meteorol Climatol 49 632ndash645 httpsdoi1011752009JAMC22081 562
Nurzyńska K M Kubo and K-i Muramoto 2012 Texture operator for snow particle 563
classification into snowflake and graupel Atmos Res 118 121-132 564
Oue M M R Kumjian Y Lu J Verlinde K Aydin and E E Clothiaux 2015 Linear 565
27
Depolarization Ratios of columnar ice crystals in a deep precipitating system over the 566
Arctic observed by Zenith-Pointing Ka-Band Doppler radar J Clim Appl Meteorol 567
54(5) 1060-1068 httpsdoiorg101175JAMC-D-15-00121 568
Pruppacher H R and J D Klett 1998 Microphysics of clouds and precipitation Kluwer 569
Academic 954 pp 570
Rasmussen R B Baker et al 2012 How well are we measuring snow the 571
NOAAFAANCAR winter precipitation test bed Bull Amer Meteor Soc 93(6) 811-829 572
httpsdoiorg101175BAMS-D-11-000521 573
Reisner J R M Rasmussen and R T Bruintjes 1998 Explicit forecasting of 574
supercooled liquid water in winter storms using the MM5 mesoscale model Q J R 575
Meteorol Soc 124 1071ndash1107 httpsdoi101256smsqj54803 576
Rosenfeld D and Ulbrich C W 2003 Cloud microphysical properties processes and 577
rainfall estimation opportunities Meteorol Monogr 30 237-237 578
httpsdoiorg101175 0065-9401(2003)030lt0237cmppargt20CO2 579
Schaefer V J 1956 The preparation of snow crystal replicas-VI Weatherwsie 9 580
132-135 581
Souverijns N A Gossart S Lhermitte I V Gorodetskaya S Kneifel M Maahn F L 582
Bliven and N P M van Lipzig (2017) Estimating radar reflectivity - Snowfall rate 583
relationships and their uncertainties over Antarctica by combining disdrometer and 584
radar observations Atmos Res 196 211-223 585
Taylor K E 2001 Summarizing multiple aspects of model performance in a single 586
diagram J Geophys Res 106 7183ndash7192 httpsdoi1010292000JD900719 587
28
Tokay A and D A Short 1996 Evidence from tropical raindrop spectra of the origin of 588
rain from stratiform versus convective clouds J Appl Meteor 35 355ndash371 589
Tokay A and D Atlas 1999 Rainfall microphysics and radar properties analysis 590
methods for drop size spectra J Appl Meteor 37 912-923 591
httpsdoiorg1011751520-0450(1998)037lt0912RMARPAgt20CO2 592
Tokay A D B Wolff et al 2014 Evaluation of the New version of the laser-optical 593
disdrometer OTT Parsivel2 J Atmos Oceanic Technol 31(6) 1276-1288 594
httpsdoiorg101175JTECH-D-13-001741 595
Ulbrich C W 1983 Natural variations in the analytical form of the raindrop size 596
distribution J Appl Meteor 5 1764-1775 597
Wen G H Xiao H Yang Y Bi and W Xu 2017 Characteristics of summer and winter 598
precipitation over northern China Atmos Res 197 390-406 599
Wu W Y Liu and A K Betts 2012 Observationally based evaluation of NWP 600
reanalyses in modeling cloud properties over the Southern Great Plains J Geophys 601
Res 117 D12202 httpsdoi1010292011JD016971 602
Yuter S E D E Kingsmill L B Nance and M Loumlffler-Mang 2006 Observations of 603
precipitation size and fall velocity characteristics within coexisting rain and wet snow J 604
Appl Meteor Climatol 45 1450ndash1464 doi httpsdoiorg101175JAM24061 605
Zhang P C and B Y Du 2000 Radar Meteorology China Meteorological Press 511pp 606
(in Chinese) 607
608
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
9
snowflake at given maximum diameters From the fall velocity distribution we can infer 177
that these hydrometeors are mainly raindrops The microscope photos obtained on the 178
ground confirm this However unlike the raindrop size and velocity distribution in 179
summer in Figure 8a of Niu et al (2010) there are some small size hydrometeors 180
(05~35mm) at very low speeds (05~2 ms) distributing among the terminal velocity 181
curves for graupel and snowflake This result implies that beside liquid raindrops 182
(including small raindrops or droplets from drizzle) some small snowflakes also exist in 183
the measurement The microscope photos also support the finding that although 184
raindrops are dominant some small plane- and column- shaped snowflakes co-exist 185
Fig 2b shows the joint hydrometeor size and fall velocity distribution during the 186
graupel event The hydrometeors are mainly symmetrically distributed around the ideal 187
terminal velocity of graupel (Locatelli and Hobbs 1974) supported by the photo-based 188
hydrometeor classification On the other hand it is found that certain small droplets 189
with the maximum dimensions among 03 to 10 mm are distributed around the liquid 190
raindrop curve suggesting that there are some raindrops and droplets coexisting in the 191
graupel dominated precipitation It is recognized that graupels grow by snow crystals 192
collecting cloud droplets and small raindrops (Pruppacher and Klett 1998) high cloud 193
top more liquid water content and presence of small raindrops (as shown in 194
microscope photography) provide favorable conditions for graupel The microscope 195
photos also display that graupelsrsquo surfaces are lumpy because of riming super cooled 196
drops during growing 197
The fall velocities of hydrometeors in Fig 2c are much smaller than the terminal 198
10
velocities of raindrop and graupel but are close to the terminal velocity curves of snow 199
of hexagonal densely rimed dendrites aggregates of dendrites Synthesizing the size 200
data the hydrometeors can be inferred as snowflakes which are further confirmed by 201
surface microscope photos From the surface observation we found many 202
rimedunrimed or aggregated dendrites or hexagonal snowflakes Although riming and 203
aggregation microphysical processes have some influence on terminal velocity 204
(Barthazy and Schefold 2006 Garrett and Yuter 2014 Heymsfield and Westbrook 205
2010) but the influences are too small to distinguish only from observed fall velocity 206
since it is a combined result of many factors When maximum dimensions are among 207
03 to 10 mm there are some small hydrometeors with fall velocities larger than 208
snowflakes which maybe graupels raindrops and droplets 209
Fig 2d is the hydrometeor size and fall velocity distribution during a mixed-phased 210
precipitation The hydrometeor fall velocities exhibit the largest spread for example 211
the fall velocities for hydrometeors with maximum dimension equaling to 3 mm 212
change from 05 to 5 ms and do not distribute along any of the ideal terminal velocity 213
curves This result suggests that different hydrometeor types might coexist during the 214
same sampling time To substantiate supercooled raindrops graupels and different 215
kinds of snowflakes are observed from the surface microscope simultaneously Similar 216
changes in particle size and fall velocity distribution documented by the disdrometer as 217
the storm transitions from rain to mixed-phase to snow were found at Marshall Field 218
site (Rasmussen et al 2012) 219
11
c Other Influencing Factors 220
The different dependence on particle size of terminal velocities for different types 221
of hydrometeors can explain some systematic distribution of the PARSIVEL-measured 222
fall velocities but the large spreads in the measurement of the instant particle fall 223
velocities await further inspection 224
According to our previous work the fall velocity (V) of a hydrometeor measured by 225
the PARSIVEL can be regarded as a combination of the terminal velocity in still air (Vt) 226
and a component Vrsquo that results from all other potential influencing factors eg type 227
turbulence organized air motions break-up and measurement errors (Niu et al 228
2010) 229
119881 = 119881119905 + 119881 prime (1) 230
The large spread of the measurements at both sides of the terminal velocity curves 231
shown in figure 2 seems compatible with the notion of nearly random collections of 232
downdraft and updraft A wider spread for fall velocities implies a wider range of 233
variation in vertical motions when hydrometeors are liquid raindrops (Niu et al 2010) 234
Solid nonspherical hydrometeors are much more complex than liquid drops and the 235
large spread of velocities may be caused by several other factors First different types 236
of hydrometeors (columns bullets plates lump graupels and hexagonal snowflakes et 237
al) have different fall speeds It is long recognized that microphysical processes in cold 238
precipitation are more complex and consequently generate more types of solid 239
hydrometeors comparing to the generation of raindrops The averaged concentration 240
distributions of large number of samples shown in Figure 2 also represents the possible 241
12
distributions of hydrometeors If there is only one kind particle the high concentration 242
would along its ideal terminal velocity very well just like the raindrop possible 243
distribution (Niu et al 2010) The concentration of mixed precipitation in Fig 2d does 244
not along any singe ideal terminal velocity further improved there are more than one 245
kind of hydrometers Coexistence of different types of hydrometeors induces larger 246
spread of fall velocities Second different degrees of riming and aggregating may affect 247
the results Densely rimed particles fall faster than unrimed particles with the same 248
maximum dimension aggregated snowflakes generally fall faster than their component 249
crystals (Barthazy and Schefold 2006 Garrett and Yuter 2014 Locatelli and Hobbs 250
1974) Third solid hydrometeors more likely occur breakup aggregation collision and 251
coalescence processes because of the large range of speeds According to prior 252
research of raindrop breakup and coalescence would lead to the ldquohigher-than-terminal 253
velocityrdquo fall velocity for small drops but ldquolower-than-terminal velocityrdquo fall velocity for 254
large drops (Niu et al 2010 Montero-Martiacutenez et al 2009 Larsen et al 2014) Similar 255
results are expected for the fall velocity of solid hydrometeors Last but not the least 256
the disdrometer may suffer from instrumental errors due to the internally assumed 257
relationship between horizontal and vertical particle dimensions likely resulting in a 258
wider spreads of fall velocities for the graupel and snowflakes as compared to the 259
raindrop counterpart as discussed in Section 2 Although the instrument error is an 260
important factor that should be considered in velocity spread as shown in Fig2b the 261
instrument error could not cause that large velocity spread The possible distributions 262
of fall velocities are the combine effects of physical and instrument principle 263
13
Further support for the possible instrumental uncertainty is from the cloud radar 264
observations Fig 3 shows the cloud reflectivity and linear depolarization ratio (LDR) in 265
lower level (less than 08 km) for the graupel snowflake and mixed-phased 266
precipitations respectively The LDR is a valuable observable in identifying the 267
hydrometeor types (Oue et al 2015) As shown in Fig 3a the cloud top height of 268
graupel precipitation was up to 7km during 1900 to 2050 Beijng Time (BT) which was 269
highest among the three events The high cloud top implies stronger updraft and 270
turbulence which further induces a larger fall velocity spread The LDR value was the 271
smallest among the three events indicating that the hydrometeors were close to 272
spherical consistent to the surface observations The cloud top height of snowflake 273
precipitation was up to 35 km (Fig 3c) which was the lowest among the three types of 274
precipitations implying weakest updraft and turbulence Notably although the 275
snowflake types are more complex than those of graupels the velocity spread was not 276
as large as that of the graupel type likely because of the weakest updraft and 277
turbulence The LDR was relatively larger consistent with the surface snowflake 278
observations (Fig 3d) The cloud top height of mixed-phase precipitation was up to 45 279
km (Fig 3e) and the LDR in lower level was largest among the three types of 280
precipitations owing to coexistence of raindrops graupels and snowflakes (Fig 3f) 281
4 Hydrometeor Size Distributions 282
a Comparison of HSDs between Different Types 283
There were four representative types of precipitations during this field experiment 284
providing us a unique opportunity to examine the HSD differences between the four 285
14
types of hydrometeors The sample numbers mean maximum dimensions and number 286
concentrations for each kind of HSDs are given in Table 2 Figure 4 is the averaged 287
distribution of all measured HSDs of 4 kinds As shown in Figure 4 on average the 288
mixed-phased precipitation tends to have most small size hydrometeors with D lt 15 289
mm while snowflake precipitation has the least small hydrometeors among the four 290
types The snowflake precipitation has more large size hydrometeors ie 3 mm lt D lt 11 291
mm Graupel size distribution tends to have two peeks around 13 mm and 26 mm The 292
mean maximum dimension is largest for snowflake (126 mm) and smallest for the 293
mixed HSD due to many small particles Similar results were found in precipitation 294
occurring in the Cascade and Rocky Mountains (Yuter et al 2006) The PARSIVEL 295
disdrometer doesnrsquot provide reliable data for small drops lower than 05 mm and tends to 296
underestimate small drops so the relatively low concentrations of small drops likely resulted 297
from the instrumentrsquos shortcomings (Tokay et al 2013 and Chen et al 2017) 298
b Evaluation of Distribution Functions for Describing HSDs 299
Over the last few decades great efforts have been devoted to finding the 300
appropriate analytical functions for describing the HSD because of its wide applications 301
in many areas including remote sensing and parameterization of precipitation (Chen et 302
al 2017) The two distribution functions mostly used up to now are the Lognormal 303
(Feingold and Levin 1986 Rosenfeld and Ulbrich 2003) and the Gamma (Ulbrich 1983) 304
distributions The Gamma distribution has been proposed as a first order generalization 305
of the Exponential distribution when μ equals 0 (Table 4) Weibull distribution is 306
another function used to describe size distributions of raindrops and cloud droplets (Liu 307
15
and Liu 1994 Liu et al 1995) Nevertheless the question as to which functions are 308
more adequate to describe HSDs of solid hydrometeors have been rarely investigated 309
systematically and quantitatively Thus the objective of this section is to examine the 310
most adequate distribution function used to describe HSDs 311
Considering size distributions of raindrops cloud droplets and aerosol particles are 312
the end results of many (stochastic) complex processes Liu (1992 1993 1994 and 313
1995) proposed a statistical method based on the relationships between the skewness 314
(S) and kurtosis (K) derived from an ensemble of particle size distribution 315
measurements and from those commonly used size distribution functions Cugerone 316
and Michele (2017) also used a similar approach based on the S-K relationships to study 317
raindrop size distributions Unlike the conventional curve-fitting of individual size 318
distributions this approach applies to an ensemble of size distribution measurements 319
and identifies the most appropriate statistical distribution pattern Here we apply this 320
approach to investigate if the statistical pattern of the HSDs of four precipitation types 321
follows the Exponential Gaussian Gamma Weibull and Lognormal distributions (Table 322
4) and if there are any pattern differences between them Briefly S and K of a HSD are 323
calculated from the corresponding HSD with the following two equations 324
23
2
3
t
iii
t
iii
dDN
)(Dn)D(D
dDN
)(Dn)D(D
S
minus
minus
=
(2) 325
32
2
4
minus
minus
minus
=
dDN
)(Dn)D(D
dDN
)(Dn)D(D
K
t
iii
t
iii
(3) 326
16
where Di is the central diameter of the i-th bin ni is the number concentration of the 327
i-th bin and Nt is total number concentration Note that each individual HSD can be 328
used to obtain a pair of S and K which is shown as a dot in Figure 5 Also noteworthy is 329
that the SndashK relationships for the families of Gamma Weibull and Lognormal are 330
described by known analytical functions (Liu 1993 1994 and 1995 Cugerone and 331
Michele 2017) represented by theoretical curves in Figure 5 The Exponential and 332
Gaussian distributions are represented by single points on the S-K diagram (S=2 and K=6 333
for Exponential) and (S=0 and K=0 for Gaussian) respectively Thus by comparing the 334
measured S and K values (points) with the known theoretical curves one can determine 335
the most proper function used to describe HSDs 336
Figure 5 shows the scatter plots of observed SndashK pairs calculated from the HSD 337
measurements for raindrop graupel snowflake mixed-phase precipitations Also 338
shown as comparison are the theoretical curves corresponding to the analytical HSD 339
functions A few points are evident First despite some occasional departures most of 340
the points fall near the theoretical lines of Gamma and Weibull distributions suggesting 341
that the HSD patterns for all the four types of precipitations well follow the Gamma and 342
Weibull distributions statistically Second HSDs of raindrops and mixed hydrometeors 343
are better described by Gamma and Weibull distribution than graupels and snowflakes 344
Third the S and K do not cluster around points (2 6) and (0 0) suggesting that the 345
Gaussian and Exponential distribution are not appropriate for describing HSDs 346
especially Gaussian distribution 347
To further evaluate the overall performance of the different distribution functions 348
17
we employ the widely used technique of Taylor diagram (Taylor 2001) and ldquoRelative 349
Euclidean Distancerdquo (RED) (Wu et al 2012) as a supplement to the Taylor diagram The 350
Taylor diagram has been widely used to visualize the statistical differences between 351
model results and observations in evaluation of model performance against 352
measurements or other benchmarks (IPCC 2001) Correlation coefficient (r) standard 353
deviation (σ) and ldquocentered root-mean-square errorrdquo (RMSE hereafter) are used in 354
the Taylor diagram The RED is introduced to add the bias as well in a dimensionless 355
framework that allows for comparison between different physical quantities with 356
different units In this study we consider the S and K values derived from the 357
distribution functions as model results and evaluate them against those derived from 358
the HSD measurements Brieflythe expressions for calculating r and σ and RMSE are 359
shown below 360
119903 =1
119873sum (119872119899minus)(119874119899minus)119873119899=1
120590119872120590119900 (4) 361
119877119872119878119864 = 1
119873sum [(119872119899 minus ) minus (119874119899 minus )]2119873119899=1
12
(5) 362
120590119872 = [1
119873sum (119872119899 minus )119873119899=1 ]
12
(6) 363
1205900 = [1
119873sum (119874119899 minus )119873119899=1 ]
12
(7) 364
where M and O denote distribution function and observed variables The RED 365
expression is shown below 366
119877119864119863 = [(minus)
]2
+ [(120590119872minus120590119874)
120590119900]2
+ (1 minus 119903)212
( 8 ) 367
Equation (8) indicates that RED considers all the components of mean bias variations 368
and correlations in a dimensionless way the distribution function performance 369
degrades as RED increases from the perfect agreement with RED=0 370
18
In the Taylor diagrams shown in Fig 6 the cosine of azimuthal angle of each point 371
gives the r between the function-calculated and observed data The distance between 372
individual point and the reference point ldquoObsrdquo represents the RMSE normalized by the 373
amplitude of the observationally based variations As this distance approaches to zero 374
the function-calculated K and S approach to the observations Clearly the values of r 375
are around 097 for Gamma and Weibull r for Lognormal function is slightly smaller 376
(095) The normalized σ are much different for Lognormal Gamma and Weibull 377
distributions with averaged value being 057 0895 and 0785 respectively Therefore 378
the Lognormal distribution exhibits the worst performance for describing HSDs and 379
Gamma and Weibull distributions appear to perform much better (Fig 6a) 380
Noticing that S and K of Gamma and Weibull distributions are equal at the point of S 381
= 2 and K = 6 and have positive relationship (If S lt 2 then K lt 6 and if S gt 2 then k gt 6) In 382
this part we further separately examine the group of data with S lt 2 and K lt 6 (Fig 6b) 383
and compare its result with those of total data The averaged normalized σ are 103 and 384
109 and r are 091 and 090 for Weibull and Gamma distributions respectively 385
suggesting that Weibull distribution performs slightly better than Gamma distribution 386
for the four HSD types in the data group of S lt 2 and K lt 6 whereas the opposite is true 387
for all data This conclusion is further substantiated by comparison of RED values for the 388
four type of precipitation (Fig7) which shows that Lognormal has the largest RED 389
Gamma the smallest and Weibull in between for four types of precipitations in all data 390
whereas Weibull (Lognormal) has smallest (largest) RED values when S lt 2 and K lt 6 It 391
can be inferred for data group of S gt 2 and k gt 6 Gamma distribution performs better 392
19
Further comparison between different precipitation types shows these functions all 393
performs better for raindrop size distributions and mixed-phase than graupel and 394
snowflake size distributions The RED for snowflakes is largest among the four types 395
The performance of Gamma is better for describing solid HSDs of all data but Weibull 396
distribution is better when S lt 2 and K lt 6 397
5 Conclusion 398
The combined measurements collected during a field experiment conducted at the 399
Haituo Mountain site using PARSIVEL disdrometer millimeter wavelength cloud radar 400
and microscope photography are analyzed to classify the precipitation hydrometeor 401
types examine the dependence of fall velocity on hydrometeor size for different 402
hydrometeor types and determine the best distribution functions to describe the 403
hydrometeor size distributions of different types 404
Analysis of the PARSIVEL-measured fall velocities show that on average the 405
dependence of fall velocity on hydrometeor size largely follow their corresponding 406
terminal velocity curves for raindrops graupels and snowflakes respectively suggesting 407
that such measurements are useful to identify the hydrometeor types The associated 408
microscope photos and cloud radar observations support the classification of 409
hydrometeor types based on the PARSIVEL-observed fall velocities Furthermore there 410
are velocity spreads in fall velocity across hydrometeor sizes for all hydrometeors and 411
the spreads for the solid hydrometeors could cause by hydrometeor type turbulence or 412
updraftdowndraft and instrument measured principle The coexistence of various 413
types of hydrometeors likely induces additional spread of fall velocity for given 414
20
hydrometeor sizes such as mixed precipitation Meanwhile complex microphysical 415
processes in cold precipitation such as riming aggregation breakup and collision and 416
coalescence influence fall velocity which likely induce larger spread of fall velocity Last 417
but not the least the disdrometer may suffer from instrumental errors due to the 418
internally assumed relationship between horizontal and vertical particle dimensions 419
Comparison of the type-averaged hydrometeor size distributions shows that the 420
mixed precipitation has more small hydrometeors with D lt 15 mm than others 421
whereas the snowflake precipitation has the least number of small hydrometeors 422
among the four types On the contrary the snowflake precipitation has more large 423
hydrometeors with D between 3 mm and 11 mm 424
The commonly used size distribution functions (Gamma Weibull and Lognormal) 425
are further examined to determine the most adequate function to describe the size 426
distribution measurements for all the hydrometeor types by use of an approach based 427
on the relationship between skewness (S) and kurtosis (K) Taylor diagram and RED are 428
further introduced to assess the performance of different size distribution functions 429
against measurements It is shown that the HSDs for the four types can all be well 430
described statistically by the Gamma and Weibull distribution but Lognormal 431
Exponential and Gaussian are not fit to describe HSDs Gamma and Weibull distribution 432
describe raindrop and mixed-phase size distribution better than snowflake and graupel 433
size distribution and their performances are worst for snowflake It may due to graupel 434
and snowflake precipitation have more big particles When S less than 2 and K less than 435
6 Weibull distribution performs better than Gamma distribution to describe HSDs but 436
21
Gamma distribution performs better for total data 437
A few points are noteworthy First although this study demonstrates the great 438
potential of combining simultaneous disdrometer measurements of particle fall velocity 439
and size distributions microscopic photography and cloud radar to address the 440
challenges facing solid precipitation the data are limited More research is needed to 441
discern such effects on the results presented here Second as the observations show 442
that in addition to sizes there are many other factors (eg hydrometeor type 443
microphysical processes turbulence and measuring principle) that can potentially 444
influence particle fall velocity as well More comprehensive research is needed to 445
further discern and separate these factors Finally the combined use of S-K diagram 446
Taylor diagram and relative Euclidean distance appears to be a powerful tool for 447
identifying the best function used to describe the HSDs and quantify the differences 448
between different precipitation types More research is in order along this direction 449
Acknowledgements 450
This study is mainly supported by the Chinese National Science Foundation under Grant 451
No 41675138 and National Key RampD Program of China (2017YFC0209604) It is partly 452
supported by Beijing National Science Foundation (8172023) the US Department 453
Energys Atmospheric System Research (ASR) Program (Liu and Jia at BNL) Lu is 454
supported by the Natural Science Foundation of Jiangsu Province (BK20160041) The 455
observation data are archived at a specialized supercomputer at Beijing Meteorology 456
Information Center (ftp10224592) which are available from the corresponding 457
author upon request The authors also thank Beijing weather modification office for 458
their support during the field experiment 459
Reference 460
22
Agosta CC Fettweis XX Datta RR 2015 Evaluation of the CMIP5 models in the 461
aim of regional modelling of the Antarctic surface mass balance Cryosphere 9 2311ndash462
2321 httpdxdoiorg105194tc-9-2311-2015 463
Barthazy E and R Schefold 2006 Fall velocity of snowflakes of different riming degree 464
and crystal types Atmos Res 82(1) 391-398 httpsdoiorg101016jatmosres 465
200512009 466
Battaglia A Rustemeier E Tokay A et al 2010 PARSIVEL snow observations a critical 467
assessment J Atmos Oceanic Technol 27(2) 333-344 doi 1011752009jtecha13321 468
Boumlhm H P 1989 A General Equation for the Terminal Fall Speed of Solid Hydrometeors 469
J Atmos Sci 46(15) 2419-2427 httpsdoiorg1011751520-0469(1989)046 lt2419A 470
GEFTTgt20CO2 471
Boudala F S G A Isaac et al 2014 Comparisons of Snowfall Measurements in 472
Complex Terrain Made During the 2010 Winter Olympics in Vancouver Pure and 473
Applied Geophysics 171(1) 113-127 474
Chen B W Hu and J Pu 2011 Characteristics of the raindrop size distribution for 475
freezing precipitation observed in southern China J Geophys Res 116 D06201 476
doi1010292010JD015305 477
Chen B Z Hu L Liu and G Zhang (2017) Raindrop Size Distribution Measurements at 478
4500m on the Tibetan Plateau during TIPEX-III J Geophys Res 122 11092-11106 479
doiorg10100 22017JD027233 480
23
Cugerone K and C De Michele 2017 Investigating raindrop size distributions in the 481
(L-)skewness-(L-)kurtosis plane Quart J Roy Meteor Soc 143(704) 1303-1312 482
httpsdoiorg101002qj3005 483
Donnadieu G 1980 Comparison of results obtained with the VIDIAZ spectro 484
pluviometer and the JossndashWaldvogel rainfall disdrometer in a ldquorain of a thundery typerdquo 485
J Appl Meteor 19 593ndash597 486
Feingold G and Levin Z 1986 The lognormal fit to raindrop spectra from frontal 487
convective clouds in Israel J Clim Appl Meteorol 25 1346ndash1363 488
httpsdoiorg1011751520-0450(1986)025lt1346tlftrsgt20CO2 489
Field P R A J Heymsfield and A Bansemer 2007 Snow Size Distribution 490
Parameterization for Midlatitude and Tropical Ice Clouds J Atmos Sci 64(12) 491
4346-4365 httpsdoiorg1011752007JAS23441 492
Garrett T J and S E Yuter 2014 Observed influence of riming temperature and 493
turbulence on the fallspeed of solid precipitation Geophysical Research Letters 41(18) 494
6515ndash6522 495
Geresdi I N Sarkadi and G Thompson 2014 Effect of the accretion by water drops 496
on the melting of snowflakes Atmos Res 149 96-110 497
Gunn R and G D Kinzer 1949 The terminal velocity of fall for water drops in stagnant 498
air J Meteor 6 243-248 httpsdoiorg1011751520-0469(1949)006lt0243TTVOFFgt 499
20CO2 500
24
Heymsfield A J and C D Westbrook 2010 Advances in the Estimation of Ice Particle 501
Fall Speeds Using Laboratory and Field Measurements J Atmos Sci 67(8) 2469-2482 502
httpsdoiorg1011752010JAS33791 503
Huang G-J C Kleinkort V N Bringi and B M Notaroš 2017 Winter precipitation 504
particle size distribution measurement by Multi-Angle Snowflake Camera Atmos Res 505
198 81-96 506
Intergovernmental Panel on Climate Change (IPCC) 2001 Climate Change 2001 The 507
Scientific Basis Contribution of Working Group I to the Third Assessment Report of the 508
Intergovernmental Panel on Climate Change edited by J T Houghton et al 881 pp 509
Cambridge Univ Press New York 510
Ishizaka M H Motoyoshi S Nakai T Shiina T Kumakura and K-i Muramoto 2013 A 511
New Method for Identifying the Main Type of Solid Hydrometeors Contributing to 512
Snowfall from Measured Size-Fall Speed Relationship Journal of the Meteorological 513
Society of Japan Ser II 91(6) 747-762 httpsdoiorg102151jmsj2013-602 514
Khvorostyanov V 2005 Fall Velocities of Hydrometeors in the Atmosphere 515
Refinements to a Continuous Analytical Power Law J Atmos Sci 62 4343-4357 516
httpsdoiorg101175JAS36221 517
Kikuchi K T Kameda K Higuchi and A Yamashita 2013 A global classification of 518
snow crystals ice crystals and solid precipitation based on observations from middle 519
latitudes to polar regions Atmos Res 132-133 460-472 520
Kneifel S A von Lerber J Tiira D Moisseev P Kollias and J Leinonen 2015 521
Observed relations between snowfall microphysics and triple-frequency radar 522
25
measurements J Geophys Res Atmos 120(12) 6034-6055 523
httpsdoi1010022015JD023156 524
Kubicek A and P K Wang 2012 A numerical study of the flow fields around a typical 525
conical graupel falling at various inclination angles Atmos Res 118 15ndash26 526
httpsdoi101016jatmosres201206001 527
Larsen M L A B Kostinski and A R Jameson (2014) Further evidence for 528
superterminal raindrops Geophys Res Lett 41(19) 6914-6918 529
Lee JE SH Jung H M Park S Kwon P L Lin and G W Lee 2015 Classification of 530
Precipitation Types Using Fall Velocity Diameter Relationships from 2D-Video 531
Distrometer Measurements Advances in Atmospheric Sciences (09) 532
Lin Y L J Donner and B A Colle 2010 Parameterization of riming intensity and its 533
impact on ice fall speed using arm data Mon Weather Rev 139(3) 1036ndash1047 534
httpsdoi1011752010MWR32991 535
Liu Y G 1992 Skewness and kurtosis of measured raindrop size distributions Atmos 536
Environ 26A 2713-2716 httpsdoiorg1010160960-1686(92)90005-6 537
Liu Y G 1993 Statistical theory of the Marshall-Parmer distribution of raindrops 538
Atmos Environ 27A 15-19 httpsdoiorg1010160960-1686(93)90066-8 539
Liu Y G and F Liu 1994 On the description of aerosol particle size distribution Atmos 540
Res 31(1-3) 187-198 httpsdoiorg1010160169-8095(94)90043-4 541
Liu Y G L You W Yang F Liu 1995 On the size distribution of cloud droplets Atmos 542
Res 35 (2-4) 201-216 httpsdoiorg1010160169-8095(94)00019-A 543
Locatelli J D and P V Hobbs 1974 Fall speeds and masses of solid precipitation 544
26
particles J Geophys Res 79(15) 2185-2197 httpsdoi101029JC079i015p02185 545
Loumlffler-Mang M and J Joss 2000 An optical disdrometer for measuring size and 546
velocity of hydrometeors J Atmos Oceanic Technol 17 130-139 547
httpsdoiorg1011751520-0426(2000)017lt0130AODFMSgt20CO2 548
Loumlffler-Mang M and U Blahak 2001 Estimation of the Equivalent Radar Reflectivity 549
Factor from Measured Snow Size Spectra J Clim Appl Meteorol 40(4) 843-849 550
httpsdoiorg1011751520-0450(2001)040lt0843EOTERRgt20CO2 551
Matrosov S Y 2007 Modeling Backscatter Properties of Snowfall at Millimeter 552
Wavelengths J Atmos Sci 64(5) 1727-1736 httpsdoiorg101175JAS39041 553
Mitchell D L 1996 Use of mass- and area-dimensional power laws for determining 554
precipitation particle terminal velocities J Atmos Sci 53 1710-1723 555
httpsdoiorg1011751520-0469(1996)053lt1710UOMAADgt20CO2 556
Montero-Martiacutenez G A B Kostinski R A Shaw and F Garciacutea-Garciacutea 2009 Do all 557
raindrops fall at terminal speed Geophys Res Lett 36 L11818 558
httpsdoiorg1010292008GL037111 559
Niu S X Jia J Sang X Liu C Lu and Y Liu 2010 Distributions of raindrop sizes and 560
fall velocities in a semiarid plateau climate Convective vs stratiform rains J Appl 561
Meteorol Climatol 49 632ndash645 httpsdoi1011752009JAMC22081 562
Nurzyńska K M Kubo and K-i Muramoto 2012 Texture operator for snow particle 563
classification into snowflake and graupel Atmos Res 118 121-132 564
Oue M M R Kumjian Y Lu J Verlinde K Aydin and E E Clothiaux 2015 Linear 565
27
Depolarization Ratios of columnar ice crystals in a deep precipitating system over the 566
Arctic observed by Zenith-Pointing Ka-Band Doppler radar J Clim Appl Meteorol 567
54(5) 1060-1068 httpsdoiorg101175JAMC-D-15-00121 568
Pruppacher H R and J D Klett 1998 Microphysics of clouds and precipitation Kluwer 569
Academic 954 pp 570
Rasmussen R B Baker et al 2012 How well are we measuring snow the 571
NOAAFAANCAR winter precipitation test bed Bull Amer Meteor Soc 93(6) 811-829 572
httpsdoiorg101175BAMS-D-11-000521 573
Reisner J R M Rasmussen and R T Bruintjes 1998 Explicit forecasting of 574
supercooled liquid water in winter storms using the MM5 mesoscale model Q J R 575
Meteorol Soc 124 1071ndash1107 httpsdoi101256smsqj54803 576
Rosenfeld D and Ulbrich C W 2003 Cloud microphysical properties processes and 577
rainfall estimation opportunities Meteorol Monogr 30 237-237 578
httpsdoiorg101175 0065-9401(2003)030lt0237cmppargt20CO2 579
Schaefer V J 1956 The preparation of snow crystal replicas-VI Weatherwsie 9 580
132-135 581
Souverijns N A Gossart S Lhermitte I V Gorodetskaya S Kneifel M Maahn F L 582
Bliven and N P M van Lipzig (2017) Estimating radar reflectivity - Snowfall rate 583
relationships and their uncertainties over Antarctica by combining disdrometer and 584
radar observations Atmos Res 196 211-223 585
Taylor K E 2001 Summarizing multiple aspects of model performance in a single 586
diagram J Geophys Res 106 7183ndash7192 httpsdoi1010292000JD900719 587
28
Tokay A and D A Short 1996 Evidence from tropical raindrop spectra of the origin of 588
rain from stratiform versus convective clouds J Appl Meteor 35 355ndash371 589
Tokay A and D Atlas 1999 Rainfall microphysics and radar properties analysis 590
methods for drop size spectra J Appl Meteor 37 912-923 591
httpsdoiorg1011751520-0450(1998)037lt0912RMARPAgt20CO2 592
Tokay A D B Wolff et al 2014 Evaluation of the New version of the laser-optical 593
disdrometer OTT Parsivel2 J Atmos Oceanic Technol 31(6) 1276-1288 594
httpsdoiorg101175JTECH-D-13-001741 595
Ulbrich C W 1983 Natural variations in the analytical form of the raindrop size 596
distribution J Appl Meteor 5 1764-1775 597
Wen G H Xiao H Yang Y Bi and W Xu 2017 Characteristics of summer and winter 598
precipitation over northern China Atmos Res 197 390-406 599
Wu W Y Liu and A K Betts 2012 Observationally based evaluation of NWP 600
reanalyses in modeling cloud properties over the Southern Great Plains J Geophys 601
Res 117 D12202 httpsdoi1010292011JD016971 602
Yuter S E D E Kingsmill L B Nance and M Loumlffler-Mang 2006 Observations of 603
precipitation size and fall velocity characteristics within coexisting rain and wet snow J 604
Appl Meteor Climatol 45 1450ndash1464 doi httpsdoiorg101175JAM24061 605
Zhang P C and B Y Du 2000 Radar Meteorology China Meteorological Press 511pp 606
(in Chinese) 607
608
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
10
velocities of raindrop and graupel but are close to the terminal velocity curves of snow 199
of hexagonal densely rimed dendrites aggregates of dendrites Synthesizing the size 200
data the hydrometeors can be inferred as snowflakes which are further confirmed by 201
surface microscope photos From the surface observation we found many 202
rimedunrimed or aggregated dendrites or hexagonal snowflakes Although riming and 203
aggregation microphysical processes have some influence on terminal velocity 204
(Barthazy and Schefold 2006 Garrett and Yuter 2014 Heymsfield and Westbrook 205
2010) but the influences are too small to distinguish only from observed fall velocity 206
since it is a combined result of many factors When maximum dimensions are among 207
03 to 10 mm there are some small hydrometeors with fall velocities larger than 208
snowflakes which maybe graupels raindrops and droplets 209
Fig 2d is the hydrometeor size and fall velocity distribution during a mixed-phased 210
precipitation The hydrometeor fall velocities exhibit the largest spread for example 211
the fall velocities for hydrometeors with maximum dimension equaling to 3 mm 212
change from 05 to 5 ms and do not distribute along any of the ideal terminal velocity 213
curves This result suggests that different hydrometeor types might coexist during the 214
same sampling time To substantiate supercooled raindrops graupels and different 215
kinds of snowflakes are observed from the surface microscope simultaneously Similar 216
changes in particle size and fall velocity distribution documented by the disdrometer as 217
the storm transitions from rain to mixed-phase to snow were found at Marshall Field 218
site (Rasmussen et al 2012) 219
11
c Other Influencing Factors 220
The different dependence on particle size of terminal velocities for different types 221
of hydrometeors can explain some systematic distribution of the PARSIVEL-measured 222
fall velocities but the large spreads in the measurement of the instant particle fall 223
velocities await further inspection 224
According to our previous work the fall velocity (V) of a hydrometeor measured by 225
the PARSIVEL can be regarded as a combination of the terminal velocity in still air (Vt) 226
and a component Vrsquo that results from all other potential influencing factors eg type 227
turbulence organized air motions break-up and measurement errors (Niu et al 228
2010) 229
119881 = 119881119905 + 119881 prime (1) 230
The large spread of the measurements at both sides of the terminal velocity curves 231
shown in figure 2 seems compatible with the notion of nearly random collections of 232
downdraft and updraft A wider spread for fall velocities implies a wider range of 233
variation in vertical motions when hydrometeors are liquid raindrops (Niu et al 2010) 234
Solid nonspherical hydrometeors are much more complex than liquid drops and the 235
large spread of velocities may be caused by several other factors First different types 236
of hydrometeors (columns bullets plates lump graupels and hexagonal snowflakes et 237
al) have different fall speeds It is long recognized that microphysical processes in cold 238
precipitation are more complex and consequently generate more types of solid 239
hydrometeors comparing to the generation of raindrops The averaged concentration 240
distributions of large number of samples shown in Figure 2 also represents the possible 241
12
distributions of hydrometeors If there is only one kind particle the high concentration 242
would along its ideal terminal velocity very well just like the raindrop possible 243
distribution (Niu et al 2010) The concentration of mixed precipitation in Fig 2d does 244
not along any singe ideal terminal velocity further improved there are more than one 245
kind of hydrometers Coexistence of different types of hydrometeors induces larger 246
spread of fall velocities Second different degrees of riming and aggregating may affect 247
the results Densely rimed particles fall faster than unrimed particles with the same 248
maximum dimension aggregated snowflakes generally fall faster than their component 249
crystals (Barthazy and Schefold 2006 Garrett and Yuter 2014 Locatelli and Hobbs 250
1974) Third solid hydrometeors more likely occur breakup aggregation collision and 251
coalescence processes because of the large range of speeds According to prior 252
research of raindrop breakup and coalescence would lead to the ldquohigher-than-terminal 253
velocityrdquo fall velocity for small drops but ldquolower-than-terminal velocityrdquo fall velocity for 254
large drops (Niu et al 2010 Montero-Martiacutenez et al 2009 Larsen et al 2014) Similar 255
results are expected for the fall velocity of solid hydrometeors Last but not the least 256
the disdrometer may suffer from instrumental errors due to the internally assumed 257
relationship between horizontal and vertical particle dimensions likely resulting in a 258
wider spreads of fall velocities for the graupel and snowflakes as compared to the 259
raindrop counterpart as discussed in Section 2 Although the instrument error is an 260
important factor that should be considered in velocity spread as shown in Fig2b the 261
instrument error could not cause that large velocity spread The possible distributions 262
of fall velocities are the combine effects of physical and instrument principle 263
13
Further support for the possible instrumental uncertainty is from the cloud radar 264
observations Fig 3 shows the cloud reflectivity and linear depolarization ratio (LDR) in 265
lower level (less than 08 km) for the graupel snowflake and mixed-phased 266
precipitations respectively The LDR is a valuable observable in identifying the 267
hydrometeor types (Oue et al 2015) As shown in Fig 3a the cloud top height of 268
graupel precipitation was up to 7km during 1900 to 2050 Beijng Time (BT) which was 269
highest among the three events The high cloud top implies stronger updraft and 270
turbulence which further induces a larger fall velocity spread The LDR value was the 271
smallest among the three events indicating that the hydrometeors were close to 272
spherical consistent to the surface observations The cloud top height of snowflake 273
precipitation was up to 35 km (Fig 3c) which was the lowest among the three types of 274
precipitations implying weakest updraft and turbulence Notably although the 275
snowflake types are more complex than those of graupels the velocity spread was not 276
as large as that of the graupel type likely because of the weakest updraft and 277
turbulence The LDR was relatively larger consistent with the surface snowflake 278
observations (Fig 3d) The cloud top height of mixed-phase precipitation was up to 45 279
km (Fig 3e) and the LDR in lower level was largest among the three types of 280
precipitations owing to coexistence of raindrops graupels and snowflakes (Fig 3f) 281
4 Hydrometeor Size Distributions 282
a Comparison of HSDs between Different Types 283
There were four representative types of precipitations during this field experiment 284
providing us a unique opportunity to examine the HSD differences between the four 285
14
types of hydrometeors The sample numbers mean maximum dimensions and number 286
concentrations for each kind of HSDs are given in Table 2 Figure 4 is the averaged 287
distribution of all measured HSDs of 4 kinds As shown in Figure 4 on average the 288
mixed-phased precipitation tends to have most small size hydrometeors with D lt 15 289
mm while snowflake precipitation has the least small hydrometeors among the four 290
types The snowflake precipitation has more large size hydrometeors ie 3 mm lt D lt 11 291
mm Graupel size distribution tends to have two peeks around 13 mm and 26 mm The 292
mean maximum dimension is largest for snowflake (126 mm) and smallest for the 293
mixed HSD due to many small particles Similar results were found in precipitation 294
occurring in the Cascade and Rocky Mountains (Yuter et al 2006) The PARSIVEL 295
disdrometer doesnrsquot provide reliable data for small drops lower than 05 mm and tends to 296
underestimate small drops so the relatively low concentrations of small drops likely resulted 297
from the instrumentrsquos shortcomings (Tokay et al 2013 and Chen et al 2017) 298
b Evaluation of Distribution Functions for Describing HSDs 299
Over the last few decades great efforts have been devoted to finding the 300
appropriate analytical functions for describing the HSD because of its wide applications 301
in many areas including remote sensing and parameterization of precipitation (Chen et 302
al 2017) The two distribution functions mostly used up to now are the Lognormal 303
(Feingold and Levin 1986 Rosenfeld and Ulbrich 2003) and the Gamma (Ulbrich 1983) 304
distributions The Gamma distribution has been proposed as a first order generalization 305
of the Exponential distribution when μ equals 0 (Table 4) Weibull distribution is 306
another function used to describe size distributions of raindrops and cloud droplets (Liu 307
15
and Liu 1994 Liu et al 1995) Nevertheless the question as to which functions are 308
more adequate to describe HSDs of solid hydrometeors have been rarely investigated 309
systematically and quantitatively Thus the objective of this section is to examine the 310
most adequate distribution function used to describe HSDs 311
Considering size distributions of raindrops cloud droplets and aerosol particles are 312
the end results of many (stochastic) complex processes Liu (1992 1993 1994 and 313
1995) proposed a statistical method based on the relationships between the skewness 314
(S) and kurtosis (K) derived from an ensemble of particle size distribution 315
measurements and from those commonly used size distribution functions Cugerone 316
and Michele (2017) also used a similar approach based on the S-K relationships to study 317
raindrop size distributions Unlike the conventional curve-fitting of individual size 318
distributions this approach applies to an ensemble of size distribution measurements 319
and identifies the most appropriate statistical distribution pattern Here we apply this 320
approach to investigate if the statistical pattern of the HSDs of four precipitation types 321
follows the Exponential Gaussian Gamma Weibull and Lognormal distributions (Table 322
4) and if there are any pattern differences between them Briefly S and K of a HSD are 323
calculated from the corresponding HSD with the following two equations 324
23
2
3
t
iii
t
iii
dDN
)(Dn)D(D
dDN
)(Dn)D(D
S
minus
minus
=
(2) 325
32
2
4
minus
minus
minus
=
dDN
)(Dn)D(D
dDN
)(Dn)D(D
K
t
iii
t
iii
(3) 326
16
where Di is the central diameter of the i-th bin ni is the number concentration of the 327
i-th bin and Nt is total number concentration Note that each individual HSD can be 328
used to obtain a pair of S and K which is shown as a dot in Figure 5 Also noteworthy is 329
that the SndashK relationships for the families of Gamma Weibull and Lognormal are 330
described by known analytical functions (Liu 1993 1994 and 1995 Cugerone and 331
Michele 2017) represented by theoretical curves in Figure 5 The Exponential and 332
Gaussian distributions are represented by single points on the S-K diagram (S=2 and K=6 333
for Exponential) and (S=0 and K=0 for Gaussian) respectively Thus by comparing the 334
measured S and K values (points) with the known theoretical curves one can determine 335
the most proper function used to describe HSDs 336
Figure 5 shows the scatter plots of observed SndashK pairs calculated from the HSD 337
measurements for raindrop graupel snowflake mixed-phase precipitations Also 338
shown as comparison are the theoretical curves corresponding to the analytical HSD 339
functions A few points are evident First despite some occasional departures most of 340
the points fall near the theoretical lines of Gamma and Weibull distributions suggesting 341
that the HSD patterns for all the four types of precipitations well follow the Gamma and 342
Weibull distributions statistically Second HSDs of raindrops and mixed hydrometeors 343
are better described by Gamma and Weibull distribution than graupels and snowflakes 344
Third the S and K do not cluster around points (2 6) and (0 0) suggesting that the 345
Gaussian and Exponential distribution are not appropriate for describing HSDs 346
especially Gaussian distribution 347
To further evaluate the overall performance of the different distribution functions 348
17
we employ the widely used technique of Taylor diagram (Taylor 2001) and ldquoRelative 349
Euclidean Distancerdquo (RED) (Wu et al 2012) as a supplement to the Taylor diagram The 350
Taylor diagram has been widely used to visualize the statistical differences between 351
model results and observations in evaluation of model performance against 352
measurements or other benchmarks (IPCC 2001) Correlation coefficient (r) standard 353
deviation (σ) and ldquocentered root-mean-square errorrdquo (RMSE hereafter) are used in 354
the Taylor diagram The RED is introduced to add the bias as well in a dimensionless 355
framework that allows for comparison between different physical quantities with 356
different units In this study we consider the S and K values derived from the 357
distribution functions as model results and evaluate them against those derived from 358
the HSD measurements Brieflythe expressions for calculating r and σ and RMSE are 359
shown below 360
119903 =1
119873sum (119872119899minus)(119874119899minus)119873119899=1
120590119872120590119900 (4) 361
119877119872119878119864 = 1
119873sum [(119872119899 minus ) minus (119874119899 minus )]2119873119899=1
12
(5) 362
120590119872 = [1
119873sum (119872119899 minus )119873119899=1 ]
12
(6) 363
1205900 = [1
119873sum (119874119899 minus )119873119899=1 ]
12
(7) 364
where M and O denote distribution function and observed variables The RED 365
expression is shown below 366
119877119864119863 = [(minus)
]2
+ [(120590119872minus120590119874)
120590119900]2
+ (1 minus 119903)212
( 8 ) 367
Equation (8) indicates that RED considers all the components of mean bias variations 368
and correlations in a dimensionless way the distribution function performance 369
degrades as RED increases from the perfect agreement with RED=0 370
18
In the Taylor diagrams shown in Fig 6 the cosine of azimuthal angle of each point 371
gives the r between the function-calculated and observed data The distance between 372
individual point and the reference point ldquoObsrdquo represents the RMSE normalized by the 373
amplitude of the observationally based variations As this distance approaches to zero 374
the function-calculated K and S approach to the observations Clearly the values of r 375
are around 097 for Gamma and Weibull r for Lognormal function is slightly smaller 376
(095) The normalized σ are much different for Lognormal Gamma and Weibull 377
distributions with averaged value being 057 0895 and 0785 respectively Therefore 378
the Lognormal distribution exhibits the worst performance for describing HSDs and 379
Gamma and Weibull distributions appear to perform much better (Fig 6a) 380
Noticing that S and K of Gamma and Weibull distributions are equal at the point of S 381
= 2 and K = 6 and have positive relationship (If S lt 2 then K lt 6 and if S gt 2 then k gt 6) In 382
this part we further separately examine the group of data with S lt 2 and K lt 6 (Fig 6b) 383
and compare its result with those of total data The averaged normalized σ are 103 and 384
109 and r are 091 and 090 for Weibull and Gamma distributions respectively 385
suggesting that Weibull distribution performs slightly better than Gamma distribution 386
for the four HSD types in the data group of S lt 2 and K lt 6 whereas the opposite is true 387
for all data This conclusion is further substantiated by comparison of RED values for the 388
four type of precipitation (Fig7) which shows that Lognormal has the largest RED 389
Gamma the smallest and Weibull in between for four types of precipitations in all data 390
whereas Weibull (Lognormal) has smallest (largest) RED values when S lt 2 and K lt 6 It 391
can be inferred for data group of S gt 2 and k gt 6 Gamma distribution performs better 392
19
Further comparison between different precipitation types shows these functions all 393
performs better for raindrop size distributions and mixed-phase than graupel and 394
snowflake size distributions The RED for snowflakes is largest among the four types 395
The performance of Gamma is better for describing solid HSDs of all data but Weibull 396
distribution is better when S lt 2 and K lt 6 397
5 Conclusion 398
The combined measurements collected during a field experiment conducted at the 399
Haituo Mountain site using PARSIVEL disdrometer millimeter wavelength cloud radar 400
and microscope photography are analyzed to classify the precipitation hydrometeor 401
types examine the dependence of fall velocity on hydrometeor size for different 402
hydrometeor types and determine the best distribution functions to describe the 403
hydrometeor size distributions of different types 404
Analysis of the PARSIVEL-measured fall velocities show that on average the 405
dependence of fall velocity on hydrometeor size largely follow their corresponding 406
terminal velocity curves for raindrops graupels and snowflakes respectively suggesting 407
that such measurements are useful to identify the hydrometeor types The associated 408
microscope photos and cloud radar observations support the classification of 409
hydrometeor types based on the PARSIVEL-observed fall velocities Furthermore there 410
are velocity spreads in fall velocity across hydrometeor sizes for all hydrometeors and 411
the spreads for the solid hydrometeors could cause by hydrometeor type turbulence or 412
updraftdowndraft and instrument measured principle The coexistence of various 413
types of hydrometeors likely induces additional spread of fall velocity for given 414
20
hydrometeor sizes such as mixed precipitation Meanwhile complex microphysical 415
processes in cold precipitation such as riming aggregation breakup and collision and 416
coalescence influence fall velocity which likely induce larger spread of fall velocity Last 417
but not the least the disdrometer may suffer from instrumental errors due to the 418
internally assumed relationship between horizontal and vertical particle dimensions 419
Comparison of the type-averaged hydrometeor size distributions shows that the 420
mixed precipitation has more small hydrometeors with D lt 15 mm than others 421
whereas the snowflake precipitation has the least number of small hydrometeors 422
among the four types On the contrary the snowflake precipitation has more large 423
hydrometeors with D between 3 mm and 11 mm 424
The commonly used size distribution functions (Gamma Weibull and Lognormal) 425
are further examined to determine the most adequate function to describe the size 426
distribution measurements for all the hydrometeor types by use of an approach based 427
on the relationship between skewness (S) and kurtosis (K) Taylor diagram and RED are 428
further introduced to assess the performance of different size distribution functions 429
against measurements It is shown that the HSDs for the four types can all be well 430
described statistically by the Gamma and Weibull distribution but Lognormal 431
Exponential and Gaussian are not fit to describe HSDs Gamma and Weibull distribution 432
describe raindrop and mixed-phase size distribution better than snowflake and graupel 433
size distribution and their performances are worst for snowflake It may due to graupel 434
and snowflake precipitation have more big particles When S less than 2 and K less than 435
6 Weibull distribution performs better than Gamma distribution to describe HSDs but 436
21
Gamma distribution performs better for total data 437
A few points are noteworthy First although this study demonstrates the great 438
potential of combining simultaneous disdrometer measurements of particle fall velocity 439
and size distributions microscopic photography and cloud radar to address the 440
challenges facing solid precipitation the data are limited More research is needed to 441
discern such effects on the results presented here Second as the observations show 442
that in addition to sizes there are many other factors (eg hydrometeor type 443
microphysical processes turbulence and measuring principle) that can potentially 444
influence particle fall velocity as well More comprehensive research is needed to 445
further discern and separate these factors Finally the combined use of S-K diagram 446
Taylor diagram and relative Euclidean distance appears to be a powerful tool for 447
identifying the best function used to describe the HSDs and quantify the differences 448
between different precipitation types More research is in order along this direction 449
Acknowledgements 450
This study is mainly supported by the Chinese National Science Foundation under Grant 451
No 41675138 and National Key RampD Program of China (2017YFC0209604) It is partly 452
supported by Beijing National Science Foundation (8172023) the US Department 453
Energys Atmospheric System Research (ASR) Program (Liu and Jia at BNL) Lu is 454
supported by the Natural Science Foundation of Jiangsu Province (BK20160041) The 455
observation data are archived at a specialized supercomputer at Beijing Meteorology 456
Information Center (ftp10224592) which are available from the corresponding 457
author upon request The authors also thank Beijing weather modification office for 458
their support during the field experiment 459
Reference 460
22
Agosta CC Fettweis XX Datta RR 2015 Evaluation of the CMIP5 models in the 461
aim of regional modelling of the Antarctic surface mass balance Cryosphere 9 2311ndash462
2321 httpdxdoiorg105194tc-9-2311-2015 463
Barthazy E and R Schefold 2006 Fall velocity of snowflakes of different riming degree 464
and crystal types Atmos Res 82(1) 391-398 httpsdoiorg101016jatmosres 465
200512009 466
Battaglia A Rustemeier E Tokay A et al 2010 PARSIVEL snow observations a critical 467
assessment J Atmos Oceanic Technol 27(2) 333-344 doi 1011752009jtecha13321 468
Boumlhm H P 1989 A General Equation for the Terminal Fall Speed of Solid Hydrometeors 469
J Atmos Sci 46(15) 2419-2427 httpsdoiorg1011751520-0469(1989)046 lt2419A 470
GEFTTgt20CO2 471
Boudala F S G A Isaac et al 2014 Comparisons of Snowfall Measurements in 472
Complex Terrain Made During the 2010 Winter Olympics in Vancouver Pure and 473
Applied Geophysics 171(1) 113-127 474
Chen B W Hu and J Pu 2011 Characteristics of the raindrop size distribution for 475
freezing precipitation observed in southern China J Geophys Res 116 D06201 476
doi1010292010JD015305 477
Chen B Z Hu L Liu and G Zhang (2017) Raindrop Size Distribution Measurements at 478
4500m on the Tibetan Plateau during TIPEX-III J Geophys Res 122 11092-11106 479
doiorg10100 22017JD027233 480
23
Cugerone K and C De Michele 2017 Investigating raindrop size distributions in the 481
(L-)skewness-(L-)kurtosis plane Quart J Roy Meteor Soc 143(704) 1303-1312 482
httpsdoiorg101002qj3005 483
Donnadieu G 1980 Comparison of results obtained with the VIDIAZ spectro 484
pluviometer and the JossndashWaldvogel rainfall disdrometer in a ldquorain of a thundery typerdquo 485
J Appl Meteor 19 593ndash597 486
Feingold G and Levin Z 1986 The lognormal fit to raindrop spectra from frontal 487
convective clouds in Israel J Clim Appl Meteorol 25 1346ndash1363 488
httpsdoiorg1011751520-0450(1986)025lt1346tlftrsgt20CO2 489
Field P R A J Heymsfield and A Bansemer 2007 Snow Size Distribution 490
Parameterization for Midlatitude and Tropical Ice Clouds J Atmos Sci 64(12) 491
4346-4365 httpsdoiorg1011752007JAS23441 492
Garrett T J and S E Yuter 2014 Observed influence of riming temperature and 493
turbulence on the fallspeed of solid precipitation Geophysical Research Letters 41(18) 494
6515ndash6522 495
Geresdi I N Sarkadi and G Thompson 2014 Effect of the accretion by water drops 496
on the melting of snowflakes Atmos Res 149 96-110 497
Gunn R and G D Kinzer 1949 The terminal velocity of fall for water drops in stagnant 498
air J Meteor 6 243-248 httpsdoiorg1011751520-0469(1949)006lt0243TTVOFFgt 499
20CO2 500
24
Heymsfield A J and C D Westbrook 2010 Advances in the Estimation of Ice Particle 501
Fall Speeds Using Laboratory and Field Measurements J Atmos Sci 67(8) 2469-2482 502
httpsdoiorg1011752010JAS33791 503
Huang G-J C Kleinkort V N Bringi and B M Notaroš 2017 Winter precipitation 504
particle size distribution measurement by Multi-Angle Snowflake Camera Atmos Res 505
198 81-96 506
Intergovernmental Panel on Climate Change (IPCC) 2001 Climate Change 2001 The 507
Scientific Basis Contribution of Working Group I to the Third Assessment Report of the 508
Intergovernmental Panel on Climate Change edited by J T Houghton et al 881 pp 509
Cambridge Univ Press New York 510
Ishizaka M H Motoyoshi S Nakai T Shiina T Kumakura and K-i Muramoto 2013 A 511
New Method for Identifying the Main Type of Solid Hydrometeors Contributing to 512
Snowfall from Measured Size-Fall Speed Relationship Journal of the Meteorological 513
Society of Japan Ser II 91(6) 747-762 httpsdoiorg102151jmsj2013-602 514
Khvorostyanov V 2005 Fall Velocities of Hydrometeors in the Atmosphere 515
Refinements to a Continuous Analytical Power Law J Atmos Sci 62 4343-4357 516
httpsdoiorg101175JAS36221 517
Kikuchi K T Kameda K Higuchi and A Yamashita 2013 A global classification of 518
snow crystals ice crystals and solid precipitation based on observations from middle 519
latitudes to polar regions Atmos Res 132-133 460-472 520
Kneifel S A von Lerber J Tiira D Moisseev P Kollias and J Leinonen 2015 521
Observed relations between snowfall microphysics and triple-frequency radar 522
25
measurements J Geophys Res Atmos 120(12) 6034-6055 523
httpsdoi1010022015JD023156 524
Kubicek A and P K Wang 2012 A numerical study of the flow fields around a typical 525
conical graupel falling at various inclination angles Atmos Res 118 15ndash26 526
httpsdoi101016jatmosres201206001 527
Larsen M L A B Kostinski and A R Jameson (2014) Further evidence for 528
superterminal raindrops Geophys Res Lett 41(19) 6914-6918 529
Lee JE SH Jung H M Park S Kwon P L Lin and G W Lee 2015 Classification of 530
Precipitation Types Using Fall Velocity Diameter Relationships from 2D-Video 531
Distrometer Measurements Advances in Atmospheric Sciences (09) 532
Lin Y L J Donner and B A Colle 2010 Parameterization of riming intensity and its 533
impact on ice fall speed using arm data Mon Weather Rev 139(3) 1036ndash1047 534
httpsdoi1011752010MWR32991 535
Liu Y G 1992 Skewness and kurtosis of measured raindrop size distributions Atmos 536
Environ 26A 2713-2716 httpsdoiorg1010160960-1686(92)90005-6 537
Liu Y G 1993 Statistical theory of the Marshall-Parmer distribution of raindrops 538
Atmos Environ 27A 15-19 httpsdoiorg1010160960-1686(93)90066-8 539
Liu Y G and F Liu 1994 On the description of aerosol particle size distribution Atmos 540
Res 31(1-3) 187-198 httpsdoiorg1010160169-8095(94)90043-4 541
Liu Y G L You W Yang F Liu 1995 On the size distribution of cloud droplets Atmos 542
Res 35 (2-4) 201-216 httpsdoiorg1010160169-8095(94)00019-A 543
Locatelli J D and P V Hobbs 1974 Fall speeds and masses of solid precipitation 544
26
particles J Geophys Res 79(15) 2185-2197 httpsdoi101029JC079i015p02185 545
Loumlffler-Mang M and J Joss 2000 An optical disdrometer for measuring size and 546
velocity of hydrometeors J Atmos Oceanic Technol 17 130-139 547
httpsdoiorg1011751520-0426(2000)017lt0130AODFMSgt20CO2 548
Loumlffler-Mang M and U Blahak 2001 Estimation of the Equivalent Radar Reflectivity 549
Factor from Measured Snow Size Spectra J Clim Appl Meteorol 40(4) 843-849 550
httpsdoiorg1011751520-0450(2001)040lt0843EOTERRgt20CO2 551
Matrosov S Y 2007 Modeling Backscatter Properties of Snowfall at Millimeter 552
Wavelengths J Atmos Sci 64(5) 1727-1736 httpsdoiorg101175JAS39041 553
Mitchell D L 1996 Use of mass- and area-dimensional power laws for determining 554
precipitation particle terminal velocities J Atmos Sci 53 1710-1723 555
httpsdoiorg1011751520-0469(1996)053lt1710UOMAADgt20CO2 556
Montero-Martiacutenez G A B Kostinski R A Shaw and F Garciacutea-Garciacutea 2009 Do all 557
raindrops fall at terminal speed Geophys Res Lett 36 L11818 558
httpsdoiorg1010292008GL037111 559
Niu S X Jia J Sang X Liu C Lu and Y Liu 2010 Distributions of raindrop sizes and 560
fall velocities in a semiarid plateau climate Convective vs stratiform rains J Appl 561
Meteorol Climatol 49 632ndash645 httpsdoi1011752009JAMC22081 562
Nurzyńska K M Kubo and K-i Muramoto 2012 Texture operator for snow particle 563
classification into snowflake and graupel Atmos Res 118 121-132 564
Oue M M R Kumjian Y Lu J Verlinde K Aydin and E E Clothiaux 2015 Linear 565
27
Depolarization Ratios of columnar ice crystals in a deep precipitating system over the 566
Arctic observed by Zenith-Pointing Ka-Band Doppler radar J Clim Appl Meteorol 567
54(5) 1060-1068 httpsdoiorg101175JAMC-D-15-00121 568
Pruppacher H R and J D Klett 1998 Microphysics of clouds and precipitation Kluwer 569
Academic 954 pp 570
Rasmussen R B Baker et al 2012 How well are we measuring snow the 571
NOAAFAANCAR winter precipitation test bed Bull Amer Meteor Soc 93(6) 811-829 572
httpsdoiorg101175BAMS-D-11-000521 573
Reisner J R M Rasmussen and R T Bruintjes 1998 Explicit forecasting of 574
supercooled liquid water in winter storms using the MM5 mesoscale model Q J R 575
Meteorol Soc 124 1071ndash1107 httpsdoi101256smsqj54803 576
Rosenfeld D and Ulbrich C W 2003 Cloud microphysical properties processes and 577
rainfall estimation opportunities Meteorol Monogr 30 237-237 578
httpsdoiorg101175 0065-9401(2003)030lt0237cmppargt20CO2 579
Schaefer V J 1956 The preparation of snow crystal replicas-VI Weatherwsie 9 580
132-135 581
Souverijns N A Gossart S Lhermitte I V Gorodetskaya S Kneifel M Maahn F L 582
Bliven and N P M van Lipzig (2017) Estimating radar reflectivity - Snowfall rate 583
relationships and their uncertainties over Antarctica by combining disdrometer and 584
radar observations Atmos Res 196 211-223 585
Taylor K E 2001 Summarizing multiple aspects of model performance in a single 586
diagram J Geophys Res 106 7183ndash7192 httpsdoi1010292000JD900719 587
28
Tokay A and D A Short 1996 Evidence from tropical raindrop spectra of the origin of 588
rain from stratiform versus convective clouds J Appl Meteor 35 355ndash371 589
Tokay A and D Atlas 1999 Rainfall microphysics and radar properties analysis 590
methods for drop size spectra J Appl Meteor 37 912-923 591
httpsdoiorg1011751520-0450(1998)037lt0912RMARPAgt20CO2 592
Tokay A D B Wolff et al 2014 Evaluation of the New version of the laser-optical 593
disdrometer OTT Parsivel2 J Atmos Oceanic Technol 31(6) 1276-1288 594
httpsdoiorg101175JTECH-D-13-001741 595
Ulbrich C W 1983 Natural variations in the analytical form of the raindrop size 596
distribution J Appl Meteor 5 1764-1775 597
Wen G H Xiao H Yang Y Bi and W Xu 2017 Characteristics of summer and winter 598
precipitation over northern China Atmos Res 197 390-406 599
Wu W Y Liu and A K Betts 2012 Observationally based evaluation of NWP 600
reanalyses in modeling cloud properties over the Southern Great Plains J Geophys 601
Res 117 D12202 httpsdoi1010292011JD016971 602
Yuter S E D E Kingsmill L B Nance and M Loumlffler-Mang 2006 Observations of 603
precipitation size and fall velocity characteristics within coexisting rain and wet snow J 604
Appl Meteor Climatol 45 1450ndash1464 doi httpsdoiorg101175JAM24061 605
Zhang P C and B Y Du 2000 Radar Meteorology China Meteorological Press 511pp 606
(in Chinese) 607
608
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
11
c Other Influencing Factors 220
The different dependence on particle size of terminal velocities for different types 221
of hydrometeors can explain some systematic distribution of the PARSIVEL-measured 222
fall velocities but the large spreads in the measurement of the instant particle fall 223
velocities await further inspection 224
According to our previous work the fall velocity (V) of a hydrometeor measured by 225
the PARSIVEL can be regarded as a combination of the terminal velocity in still air (Vt) 226
and a component Vrsquo that results from all other potential influencing factors eg type 227
turbulence organized air motions break-up and measurement errors (Niu et al 228
2010) 229
119881 = 119881119905 + 119881 prime (1) 230
The large spread of the measurements at both sides of the terminal velocity curves 231
shown in figure 2 seems compatible with the notion of nearly random collections of 232
downdraft and updraft A wider spread for fall velocities implies a wider range of 233
variation in vertical motions when hydrometeors are liquid raindrops (Niu et al 2010) 234
Solid nonspherical hydrometeors are much more complex than liquid drops and the 235
large spread of velocities may be caused by several other factors First different types 236
of hydrometeors (columns bullets plates lump graupels and hexagonal snowflakes et 237
al) have different fall speeds It is long recognized that microphysical processes in cold 238
precipitation are more complex and consequently generate more types of solid 239
hydrometeors comparing to the generation of raindrops The averaged concentration 240
distributions of large number of samples shown in Figure 2 also represents the possible 241
12
distributions of hydrometeors If there is only one kind particle the high concentration 242
would along its ideal terminal velocity very well just like the raindrop possible 243
distribution (Niu et al 2010) The concentration of mixed precipitation in Fig 2d does 244
not along any singe ideal terminal velocity further improved there are more than one 245
kind of hydrometers Coexistence of different types of hydrometeors induces larger 246
spread of fall velocities Second different degrees of riming and aggregating may affect 247
the results Densely rimed particles fall faster than unrimed particles with the same 248
maximum dimension aggregated snowflakes generally fall faster than their component 249
crystals (Barthazy and Schefold 2006 Garrett and Yuter 2014 Locatelli and Hobbs 250
1974) Third solid hydrometeors more likely occur breakup aggregation collision and 251
coalescence processes because of the large range of speeds According to prior 252
research of raindrop breakup and coalescence would lead to the ldquohigher-than-terminal 253
velocityrdquo fall velocity for small drops but ldquolower-than-terminal velocityrdquo fall velocity for 254
large drops (Niu et al 2010 Montero-Martiacutenez et al 2009 Larsen et al 2014) Similar 255
results are expected for the fall velocity of solid hydrometeors Last but not the least 256
the disdrometer may suffer from instrumental errors due to the internally assumed 257
relationship between horizontal and vertical particle dimensions likely resulting in a 258
wider spreads of fall velocities for the graupel and snowflakes as compared to the 259
raindrop counterpart as discussed in Section 2 Although the instrument error is an 260
important factor that should be considered in velocity spread as shown in Fig2b the 261
instrument error could not cause that large velocity spread The possible distributions 262
of fall velocities are the combine effects of physical and instrument principle 263
13
Further support for the possible instrumental uncertainty is from the cloud radar 264
observations Fig 3 shows the cloud reflectivity and linear depolarization ratio (LDR) in 265
lower level (less than 08 km) for the graupel snowflake and mixed-phased 266
precipitations respectively The LDR is a valuable observable in identifying the 267
hydrometeor types (Oue et al 2015) As shown in Fig 3a the cloud top height of 268
graupel precipitation was up to 7km during 1900 to 2050 Beijng Time (BT) which was 269
highest among the three events The high cloud top implies stronger updraft and 270
turbulence which further induces a larger fall velocity spread The LDR value was the 271
smallest among the three events indicating that the hydrometeors were close to 272
spherical consistent to the surface observations The cloud top height of snowflake 273
precipitation was up to 35 km (Fig 3c) which was the lowest among the three types of 274
precipitations implying weakest updraft and turbulence Notably although the 275
snowflake types are more complex than those of graupels the velocity spread was not 276
as large as that of the graupel type likely because of the weakest updraft and 277
turbulence The LDR was relatively larger consistent with the surface snowflake 278
observations (Fig 3d) The cloud top height of mixed-phase precipitation was up to 45 279
km (Fig 3e) and the LDR in lower level was largest among the three types of 280
precipitations owing to coexistence of raindrops graupels and snowflakes (Fig 3f) 281
4 Hydrometeor Size Distributions 282
a Comparison of HSDs between Different Types 283
There were four representative types of precipitations during this field experiment 284
providing us a unique opportunity to examine the HSD differences between the four 285
14
types of hydrometeors The sample numbers mean maximum dimensions and number 286
concentrations for each kind of HSDs are given in Table 2 Figure 4 is the averaged 287
distribution of all measured HSDs of 4 kinds As shown in Figure 4 on average the 288
mixed-phased precipitation tends to have most small size hydrometeors with D lt 15 289
mm while snowflake precipitation has the least small hydrometeors among the four 290
types The snowflake precipitation has more large size hydrometeors ie 3 mm lt D lt 11 291
mm Graupel size distribution tends to have two peeks around 13 mm and 26 mm The 292
mean maximum dimension is largest for snowflake (126 mm) and smallest for the 293
mixed HSD due to many small particles Similar results were found in precipitation 294
occurring in the Cascade and Rocky Mountains (Yuter et al 2006) The PARSIVEL 295
disdrometer doesnrsquot provide reliable data for small drops lower than 05 mm and tends to 296
underestimate small drops so the relatively low concentrations of small drops likely resulted 297
from the instrumentrsquos shortcomings (Tokay et al 2013 and Chen et al 2017) 298
b Evaluation of Distribution Functions for Describing HSDs 299
Over the last few decades great efforts have been devoted to finding the 300
appropriate analytical functions for describing the HSD because of its wide applications 301
in many areas including remote sensing and parameterization of precipitation (Chen et 302
al 2017) The two distribution functions mostly used up to now are the Lognormal 303
(Feingold and Levin 1986 Rosenfeld and Ulbrich 2003) and the Gamma (Ulbrich 1983) 304
distributions The Gamma distribution has been proposed as a first order generalization 305
of the Exponential distribution when μ equals 0 (Table 4) Weibull distribution is 306
another function used to describe size distributions of raindrops and cloud droplets (Liu 307
15
and Liu 1994 Liu et al 1995) Nevertheless the question as to which functions are 308
more adequate to describe HSDs of solid hydrometeors have been rarely investigated 309
systematically and quantitatively Thus the objective of this section is to examine the 310
most adequate distribution function used to describe HSDs 311
Considering size distributions of raindrops cloud droplets and aerosol particles are 312
the end results of many (stochastic) complex processes Liu (1992 1993 1994 and 313
1995) proposed a statistical method based on the relationships between the skewness 314
(S) and kurtosis (K) derived from an ensemble of particle size distribution 315
measurements and from those commonly used size distribution functions Cugerone 316
and Michele (2017) also used a similar approach based on the S-K relationships to study 317
raindrop size distributions Unlike the conventional curve-fitting of individual size 318
distributions this approach applies to an ensemble of size distribution measurements 319
and identifies the most appropriate statistical distribution pattern Here we apply this 320
approach to investigate if the statistical pattern of the HSDs of four precipitation types 321
follows the Exponential Gaussian Gamma Weibull and Lognormal distributions (Table 322
4) and if there are any pattern differences between them Briefly S and K of a HSD are 323
calculated from the corresponding HSD with the following two equations 324
23
2
3
t
iii
t
iii
dDN
)(Dn)D(D
dDN
)(Dn)D(D
S
minus
minus
=
(2) 325
32
2
4
minus
minus
minus
=
dDN
)(Dn)D(D
dDN
)(Dn)D(D
K
t
iii
t
iii
(3) 326
16
where Di is the central diameter of the i-th bin ni is the number concentration of the 327
i-th bin and Nt is total number concentration Note that each individual HSD can be 328
used to obtain a pair of S and K which is shown as a dot in Figure 5 Also noteworthy is 329
that the SndashK relationships for the families of Gamma Weibull and Lognormal are 330
described by known analytical functions (Liu 1993 1994 and 1995 Cugerone and 331
Michele 2017) represented by theoretical curves in Figure 5 The Exponential and 332
Gaussian distributions are represented by single points on the S-K diagram (S=2 and K=6 333
for Exponential) and (S=0 and K=0 for Gaussian) respectively Thus by comparing the 334
measured S and K values (points) with the known theoretical curves one can determine 335
the most proper function used to describe HSDs 336
Figure 5 shows the scatter plots of observed SndashK pairs calculated from the HSD 337
measurements for raindrop graupel snowflake mixed-phase precipitations Also 338
shown as comparison are the theoretical curves corresponding to the analytical HSD 339
functions A few points are evident First despite some occasional departures most of 340
the points fall near the theoretical lines of Gamma and Weibull distributions suggesting 341
that the HSD patterns for all the four types of precipitations well follow the Gamma and 342
Weibull distributions statistically Second HSDs of raindrops and mixed hydrometeors 343
are better described by Gamma and Weibull distribution than graupels and snowflakes 344
Third the S and K do not cluster around points (2 6) and (0 0) suggesting that the 345
Gaussian and Exponential distribution are not appropriate for describing HSDs 346
especially Gaussian distribution 347
To further evaluate the overall performance of the different distribution functions 348
17
we employ the widely used technique of Taylor diagram (Taylor 2001) and ldquoRelative 349
Euclidean Distancerdquo (RED) (Wu et al 2012) as a supplement to the Taylor diagram The 350
Taylor diagram has been widely used to visualize the statistical differences between 351
model results and observations in evaluation of model performance against 352
measurements or other benchmarks (IPCC 2001) Correlation coefficient (r) standard 353
deviation (σ) and ldquocentered root-mean-square errorrdquo (RMSE hereafter) are used in 354
the Taylor diagram The RED is introduced to add the bias as well in a dimensionless 355
framework that allows for comparison between different physical quantities with 356
different units In this study we consider the S and K values derived from the 357
distribution functions as model results and evaluate them against those derived from 358
the HSD measurements Brieflythe expressions for calculating r and σ and RMSE are 359
shown below 360
119903 =1
119873sum (119872119899minus)(119874119899minus)119873119899=1
120590119872120590119900 (4) 361
119877119872119878119864 = 1
119873sum [(119872119899 minus ) minus (119874119899 minus )]2119873119899=1
12
(5) 362
120590119872 = [1
119873sum (119872119899 minus )119873119899=1 ]
12
(6) 363
1205900 = [1
119873sum (119874119899 minus )119873119899=1 ]
12
(7) 364
where M and O denote distribution function and observed variables The RED 365
expression is shown below 366
119877119864119863 = [(minus)
]2
+ [(120590119872minus120590119874)
120590119900]2
+ (1 minus 119903)212
( 8 ) 367
Equation (8) indicates that RED considers all the components of mean bias variations 368
and correlations in a dimensionless way the distribution function performance 369
degrades as RED increases from the perfect agreement with RED=0 370
18
In the Taylor diagrams shown in Fig 6 the cosine of azimuthal angle of each point 371
gives the r between the function-calculated and observed data The distance between 372
individual point and the reference point ldquoObsrdquo represents the RMSE normalized by the 373
amplitude of the observationally based variations As this distance approaches to zero 374
the function-calculated K and S approach to the observations Clearly the values of r 375
are around 097 for Gamma and Weibull r for Lognormal function is slightly smaller 376
(095) The normalized σ are much different for Lognormal Gamma and Weibull 377
distributions with averaged value being 057 0895 and 0785 respectively Therefore 378
the Lognormal distribution exhibits the worst performance for describing HSDs and 379
Gamma and Weibull distributions appear to perform much better (Fig 6a) 380
Noticing that S and K of Gamma and Weibull distributions are equal at the point of S 381
= 2 and K = 6 and have positive relationship (If S lt 2 then K lt 6 and if S gt 2 then k gt 6) In 382
this part we further separately examine the group of data with S lt 2 and K lt 6 (Fig 6b) 383
and compare its result with those of total data The averaged normalized σ are 103 and 384
109 and r are 091 and 090 for Weibull and Gamma distributions respectively 385
suggesting that Weibull distribution performs slightly better than Gamma distribution 386
for the four HSD types in the data group of S lt 2 and K lt 6 whereas the opposite is true 387
for all data This conclusion is further substantiated by comparison of RED values for the 388
four type of precipitation (Fig7) which shows that Lognormal has the largest RED 389
Gamma the smallest and Weibull in between for four types of precipitations in all data 390
whereas Weibull (Lognormal) has smallest (largest) RED values when S lt 2 and K lt 6 It 391
can be inferred for data group of S gt 2 and k gt 6 Gamma distribution performs better 392
19
Further comparison between different precipitation types shows these functions all 393
performs better for raindrop size distributions and mixed-phase than graupel and 394
snowflake size distributions The RED for snowflakes is largest among the four types 395
The performance of Gamma is better for describing solid HSDs of all data but Weibull 396
distribution is better when S lt 2 and K lt 6 397
5 Conclusion 398
The combined measurements collected during a field experiment conducted at the 399
Haituo Mountain site using PARSIVEL disdrometer millimeter wavelength cloud radar 400
and microscope photography are analyzed to classify the precipitation hydrometeor 401
types examine the dependence of fall velocity on hydrometeor size for different 402
hydrometeor types and determine the best distribution functions to describe the 403
hydrometeor size distributions of different types 404
Analysis of the PARSIVEL-measured fall velocities show that on average the 405
dependence of fall velocity on hydrometeor size largely follow their corresponding 406
terminal velocity curves for raindrops graupels and snowflakes respectively suggesting 407
that such measurements are useful to identify the hydrometeor types The associated 408
microscope photos and cloud radar observations support the classification of 409
hydrometeor types based on the PARSIVEL-observed fall velocities Furthermore there 410
are velocity spreads in fall velocity across hydrometeor sizes for all hydrometeors and 411
the spreads for the solid hydrometeors could cause by hydrometeor type turbulence or 412
updraftdowndraft and instrument measured principle The coexistence of various 413
types of hydrometeors likely induces additional spread of fall velocity for given 414
20
hydrometeor sizes such as mixed precipitation Meanwhile complex microphysical 415
processes in cold precipitation such as riming aggregation breakup and collision and 416
coalescence influence fall velocity which likely induce larger spread of fall velocity Last 417
but not the least the disdrometer may suffer from instrumental errors due to the 418
internally assumed relationship between horizontal and vertical particle dimensions 419
Comparison of the type-averaged hydrometeor size distributions shows that the 420
mixed precipitation has more small hydrometeors with D lt 15 mm than others 421
whereas the snowflake precipitation has the least number of small hydrometeors 422
among the four types On the contrary the snowflake precipitation has more large 423
hydrometeors with D between 3 mm and 11 mm 424
The commonly used size distribution functions (Gamma Weibull and Lognormal) 425
are further examined to determine the most adequate function to describe the size 426
distribution measurements for all the hydrometeor types by use of an approach based 427
on the relationship between skewness (S) and kurtosis (K) Taylor diagram and RED are 428
further introduced to assess the performance of different size distribution functions 429
against measurements It is shown that the HSDs for the four types can all be well 430
described statistically by the Gamma and Weibull distribution but Lognormal 431
Exponential and Gaussian are not fit to describe HSDs Gamma and Weibull distribution 432
describe raindrop and mixed-phase size distribution better than snowflake and graupel 433
size distribution and their performances are worst for snowflake It may due to graupel 434
and snowflake precipitation have more big particles When S less than 2 and K less than 435
6 Weibull distribution performs better than Gamma distribution to describe HSDs but 436
21
Gamma distribution performs better for total data 437
A few points are noteworthy First although this study demonstrates the great 438
potential of combining simultaneous disdrometer measurements of particle fall velocity 439
and size distributions microscopic photography and cloud radar to address the 440
challenges facing solid precipitation the data are limited More research is needed to 441
discern such effects on the results presented here Second as the observations show 442
that in addition to sizes there are many other factors (eg hydrometeor type 443
microphysical processes turbulence and measuring principle) that can potentially 444
influence particle fall velocity as well More comprehensive research is needed to 445
further discern and separate these factors Finally the combined use of S-K diagram 446
Taylor diagram and relative Euclidean distance appears to be a powerful tool for 447
identifying the best function used to describe the HSDs and quantify the differences 448
between different precipitation types More research is in order along this direction 449
Acknowledgements 450
This study is mainly supported by the Chinese National Science Foundation under Grant 451
No 41675138 and National Key RampD Program of China (2017YFC0209604) It is partly 452
supported by Beijing National Science Foundation (8172023) the US Department 453
Energys Atmospheric System Research (ASR) Program (Liu and Jia at BNL) Lu is 454
supported by the Natural Science Foundation of Jiangsu Province (BK20160041) The 455
observation data are archived at a specialized supercomputer at Beijing Meteorology 456
Information Center (ftp10224592) which are available from the corresponding 457
author upon request The authors also thank Beijing weather modification office for 458
their support during the field experiment 459
Reference 460
22
Agosta CC Fettweis XX Datta RR 2015 Evaluation of the CMIP5 models in the 461
aim of regional modelling of the Antarctic surface mass balance Cryosphere 9 2311ndash462
2321 httpdxdoiorg105194tc-9-2311-2015 463
Barthazy E and R Schefold 2006 Fall velocity of snowflakes of different riming degree 464
and crystal types Atmos Res 82(1) 391-398 httpsdoiorg101016jatmosres 465
200512009 466
Battaglia A Rustemeier E Tokay A et al 2010 PARSIVEL snow observations a critical 467
assessment J Atmos Oceanic Technol 27(2) 333-344 doi 1011752009jtecha13321 468
Boumlhm H P 1989 A General Equation for the Terminal Fall Speed of Solid Hydrometeors 469
J Atmos Sci 46(15) 2419-2427 httpsdoiorg1011751520-0469(1989)046 lt2419A 470
GEFTTgt20CO2 471
Boudala F S G A Isaac et al 2014 Comparisons of Snowfall Measurements in 472
Complex Terrain Made During the 2010 Winter Olympics in Vancouver Pure and 473
Applied Geophysics 171(1) 113-127 474
Chen B W Hu and J Pu 2011 Characteristics of the raindrop size distribution for 475
freezing precipitation observed in southern China J Geophys Res 116 D06201 476
doi1010292010JD015305 477
Chen B Z Hu L Liu and G Zhang (2017) Raindrop Size Distribution Measurements at 478
4500m on the Tibetan Plateau during TIPEX-III J Geophys Res 122 11092-11106 479
doiorg10100 22017JD027233 480
23
Cugerone K and C De Michele 2017 Investigating raindrop size distributions in the 481
(L-)skewness-(L-)kurtosis plane Quart J Roy Meteor Soc 143(704) 1303-1312 482
httpsdoiorg101002qj3005 483
Donnadieu G 1980 Comparison of results obtained with the VIDIAZ spectro 484
pluviometer and the JossndashWaldvogel rainfall disdrometer in a ldquorain of a thundery typerdquo 485
J Appl Meteor 19 593ndash597 486
Feingold G and Levin Z 1986 The lognormal fit to raindrop spectra from frontal 487
convective clouds in Israel J Clim Appl Meteorol 25 1346ndash1363 488
httpsdoiorg1011751520-0450(1986)025lt1346tlftrsgt20CO2 489
Field P R A J Heymsfield and A Bansemer 2007 Snow Size Distribution 490
Parameterization for Midlatitude and Tropical Ice Clouds J Atmos Sci 64(12) 491
4346-4365 httpsdoiorg1011752007JAS23441 492
Garrett T J and S E Yuter 2014 Observed influence of riming temperature and 493
turbulence on the fallspeed of solid precipitation Geophysical Research Letters 41(18) 494
6515ndash6522 495
Geresdi I N Sarkadi and G Thompson 2014 Effect of the accretion by water drops 496
on the melting of snowflakes Atmos Res 149 96-110 497
Gunn R and G D Kinzer 1949 The terminal velocity of fall for water drops in stagnant 498
air J Meteor 6 243-248 httpsdoiorg1011751520-0469(1949)006lt0243TTVOFFgt 499
20CO2 500
24
Heymsfield A J and C D Westbrook 2010 Advances in the Estimation of Ice Particle 501
Fall Speeds Using Laboratory and Field Measurements J Atmos Sci 67(8) 2469-2482 502
httpsdoiorg1011752010JAS33791 503
Huang G-J C Kleinkort V N Bringi and B M Notaroš 2017 Winter precipitation 504
particle size distribution measurement by Multi-Angle Snowflake Camera Atmos Res 505
198 81-96 506
Intergovernmental Panel on Climate Change (IPCC) 2001 Climate Change 2001 The 507
Scientific Basis Contribution of Working Group I to the Third Assessment Report of the 508
Intergovernmental Panel on Climate Change edited by J T Houghton et al 881 pp 509
Cambridge Univ Press New York 510
Ishizaka M H Motoyoshi S Nakai T Shiina T Kumakura and K-i Muramoto 2013 A 511
New Method for Identifying the Main Type of Solid Hydrometeors Contributing to 512
Snowfall from Measured Size-Fall Speed Relationship Journal of the Meteorological 513
Society of Japan Ser II 91(6) 747-762 httpsdoiorg102151jmsj2013-602 514
Khvorostyanov V 2005 Fall Velocities of Hydrometeors in the Atmosphere 515
Refinements to a Continuous Analytical Power Law J Atmos Sci 62 4343-4357 516
httpsdoiorg101175JAS36221 517
Kikuchi K T Kameda K Higuchi and A Yamashita 2013 A global classification of 518
snow crystals ice crystals and solid precipitation based on observations from middle 519
latitudes to polar regions Atmos Res 132-133 460-472 520
Kneifel S A von Lerber J Tiira D Moisseev P Kollias and J Leinonen 2015 521
Observed relations between snowfall microphysics and triple-frequency radar 522
25
measurements J Geophys Res Atmos 120(12) 6034-6055 523
httpsdoi1010022015JD023156 524
Kubicek A and P K Wang 2012 A numerical study of the flow fields around a typical 525
conical graupel falling at various inclination angles Atmos Res 118 15ndash26 526
httpsdoi101016jatmosres201206001 527
Larsen M L A B Kostinski and A R Jameson (2014) Further evidence for 528
superterminal raindrops Geophys Res Lett 41(19) 6914-6918 529
Lee JE SH Jung H M Park S Kwon P L Lin and G W Lee 2015 Classification of 530
Precipitation Types Using Fall Velocity Diameter Relationships from 2D-Video 531
Distrometer Measurements Advances in Atmospheric Sciences (09) 532
Lin Y L J Donner and B A Colle 2010 Parameterization of riming intensity and its 533
impact on ice fall speed using arm data Mon Weather Rev 139(3) 1036ndash1047 534
httpsdoi1011752010MWR32991 535
Liu Y G 1992 Skewness and kurtosis of measured raindrop size distributions Atmos 536
Environ 26A 2713-2716 httpsdoiorg1010160960-1686(92)90005-6 537
Liu Y G 1993 Statistical theory of the Marshall-Parmer distribution of raindrops 538
Atmos Environ 27A 15-19 httpsdoiorg1010160960-1686(93)90066-8 539
Liu Y G and F Liu 1994 On the description of aerosol particle size distribution Atmos 540
Res 31(1-3) 187-198 httpsdoiorg1010160169-8095(94)90043-4 541
Liu Y G L You W Yang F Liu 1995 On the size distribution of cloud droplets Atmos 542
Res 35 (2-4) 201-216 httpsdoiorg1010160169-8095(94)00019-A 543
Locatelli J D and P V Hobbs 1974 Fall speeds and masses of solid precipitation 544
26
particles J Geophys Res 79(15) 2185-2197 httpsdoi101029JC079i015p02185 545
Loumlffler-Mang M and J Joss 2000 An optical disdrometer for measuring size and 546
velocity of hydrometeors J Atmos Oceanic Technol 17 130-139 547
httpsdoiorg1011751520-0426(2000)017lt0130AODFMSgt20CO2 548
Loumlffler-Mang M and U Blahak 2001 Estimation of the Equivalent Radar Reflectivity 549
Factor from Measured Snow Size Spectra J Clim Appl Meteorol 40(4) 843-849 550
httpsdoiorg1011751520-0450(2001)040lt0843EOTERRgt20CO2 551
Matrosov S Y 2007 Modeling Backscatter Properties of Snowfall at Millimeter 552
Wavelengths J Atmos Sci 64(5) 1727-1736 httpsdoiorg101175JAS39041 553
Mitchell D L 1996 Use of mass- and area-dimensional power laws for determining 554
precipitation particle terminal velocities J Atmos Sci 53 1710-1723 555
httpsdoiorg1011751520-0469(1996)053lt1710UOMAADgt20CO2 556
Montero-Martiacutenez G A B Kostinski R A Shaw and F Garciacutea-Garciacutea 2009 Do all 557
raindrops fall at terminal speed Geophys Res Lett 36 L11818 558
httpsdoiorg1010292008GL037111 559
Niu S X Jia J Sang X Liu C Lu and Y Liu 2010 Distributions of raindrop sizes and 560
fall velocities in a semiarid plateau climate Convective vs stratiform rains J Appl 561
Meteorol Climatol 49 632ndash645 httpsdoi1011752009JAMC22081 562
Nurzyńska K M Kubo and K-i Muramoto 2012 Texture operator for snow particle 563
classification into snowflake and graupel Atmos Res 118 121-132 564
Oue M M R Kumjian Y Lu J Verlinde K Aydin and E E Clothiaux 2015 Linear 565
27
Depolarization Ratios of columnar ice crystals in a deep precipitating system over the 566
Arctic observed by Zenith-Pointing Ka-Band Doppler radar J Clim Appl Meteorol 567
54(5) 1060-1068 httpsdoiorg101175JAMC-D-15-00121 568
Pruppacher H R and J D Klett 1998 Microphysics of clouds and precipitation Kluwer 569
Academic 954 pp 570
Rasmussen R B Baker et al 2012 How well are we measuring snow the 571
NOAAFAANCAR winter precipitation test bed Bull Amer Meteor Soc 93(6) 811-829 572
httpsdoiorg101175BAMS-D-11-000521 573
Reisner J R M Rasmussen and R T Bruintjes 1998 Explicit forecasting of 574
supercooled liquid water in winter storms using the MM5 mesoscale model Q J R 575
Meteorol Soc 124 1071ndash1107 httpsdoi101256smsqj54803 576
Rosenfeld D and Ulbrich C W 2003 Cloud microphysical properties processes and 577
rainfall estimation opportunities Meteorol Monogr 30 237-237 578
httpsdoiorg101175 0065-9401(2003)030lt0237cmppargt20CO2 579
Schaefer V J 1956 The preparation of snow crystal replicas-VI Weatherwsie 9 580
132-135 581
Souverijns N A Gossart S Lhermitte I V Gorodetskaya S Kneifel M Maahn F L 582
Bliven and N P M van Lipzig (2017) Estimating radar reflectivity - Snowfall rate 583
relationships and their uncertainties over Antarctica by combining disdrometer and 584
radar observations Atmos Res 196 211-223 585
Taylor K E 2001 Summarizing multiple aspects of model performance in a single 586
diagram J Geophys Res 106 7183ndash7192 httpsdoi1010292000JD900719 587
28
Tokay A and D A Short 1996 Evidence from tropical raindrop spectra of the origin of 588
rain from stratiform versus convective clouds J Appl Meteor 35 355ndash371 589
Tokay A and D Atlas 1999 Rainfall microphysics and radar properties analysis 590
methods for drop size spectra J Appl Meteor 37 912-923 591
httpsdoiorg1011751520-0450(1998)037lt0912RMARPAgt20CO2 592
Tokay A D B Wolff et al 2014 Evaluation of the New version of the laser-optical 593
disdrometer OTT Parsivel2 J Atmos Oceanic Technol 31(6) 1276-1288 594
httpsdoiorg101175JTECH-D-13-001741 595
Ulbrich C W 1983 Natural variations in the analytical form of the raindrop size 596
distribution J Appl Meteor 5 1764-1775 597
Wen G H Xiao H Yang Y Bi and W Xu 2017 Characteristics of summer and winter 598
precipitation over northern China Atmos Res 197 390-406 599
Wu W Y Liu and A K Betts 2012 Observationally based evaluation of NWP 600
reanalyses in modeling cloud properties over the Southern Great Plains J Geophys 601
Res 117 D12202 httpsdoi1010292011JD016971 602
Yuter S E D E Kingsmill L B Nance and M Loumlffler-Mang 2006 Observations of 603
precipitation size and fall velocity characteristics within coexisting rain and wet snow J 604
Appl Meteor Climatol 45 1450ndash1464 doi httpsdoiorg101175JAM24061 605
Zhang P C and B Y Du 2000 Radar Meteorology China Meteorological Press 511pp 606
(in Chinese) 607
608
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
12
distributions of hydrometeors If there is only one kind particle the high concentration 242
would along its ideal terminal velocity very well just like the raindrop possible 243
distribution (Niu et al 2010) The concentration of mixed precipitation in Fig 2d does 244
not along any singe ideal terminal velocity further improved there are more than one 245
kind of hydrometers Coexistence of different types of hydrometeors induces larger 246
spread of fall velocities Second different degrees of riming and aggregating may affect 247
the results Densely rimed particles fall faster than unrimed particles with the same 248
maximum dimension aggregated snowflakes generally fall faster than their component 249
crystals (Barthazy and Schefold 2006 Garrett and Yuter 2014 Locatelli and Hobbs 250
1974) Third solid hydrometeors more likely occur breakup aggregation collision and 251
coalescence processes because of the large range of speeds According to prior 252
research of raindrop breakup and coalescence would lead to the ldquohigher-than-terminal 253
velocityrdquo fall velocity for small drops but ldquolower-than-terminal velocityrdquo fall velocity for 254
large drops (Niu et al 2010 Montero-Martiacutenez et al 2009 Larsen et al 2014) Similar 255
results are expected for the fall velocity of solid hydrometeors Last but not the least 256
the disdrometer may suffer from instrumental errors due to the internally assumed 257
relationship between horizontal and vertical particle dimensions likely resulting in a 258
wider spreads of fall velocities for the graupel and snowflakes as compared to the 259
raindrop counterpart as discussed in Section 2 Although the instrument error is an 260
important factor that should be considered in velocity spread as shown in Fig2b the 261
instrument error could not cause that large velocity spread The possible distributions 262
of fall velocities are the combine effects of physical and instrument principle 263
13
Further support for the possible instrumental uncertainty is from the cloud radar 264
observations Fig 3 shows the cloud reflectivity and linear depolarization ratio (LDR) in 265
lower level (less than 08 km) for the graupel snowflake and mixed-phased 266
precipitations respectively The LDR is a valuable observable in identifying the 267
hydrometeor types (Oue et al 2015) As shown in Fig 3a the cloud top height of 268
graupel precipitation was up to 7km during 1900 to 2050 Beijng Time (BT) which was 269
highest among the three events The high cloud top implies stronger updraft and 270
turbulence which further induces a larger fall velocity spread The LDR value was the 271
smallest among the three events indicating that the hydrometeors were close to 272
spherical consistent to the surface observations The cloud top height of snowflake 273
precipitation was up to 35 km (Fig 3c) which was the lowest among the three types of 274
precipitations implying weakest updraft and turbulence Notably although the 275
snowflake types are more complex than those of graupels the velocity spread was not 276
as large as that of the graupel type likely because of the weakest updraft and 277
turbulence The LDR was relatively larger consistent with the surface snowflake 278
observations (Fig 3d) The cloud top height of mixed-phase precipitation was up to 45 279
km (Fig 3e) and the LDR in lower level was largest among the three types of 280
precipitations owing to coexistence of raindrops graupels and snowflakes (Fig 3f) 281
4 Hydrometeor Size Distributions 282
a Comparison of HSDs between Different Types 283
There were four representative types of precipitations during this field experiment 284
providing us a unique opportunity to examine the HSD differences between the four 285
14
types of hydrometeors The sample numbers mean maximum dimensions and number 286
concentrations for each kind of HSDs are given in Table 2 Figure 4 is the averaged 287
distribution of all measured HSDs of 4 kinds As shown in Figure 4 on average the 288
mixed-phased precipitation tends to have most small size hydrometeors with D lt 15 289
mm while snowflake precipitation has the least small hydrometeors among the four 290
types The snowflake precipitation has more large size hydrometeors ie 3 mm lt D lt 11 291
mm Graupel size distribution tends to have two peeks around 13 mm and 26 mm The 292
mean maximum dimension is largest for snowflake (126 mm) and smallest for the 293
mixed HSD due to many small particles Similar results were found in precipitation 294
occurring in the Cascade and Rocky Mountains (Yuter et al 2006) The PARSIVEL 295
disdrometer doesnrsquot provide reliable data for small drops lower than 05 mm and tends to 296
underestimate small drops so the relatively low concentrations of small drops likely resulted 297
from the instrumentrsquos shortcomings (Tokay et al 2013 and Chen et al 2017) 298
b Evaluation of Distribution Functions for Describing HSDs 299
Over the last few decades great efforts have been devoted to finding the 300
appropriate analytical functions for describing the HSD because of its wide applications 301
in many areas including remote sensing and parameterization of precipitation (Chen et 302
al 2017) The two distribution functions mostly used up to now are the Lognormal 303
(Feingold and Levin 1986 Rosenfeld and Ulbrich 2003) and the Gamma (Ulbrich 1983) 304
distributions The Gamma distribution has been proposed as a first order generalization 305
of the Exponential distribution when μ equals 0 (Table 4) Weibull distribution is 306
another function used to describe size distributions of raindrops and cloud droplets (Liu 307
15
and Liu 1994 Liu et al 1995) Nevertheless the question as to which functions are 308
more adequate to describe HSDs of solid hydrometeors have been rarely investigated 309
systematically and quantitatively Thus the objective of this section is to examine the 310
most adequate distribution function used to describe HSDs 311
Considering size distributions of raindrops cloud droplets and aerosol particles are 312
the end results of many (stochastic) complex processes Liu (1992 1993 1994 and 313
1995) proposed a statistical method based on the relationships between the skewness 314
(S) and kurtosis (K) derived from an ensemble of particle size distribution 315
measurements and from those commonly used size distribution functions Cugerone 316
and Michele (2017) also used a similar approach based on the S-K relationships to study 317
raindrop size distributions Unlike the conventional curve-fitting of individual size 318
distributions this approach applies to an ensemble of size distribution measurements 319
and identifies the most appropriate statistical distribution pattern Here we apply this 320
approach to investigate if the statistical pattern of the HSDs of four precipitation types 321
follows the Exponential Gaussian Gamma Weibull and Lognormal distributions (Table 322
4) and if there are any pattern differences between them Briefly S and K of a HSD are 323
calculated from the corresponding HSD with the following two equations 324
23
2
3
t
iii
t
iii
dDN
)(Dn)D(D
dDN
)(Dn)D(D
S
minus
minus
=
(2) 325
32
2
4
minus
minus
minus
=
dDN
)(Dn)D(D
dDN
)(Dn)D(D
K
t
iii
t
iii
(3) 326
16
where Di is the central diameter of the i-th bin ni is the number concentration of the 327
i-th bin and Nt is total number concentration Note that each individual HSD can be 328
used to obtain a pair of S and K which is shown as a dot in Figure 5 Also noteworthy is 329
that the SndashK relationships for the families of Gamma Weibull and Lognormal are 330
described by known analytical functions (Liu 1993 1994 and 1995 Cugerone and 331
Michele 2017) represented by theoretical curves in Figure 5 The Exponential and 332
Gaussian distributions are represented by single points on the S-K diagram (S=2 and K=6 333
for Exponential) and (S=0 and K=0 for Gaussian) respectively Thus by comparing the 334
measured S and K values (points) with the known theoretical curves one can determine 335
the most proper function used to describe HSDs 336
Figure 5 shows the scatter plots of observed SndashK pairs calculated from the HSD 337
measurements for raindrop graupel snowflake mixed-phase precipitations Also 338
shown as comparison are the theoretical curves corresponding to the analytical HSD 339
functions A few points are evident First despite some occasional departures most of 340
the points fall near the theoretical lines of Gamma and Weibull distributions suggesting 341
that the HSD patterns for all the four types of precipitations well follow the Gamma and 342
Weibull distributions statistically Second HSDs of raindrops and mixed hydrometeors 343
are better described by Gamma and Weibull distribution than graupels and snowflakes 344
Third the S and K do not cluster around points (2 6) and (0 0) suggesting that the 345
Gaussian and Exponential distribution are not appropriate for describing HSDs 346
especially Gaussian distribution 347
To further evaluate the overall performance of the different distribution functions 348
17
we employ the widely used technique of Taylor diagram (Taylor 2001) and ldquoRelative 349
Euclidean Distancerdquo (RED) (Wu et al 2012) as a supplement to the Taylor diagram The 350
Taylor diagram has been widely used to visualize the statistical differences between 351
model results and observations in evaluation of model performance against 352
measurements or other benchmarks (IPCC 2001) Correlation coefficient (r) standard 353
deviation (σ) and ldquocentered root-mean-square errorrdquo (RMSE hereafter) are used in 354
the Taylor diagram The RED is introduced to add the bias as well in a dimensionless 355
framework that allows for comparison between different physical quantities with 356
different units In this study we consider the S and K values derived from the 357
distribution functions as model results and evaluate them against those derived from 358
the HSD measurements Brieflythe expressions for calculating r and σ and RMSE are 359
shown below 360
119903 =1
119873sum (119872119899minus)(119874119899minus)119873119899=1
120590119872120590119900 (4) 361
119877119872119878119864 = 1
119873sum [(119872119899 minus ) minus (119874119899 minus )]2119873119899=1
12
(5) 362
120590119872 = [1
119873sum (119872119899 minus )119873119899=1 ]
12
(6) 363
1205900 = [1
119873sum (119874119899 minus )119873119899=1 ]
12
(7) 364
where M and O denote distribution function and observed variables The RED 365
expression is shown below 366
119877119864119863 = [(minus)
]2
+ [(120590119872minus120590119874)
120590119900]2
+ (1 minus 119903)212
( 8 ) 367
Equation (8) indicates that RED considers all the components of mean bias variations 368
and correlations in a dimensionless way the distribution function performance 369
degrades as RED increases from the perfect agreement with RED=0 370
18
In the Taylor diagrams shown in Fig 6 the cosine of azimuthal angle of each point 371
gives the r between the function-calculated and observed data The distance between 372
individual point and the reference point ldquoObsrdquo represents the RMSE normalized by the 373
amplitude of the observationally based variations As this distance approaches to zero 374
the function-calculated K and S approach to the observations Clearly the values of r 375
are around 097 for Gamma and Weibull r for Lognormal function is slightly smaller 376
(095) The normalized σ are much different for Lognormal Gamma and Weibull 377
distributions with averaged value being 057 0895 and 0785 respectively Therefore 378
the Lognormal distribution exhibits the worst performance for describing HSDs and 379
Gamma and Weibull distributions appear to perform much better (Fig 6a) 380
Noticing that S and K of Gamma and Weibull distributions are equal at the point of S 381
= 2 and K = 6 and have positive relationship (If S lt 2 then K lt 6 and if S gt 2 then k gt 6) In 382
this part we further separately examine the group of data with S lt 2 and K lt 6 (Fig 6b) 383
and compare its result with those of total data The averaged normalized σ are 103 and 384
109 and r are 091 and 090 for Weibull and Gamma distributions respectively 385
suggesting that Weibull distribution performs slightly better than Gamma distribution 386
for the four HSD types in the data group of S lt 2 and K lt 6 whereas the opposite is true 387
for all data This conclusion is further substantiated by comparison of RED values for the 388
four type of precipitation (Fig7) which shows that Lognormal has the largest RED 389
Gamma the smallest and Weibull in between for four types of precipitations in all data 390
whereas Weibull (Lognormal) has smallest (largest) RED values when S lt 2 and K lt 6 It 391
can be inferred for data group of S gt 2 and k gt 6 Gamma distribution performs better 392
19
Further comparison between different precipitation types shows these functions all 393
performs better for raindrop size distributions and mixed-phase than graupel and 394
snowflake size distributions The RED for snowflakes is largest among the four types 395
The performance of Gamma is better for describing solid HSDs of all data but Weibull 396
distribution is better when S lt 2 and K lt 6 397
5 Conclusion 398
The combined measurements collected during a field experiment conducted at the 399
Haituo Mountain site using PARSIVEL disdrometer millimeter wavelength cloud radar 400
and microscope photography are analyzed to classify the precipitation hydrometeor 401
types examine the dependence of fall velocity on hydrometeor size for different 402
hydrometeor types and determine the best distribution functions to describe the 403
hydrometeor size distributions of different types 404
Analysis of the PARSIVEL-measured fall velocities show that on average the 405
dependence of fall velocity on hydrometeor size largely follow their corresponding 406
terminal velocity curves for raindrops graupels and snowflakes respectively suggesting 407
that such measurements are useful to identify the hydrometeor types The associated 408
microscope photos and cloud radar observations support the classification of 409
hydrometeor types based on the PARSIVEL-observed fall velocities Furthermore there 410
are velocity spreads in fall velocity across hydrometeor sizes for all hydrometeors and 411
the spreads for the solid hydrometeors could cause by hydrometeor type turbulence or 412
updraftdowndraft and instrument measured principle The coexistence of various 413
types of hydrometeors likely induces additional spread of fall velocity for given 414
20
hydrometeor sizes such as mixed precipitation Meanwhile complex microphysical 415
processes in cold precipitation such as riming aggregation breakup and collision and 416
coalescence influence fall velocity which likely induce larger spread of fall velocity Last 417
but not the least the disdrometer may suffer from instrumental errors due to the 418
internally assumed relationship between horizontal and vertical particle dimensions 419
Comparison of the type-averaged hydrometeor size distributions shows that the 420
mixed precipitation has more small hydrometeors with D lt 15 mm than others 421
whereas the snowflake precipitation has the least number of small hydrometeors 422
among the four types On the contrary the snowflake precipitation has more large 423
hydrometeors with D between 3 mm and 11 mm 424
The commonly used size distribution functions (Gamma Weibull and Lognormal) 425
are further examined to determine the most adequate function to describe the size 426
distribution measurements for all the hydrometeor types by use of an approach based 427
on the relationship between skewness (S) and kurtosis (K) Taylor diagram and RED are 428
further introduced to assess the performance of different size distribution functions 429
against measurements It is shown that the HSDs for the four types can all be well 430
described statistically by the Gamma and Weibull distribution but Lognormal 431
Exponential and Gaussian are not fit to describe HSDs Gamma and Weibull distribution 432
describe raindrop and mixed-phase size distribution better than snowflake and graupel 433
size distribution and their performances are worst for snowflake It may due to graupel 434
and snowflake precipitation have more big particles When S less than 2 and K less than 435
6 Weibull distribution performs better than Gamma distribution to describe HSDs but 436
21
Gamma distribution performs better for total data 437
A few points are noteworthy First although this study demonstrates the great 438
potential of combining simultaneous disdrometer measurements of particle fall velocity 439
and size distributions microscopic photography and cloud radar to address the 440
challenges facing solid precipitation the data are limited More research is needed to 441
discern such effects on the results presented here Second as the observations show 442
that in addition to sizes there are many other factors (eg hydrometeor type 443
microphysical processes turbulence and measuring principle) that can potentially 444
influence particle fall velocity as well More comprehensive research is needed to 445
further discern and separate these factors Finally the combined use of S-K diagram 446
Taylor diagram and relative Euclidean distance appears to be a powerful tool for 447
identifying the best function used to describe the HSDs and quantify the differences 448
between different precipitation types More research is in order along this direction 449
Acknowledgements 450
This study is mainly supported by the Chinese National Science Foundation under Grant 451
No 41675138 and National Key RampD Program of China (2017YFC0209604) It is partly 452
supported by Beijing National Science Foundation (8172023) the US Department 453
Energys Atmospheric System Research (ASR) Program (Liu and Jia at BNL) Lu is 454
supported by the Natural Science Foundation of Jiangsu Province (BK20160041) The 455
observation data are archived at a specialized supercomputer at Beijing Meteorology 456
Information Center (ftp10224592) which are available from the corresponding 457
author upon request The authors also thank Beijing weather modification office for 458
their support during the field experiment 459
Reference 460
22
Agosta CC Fettweis XX Datta RR 2015 Evaluation of the CMIP5 models in the 461
aim of regional modelling of the Antarctic surface mass balance Cryosphere 9 2311ndash462
2321 httpdxdoiorg105194tc-9-2311-2015 463
Barthazy E and R Schefold 2006 Fall velocity of snowflakes of different riming degree 464
and crystal types Atmos Res 82(1) 391-398 httpsdoiorg101016jatmosres 465
200512009 466
Battaglia A Rustemeier E Tokay A et al 2010 PARSIVEL snow observations a critical 467
assessment J Atmos Oceanic Technol 27(2) 333-344 doi 1011752009jtecha13321 468
Boumlhm H P 1989 A General Equation for the Terminal Fall Speed of Solid Hydrometeors 469
J Atmos Sci 46(15) 2419-2427 httpsdoiorg1011751520-0469(1989)046 lt2419A 470
GEFTTgt20CO2 471
Boudala F S G A Isaac et al 2014 Comparisons of Snowfall Measurements in 472
Complex Terrain Made During the 2010 Winter Olympics in Vancouver Pure and 473
Applied Geophysics 171(1) 113-127 474
Chen B W Hu and J Pu 2011 Characteristics of the raindrop size distribution for 475
freezing precipitation observed in southern China J Geophys Res 116 D06201 476
doi1010292010JD015305 477
Chen B Z Hu L Liu and G Zhang (2017) Raindrop Size Distribution Measurements at 478
4500m on the Tibetan Plateau during TIPEX-III J Geophys Res 122 11092-11106 479
doiorg10100 22017JD027233 480
23
Cugerone K and C De Michele 2017 Investigating raindrop size distributions in the 481
(L-)skewness-(L-)kurtosis plane Quart J Roy Meteor Soc 143(704) 1303-1312 482
httpsdoiorg101002qj3005 483
Donnadieu G 1980 Comparison of results obtained with the VIDIAZ spectro 484
pluviometer and the JossndashWaldvogel rainfall disdrometer in a ldquorain of a thundery typerdquo 485
J Appl Meteor 19 593ndash597 486
Feingold G and Levin Z 1986 The lognormal fit to raindrop spectra from frontal 487
convective clouds in Israel J Clim Appl Meteorol 25 1346ndash1363 488
httpsdoiorg1011751520-0450(1986)025lt1346tlftrsgt20CO2 489
Field P R A J Heymsfield and A Bansemer 2007 Snow Size Distribution 490
Parameterization for Midlatitude and Tropical Ice Clouds J Atmos Sci 64(12) 491
4346-4365 httpsdoiorg1011752007JAS23441 492
Garrett T J and S E Yuter 2014 Observed influence of riming temperature and 493
turbulence on the fallspeed of solid precipitation Geophysical Research Letters 41(18) 494
6515ndash6522 495
Geresdi I N Sarkadi and G Thompson 2014 Effect of the accretion by water drops 496
on the melting of snowflakes Atmos Res 149 96-110 497
Gunn R and G D Kinzer 1949 The terminal velocity of fall for water drops in stagnant 498
air J Meteor 6 243-248 httpsdoiorg1011751520-0469(1949)006lt0243TTVOFFgt 499
20CO2 500
24
Heymsfield A J and C D Westbrook 2010 Advances in the Estimation of Ice Particle 501
Fall Speeds Using Laboratory and Field Measurements J Atmos Sci 67(8) 2469-2482 502
httpsdoiorg1011752010JAS33791 503
Huang G-J C Kleinkort V N Bringi and B M Notaroš 2017 Winter precipitation 504
particle size distribution measurement by Multi-Angle Snowflake Camera Atmos Res 505
198 81-96 506
Intergovernmental Panel on Climate Change (IPCC) 2001 Climate Change 2001 The 507
Scientific Basis Contribution of Working Group I to the Third Assessment Report of the 508
Intergovernmental Panel on Climate Change edited by J T Houghton et al 881 pp 509
Cambridge Univ Press New York 510
Ishizaka M H Motoyoshi S Nakai T Shiina T Kumakura and K-i Muramoto 2013 A 511
New Method for Identifying the Main Type of Solid Hydrometeors Contributing to 512
Snowfall from Measured Size-Fall Speed Relationship Journal of the Meteorological 513
Society of Japan Ser II 91(6) 747-762 httpsdoiorg102151jmsj2013-602 514
Khvorostyanov V 2005 Fall Velocities of Hydrometeors in the Atmosphere 515
Refinements to a Continuous Analytical Power Law J Atmos Sci 62 4343-4357 516
httpsdoiorg101175JAS36221 517
Kikuchi K T Kameda K Higuchi and A Yamashita 2013 A global classification of 518
snow crystals ice crystals and solid precipitation based on observations from middle 519
latitudes to polar regions Atmos Res 132-133 460-472 520
Kneifel S A von Lerber J Tiira D Moisseev P Kollias and J Leinonen 2015 521
Observed relations between snowfall microphysics and triple-frequency radar 522
25
measurements J Geophys Res Atmos 120(12) 6034-6055 523
httpsdoi1010022015JD023156 524
Kubicek A and P K Wang 2012 A numerical study of the flow fields around a typical 525
conical graupel falling at various inclination angles Atmos Res 118 15ndash26 526
httpsdoi101016jatmosres201206001 527
Larsen M L A B Kostinski and A R Jameson (2014) Further evidence for 528
superterminal raindrops Geophys Res Lett 41(19) 6914-6918 529
Lee JE SH Jung H M Park S Kwon P L Lin and G W Lee 2015 Classification of 530
Precipitation Types Using Fall Velocity Diameter Relationships from 2D-Video 531
Distrometer Measurements Advances in Atmospheric Sciences (09) 532
Lin Y L J Donner and B A Colle 2010 Parameterization of riming intensity and its 533
impact on ice fall speed using arm data Mon Weather Rev 139(3) 1036ndash1047 534
httpsdoi1011752010MWR32991 535
Liu Y G 1992 Skewness and kurtosis of measured raindrop size distributions Atmos 536
Environ 26A 2713-2716 httpsdoiorg1010160960-1686(92)90005-6 537
Liu Y G 1993 Statistical theory of the Marshall-Parmer distribution of raindrops 538
Atmos Environ 27A 15-19 httpsdoiorg1010160960-1686(93)90066-8 539
Liu Y G and F Liu 1994 On the description of aerosol particle size distribution Atmos 540
Res 31(1-3) 187-198 httpsdoiorg1010160169-8095(94)90043-4 541
Liu Y G L You W Yang F Liu 1995 On the size distribution of cloud droplets Atmos 542
Res 35 (2-4) 201-216 httpsdoiorg1010160169-8095(94)00019-A 543
Locatelli J D and P V Hobbs 1974 Fall speeds and masses of solid precipitation 544
26
particles J Geophys Res 79(15) 2185-2197 httpsdoi101029JC079i015p02185 545
Loumlffler-Mang M and J Joss 2000 An optical disdrometer for measuring size and 546
velocity of hydrometeors J Atmos Oceanic Technol 17 130-139 547
httpsdoiorg1011751520-0426(2000)017lt0130AODFMSgt20CO2 548
Loumlffler-Mang M and U Blahak 2001 Estimation of the Equivalent Radar Reflectivity 549
Factor from Measured Snow Size Spectra J Clim Appl Meteorol 40(4) 843-849 550
httpsdoiorg1011751520-0450(2001)040lt0843EOTERRgt20CO2 551
Matrosov S Y 2007 Modeling Backscatter Properties of Snowfall at Millimeter 552
Wavelengths J Atmos Sci 64(5) 1727-1736 httpsdoiorg101175JAS39041 553
Mitchell D L 1996 Use of mass- and area-dimensional power laws for determining 554
precipitation particle terminal velocities J Atmos Sci 53 1710-1723 555
httpsdoiorg1011751520-0469(1996)053lt1710UOMAADgt20CO2 556
Montero-Martiacutenez G A B Kostinski R A Shaw and F Garciacutea-Garciacutea 2009 Do all 557
raindrops fall at terminal speed Geophys Res Lett 36 L11818 558
httpsdoiorg1010292008GL037111 559
Niu S X Jia J Sang X Liu C Lu and Y Liu 2010 Distributions of raindrop sizes and 560
fall velocities in a semiarid plateau climate Convective vs stratiform rains J Appl 561
Meteorol Climatol 49 632ndash645 httpsdoi1011752009JAMC22081 562
Nurzyńska K M Kubo and K-i Muramoto 2012 Texture operator for snow particle 563
classification into snowflake and graupel Atmos Res 118 121-132 564
Oue M M R Kumjian Y Lu J Verlinde K Aydin and E E Clothiaux 2015 Linear 565
27
Depolarization Ratios of columnar ice crystals in a deep precipitating system over the 566
Arctic observed by Zenith-Pointing Ka-Band Doppler radar J Clim Appl Meteorol 567
54(5) 1060-1068 httpsdoiorg101175JAMC-D-15-00121 568
Pruppacher H R and J D Klett 1998 Microphysics of clouds and precipitation Kluwer 569
Academic 954 pp 570
Rasmussen R B Baker et al 2012 How well are we measuring snow the 571
NOAAFAANCAR winter precipitation test bed Bull Amer Meteor Soc 93(6) 811-829 572
httpsdoiorg101175BAMS-D-11-000521 573
Reisner J R M Rasmussen and R T Bruintjes 1998 Explicit forecasting of 574
supercooled liquid water in winter storms using the MM5 mesoscale model Q J R 575
Meteorol Soc 124 1071ndash1107 httpsdoi101256smsqj54803 576
Rosenfeld D and Ulbrich C W 2003 Cloud microphysical properties processes and 577
rainfall estimation opportunities Meteorol Monogr 30 237-237 578
httpsdoiorg101175 0065-9401(2003)030lt0237cmppargt20CO2 579
Schaefer V J 1956 The preparation of snow crystal replicas-VI Weatherwsie 9 580
132-135 581
Souverijns N A Gossart S Lhermitte I V Gorodetskaya S Kneifel M Maahn F L 582
Bliven and N P M van Lipzig (2017) Estimating radar reflectivity - Snowfall rate 583
relationships and their uncertainties over Antarctica by combining disdrometer and 584
radar observations Atmos Res 196 211-223 585
Taylor K E 2001 Summarizing multiple aspects of model performance in a single 586
diagram J Geophys Res 106 7183ndash7192 httpsdoi1010292000JD900719 587
28
Tokay A and D A Short 1996 Evidence from tropical raindrop spectra of the origin of 588
rain from stratiform versus convective clouds J Appl Meteor 35 355ndash371 589
Tokay A and D Atlas 1999 Rainfall microphysics and radar properties analysis 590
methods for drop size spectra J Appl Meteor 37 912-923 591
httpsdoiorg1011751520-0450(1998)037lt0912RMARPAgt20CO2 592
Tokay A D B Wolff et al 2014 Evaluation of the New version of the laser-optical 593
disdrometer OTT Parsivel2 J Atmos Oceanic Technol 31(6) 1276-1288 594
httpsdoiorg101175JTECH-D-13-001741 595
Ulbrich C W 1983 Natural variations in the analytical form of the raindrop size 596
distribution J Appl Meteor 5 1764-1775 597
Wen G H Xiao H Yang Y Bi and W Xu 2017 Characteristics of summer and winter 598
precipitation over northern China Atmos Res 197 390-406 599
Wu W Y Liu and A K Betts 2012 Observationally based evaluation of NWP 600
reanalyses in modeling cloud properties over the Southern Great Plains J Geophys 601
Res 117 D12202 httpsdoi1010292011JD016971 602
Yuter S E D E Kingsmill L B Nance and M Loumlffler-Mang 2006 Observations of 603
precipitation size and fall velocity characteristics within coexisting rain and wet snow J 604
Appl Meteor Climatol 45 1450ndash1464 doi httpsdoiorg101175JAM24061 605
Zhang P C and B Y Du 2000 Radar Meteorology China Meteorological Press 511pp 606
(in Chinese) 607
608
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
13
Further support for the possible instrumental uncertainty is from the cloud radar 264
observations Fig 3 shows the cloud reflectivity and linear depolarization ratio (LDR) in 265
lower level (less than 08 km) for the graupel snowflake and mixed-phased 266
precipitations respectively The LDR is a valuable observable in identifying the 267
hydrometeor types (Oue et al 2015) As shown in Fig 3a the cloud top height of 268
graupel precipitation was up to 7km during 1900 to 2050 Beijng Time (BT) which was 269
highest among the three events The high cloud top implies stronger updraft and 270
turbulence which further induces a larger fall velocity spread The LDR value was the 271
smallest among the three events indicating that the hydrometeors were close to 272
spherical consistent to the surface observations The cloud top height of snowflake 273
precipitation was up to 35 km (Fig 3c) which was the lowest among the three types of 274
precipitations implying weakest updraft and turbulence Notably although the 275
snowflake types are more complex than those of graupels the velocity spread was not 276
as large as that of the graupel type likely because of the weakest updraft and 277
turbulence The LDR was relatively larger consistent with the surface snowflake 278
observations (Fig 3d) The cloud top height of mixed-phase precipitation was up to 45 279
km (Fig 3e) and the LDR in lower level was largest among the three types of 280
precipitations owing to coexistence of raindrops graupels and snowflakes (Fig 3f) 281
4 Hydrometeor Size Distributions 282
a Comparison of HSDs between Different Types 283
There were four representative types of precipitations during this field experiment 284
providing us a unique opportunity to examine the HSD differences between the four 285
14
types of hydrometeors The sample numbers mean maximum dimensions and number 286
concentrations for each kind of HSDs are given in Table 2 Figure 4 is the averaged 287
distribution of all measured HSDs of 4 kinds As shown in Figure 4 on average the 288
mixed-phased precipitation tends to have most small size hydrometeors with D lt 15 289
mm while snowflake precipitation has the least small hydrometeors among the four 290
types The snowflake precipitation has more large size hydrometeors ie 3 mm lt D lt 11 291
mm Graupel size distribution tends to have two peeks around 13 mm and 26 mm The 292
mean maximum dimension is largest for snowflake (126 mm) and smallest for the 293
mixed HSD due to many small particles Similar results were found in precipitation 294
occurring in the Cascade and Rocky Mountains (Yuter et al 2006) The PARSIVEL 295
disdrometer doesnrsquot provide reliable data for small drops lower than 05 mm and tends to 296
underestimate small drops so the relatively low concentrations of small drops likely resulted 297
from the instrumentrsquos shortcomings (Tokay et al 2013 and Chen et al 2017) 298
b Evaluation of Distribution Functions for Describing HSDs 299
Over the last few decades great efforts have been devoted to finding the 300
appropriate analytical functions for describing the HSD because of its wide applications 301
in many areas including remote sensing and parameterization of precipitation (Chen et 302
al 2017) The two distribution functions mostly used up to now are the Lognormal 303
(Feingold and Levin 1986 Rosenfeld and Ulbrich 2003) and the Gamma (Ulbrich 1983) 304
distributions The Gamma distribution has been proposed as a first order generalization 305
of the Exponential distribution when μ equals 0 (Table 4) Weibull distribution is 306
another function used to describe size distributions of raindrops and cloud droplets (Liu 307
15
and Liu 1994 Liu et al 1995) Nevertheless the question as to which functions are 308
more adequate to describe HSDs of solid hydrometeors have been rarely investigated 309
systematically and quantitatively Thus the objective of this section is to examine the 310
most adequate distribution function used to describe HSDs 311
Considering size distributions of raindrops cloud droplets and aerosol particles are 312
the end results of many (stochastic) complex processes Liu (1992 1993 1994 and 313
1995) proposed a statistical method based on the relationships between the skewness 314
(S) and kurtosis (K) derived from an ensemble of particle size distribution 315
measurements and from those commonly used size distribution functions Cugerone 316
and Michele (2017) also used a similar approach based on the S-K relationships to study 317
raindrop size distributions Unlike the conventional curve-fitting of individual size 318
distributions this approach applies to an ensemble of size distribution measurements 319
and identifies the most appropriate statistical distribution pattern Here we apply this 320
approach to investigate if the statistical pattern of the HSDs of four precipitation types 321
follows the Exponential Gaussian Gamma Weibull and Lognormal distributions (Table 322
4) and if there are any pattern differences between them Briefly S and K of a HSD are 323
calculated from the corresponding HSD with the following two equations 324
23
2
3
t
iii
t
iii
dDN
)(Dn)D(D
dDN
)(Dn)D(D
S
minus
minus
=
(2) 325
32
2
4
minus
minus
minus
=
dDN
)(Dn)D(D
dDN
)(Dn)D(D
K
t
iii
t
iii
(3) 326
16
where Di is the central diameter of the i-th bin ni is the number concentration of the 327
i-th bin and Nt is total number concentration Note that each individual HSD can be 328
used to obtain a pair of S and K which is shown as a dot in Figure 5 Also noteworthy is 329
that the SndashK relationships for the families of Gamma Weibull and Lognormal are 330
described by known analytical functions (Liu 1993 1994 and 1995 Cugerone and 331
Michele 2017) represented by theoretical curves in Figure 5 The Exponential and 332
Gaussian distributions are represented by single points on the S-K diagram (S=2 and K=6 333
for Exponential) and (S=0 and K=0 for Gaussian) respectively Thus by comparing the 334
measured S and K values (points) with the known theoretical curves one can determine 335
the most proper function used to describe HSDs 336
Figure 5 shows the scatter plots of observed SndashK pairs calculated from the HSD 337
measurements for raindrop graupel snowflake mixed-phase precipitations Also 338
shown as comparison are the theoretical curves corresponding to the analytical HSD 339
functions A few points are evident First despite some occasional departures most of 340
the points fall near the theoretical lines of Gamma and Weibull distributions suggesting 341
that the HSD patterns for all the four types of precipitations well follow the Gamma and 342
Weibull distributions statistically Second HSDs of raindrops and mixed hydrometeors 343
are better described by Gamma and Weibull distribution than graupels and snowflakes 344
Third the S and K do not cluster around points (2 6) and (0 0) suggesting that the 345
Gaussian and Exponential distribution are not appropriate for describing HSDs 346
especially Gaussian distribution 347
To further evaluate the overall performance of the different distribution functions 348
17
we employ the widely used technique of Taylor diagram (Taylor 2001) and ldquoRelative 349
Euclidean Distancerdquo (RED) (Wu et al 2012) as a supplement to the Taylor diagram The 350
Taylor diagram has been widely used to visualize the statistical differences between 351
model results and observations in evaluation of model performance against 352
measurements or other benchmarks (IPCC 2001) Correlation coefficient (r) standard 353
deviation (σ) and ldquocentered root-mean-square errorrdquo (RMSE hereafter) are used in 354
the Taylor diagram The RED is introduced to add the bias as well in a dimensionless 355
framework that allows for comparison between different physical quantities with 356
different units In this study we consider the S and K values derived from the 357
distribution functions as model results and evaluate them against those derived from 358
the HSD measurements Brieflythe expressions for calculating r and σ and RMSE are 359
shown below 360
119903 =1
119873sum (119872119899minus)(119874119899minus)119873119899=1
120590119872120590119900 (4) 361
119877119872119878119864 = 1
119873sum [(119872119899 minus ) minus (119874119899 minus )]2119873119899=1
12
(5) 362
120590119872 = [1
119873sum (119872119899 minus )119873119899=1 ]
12
(6) 363
1205900 = [1
119873sum (119874119899 minus )119873119899=1 ]
12
(7) 364
where M and O denote distribution function and observed variables The RED 365
expression is shown below 366
119877119864119863 = [(minus)
]2
+ [(120590119872minus120590119874)
120590119900]2
+ (1 minus 119903)212
( 8 ) 367
Equation (8) indicates that RED considers all the components of mean bias variations 368
and correlations in a dimensionless way the distribution function performance 369
degrades as RED increases from the perfect agreement with RED=0 370
18
In the Taylor diagrams shown in Fig 6 the cosine of azimuthal angle of each point 371
gives the r between the function-calculated and observed data The distance between 372
individual point and the reference point ldquoObsrdquo represents the RMSE normalized by the 373
amplitude of the observationally based variations As this distance approaches to zero 374
the function-calculated K and S approach to the observations Clearly the values of r 375
are around 097 for Gamma and Weibull r for Lognormal function is slightly smaller 376
(095) The normalized σ are much different for Lognormal Gamma and Weibull 377
distributions with averaged value being 057 0895 and 0785 respectively Therefore 378
the Lognormal distribution exhibits the worst performance for describing HSDs and 379
Gamma and Weibull distributions appear to perform much better (Fig 6a) 380
Noticing that S and K of Gamma and Weibull distributions are equal at the point of S 381
= 2 and K = 6 and have positive relationship (If S lt 2 then K lt 6 and if S gt 2 then k gt 6) In 382
this part we further separately examine the group of data with S lt 2 and K lt 6 (Fig 6b) 383
and compare its result with those of total data The averaged normalized σ are 103 and 384
109 and r are 091 and 090 for Weibull and Gamma distributions respectively 385
suggesting that Weibull distribution performs slightly better than Gamma distribution 386
for the four HSD types in the data group of S lt 2 and K lt 6 whereas the opposite is true 387
for all data This conclusion is further substantiated by comparison of RED values for the 388
four type of precipitation (Fig7) which shows that Lognormal has the largest RED 389
Gamma the smallest and Weibull in between for four types of precipitations in all data 390
whereas Weibull (Lognormal) has smallest (largest) RED values when S lt 2 and K lt 6 It 391
can be inferred for data group of S gt 2 and k gt 6 Gamma distribution performs better 392
19
Further comparison between different precipitation types shows these functions all 393
performs better for raindrop size distributions and mixed-phase than graupel and 394
snowflake size distributions The RED for snowflakes is largest among the four types 395
The performance of Gamma is better for describing solid HSDs of all data but Weibull 396
distribution is better when S lt 2 and K lt 6 397
5 Conclusion 398
The combined measurements collected during a field experiment conducted at the 399
Haituo Mountain site using PARSIVEL disdrometer millimeter wavelength cloud radar 400
and microscope photography are analyzed to classify the precipitation hydrometeor 401
types examine the dependence of fall velocity on hydrometeor size for different 402
hydrometeor types and determine the best distribution functions to describe the 403
hydrometeor size distributions of different types 404
Analysis of the PARSIVEL-measured fall velocities show that on average the 405
dependence of fall velocity on hydrometeor size largely follow their corresponding 406
terminal velocity curves for raindrops graupels and snowflakes respectively suggesting 407
that such measurements are useful to identify the hydrometeor types The associated 408
microscope photos and cloud radar observations support the classification of 409
hydrometeor types based on the PARSIVEL-observed fall velocities Furthermore there 410
are velocity spreads in fall velocity across hydrometeor sizes for all hydrometeors and 411
the spreads for the solid hydrometeors could cause by hydrometeor type turbulence or 412
updraftdowndraft and instrument measured principle The coexistence of various 413
types of hydrometeors likely induces additional spread of fall velocity for given 414
20
hydrometeor sizes such as mixed precipitation Meanwhile complex microphysical 415
processes in cold precipitation such as riming aggregation breakup and collision and 416
coalescence influence fall velocity which likely induce larger spread of fall velocity Last 417
but not the least the disdrometer may suffer from instrumental errors due to the 418
internally assumed relationship between horizontal and vertical particle dimensions 419
Comparison of the type-averaged hydrometeor size distributions shows that the 420
mixed precipitation has more small hydrometeors with D lt 15 mm than others 421
whereas the snowflake precipitation has the least number of small hydrometeors 422
among the four types On the contrary the snowflake precipitation has more large 423
hydrometeors with D between 3 mm and 11 mm 424
The commonly used size distribution functions (Gamma Weibull and Lognormal) 425
are further examined to determine the most adequate function to describe the size 426
distribution measurements for all the hydrometeor types by use of an approach based 427
on the relationship between skewness (S) and kurtosis (K) Taylor diagram and RED are 428
further introduced to assess the performance of different size distribution functions 429
against measurements It is shown that the HSDs for the four types can all be well 430
described statistically by the Gamma and Weibull distribution but Lognormal 431
Exponential and Gaussian are not fit to describe HSDs Gamma and Weibull distribution 432
describe raindrop and mixed-phase size distribution better than snowflake and graupel 433
size distribution and their performances are worst for snowflake It may due to graupel 434
and snowflake precipitation have more big particles When S less than 2 and K less than 435
6 Weibull distribution performs better than Gamma distribution to describe HSDs but 436
21
Gamma distribution performs better for total data 437
A few points are noteworthy First although this study demonstrates the great 438
potential of combining simultaneous disdrometer measurements of particle fall velocity 439
and size distributions microscopic photography and cloud radar to address the 440
challenges facing solid precipitation the data are limited More research is needed to 441
discern such effects on the results presented here Second as the observations show 442
that in addition to sizes there are many other factors (eg hydrometeor type 443
microphysical processes turbulence and measuring principle) that can potentially 444
influence particle fall velocity as well More comprehensive research is needed to 445
further discern and separate these factors Finally the combined use of S-K diagram 446
Taylor diagram and relative Euclidean distance appears to be a powerful tool for 447
identifying the best function used to describe the HSDs and quantify the differences 448
between different precipitation types More research is in order along this direction 449
Acknowledgements 450
This study is mainly supported by the Chinese National Science Foundation under Grant 451
No 41675138 and National Key RampD Program of China (2017YFC0209604) It is partly 452
supported by Beijing National Science Foundation (8172023) the US Department 453
Energys Atmospheric System Research (ASR) Program (Liu and Jia at BNL) Lu is 454
supported by the Natural Science Foundation of Jiangsu Province (BK20160041) The 455
observation data are archived at a specialized supercomputer at Beijing Meteorology 456
Information Center (ftp10224592) which are available from the corresponding 457
author upon request The authors also thank Beijing weather modification office for 458
their support during the field experiment 459
Reference 460
22
Agosta CC Fettweis XX Datta RR 2015 Evaluation of the CMIP5 models in the 461
aim of regional modelling of the Antarctic surface mass balance Cryosphere 9 2311ndash462
2321 httpdxdoiorg105194tc-9-2311-2015 463
Barthazy E and R Schefold 2006 Fall velocity of snowflakes of different riming degree 464
and crystal types Atmos Res 82(1) 391-398 httpsdoiorg101016jatmosres 465
200512009 466
Battaglia A Rustemeier E Tokay A et al 2010 PARSIVEL snow observations a critical 467
assessment J Atmos Oceanic Technol 27(2) 333-344 doi 1011752009jtecha13321 468
Boumlhm H P 1989 A General Equation for the Terminal Fall Speed of Solid Hydrometeors 469
J Atmos Sci 46(15) 2419-2427 httpsdoiorg1011751520-0469(1989)046 lt2419A 470
GEFTTgt20CO2 471
Boudala F S G A Isaac et al 2014 Comparisons of Snowfall Measurements in 472
Complex Terrain Made During the 2010 Winter Olympics in Vancouver Pure and 473
Applied Geophysics 171(1) 113-127 474
Chen B W Hu and J Pu 2011 Characteristics of the raindrop size distribution for 475
freezing precipitation observed in southern China J Geophys Res 116 D06201 476
doi1010292010JD015305 477
Chen B Z Hu L Liu and G Zhang (2017) Raindrop Size Distribution Measurements at 478
4500m on the Tibetan Plateau during TIPEX-III J Geophys Res 122 11092-11106 479
doiorg10100 22017JD027233 480
23
Cugerone K and C De Michele 2017 Investigating raindrop size distributions in the 481
(L-)skewness-(L-)kurtosis plane Quart J Roy Meteor Soc 143(704) 1303-1312 482
httpsdoiorg101002qj3005 483
Donnadieu G 1980 Comparison of results obtained with the VIDIAZ spectro 484
pluviometer and the JossndashWaldvogel rainfall disdrometer in a ldquorain of a thundery typerdquo 485
J Appl Meteor 19 593ndash597 486
Feingold G and Levin Z 1986 The lognormal fit to raindrop spectra from frontal 487
convective clouds in Israel J Clim Appl Meteorol 25 1346ndash1363 488
httpsdoiorg1011751520-0450(1986)025lt1346tlftrsgt20CO2 489
Field P R A J Heymsfield and A Bansemer 2007 Snow Size Distribution 490
Parameterization for Midlatitude and Tropical Ice Clouds J Atmos Sci 64(12) 491
4346-4365 httpsdoiorg1011752007JAS23441 492
Garrett T J and S E Yuter 2014 Observed influence of riming temperature and 493
turbulence on the fallspeed of solid precipitation Geophysical Research Letters 41(18) 494
6515ndash6522 495
Geresdi I N Sarkadi and G Thompson 2014 Effect of the accretion by water drops 496
on the melting of snowflakes Atmos Res 149 96-110 497
Gunn R and G D Kinzer 1949 The terminal velocity of fall for water drops in stagnant 498
air J Meteor 6 243-248 httpsdoiorg1011751520-0469(1949)006lt0243TTVOFFgt 499
20CO2 500
24
Heymsfield A J and C D Westbrook 2010 Advances in the Estimation of Ice Particle 501
Fall Speeds Using Laboratory and Field Measurements J Atmos Sci 67(8) 2469-2482 502
httpsdoiorg1011752010JAS33791 503
Huang G-J C Kleinkort V N Bringi and B M Notaroš 2017 Winter precipitation 504
particle size distribution measurement by Multi-Angle Snowflake Camera Atmos Res 505
198 81-96 506
Intergovernmental Panel on Climate Change (IPCC) 2001 Climate Change 2001 The 507
Scientific Basis Contribution of Working Group I to the Third Assessment Report of the 508
Intergovernmental Panel on Climate Change edited by J T Houghton et al 881 pp 509
Cambridge Univ Press New York 510
Ishizaka M H Motoyoshi S Nakai T Shiina T Kumakura and K-i Muramoto 2013 A 511
New Method for Identifying the Main Type of Solid Hydrometeors Contributing to 512
Snowfall from Measured Size-Fall Speed Relationship Journal of the Meteorological 513
Society of Japan Ser II 91(6) 747-762 httpsdoiorg102151jmsj2013-602 514
Khvorostyanov V 2005 Fall Velocities of Hydrometeors in the Atmosphere 515
Refinements to a Continuous Analytical Power Law J Atmos Sci 62 4343-4357 516
httpsdoiorg101175JAS36221 517
Kikuchi K T Kameda K Higuchi and A Yamashita 2013 A global classification of 518
snow crystals ice crystals and solid precipitation based on observations from middle 519
latitudes to polar regions Atmos Res 132-133 460-472 520
Kneifel S A von Lerber J Tiira D Moisseev P Kollias and J Leinonen 2015 521
Observed relations between snowfall microphysics and triple-frequency radar 522
25
measurements J Geophys Res Atmos 120(12) 6034-6055 523
httpsdoi1010022015JD023156 524
Kubicek A and P K Wang 2012 A numerical study of the flow fields around a typical 525
conical graupel falling at various inclination angles Atmos Res 118 15ndash26 526
httpsdoi101016jatmosres201206001 527
Larsen M L A B Kostinski and A R Jameson (2014) Further evidence for 528
superterminal raindrops Geophys Res Lett 41(19) 6914-6918 529
Lee JE SH Jung H M Park S Kwon P L Lin and G W Lee 2015 Classification of 530
Precipitation Types Using Fall Velocity Diameter Relationships from 2D-Video 531
Distrometer Measurements Advances in Atmospheric Sciences (09) 532
Lin Y L J Donner and B A Colle 2010 Parameterization of riming intensity and its 533
impact on ice fall speed using arm data Mon Weather Rev 139(3) 1036ndash1047 534
httpsdoi1011752010MWR32991 535
Liu Y G 1992 Skewness and kurtosis of measured raindrop size distributions Atmos 536
Environ 26A 2713-2716 httpsdoiorg1010160960-1686(92)90005-6 537
Liu Y G 1993 Statistical theory of the Marshall-Parmer distribution of raindrops 538
Atmos Environ 27A 15-19 httpsdoiorg1010160960-1686(93)90066-8 539
Liu Y G and F Liu 1994 On the description of aerosol particle size distribution Atmos 540
Res 31(1-3) 187-198 httpsdoiorg1010160169-8095(94)90043-4 541
Liu Y G L You W Yang F Liu 1995 On the size distribution of cloud droplets Atmos 542
Res 35 (2-4) 201-216 httpsdoiorg1010160169-8095(94)00019-A 543
Locatelli J D and P V Hobbs 1974 Fall speeds and masses of solid precipitation 544
26
particles J Geophys Res 79(15) 2185-2197 httpsdoi101029JC079i015p02185 545
Loumlffler-Mang M and J Joss 2000 An optical disdrometer for measuring size and 546
velocity of hydrometeors J Atmos Oceanic Technol 17 130-139 547
httpsdoiorg1011751520-0426(2000)017lt0130AODFMSgt20CO2 548
Loumlffler-Mang M and U Blahak 2001 Estimation of the Equivalent Radar Reflectivity 549
Factor from Measured Snow Size Spectra J Clim Appl Meteorol 40(4) 843-849 550
httpsdoiorg1011751520-0450(2001)040lt0843EOTERRgt20CO2 551
Matrosov S Y 2007 Modeling Backscatter Properties of Snowfall at Millimeter 552
Wavelengths J Atmos Sci 64(5) 1727-1736 httpsdoiorg101175JAS39041 553
Mitchell D L 1996 Use of mass- and area-dimensional power laws for determining 554
precipitation particle terminal velocities J Atmos Sci 53 1710-1723 555
httpsdoiorg1011751520-0469(1996)053lt1710UOMAADgt20CO2 556
Montero-Martiacutenez G A B Kostinski R A Shaw and F Garciacutea-Garciacutea 2009 Do all 557
raindrops fall at terminal speed Geophys Res Lett 36 L11818 558
httpsdoiorg1010292008GL037111 559
Niu S X Jia J Sang X Liu C Lu and Y Liu 2010 Distributions of raindrop sizes and 560
fall velocities in a semiarid plateau climate Convective vs stratiform rains J Appl 561
Meteorol Climatol 49 632ndash645 httpsdoi1011752009JAMC22081 562
Nurzyńska K M Kubo and K-i Muramoto 2012 Texture operator for snow particle 563
classification into snowflake and graupel Atmos Res 118 121-132 564
Oue M M R Kumjian Y Lu J Verlinde K Aydin and E E Clothiaux 2015 Linear 565
27
Depolarization Ratios of columnar ice crystals in a deep precipitating system over the 566
Arctic observed by Zenith-Pointing Ka-Band Doppler radar J Clim Appl Meteorol 567
54(5) 1060-1068 httpsdoiorg101175JAMC-D-15-00121 568
Pruppacher H R and J D Klett 1998 Microphysics of clouds and precipitation Kluwer 569
Academic 954 pp 570
Rasmussen R B Baker et al 2012 How well are we measuring snow the 571
NOAAFAANCAR winter precipitation test bed Bull Amer Meteor Soc 93(6) 811-829 572
httpsdoiorg101175BAMS-D-11-000521 573
Reisner J R M Rasmussen and R T Bruintjes 1998 Explicit forecasting of 574
supercooled liquid water in winter storms using the MM5 mesoscale model Q J R 575
Meteorol Soc 124 1071ndash1107 httpsdoi101256smsqj54803 576
Rosenfeld D and Ulbrich C W 2003 Cloud microphysical properties processes and 577
rainfall estimation opportunities Meteorol Monogr 30 237-237 578
httpsdoiorg101175 0065-9401(2003)030lt0237cmppargt20CO2 579
Schaefer V J 1956 The preparation of snow crystal replicas-VI Weatherwsie 9 580
132-135 581
Souverijns N A Gossart S Lhermitte I V Gorodetskaya S Kneifel M Maahn F L 582
Bliven and N P M van Lipzig (2017) Estimating radar reflectivity - Snowfall rate 583
relationships and their uncertainties over Antarctica by combining disdrometer and 584
radar observations Atmos Res 196 211-223 585
Taylor K E 2001 Summarizing multiple aspects of model performance in a single 586
diagram J Geophys Res 106 7183ndash7192 httpsdoi1010292000JD900719 587
28
Tokay A and D A Short 1996 Evidence from tropical raindrop spectra of the origin of 588
rain from stratiform versus convective clouds J Appl Meteor 35 355ndash371 589
Tokay A and D Atlas 1999 Rainfall microphysics and radar properties analysis 590
methods for drop size spectra J Appl Meteor 37 912-923 591
httpsdoiorg1011751520-0450(1998)037lt0912RMARPAgt20CO2 592
Tokay A D B Wolff et al 2014 Evaluation of the New version of the laser-optical 593
disdrometer OTT Parsivel2 J Atmos Oceanic Technol 31(6) 1276-1288 594
httpsdoiorg101175JTECH-D-13-001741 595
Ulbrich C W 1983 Natural variations in the analytical form of the raindrop size 596
distribution J Appl Meteor 5 1764-1775 597
Wen G H Xiao H Yang Y Bi and W Xu 2017 Characteristics of summer and winter 598
precipitation over northern China Atmos Res 197 390-406 599
Wu W Y Liu and A K Betts 2012 Observationally based evaluation of NWP 600
reanalyses in modeling cloud properties over the Southern Great Plains J Geophys 601
Res 117 D12202 httpsdoi1010292011JD016971 602
Yuter S E D E Kingsmill L B Nance and M Loumlffler-Mang 2006 Observations of 603
precipitation size and fall velocity characteristics within coexisting rain and wet snow J 604
Appl Meteor Climatol 45 1450ndash1464 doi httpsdoiorg101175JAM24061 605
Zhang P C and B Y Du 2000 Radar Meteorology China Meteorological Press 511pp 606
(in Chinese) 607
608
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
14
types of hydrometeors The sample numbers mean maximum dimensions and number 286
concentrations for each kind of HSDs are given in Table 2 Figure 4 is the averaged 287
distribution of all measured HSDs of 4 kinds As shown in Figure 4 on average the 288
mixed-phased precipitation tends to have most small size hydrometeors with D lt 15 289
mm while snowflake precipitation has the least small hydrometeors among the four 290
types The snowflake precipitation has more large size hydrometeors ie 3 mm lt D lt 11 291
mm Graupel size distribution tends to have two peeks around 13 mm and 26 mm The 292
mean maximum dimension is largest for snowflake (126 mm) and smallest for the 293
mixed HSD due to many small particles Similar results were found in precipitation 294
occurring in the Cascade and Rocky Mountains (Yuter et al 2006) The PARSIVEL 295
disdrometer doesnrsquot provide reliable data for small drops lower than 05 mm and tends to 296
underestimate small drops so the relatively low concentrations of small drops likely resulted 297
from the instrumentrsquos shortcomings (Tokay et al 2013 and Chen et al 2017) 298
b Evaluation of Distribution Functions for Describing HSDs 299
Over the last few decades great efforts have been devoted to finding the 300
appropriate analytical functions for describing the HSD because of its wide applications 301
in many areas including remote sensing and parameterization of precipitation (Chen et 302
al 2017) The two distribution functions mostly used up to now are the Lognormal 303
(Feingold and Levin 1986 Rosenfeld and Ulbrich 2003) and the Gamma (Ulbrich 1983) 304
distributions The Gamma distribution has been proposed as a first order generalization 305
of the Exponential distribution when μ equals 0 (Table 4) Weibull distribution is 306
another function used to describe size distributions of raindrops and cloud droplets (Liu 307
15
and Liu 1994 Liu et al 1995) Nevertheless the question as to which functions are 308
more adequate to describe HSDs of solid hydrometeors have been rarely investigated 309
systematically and quantitatively Thus the objective of this section is to examine the 310
most adequate distribution function used to describe HSDs 311
Considering size distributions of raindrops cloud droplets and aerosol particles are 312
the end results of many (stochastic) complex processes Liu (1992 1993 1994 and 313
1995) proposed a statistical method based on the relationships between the skewness 314
(S) and kurtosis (K) derived from an ensemble of particle size distribution 315
measurements and from those commonly used size distribution functions Cugerone 316
and Michele (2017) also used a similar approach based on the S-K relationships to study 317
raindrop size distributions Unlike the conventional curve-fitting of individual size 318
distributions this approach applies to an ensemble of size distribution measurements 319
and identifies the most appropriate statistical distribution pattern Here we apply this 320
approach to investigate if the statistical pattern of the HSDs of four precipitation types 321
follows the Exponential Gaussian Gamma Weibull and Lognormal distributions (Table 322
4) and if there are any pattern differences between them Briefly S and K of a HSD are 323
calculated from the corresponding HSD with the following two equations 324
23
2
3
t
iii
t
iii
dDN
)(Dn)D(D
dDN
)(Dn)D(D
S
minus
minus
=
(2) 325
32
2
4
minus
minus
minus
=
dDN
)(Dn)D(D
dDN
)(Dn)D(D
K
t
iii
t
iii
(3) 326
16
where Di is the central diameter of the i-th bin ni is the number concentration of the 327
i-th bin and Nt is total number concentration Note that each individual HSD can be 328
used to obtain a pair of S and K which is shown as a dot in Figure 5 Also noteworthy is 329
that the SndashK relationships for the families of Gamma Weibull and Lognormal are 330
described by known analytical functions (Liu 1993 1994 and 1995 Cugerone and 331
Michele 2017) represented by theoretical curves in Figure 5 The Exponential and 332
Gaussian distributions are represented by single points on the S-K diagram (S=2 and K=6 333
for Exponential) and (S=0 and K=0 for Gaussian) respectively Thus by comparing the 334
measured S and K values (points) with the known theoretical curves one can determine 335
the most proper function used to describe HSDs 336
Figure 5 shows the scatter plots of observed SndashK pairs calculated from the HSD 337
measurements for raindrop graupel snowflake mixed-phase precipitations Also 338
shown as comparison are the theoretical curves corresponding to the analytical HSD 339
functions A few points are evident First despite some occasional departures most of 340
the points fall near the theoretical lines of Gamma and Weibull distributions suggesting 341
that the HSD patterns for all the four types of precipitations well follow the Gamma and 342
Weibull distributions statistically Second HSDs of raindrops and mixed hydrometeors 343
are better described by Gamma and Weibull distribution than graupels and snowflakes 344
Third the S and K do not cluster around points (2 6) and (0 0) suggesting that the 345
Gaussian and Exponential distribution are not appropriate for describing HSDs 346
especially Gaussian distribution 347
To further evaluate the overall performance of the different distribution functions 348
17
we employ the widely used technique of Taylor diagram (Taylor 2001) and ldquoRelative 349
Euclidean Distancerdquo (RED) (Wu et al 2012) as a supplement to the Taylor diagram The 350
Taylor diagram has been widely used to visualize the statistical differences between 351
model results and observations in evaluation of model performance against 352
measurements or other benchmarks (IPCC 2001) Correlation coefficient (r) standard 353
deviation (σ) and ldquocentered root-mean-square errorrdquo (RMSE hereafter) are used in 354
the Taylor diagram The RED is introduced to add the bias as well in a dimensionless 355
framework that allows for comparison between different physical quantities with 356
different units In this study we consider the S and K values derived from the 357
distribution functions as model results and evaluate them against those derived from 358
the HSD measurements Brieflythe expressions for calculating r and σ and RMSE are 359
shown below 360
119903 =1
119873sum (119872119899minus)(119874119899minus)119873119899=1
120590119872120590119900 (4) 361
119877119872119878119864 = 1
119873sum [(119872119899 minus ) minus (119874119899 minus )]2119873119899=1
12
(5) 362
120590119872 = [1
119873sum (119872119899 minus )119873119899=1 ]
12
(6) 363
1205900 = [1
119873sum (119874119899 minus )119873119899=1 ]
12
(7) 364
where M and O denote distribution function and observed variables The RED 365
expression is shown below 366
119877119864119863 = [(minus)
]2
+ [(120590119872minus120590119874)
120590119900]2
+ (1 minus 119903)212
( 8 ) 367
Equation (8) indicates that RED considers all the components of mean bias variations 368
and correlations in a dimensionless way the distribution function performance 369
degrades as RED increases from the perfect agreement with RED=0 370
18
In the Taylor diagrams shown in Fig 6 the cosine of azimuthal angle of each point 371
gives the r between the function-calculated and observed data The distance between 372
individual point and the reference point ldquoObsrdquo represents the RMSE normalized by the 373
amplitude of the observationally based variations As this distance approaches to zero 374
the function-calculated K and S approach to the observations Clearly the values of r 375
are around 097 for Gamma and Weibull r for Lognormal function is slightly smaller 376
(095) The normalized σ are much different for Lognormal Gamma and Weibull 377
distributions with averaged value being 057 0895 and 0785 respectively Therefore 378
the Lognormal distribution exhibits the worst performance for describing HSDs and 379
Gamma and Weibull distributions appear to perform much better (Fig 6a) 380
Noticing that S and K of Gamma and Weibull distributions are equal at the point of S 381
= 2 and K = 6 and have positive relationship (If S lt 2 then K lt 6 and if S gt 2 then k gt 6) In 382
this part we further separately examine the group of data with S lt 2 and K lt 6 (Fig 6b) 383
and compare its result with those of total data The averaged normalized σ are 103 and 384
109 and r are 091 and 090 for Weibull and Gamma distributions respectively 385
suggesting that Weibull distribution performs slightly better than Gamma distribution 386
for the four HSD types in the data group of S lt 2 and K lt 6 whereas the opposite is true 387
for all data This conclusion is further substantiated by comparison of RED values for the 388
four type of precipitation (Fig7) which shows that Lognormal has the largest RED 389
Gamma the smallest and Weibull in between for four types of precipitations in all data 390
whereas Weibull (Lognormal) has smallest (largest) RED values when S lt 2 and K lt 6 It 391
can be inferred for data group of S gt 2 and k gt 6 Gamma distribution performs better 392
19
Further comparison between different precipitation types shows these functions all 393
performs better for raindrop size distributions and mixed-phase than graupel and 394
snowflake size distributions The RED for snowflakes is largest among the four types 395
The performance of Gamma is better for describing solid HSDs of all data but Weibull 396
distribution is better when S lt 2 and K lt 6 397
5 Conclusion 398
The combined measurements collected during a field experiment conducted at the 399
Haituo Mountain site using PARSIVEL disdrometer millimeter wavelength cloud radar 400
and microscope photography are analyzed to classify the precipitation hydrometeor 401
types examine the dependence of fall velocity on hydrometeor size for different 402
hydrometeor types and determine the best distribution functions to describe the 403
hydrometeor size distributions of different types 404
Analysis of the PARSIVEL-measured fall velocities show that on average the 405
dependence of fall velocity on hydrometeor size largely follow their corresponding 406
terminal velocity curves for raindrops graupels and snowflakes respectively suggesting 407
that such measurements are useful to identify the hydrometeor types The associated 408
microscope photos and cloud radar observations support the classification of 409
hydrometeor types based on the PARSIVEL-observed fall velocities Furthermore there 410
are velocity spreads in fall velocity across hydrometeor sizes for all hydrometeors and 411
the spreads for the solid hydrometeors could cause by hydrometeor type turbulence or 412
updraftdowndraft and instrument measured principle The coexistence of various 413
types of hydrometeors likely induces additional spread of fall velocity for given 414
20
hydrometeor sizes such as mixed precipitation Meanwhile complex microphysical 415
processes in cold precipitation such as riming aggregation breakup and collision and 416
coalescence influence fall velocity which likely induce larger spread of fall velocity Last 417
but not the least the disdrometer may suffer from instrumental errors due to the 418
internally assumed relationship between horizontal and vertical particle dimensions 419
Comparison of the type-averaged hydrometeor size distributions shows that the 420
mixed precipitation has more small hydrometeors with D lt 15 mm than others 421
whereas the snowflake precipitation has the least number of small hydrometeors 422
among the four types On the contrary the snowflake precipitation has more large 423
hydrometeors with D between 3 mm and 11 mm 424
The commonly used size distribution functions (Gamma Weibull and Lognormal) 425
are further examined to determine the most adequate function to describe the size 426
distribution measurements for all the hydrometeor types by use of an approach based 427
on the relationship between skewness (S) and kurtosis (K) Taylor diagram and RED are 428
further introduced to assess the performance of different size distribution functions 429
against measurements It is shown that the HSDs for the four types can all be well 430
described statistically by the Gamma and Weibull distribution but Lognormal 431
Exponential and Gaussian are not fit to describe HSDs Gamma and Weibull distribution 432
describe raindrop and mixed-phase size distribution better than snowflake and graupel 433
size distribution and their performances are worst for snowflake It may due to graupel 434
and snowflake precipitation have more big particles When S less than 2 and K less than 435
6 Weibull distribution performs better than Gamma distribution to describe HSDs but 436
21
Gamma distribution performs better for total data 437
A few points are noteworthy First although this study demonstrates the great 438
potential of combining simultaneous disdrometer measurements of particle fall velocity 439
and size distributions microscopic photography and cloud radar to address the 440
challenges facing solid precipitation the data are limited More research is needed to 441
discern such effects on the results presented here Second as the observations show 442
that in addition to sizes there are many other factors (eg hydrometeor type 443
microphysical processes turbulence and measuring principle) that can potentially 444
influence particle fall velocity as well More comprehensive research is needed to 445
further discern and separate these factors Finally the combined use of S-K diagram 446
Taylor diagram and relative Euclidean distance appears to be a powerful tool for 447
identifying the best function used to describe the HSDs and quantify the differences 448
between different precipitation types More research is in order along this direction 449
Acknowledgements 450
This study is mainly supported by the Chinese National Science Foundation under Grant 451
No 41675138 and National Key RampD Program of China (2017YFC0209604) It is partly 452
supported by Beijing National Science Foundation (8172023) the US Department 453
Energys Atmospheric System Research (ASR) Program (Liu and Jia at BNL) Lu is 454
supported by the Natural Science Foundation of Jiangsu Province (BK20160041) The 455
observation data are archived at a specialized supercomputer at Beijing Meteorology 456
Information Center (ftp10224592) which are available from the corresponding 457
author upon request The authors also thank Beijing weather modification office for 458
their support during the field experiment 459
Reference 460
22
Agosta CC Fettweis XX Datta RR 2015 Evaluation of the CMIP5 models in the 461
aim of regional modelling of the Antarctic surface mass balance Cryosphere 9 2311ndash462
2321 httpdxdoiorg105194tc-9-2311-2015 463
Barthazy E and R Schefold 2006 Fall velocity of snowflakes of different riming degree 464
and crystal types Atmos Res 82(1) 391-398 httpsdoiorg101016jatmosres 465
200512009 466
Battaglia A Rustemeier E Tokay A et al 2010 PARSIVEL snow observations a critical 467
assessment J Atmos Oceanic Technol 27(2) 333-344 doi 1011752009jtecha13321 468
Boumlhm H P 1989 A General Equation for the Terminal Fall Speed of Solid Hydrometeors 469
J Atmos Sci 46(15) 2419-2427 httpsdoiorg1011751520-0469(1989)046 lt2419A 470
GEFTTgt20CO2 471
Boudala F S G A Isaac et al 2014 Comparisons of Snowfall Measurements in 472
Complex Terrain Made During the 2010 Winter Olympics in Vancouver Pure and 473
Applied Geophysics 171(1) 113-127 474
Chen B W Hu and J Pu 2011 Characteristics of the raindrop size distribution for 475
freezing precipitation observed in southern China J Geophys Res 116 D06201 476
doi1010292010JD015305 477
Chen B Z Hu L Liu and G Zhang (2017) Raindrop Size Distribution Measurements at 478
4500m on the Tibetan Plateau during TIPEX-III J Geophys Res 122 11092-11106 479
doiorg10100 22017JD027233 480
23
Cugerone K and C De Michele 2017 Investigating raindrop size distributions in the 481
(L-)skewness-(L-)kurtosis plane Quart J Roy Meteor Soc 143(704) 1303-1312 482
httpsdoiorg101002qj3005 483
Donnadieu G 1980 Comparison of results obtained with the VIDIAZ spectro 484
pluviometer and the JossndashWaldvogel rainfall disdrometer in a ldquorain of a thundery typerdquo 485
J Appl Meteor 19 593ndash597 486
Feingold G and Levin Z 1986 The lognormal fit to raindrop spectra from frontal 487
convective clouds in Israel J Clim Appl Meteorol 25 1346ndash1363 488
httpsdoiorg1011751520-0450(1986)025lt1346tlftrsgt20CO2 489
Field P R A J Heymsfield and A Bansemer 2007 Snow Size Distribution 490
Parameterization for Midlatitude and Tropical Ice Clouds J Atmos Sci 64(12) 491
4346-4365 httpsdoiorg1011752007JAS23441 492
Garrett T J and S E Yuter 2014 Observed influence of riming temperature and 493
turbulence on the fallspeed of solid precipitation Geophysical Research Letters 41(18) 494
6515ndash6522 495
Geresdi I N Sarkadi and G Thompson 2014 Effect of the accretion by water drops 496
on the melting of snowflakes Atmos Res 149 96-110 497
Gunn R and G D Kinzer 1949 The terminal velocity of fall for water drops in stagnant 498
air J Meteor 6 243-248 httpsdoiorg1011751520-0469(1949)006lt0243TTVOFFgt 499
20CO2 500
24
Heymsfield A J and C D Westbrook 2010 Advances in the Estimation of Ice Particle 501
Fall Speeds Using Laboratory and Field Measurements J Atmos Sci 67(8) 2469-2482 502
httpsdoiorg1011752010JAS33791 503
Huang G-J C Kleinkort V N Bringi and B M Notaroš 2017 Winter precipitation 504
particle size distribution measurement by Multi-Angle Snowflake Camera Atmos Res 505
198 81-96 506
Intergovernmental Panel on Climate Change (IPCC) 2001 Climate Change 2001 The 507
Scientific Basis Contribution of Working Group I to the Third Assessment Report of the 508
Intergovernmental Panel on Climate Change edited by J T Houghton et al 881 pp 509
Cambridge Univ Press New York 510
Ishizaka M H Motoyoshi S Nakai T Shiina T Kumakura and K-i Muramoto 2013 A 511
New Method for Identifying the Main Type of Solid Hydrometeors Contributing to 512
Snowfall from Measured Size-Fall Speed Relationship Journal of the Meteorological 513
Society of Japan Ser II 91(6) 747-762 httpsdoiorg102151jmsj2013-602 514
Khvorostyanov V 2005 Fall Velocities of Hydrometeors in the Atmosphere 515
Refinements to a Continuous Analytical Power Law J Atmos Sci 62 4343-4357 516
httpsdoiorg101175JAS36221 517
Kikuchi K T Kameda K Higuchi and A Yamashita 2013 A global classification of 518
snow crystals ice crystals and solid precipitation based on observations from middle 519
latitudes to polar regions Atmos Res 132-133 460-472 520
Kneifel S A von Lerber J Tiira D Moisseev P Kollias and J Leinonen 2015 521
Observed relations between snowfall microphysics and triple-frequency radar 522
25
measurements J Geophys Res Atmos 120(12) 6034-6055 523
httpsdoi1010022015JD023156 524
Kubicek A and P K Wang 2012 A numerical study of the flow fields around a typical 525
conical graupel falling at various inclination angles Atmos Res 118 15ndash26 526
httpsdoi101016jatmosres201206001 527
Larsen M L A B Kostinski and A R Jameson (2014) Further evidence for 528
superterminal raindrops Geophys Res Lett 41(19) 6914-6918 529
Lee JE SH Jung H M Park S Kwon P L Lin and G W Lee 2015 Classification of 530
Precipitation Types Using Fall Velocity Diameter Relationships from 2D-Video 531
Distrometer Measurements Advances in Atmospheric Sciences (09) 532
Lin Y L J Donner and B A Colle 2010 Parameterization of riming intensity and its 533
impact on ice fall speed using arm data Mon Weather Rev 139(3) 1036ndash1047 534
httpsdoi1011752010MWR32991 535
Liu Y G 1992 Skewness and kurtosis of measured raindrop size distributions Atmos 536
Environ 26A 2713-2716 httpsdoiorg1010160960-1686(92)90005-6 537
Liu Y G 1993 Statistical theory of the Marshall-Parmer distribution of raindrops 538
Atmos Environ 27A 15-19 httpsdoiorg1010160960-1686(93)90066-8 539
Liu Y G and F Liu 1994 On the description of aerosol particle size distribution Atmos 540
Res 31(1-3) 187-198 httpsdoiorg1010160169-8095(94)90043-4 541
Liu Y G L You W Yang F Liu 1995 On the size distribution of cloud droplets Atmos 542
Res 35 (2-4) 201-216 httpsdoiorg1010160169-8095(94)00019-A 543
Locatelli J D and P V Hobbs 1974 Fall speeds and masses of solid precipitation 544
26
particles J Geophys Res 79(15) 2185-2197 httpsdoi101029JC079i015p02185 545
Loumlffler-Mang M and J Joss 2000 An optical disdrometer for measuring size and 546
velocity of hydrometeors J Atmos Oceanic Technol 17 130-139 547
httpsdoiorg1011751520-0426(2000)017lt0130AODFMSgt20CO2 548
Loumlffler-Mang M and U Blahak 2001 Estimation of the Equivalent Radar Reflectivity 549
Factor from Measured Snow Size Spectra J Clim Appl Meteorol 40(4) 843-849 550
httpsdoiorg1011751520-0450(2001)040lt0843EOTERRgt20CO2 551
Matrosov S Y 2007 Modeling Backscatter Properties of Snowfall at Millimeter 552
Wavelengths J Atmos Sci 64(5) 1727-1736 httpsdoiorg101175JAS39041 553
Mitchell D L 1996 Use of mass- and area-dimensional power laws for determining 554
precipitation particle terminal velocities J Atmos Sci 53 1710-1723 555
httpsdoiorg1011751520-0469(1996)053lt1710UOMAADgt20CO2 556
Montero-Martiacutenez G A B Kostinski R A Shaw and F Garciacutea-Garciacutea 2009 Do all 557
raindrops fall at terminal speed Geophys Res Lett 36 L11818 558
httpsdoiorg1010292008GL037111 559
Niu S X Jia J Sang X Liu C Lu and Y Liu 2010 Distributions of raindrop sizes and 560
fall velocities in a semiarid plateau climate Convective vs stratiform rains J Appl 561
Meteorol Climatol 49 632ndash645 httpsdoi1011752009JAMC22081 562
Nurzyńska K M Kubo and K-i Muramoto 2012 Texture operator for snow particle 563
classification into snowflake and graupel Atmos Res 118 121-132 564
Oue M M R Kumjian Y Lu J Verlinde K Aydin and E E Clothiaux 2015 Linear 565
27
Depolarization Ratios of columnar ice crystals in a deep precipitating system over the 566
Arctic observed by Zenith-Pointing Ka-Band Doppler radar J Clim Appl Meteorol 567
54(5) 1060-1068 httpsdoiorg101175JAMC-D-15-00121 568
Pruppacher H R and J D Klett 1998 Microphysics of clouds and precipitation Kluwer 569
Academic 954 pp 570
Rasmussen R B Baker et al 2012 How well are we measuring snow the 571
NOAAFAANCAR winter precipitation test bed Bull Amer Meteor Soc 93(6) 811-829 572
httpsdoiorg101175BAMS-D-11-000521 573
Reisner J R M Rasmussen and R T Bruintjes 1998 Explicit forecasting of 574
supercooled liquid water in winter storms using the MM5 mesoscale model Q J R 575
Meteorol Soc 124 1071ndash1107 httpsdoi101256smsqj54803 576
Rosenfeld D and Ulbrich C W 2003 Cloud microphysical properties processes and 577
rainfall estimation opportunities Meteorol Monogr 30 237-237 578
httpsdoiorg101175 0065-9401(2003)030lt0237cmppargt20CO2 579
Schaefer V J 1956 The preparation of snow crystal replicas-VI Weatherwsie 9 580
132-135 581
Souverijns N A Gossart S Lhermitte I V Gorodetskaya S Kneifel M Maahn F L 582
Bliven and N P M van Lipzig (2017) Estimating radar reflectivity - Snowfall rate 583
relationships and their uncertainties over Antarctica by combining disdrometer and 584
radar observations Atmos Res 196 211-223 585
Taylor K E 2001 Summarizing multiple aspects of model performance in a single 586
diagram J Geophys Res 106 7183ndash7192 httpsdoi1010292000JD900719 587
28
Tokay A and D A Short 1996 Evidence from tropical raindrop spectra of the origin of 588
rain from stratiform versus convective clouds J Appl Meteor 35 355ndash371 589
Tokay A and D Atlas 1999 Rainfall microphysics and radar properties analysis 590
methods for drop size spectra J Appl Meteor 37 912-923 591
httpsdoiorg1011751520-0450(1998)037lt0912RMARPAgt20CO2 592
Tokay A D B Wolff et al 2014 Evaluation of the New version of the laser-optical 593
disdrometer OTT Parsivel2 J Atmos Oceanic Technol 31(6) 1276-1288 594
httpsdoiorg101175JTECH-D-13-001741 595
Ulbrich C W 1983 Natural variations in the analytical form of the raindrop size 596
distribution J Appl Meteor 5 1764-1775 597
Wen G H Xiao H Yang Y Bi and W Xu 2017 Characteristics of summer and winter 598
precipitation over northern China Atmos Res 197 390-406 599
Wu W Y Liu and A K Betts 2012 Observationally based evaluation of NWP 600
reanalyses in modeling cloud properties over the Southern Great Plains J Geophys 601
Res 117 D12202 httpsdoi1010292011JD016971 602
Yuter S E D E Kingsmill L B Nance and M Loumlffler-Mang 2006 Observations of 603
precipitation size and fall velocity characteristics within coexisting rain and wet snow J 604
Appl Meteor Climatol 45 1450ndash1464 doi httpsdoiorg101175JAM24061 605
Zhang P C and B Y Du 2000 Radar Meteorology China Meteorological Press 511pp 606
(in Chinese) 607
608
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
15
and Liu 1994 Liu et al 1995) Nevertheless the question as to which functions are 308
more adequate to describe HSDs of solid hydrometeors have been rarely investigated 309
systematically and quantitatively Thus the objective of this section is to examine the 310
most adequate distribution function used to describe HSDs 311
Considering size distributions of raindrops cloud droplets and aerosol particles are 312
the end results of many (stochastic) complex processes Liu (1992 1993 1994 and 313
1995) proposed a statistical method based on the relationships between the skewness 314
(S) and kurtosis (K) derived from an ensemble of particle size distribution 315
measurements and from those commonly used size distribution functions Cugerone 316
and Michele (2017) also used a similar approach based on the S-K relationships to study 317
raindrop size distributions Unlike the conventional curve-fitting of individual size 318
distributions this approach applies to an ensemble of size distribution measurements 319
and identifies the most appropriate statistical distribution pattern Here we apply this 320
approach to investigate if the statistical pattern of the HSDs of four precipitation types 321
follows the Exponential Gaussian Gamma Weibull and Lognormal distributions (Table 322
4) and if there are any pattern differences between them Briefly S and K of a HSD are 323
calculated from the corresponding HSD with the following two equations 324
23
2
3
t
iii
t
iii
dDN
)(Dn)D(D
dDN
)(Dn)D(D
S
minus
minus
=
(2) 325
32
2
4
minus
minus
minus
=
dDN
)(Dn)D(D
dDN
)(Dn)D(D
K
t
iii
t
iii
(3) 326
16
where Di is the central diameter of the i-th bin ni is the number concentration of the 327
i-th bin and Nt is total number concentration Note that each individual HSD can be 328
used to obtain a pair of S and K which is shown as a dot in Figure 5 Also noteworthy is 329
that the SndashK relationships for the families of Gamma Weibull and Lognormal are 330
described by known analytical functions (Liu 1993 1994 and 1995 Cugerone and 331
Michele 2017) represented by theoretical curves in Figure 5 The Exponential and 332
Gaussian distributions are represented by single points on the S-K diagram (S=2 and K=6 333
for Exponential) and (S=0 and K=0 for Gaussian) respectively Thus by comparing the 334
measured S and K values (points) with the known theoretical curves one can determine 335
the most proper function used to describe HSDs 336
Figure 5 shows the scatter plots of observed SndashK pairs calculated from the HSD 337
measurements for raindrop graupel snowflake mixed-phase precipitations Also 338
shown as comparison are the theoretical curves corresponding to the analytical HSD 339
functions A few points are evident First despite some occasional departures most of 340
the points fall near the theoretical lines of Gamma and Weibull distributions suggesting 341
that the HSD patterns for all the four types of precipitations well follow the Gamma and 342
Weibull distributions statistically Second HSDs of raindrops and mixed hydrometeors 343
are better described by Gamma and Weibull distribution than graupels and snowflakes 344
Third the S and K do not cluster around points (2 6) and (0 0) suggesting that the 345
Gaussian and Exponential distribution are not appropriate for describing HSDs 346
especially Gaussian distribution 347
To further evaluate the overall performance of the different distribution functions 348
17
we employ the widely used technique of Taylor diagram (Taylor 2001) and ldquoRelative 349
Euclidean Distancerdquo (RED) (Wu et al 2012) as a supplement to the Taylor diagram The 350
Taylor diagram has been widely used to visualize the statistical differences between 351
model results and observations in evaluation of model performance against 352
measurements or other benchmarks (IPCC 2001) Correlation coefficient (r) standard 353
deviation (σ) and ldquocentered root-mean-square errorrdquo (RMSE hereafter) are used in 354
the Taylor diagram The RED is introduced to add the bias as well in a dimensionless 355
framework that allows for comparison between different physical quantities with 356
different units In this study we consider the S and K values derived from the 357
distribution functions as model results and evaluate them against those derived from 358
the HSD measurements Brieflythe expressions for calculating r and σ and RMSE are 359
shown below 360
119903 =1
119873sum (119872119899minus)(119874119899minus)119873119899=1
120590119872120590119900 (4) 361
119877119872119878119864 = 1
119873sum [(119872119899 minus ) minus (119874119899 minus )]2119873119899=1
12
(5) 362
120590119872 = [1
119873sum (119872119899 minus )119873119899=1 ]
12
(6) 363
1205900 = [1
119873sum (119874119899 minus )119873119899=1 ]
12
(7) 364
where M and O denote distribution function and observed variables The RED 365
expression is shown below 366
119877119864119863 = [(minus)
]2
+ [(120590119872minus120590119874)
120590119900]2
+ (1 minus 119903)212
( 8 ) 367
Equation (8) indicates that RED considers all the components of mean bias variations 368
and correlations in a dimensionless way the distribution function performance 369
degrades as RED increases from the perfect agreement with RED=0 370
18
In the Taylor diagrams shown in Fig 6 the cosine of azimuthal angle of each point 371
gives the r between the function-calculated and observed data The distance between 372
individual point and the reference point ldquoObsrdquo represents the RMSE normalized by the 373
amplitude of the observationally based variations As this distance approaches to zero 374
the function-calculated K and S approach to the observations Clearly the values of r 375
are around 097 for Gamma and Weibull r for Lognormal function is slightly smaller 376
(095) The normalized σ are much different for Lognormal Gamma and Weibull 377
distributions with averaged value being 057 0895 and 0785 respectively Therefore 378
the Lognormal distribution exhibits the worst performance for describing HSDs and 379
Gamma and Weibull distributions appear to perform much better (Fig 6a) 380
Noticing that S and K of Gamma and Weibull distributions are equal at the point of S 381
= 2 and K = 6 and have positive relationship (If S lt 2 then K lt 6 and if S gt 2 then k gt 6) In 382
this part we further separately examine the group of data with S lt 2 and K lt 6 (Fig 6b) 383
and compare its result with those of total data The averaged normalized σ are 103 and 384
109 and r are 091 and 090 for Weibull and Gamma distributions respectively 385
suggesting that Weibull distribution performs slightly better than Gamma distribution 386
for the four HSD types in the data group of S lt 2 and K lt 6 whereas the opposite is true 387
for all data This conclusion is further substantiated by comparison of RED values for the 388
four type of precipitation (Fig7) which shows that Lognormal has the largest RED 389
Gamma the smallest and Weibull in between for four types of precipitations in all data 390
whereas Weibull (Lognormal) has smallest (largest) RED values when S lt 2 and K lt 6 It 391
can be inferred for data group of S gt 2 and k gt 6 Gamma distribution performs better 392
19
Further comparison between different precipitation types shows these functions all 393
performs better for raindrop size distributions and mixed-phase than graupel and 394
snowflake size distributions The RED for snowflakes is largest among the four types 395
The performance of Gamma is better for describing solid HSDs of all data but Weibull 396
distribution is better when S lt 2 and K lt 6 397
5 Conclusion 398
The combined measurements collected during a field experiment conducted at the 399
Haituo Mountain site using PARSIVEL disdrometer millimeter wavelength cloud radar 400
and microscope photography are analyzed to classify the precipitation hydrometeor 401
types examine the dependence of fall velocity on hydrometeor size for different 402
hydrometeor types and determine the best distribution functions to describe the 403
hydrometeor size distributions of different types 404
Analysis of the PARSIVEL-measured fall velocities show that on average the 405
dependence of fall velocity on hydrometeor size largely follow their corresponding 406
terminal velocity curves for raindrops graupels and snowflakes respectively suggesting 407
that such measurements are useful to identify the hydrometeor types The associated 408
microscope photos and cloud radar observations support the classification of 409
hydrometeor types based on the PARSIVEL-observed fall velocities Furthermore there 410
are velocity spreads in fall velocity across hydrometeor sizes for all hydrometeors and 411
the spreads for the solid hydrometeors could cause by hydrometeor type turbulence or 412
updraftdowndraft and instrument measured principle The coexistence of various 413
types of hydrometeors likely induces additional spread of fall velocity for given 414
20
hydrometeor sizes such as mixed precipitation Meanwhile complex microphysical 415
processes in cold precipitation such as riming aggregation breakup and collision and 416
coalescence influence fall velocity which likely induce larger spread of fall velocity Last 417
but not the least the disdrometer may suffer from instrumental errors due to the 418
internally assumed relationship between horizontal and vertical particle dimensions 419
Comparison of the type-averaged hydrometeor size distributions shows that the 420
mixed precipitation has more small hydrometeors with D lt 15 mm than others 421
whereas the snowflake precipitation has the least number of small hydrometeors 422
among the four types On the contrary the snowflake precipitation has more large 423
hydrometeors with D between 3 mm and 11 mm 424
The commonly used size distribution functions (Gamma Weibull and Lognormal) 425
are further examined to determine the most adequate function to describe the size 426
distribution measurements for all the hydrometeor types by use of an approach based 427
on the relationship between skewness (S) and kurtosis (K) Taylor diagram and RED are 428
further introduced to assess the performance of different size distribution functions 429
against measurements It is shown that the HSDs for the four types can all be well 430
described statistically by the Gamma and Weibull distribution but Lognormal 431
Exponential and Gaussian are not fit to describe HSDs Gamma and Weibull distribution 432
describe raindrop and mixed-phase size distribution better than snowflake and graupel 433
size distribution and their performances are worst for snowflake It may due to graupel 434
and snowflake precipitation have more big particles When S less than 2 and K less than 435
6 Weibull distribution performs better than Gamma distribution to describe HSDs but 436
21
Gamma distribution performs better for total data 437
A few points are noteworthy First although this study demonstrates the great 438
potential of combining simultaneous disdrometer measurements of particle fall velocity 439
and size distributions microscopic photography and cloud radar to address the 440
challenges facing solid precipitation the data are limited More research is needed to 441
discern such effects on the results presented here Second as the observations show 442
that in addition to sizes there are many other factors (eg hydrometeor type 443
microphysical processes turbulence and measuring principle) that can potentially 444
influence particle fall velocity as well More comprehensive research is needed to 445
further discern and separate these factors Finally the combined use of S-K diagram 446
Taylor diagram and relative Euclidean distance appears to be a powerful tool for 447
identifying the best function used to describe the HSDs and quantify the differences 448
between different precipitation types More research is in order along this direction 449
Acknowledgements 450
This study is mainly supported by the Chinese National Science Foundation under Grant 451
No 41675138 and National Key RampD Program of China (2017YFC0209604) It is partly 452
supported by Beijing National Science Foundation (8172023) the US Department 453
Energys Atmospheric System Research (ASR) Program (Liu and Jia at BNL) Lu is 454
supported by the Natural Science Foundation of Jiangsu Province (BK20160041) The 455
observation data are archived at a specialized supercomputer at Beijing Meteorology 456
Information Center (ftp10224592) which are available from the corresponding 457
author upon request The authors also thank Beijing weather modification office for 458
their support during the field experiment 459
Reference 460
22
Agosta CC Fettweis XX Datta RR 2015 Evaluation of the CMIP5 models in the 461
aim of regional modelling of the Antarctic surface mass balance Cryosphere 9 2311ndash462
2321 httpdxdoiorg105194tc-9-2311-2015 463
Barthazy E and R Schefold 2006 Fall velocity of snowflakes of different riming degree 464
and crystal types Atmos Res 82(1) 391-398 httpsdoiorg101016jatmosres 465
200512009 466
Battaglia A Rustemeier E Tokay A et al 2010 PARSIVEL snow observations a critical 467
assessment J Atmos Oceanic Technol 27(2) 333-344 doi 1011752009jtecha13321 468
Boumlhm H P 1989 A General Equation for the Terminal Fall Speed of Solid Hydrometeors 469
J Atmos Sci 46(15) 2419-2427 httpsdoiorg1011751520-0469(1989)046 lt2419A 470
GEFTTgt20CO2 471
Boudala F S G A Isaac et al 2014 Comparisons of Snowfall Measurements in 472
Complex Terrain Made During the 2010 Winter Olympics in Vancouver Pure and 473
Applied Geophysics 171(1) 113-127 474
Chen B W Hu and J Pu 2011 Characteristics of the raindrop size distribution for 475
freezing precipitation observed in southern China J Geophys Res 116 D06201 476
doi1010292010JD015305 477
Chen B Z Hu L Liu and G Zhang (2017) Raindrop Size Distribution Measurements at 478
4500m on the Tibetan Plateau during TIPEX-III J Geophys Res 122 11092-11106 479
doiorg10100 22017JD027233 480
23
Cugerone K and C De Michele 2017 Investigating raindrop size distributions in the 481
(L-)skewness-(L-)kurtosis plane Quart J Roy Meteor Soc 143(704) 1303-1312 482
httpsdoiorg101002qj3005 483
Donnadieu G 1980 Comparison of results obtained with the VIDIAZ spectro 484
pluviometer and the JossndashWaldvogel rainfall disdrometer in a ldquorain of a thundery typerdquo 485
J Appl Meteor 19 593ndash597 486
Feingold G and Levin Z 1986 The lognormal fit to raindrop spectra from frontal 487
convective clouds in Israel J Clim Appl Meteorol 25 1346ndash1363 488
httpsdoiorg1011751520-0450(1986)025lt1346tlftrsgt20CO2 489
Field P R A J Heymsfield and A Bansemer 2007 Snow Size Distribution 490
Parameterization for Midlatitude and Tropical Ice Clouds J Atmos Sci 64(12) 491
4346-4365 httpsdoiorg1011752007JAS23441 492
Garrett T J and S E Yuter 2014 Observed influence of riming temperature and 493
turbulence on the fallspeed of solid precipitation Geophysical Research Letters 41(18) 494
6515ndash6522 495
Geresdi I N Sarkadi and G Thompson 2014 Effect of the accretion by water drops 496
on the melting of snowflakes Atmos Res 149 96-110 497
Gunn R and G D Kinzer 1949 The terminal velocity of fall for water drops in stagnant 498
air J Meteor 6 243-248 httpsdoiorg1011751520-0469(1949)006lt0243TTVOFFgt 499
20CO2 500
24
Heymsfield A J and C D Westbrook 2010 Advances in the Estimation of Ice Particle 501
Fall Speeds Using Laboratory and Field Measurements J Atmos Sci 67(8) 2469-2482 502
httpsdoiorg1011752010JAS33791 503
Huang G-J C Kleinkort V N Bringi and B M Notaroš 2017 Winter precipitation 504
particle size distribution measurement by Multi-Angle Snowflake Camera Atmos Res 505
198 81-96 506
Intergovernmental Panel on Climate Change (IPCC) 2001 Climate Change 2001 The 507
Scientific Basis Contribution of Working Group I to the Third Assessment Report of the 508
Intergovernmental Panel on Climate Change edited by J T Houghton et al 881 pp 509
Cambridge Univ Press New York 510
Ishizaka M H Motoyoshi S Nakai T Shiina T Kumakura and K-i Muramoto 2013 A 511
New Method for Identifying the Main Type of Solid Hydrometeors Contributing to 512
Snowfall from Measured Size-Fall Speed Relationship Journal of the Meteorological 513
Society of Japan Ser II 91(6) 747-762 httpsdoiorg102151jmsj2013-602 514
Khvorostyanov V 2005 Fall Velocities of Hydrometeors in the Atmosphere 515
Refinements to a Continuous Analytical Power Law J Atmos Sci 62 4343-4357 516
httpsdoiorg101175JAS36221 517
Kikuchi K T Kameda K Higuchi and A Yamashita 2013 A global classification of 518
snow crystals ice crystals and solid precipitation based on observations from middle 519
latitudes to polar regions Atmos Res 132-133 460-472 520
Kneifel S A von Lerber J Tiira D Moisseev P Kollias and J Leinonen 2015 521
Observed relations between snowfall microphysics and triple-frequency radar 522
25
measurements J Geophys Res Atmos 120(12) 6034-6055 523
httpsdoi1010022015JD023156 524
Kubicek A and P K Wang 2012 A numerical study of the flow fields around a typical 525
conical graupel falling at various inclination angles Atmos Res 118 15ndash26 526
httpsdoi101016jatmosres201206001 527
Larsen M L A B Kostinski and A R Jameson (2014) Further evidence for 528
superterminal raindrops Geophys Res Lett 41(19) 6914-6918 529
Lee JE SH Jung H M Park S Kwon P L Lin and G W Lee 2015 Classification of 530
Precipitation Types Using Fall Velocity Diameter Relationships from 2D-Video 531
Distrometer Measurements Advances in Atmospheric Sciences (09) 532
Lin Y L J Donner and B A Colle 2010 Parameterization of riming intensity and its 533
impact on ice fall speed using arm data Mon Weather Rev 139(3) 1036ndash1047 534
httpsdoi1011752010MWR32991 535
Liu Y G 1992 Skewness and kurtosis of measured raindrop size distributions Atmos 536
Environ 26A 2713-2716 httpsdoiorg1010160960-1686(92)90005-6 537
Liu Y G 1993 Statistical theory of the Marshall-Parmer distribution of raindrops 538
Atmos Environ 27A 15-19 httpsdoiorg1010160960-1686(93)90066-8 539
Liu Y G and F Liu 1994 On the description of aerosol particle size distribution Atmos 540
Res 31(1-3) 187-198 httpsdoiorg1010160169-8095(94)90043-4 541
Liu Y G L You W Yang F Liu 1995 On the size distribution of cloud droplets Atmos 542
Res 35 (2-4) 201-216 httpsdoiorg1010160169-8095(94)00019-A 543
Locatelli J D and P V Hobbs 1974 Fall speeds and masses of solid precipitation 544
26
particles J Geophys Res 79(15) 2185-2197 httpsdoi101029JC079i015p02185 545
Loumlffler-Mang M and J Joss 2000 An optical disdrometer for measuring size and 546
velocity of hydrometeors J Atmos Oceanic Technol 17 130-139 547
httpsdoiorg1011751520-0426(2000)017lt0130AODFMSgt20CO2 548
Loumlffler-Mang M and U Blahak 2001 Estimation of the Equivalent Radar Reflectivity 549
Factor from Measured Snow Size Spectra J Clim Appl Meteorol 40(4) 843-849 550
httpsdoiorg1011751520-0450(2001)040lt0843EOTERRgt20CO2 551
Matrosov S Y 2007 Modeling Backscatter Properties of Snowfall at Millimeter 552
Wavelengths J Atmos Sci 64(5) 1727-1736 httpsdoiorg101175JAS39041 553
Mitchell D L 1996 Use of mass- and area-dimensional power laws for determining 554
precipitation particle terminal velocities J Atmos Sci 53 1710-1723 555
httpsdoiorg1011751520-0469(1996)053lt1710UOMAADgt20CO2 556
Montero-Martiacutenez G A B Kostinski R A Shaw and F Garciacutea-Garciacutea 2009 Do all 557
raindrops fall at terminal speed Geophys Res Lett 36 L11818 558
httpsdoiorg1010292008GL037111 559
Niu S X Jia J Sang X Liu C Lu and Y Liu 2010 Distributions of raindrop sizes and 560
fall velocities in a semiarid plateau climate Convective vs stratiform rains J Appl 561
Meteorol Climatol 49 632ndash645 httpsdoi1011752009JAMC22081 562
Nurzyńska K M Kubo and K-i Muramoto 2012 Texture operator for snow particle 563
classification into snowflake and graupel Atmos Res 118 121-132 564
Oue M M R Kumjian Y Lu J Verlinde K Aydin and E E Clothiaux 2015 Linear 565
27
Depolarization Ratios of columnar ice crystals in a deep precipitating system over the 566
Arctic observed by Zenith-Pointing Ka-Band Doppler radar J Clim Appl Meteorol 567
54(5) 1060-1068 httpsdoiorg101175JAMC-D-15-00121 568
Pruppacher H R and J D Klett 1998 Microphysics of clouds and precipitation Kluwer 569
Academic 954 pp 570
Rasmussen R B Baker et al 2012 How well are we measuring snow the 571
NOAAFAANCAR winter precipitation test bed Bull Amer Meteor Soc 93(6) 811-829 572
httpsdoiorg101175BAMS-D-11-000521 573
Reisner J R M Rasmussen and R T Bruintjes 1998 Explicit forecasting of 574
supercooled liquid water in winter storms using the MM5 mesoscale model Q J R 575
Meteorol Soc 124 1071ndash1107 httpsdoi101256smsqj54803 576
Rosenfeld D and Ulbrich C W 2003 Cloud microphysical properties processes and 577
rainfall estimation opportunities Meteorol Monogr 30 237-237 578
httpsdoiorg101175 0065-9401(2003)030lt0237cmppargt20CO2 579
Schaefer V J 1956 The preparation of snow crystal replicas-VI Weatherwsie 9 580
132-135 581
Souverijns N A Gossart S Lhermitte I V Gorodetskaya S Kneifel M Maahn F L 582
Bliven and N P M van Lipzig (2017) Estimating radar reflectivity - Snowfall rate 583
relationships and their uncertainties over Antarctica by combining disdrometer and 584
radar observations Atmos Res 196 211-223 585
Taylor K E 2001 Summarizing multiple aspects of model performance in a single 586
diagram J Geophys Res 106 7183ndash7192 httpsdoi1010292000JD900719 587
28
Tokay A and D A Short 1996 Evidence from tropical raindrop spectra of the origin of 588
rain from stratiform versus convective clouds J Appl Meteor 35 355ndash371 589
Tokay A and D Atlas 1999 Rainfall microphysics and radar properties analysis 590
methods for drop size spectra J Appl Meteor 37 912-923 591
httpsdoiorg1011751520-0450(1998)037lt0912RMARPAgt20CO2 592
Tokay A D B Wolff et al 2014 Evaluation of the New version of the laser-optical 593
disdrometer OTT Parsivel2 J Atmos Oceanic Technol 31(6) 1276-1288 594
httpsdoiorg101175JTECH-D-13-001741 595
Ulbrich C W 1983 Natural variations in the analytical form of the raindrop size 596
distribution J Appl Meteor 5 1764-1775 597
Wen G H Xiao H Yang Y Bi and W Xu 2017 Characteristics of summer and winter 598
precipitation over northern China Atmos Res 197 390-406 599
Wu W Y Liu and A K Betts 2012 Observationally based evaluation of NWP 600
reanalyses in modeling cloud properties over the Southern Great Plains J Geophys 601
Res 117 D12202 httpsdoi1010292011JD016971 602
Yuter S E D E Kingsmill L B Nance and M Loumlffler-Mang 2006 Observations of 603
precipitation size and fall velocity characteristics within coexisting rain and wet snow J 604
Appl Meteor Climatol 45 1450ndash1464 doi httpsdoiorg101175JAM24061 605
Zhang P C and B Y Du 2000 Radar Meteorology China Meteorological Press 511pp 606
(in Chinese) 607
608
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
16
where Di is the central diameter of the i-th bin ni is the number concentration of the 327
i-th bin and Nt is total number concentration Note that each individual HSD can be 328
used to obtain a pair of S and K which is shown as a dot in Figure 5 Also noteworthy is 329
that the SndashK relationships for the families of Gamma Weibull and Lognormal are 330
described by known analytical functions (Liu 1993 1994 and 1995 Cugerone and 331
Michele 2017) represented by theoretical curves in Figure 5 The Exponential and 332
Gaussian distributions are represented by single points on the S-K diagram (S=2 and K=6 333
for Exponential) and (S=0 and K=0 for Gaussian) respectively Thus by comparing the 334
measured S and K values (points) with the known theoretical curves one can determine 335
the most proper function used to describe HSDs 336
Figure 5 shows the scatter plots of observed SndashK pairs calculated from the HSD 337
measurements for raindrop graupel snowflake mixed-phase precipitations Also 338
shown as comparison are the theoretical curves corresponding to the analytical HSD 339
functions A few points are evident First despite some occasional departures most of 340
the points fall near the theoretical lines of Gamma and Weibull distributions suggesting 341
that the HSD patterns for all the four types of precipitations well follow the Gamma and 342
Weibull distributions statistically Second HSDs of raindrops and mixed hydrometeors 343
are better described by Gamma and Weibull distribution than graupels and snowflakes 344
Third the S and K do not cluster around points (2 6) and (0 0) suggesting that the 345
Gaussian and Exponential distribution are not appropriate for describing HSDs 346
especially Gaussian distribution 347
To further evaluate the overall performance of the different distribution functions 348
17
we employ the widely used technique of Taylor diagram (Taylor 2001) and ldquoRelative 349
Euclidean Distancerdquo (RED) (Wu et al 2012) as a supplement to the Taylor diagram The 350
Taylor diagram has been widely used to visualize the statistical differences between 351
model results and observations in evaluation of model performance against 352
measurements or other benchmarks (IPCC 2001) Correlation coefficient (r) standard 353
deviation (σ) and ldquocentered root-mean-square errorrdquo (RMSE hereafter) are used in 354
the Taylor diagram The RED is introduced to add the bias as well in a dimensionless 355
framework that allows for comparison between different physical quantities with 356
different units In this study we consider the S and K values derived from the 357
distribution functions as model results and evaluate them against those derived from 358
the HSD measurements Brieflythe expressions for calculating r and σ and RMSE are 359
shown below 360
119903 =1
119873sum (119872119899minus)(119874119899minus)119873119899=1
120590119872120590119900 (4) 361
119877119872119878119864 = 1
119873sum [(119872119899 minus ) minus (119874119899 minus )]2119873119899=1
12
(5) 362
120590119872 = [1
119873sum (119872119899 minus )119873119899=1 ]
12
(6) 363
1205900 = [1
119873sum (119874119899 minus )119873119899=1 ]
12
(7) 364
where M and O denote distribution function and observed variables The RED 365
expression is shown below 366
119877119864119863 = [(minus)
]2
+ [(120590119872minus120590119874)
120590119900]2
+ (1 minus 119903)212
( 8 ) 367
Equation (8) indicates that RED considers all the components of mean bias variations 368
and correlations in a dimensionless way the distribution function performance 369
degrades as RED increases from the perfect agreement with RED=0 370
18
In the Taylor diagrams shown in Fig 6 the cosine of azimuthal angle of each point 371
gives the r between the function-calculated and observed data The distance between 372
individual point and the reference point ldquoObsrdquo represents the RMSE normalized by the 373
amplitude of the observationally based variations As this distance approaches to zero 374
the function-calculated K and S approach to the observations Clearly the values of r 375
are around 097 for Gamma and Weibull r for Lognormal function is slightly smaller 376
(095) The normalized σ are much different for Lognormal Gamma and Weibull 377
distributions with averaged value being 057 0895 and 0785 respectively Therefore 378
the Lognormal distribution exhibits the worst performance for describing HSDs and 379
Gamma and Weibull distributions appear to perform much better (Fig 6a) 380
Noticing that S and K of Gamma and Weibull distributions are equal at the point of S 381
= 2 and K = 6 and have positive relationship (If S lt 2 then K lt 6 and if S gt 2 then k gt 6) In 382
this part we further separately examine the group of data with S lt 2 and K lt 6 (Fig 6b) 383
and compare its result with those of total data The averaged normalized σ are 103 and 384
109 and r are 091 and 090 for Weibull and Gamma distributions respectively 385
suggesting that Weibull distribution performs slightly better than Gamma distribution 386
for the four HSD types in the data group of S lt 2 and K lt 6 whereas the opposite is true 387
for all data This conclusion is further substantiated by comparison of RED values for the 388
four type of precipitation (Fig7) which shows that Lognormal has the largest RED 389
Gamma the smallest and Weibull in between for four types of precipitations in all data 390
whereas Weibull (Lognormal) has smallest (largest) RED values when S lt 2 and K lt 6 It 391
can be inferred for data group of S gt 2 and k gt 6 Gamma distribution performs better 392
19
Further comparison between different precipitation types shows these functions all 393
performs better for raindrop size distributions and mixed-phase than graupel and 394
snowflake size distributions The RED for snowflakes is largest among the four types 395
The performance of Gamma is better for describing solid HSDs of all data but Weibull 396
distribution is better when S lt 2 and K lt 6 397
5 Conclusion 398
The combined measurements collected during a field experiment conducted at the 399
Haituo Mountain site using PARSIVEL disdrometer millimeter wavelength cloud radar 400
and microscope photography are analyzed to classify the precipitation hydrometeor 401
types examine the dependence of fall velocity on hydrometeor size for different 402
hydrometeor types and determine the best distribution functions to describe the 403
hydrometeor size distributions of different types 404
Analysis of the PARSIVEL-measured fall velocities show that on average the 405
dependence of fall velocity on hydrometeor size largely follow their corresponding 406
terminal velocity curves for raindrops graupels and snowflakes respectively suggesting 407
that such measurements are useful to identify the hydrometeor types The associated 408
microscope photos and cloud radar observations support the classification of 409
hydrometeor types based on the PARSIVEL-observed fall velocities Furthermore there 410
are velocity spreads in fall velocity across hydrometeor sizes for all hydrometeors and 411
the spreads for the solid hydrometeors could cause by hydrometeor type turbulence or 412
updraftdowndraft and instrument measured principle The coexistence of various 413
types of hydrometeors likely induces additional spread of fall velocity for given 414
20
hydrometeor sizes such as mixed precipitation Meanwhile complex microphysical 415
processes in cold precipitation such as riming aggregation breakup and collision and 416
coalescence influence fall velocity which likely induce larger spread of fall velocity Last 417
but not the least the disdrometer may suffer from instrumental errors due to the 418
internally assumed relationship between horizontal and vertical particle dimensions 419
Comparison of the type-averaged hydrometeor size distributions shows that the 420
mixed precipitation has more small hydrometeors with D lt 15 mm than others 421
whereas the snowflake precipitation has the least number of small hydrometeors 422
among the four types On the contrary the snowflake precipitation has more large 423
hydrometeors with D between 3 mm and 11 mm 424
The commonly used size distribution functions (Gamma Weibull and Lognormal) 425
are further examined to determine the most adequate function to describe the size 426
distribution measurements for all the hydrometeor types by use of an approach based 427
on the relationship between skewness (S) and kurtosis (K) Taylor diagram and RED are 428
further introduced to assess the performance of different size distribution functions 429
against measurements It is shown that the HSDs for the four types can all be well 430
described statistically by the Gamma and Weibull distribution but Lognormal 431
Exponential and Gaussian are not fit to describe HSDs Gamma and Weibull distribution 432
describe raindrop and mixed-phase size distribution better than snowflake and graupel 433
size distribution and their performances are worst for snowflake It may due to graupel 434
and snowflake precipitation have more big particles When S less than 2 and K less than 435
6 Weibull distribution performs better than Gamma distribution to describe HSDs but 436
21
Gamma distribution performs better for total data 437
A few points are noteworthy First although this study demonstrates the great 438
potential of combining simultaneous disdrometer measurements of particle fall velocity 439
and size distributions microscopic photography and cloud radar to address the 440
challenges facing solid precipitation the data are limited More research is needed to 441
discern such effects on the results presented here Second as the observations show 442
that in addition to sizes there are many other factors (eg hydrometeor type 443
microphysical processes turbulence and measuring principle) that can potentially 444
influence particle fall velocity as well More comprehensive research is needed to 445
further discern and separate these factors Finally the combined use of S-K diagram 446
Taylor diagram and relative Euclidean distance appears to be a powerful tool for 447
identifying the best function used to describe the HSDs and quantify the differences 448
between different precipitation types More research is in order along this direction 449
Acknowledgements 450
This study is mainly supported by the Chinese National Science Foundation under Grant 451
No 41675138 and National Key RampD Program of China (2017YFC0209604) It is partly 452
supported by Beijing National Science Foundation (8172023) the US Department 453
Energys Atmospheric System Research (ASR) Program (Liu and Jia at BNL) Lu is 454
supported by the Natural Science Foundation of Jiangsu Province (BK20160041) The 455
observation data are archived at a specialized supercomputer at Beijing Meteorology 456
Information Center (ftp10224592) which are available from the corresponding 457
author upon request The authors also thank Beijing weather modification office for 458
their support during the field experiment 459
Reference 460
22
Agosta CC Fettweis XX Datta RR 2015 Evaluation of the CMIP5 models in the 461
aim of regional modelling of the Antarctic surface mass balance Cryosphere 9 2311ndash462
2321 httpdxdoiorg105194tc-9-2311-2015 463
Barthazy E and R Schefold 2006 Fall velocity of snowflakes of different riming degree 464
and crystal types Atmos Res 82(1) 391-398 httpsdoiorg101016jatmosres 465
200512009 466
Battaglia A Rustemeier E Tokay A et al 2010 PARSIVEL snow observations a critical 467
assessment J Atmos Oceanic Technol 27(2) 333-344 doi 1011752009jtecha13321 468
Boumlhm H P 1989 A General Equation for the Terminal Fall Speed of Solid Hydrometeors 469
J Atmos Sci 46(15) 2419-2427 httpsdoiorg1011751520-0469(1989)046 lt2419A 470
GEFTTgt20CO2 471
Boudala F S G A Isaac et al 2014 Comparisons of Snowfall Measurements in 472
Complex Terrain Made During the 2010 Winter Olympics in Vancouver Pure and 473
Applied Geophysics 171(1) 113-127 474
Chen B W Hu and J Pu 2011 Characteristics of the raindrop size distribution for 475
freezing precipitation observed in southern China J Geophys Res 116 D06201 476
doi1010292010JD015305 477
Chen B Z Hu L Liu and G Zhang (2017) Raindrop Size Distribution Measurements at 478
4500m on the Tibetan Plateau during TIPEX-III J Geophys Res 122 11092-11106 479
doiorg10100 22017JD027233 480
23
Cugerone K and C De Michele 2017 Investigating raindrop size distributions in the 481
(L-)skewness-(L-)kurtosis plane Quart J Roy Meteor Soc 143(704) 1303-1312 482
httpsdoiorg101002qj3005 483
Donnadieu G 1980 Comparison of results obtained with the VIDIAZ spectro 484
pluviometer and the JossndashWaldvogel rainfall disdrometer in a ldquorain of a thundery typerdquo 485
J Appl Meteor 19 593ndash597 486
Feingold G and Levin Z 1986 The lognormal fit to raindrop spectra from frontal 487
convective clouds in Israel J Clim Appl Meteorol 25 1346ndash1363 488
httpsdoiorg1011751520-0450(1986)025lt1346tlftrsgt20CO2 489
Field P R A J Heymsfield and A Bansemer 2007 Snow Size Distribution 490
Parameterization for Midlatitude and Tropical Ice Clouds J Atmos Sci 64(12) 491
4346-4365 httpsdoiorg1011752007JAS23441 492
Garrett T J and S E Yuter 2014 Observed influence of riming temperature and 493
turbulence on the fallspeed of solid precipitation Geophysical Research Letters 41(18) 494
6515ndash6522 495
Geresdi I N Sarkadi and G Thompson 2014 Effect of the accretion by water drops 496
on the melting of snowflakes Atmos Res 149 96-110 497
Gunn R and G D Kinzer 1949 The terminal velocity of fall for water drops in stagnant 498
air J Meteor 6 243-248 httpsdoiorg1011751520-0469(1949)006lt0243TTVOFFgt 499
20CO2 500
24
Heymsfield A J and C D Westbrook 2010 Advances in the Estimation of Ice Particle 501
Fall Speeds Using Laboratory and Field Measurements J Atmos Sci 67(8) 2469-2482 502
httpsdoiorg1011752010JAS33791 503
Huang G-J C Kleinkort V N Bringi and B M Notaroš 2017 Winter precipitation 504
particle size distribution measurement by Multi-Angle Snowflake Camera Atmos Res 505
198 81-96 506
Intergovernmental Panel on Climate Change (IPCC) 2001 Climate Change 2001 The 507
Scientific Basis Contribution of Working Group I to the Third Assessment Report of the 508
Intergovernmental Panel on Climate Change edited by J T Houghton et al 881 pp 509
Cambridge Univ Press New York 510
Ishizaka M H Motoyoshi S Nakai T Shiina T Kumakura and K-i Muramoto 2013 A 511
New Method for Identifying the Main Type of Solid Hydrometeors Contributing to 512
Snowfall from Measured Size-Fall Speed Relationship Journal of the Meteorological 513
Society of Japan Ser II 91(6) 747-762 httpsdoiorg102151jmsj2013-602 514
Khvorostyanov V 2005 Fall Velocities of Hydrometeors in the Atmosphere 515
Refinements to a Continuous Analytical Power Law J Atmos Sci 62 4343-4357 516
httpsdoiorg101175JAS36221 517
Kikuchi K T Kameda K Higuchi and A Yamashita 2013 A global classification of 518
snow crystals ice crystals and solid precipitation based on observations from middle 519
latitudes to polar regions Atmos Res 132-133 460-472 520
Kneifel S A von Lerber J Tiira D Moisseev P Kollias and J Leinonen 2015 521
Observed relations between snowfall microphysics and triple-frequency radar 522
25
measurements J Geophys Res Atmos 120(12) 6034-6055 523
httpsdoi1010022015JD023156 524
Kubicek A and P K Wang 2012 A numerical study of the flow fields around a typical 525
conical graupel falling at various inclination angles Atmos Res 118 15ndash26 526
httpsdoi101016jatmosres201206001 527
Larsen M L A B Kostinski and A R Jameson (2014) Further evidence for 528
superterminal raindrops Geophys Res Lett 41(19) 6914-6918 529
Lee JE SH Jung H M Park S Kwon P L Lin and G W Lee 2015 Classification of 530
Precipitation Types Using Fall Velocity Diameter Relationships from 2D-Video 531
Distrometer Measurements Advances in Atmospheric Sciences (09) 532
Lin Y L J Donner and B A Colle 2010 Parameterization of riming intensity and its 533
impact on ice fall speed using arm data Mon Weather Rev 139(3) 1036ndash1047 534
httpsdoi1011752010MWR32991 535
Liu Y G 1992 Skewness and kurtosis of measured raindrop size distributions Atmos 536
Environ 26A 2713-2716 httpsdoiorg1010160960-1686(92)90005-6 537
Liu Y G 1993 Statistical theory of the Marshall-Parmer distribution of raindrops 538
Atmos Environ 27A 15-19 httpsdoiorg1010160960-1686(93)90066-8 539
Liu Y G and F Liu 1994 On the description of aerosol particle size distribution Atmos 540
Res 31(1-3) 187-198 httpsdoiorg1010160169-8095(94)90043-4 541
Liu Y G L You W Yang F Liu 1995 On the size distribution of cloud droplets Atmos 542
Res 35 (2-4) 201-216 httpsdoiorg1010160169-8095(94)00019-A 543
Locatelli J D and P V Hobbs 1974 Fall speeds and masses of solid precipitation 544
26
particles J Geophys Res 79(15) 2185-2197 httpsdoi101029JC079i015p02185 545
Loumlffler-Mang M and J Joss 2000 An optical disdrometer for measuring size and 546
velocity of hydrometeors J Atmos Oceanic Technol 17 130-139 547
httpsdoiorg1011751520-0426(2000)017lt0130AODFMSgt20CO2 548
Loumlffler-Mang M and U Blahak 2001 Estimation of the Equivalent Radar Reflectivity 549
Factor from Measured Snow Size Spectra J Clim Appl Meteorol 40(4) 843-849 550
httpsdoiorg1011751520-0450(2001)040lt0843EOTERRgt20CO2 551
Matrosov S Y 2007 Modeling Backscatter Properties of Snowfall at Millimeter 552
Wavelengths J Atmos Sci 64(5) 1727-1736 httpsdoiorg101175JAS39041 553
Mitchell D L 1996 Use of mass- and area-dimensional power laws for determining 554
precipitation particle terminal velocities J Atmos Sci 53 1710-1723 555
httpsdoiorg1011751520-0469(1996)053lt1710UOMAADgt20CO2 556
Montero-Martiacutenez G A B Kostinski R A Shaw and F Garciacutea-Garciacutea 2009 Do all 557
raindrops fall at terminal speed Geophys Res Lett 36 L11818 558
httpsdoiorg1010292008GL037111 559
Niu S X Jia J Sang X Liu C Lu and Y Liu 2010 Distributions of raindrop sizes and 560
fall velocities in a semiarid plateau climate Convective vs stratiform rains J Appl 561
Meteorol Climatol 49 632ndash645 httpsdoi1011752009JAMC22081 562
Nurzyńska K M Kubo and K-i Muramoto 2012 Texture operator for snow particle 563
classification into snowflake and graupel Atmos Res 118 121-132 564
Oue M M R Kumjian Y Lu J Verlinde K Aydin and E E Clothiaux 2015 Linear 565
27
Depolarization Ratios of columnar ice crystals in a deep precipitating system over the 566
Arctic observed by Zenith-Pointing Ka-Band Doppler radar J Clim Appl Meteorol 567
54(5) 1060-1068 httpsdoiorg101175JAMC-D-15-00121 568
Pruppacher H R and J D Klett 1998 Microphysics of clouds and precipitation Kluwer 569
Academic 954 pp 570
Rasmussen R B Baker et al 2012 How well are we measuring snow the 571
NOAAFAANCAR winter precipitation test bed Bull Amer Meteor Soc 93(6) 811-829 572
httpsdoiorg101175BAMS-D-11-000521 573
Reisner J R M Rasmussen and R T Bruintjes 1998 Explicit forecasting of 574
supercooled liquid water in winter storms using the MM5 mesoscale model Q J R 575
Meteorol Soc 124 1071ndash1107 httpsdoi101256smsqj54803 576
Rosenfeld D and Ulbrich C W 2003 Cloud microphysical properties processes and 577
rainfall estimation opportunities Meteorol Monogr 30 237-237 578
httpsdoiorg101175 0065-9401(2003)030lt0237cmppargt20CO2 579
Schaefer V J 1956 The preparation of snow crystal replicas-VI Weatherwsie 9 580
132-135 581
Souverijns N A Gossart S Lhermitte I V Gorodetskaya S Kneifel M Maahn F L 582
Bliven and N P M van Lipzig (2017) Estimating radar reflectivity - Snowfall rate 583
relationships and their uncertainties over Antarctica by combining disdrometer and 584
radar observations Atmos Res 196 211-223 585
Taylor K E 2001 Summarizing multiple aspects of model performance in a single 586
diagram J Geophys Res 106 7183ndash7192 httpsdoi1010292000JD900719 587
28
Tokay A and D A Short 1996 Evidence from tropical raindrop spectra of the origin of 588
rain from stratiform versus convective clouds J Appl Meteor 35 355ndash371 589
Tokay A and D Atlas 1999 Rainfall microphysics and radar properties analysis 590
methods for drop size spectra J Appl Meteor 37 912-923 591
httpsdoiorg1011751520-0450(1998)037lt0912RMARPAgt20CO2 592
Tokay A D B Wolff et al 2014 Evaluation of the New version of the laser-optical 593
disdrometer OTT Parsivel2 J Atmos Oceanic Technol 31(6) 1276-1288 594
httpsdoiorg101175JTECH-D-13-001741 595
Ulbrich C W 1983 Natural variations in the analytical form of the raindrop size 596
distribution J Appl Meteor 5 1764-1775 597
Wen G H Xiao H Yang Y Bi and W Xu 2017 Characteristics of summer and winter 598
precipitation over northern China Atmos Res 197 390-406 599
Wu W Y Liu and A K Betts 2012 Observationally based evaluation of NWP 600
reanalyses in modeling cloud properties over the Southern Great Plains J Geophys 601
Res 117 D12202 httpsdoi1010292011JD016971 602
Yuter S E D E Kingsmill L B Nance and M Loumlffler-Mang 2006 Observations of 603
precipitation size and fall velocity characteristics within coexisting rain and wet snow J 604
Appl Meteor Climatol 45 1450ndash1464 doi httpsdoiorg101175JAM24061 605
Zhang P C and B Y Du 2000 Radar Meteorology China Meteorological Press 511pp 606
(in Chinese) 607
608
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
17
we employ the widely used technique of Taylor diagram (Taylor 2001) and ldquoRelative 349
Euclidean Distancerdquo (RED) (Wu et al 2012) as a supplement to the Taylor diagram The 350
Taylor diagram has been widely used to visualize the statistical differences between 351
model results and observations in evaluation of model performance against 352
measurements or other benchmarks (IPCC 2001) Correlation coefficient (r) standard 353
deviation (σ) and ldquocentered root-mean-square errorrdquo (RMSE hereafter) are used in 354
the Taylor diagram The RED is introduced to add the bias as well in a dimensionless 355
framework that allows for comparison between different physical quantities with 356
different units In this study we consider the S and K values derived from the 357
distribution functions as model results and evaluate them against those derived from 358
the HSD measurements Brieflythe expressions for calculating r and σ and RMSE are 359
shown below 360
119903 =1
119873sum (119872119899minus)(119874119899minus)119873119899=1
120590119872120590119900 (4) 361
119877119872119878119864 = 1
119873sum [(119872119899 minus ) minus (119874119899 minus )]2119873119899=1
12
(5) 362
120590119872 = [1
119873sum (119872119899 minus )119873119899=1 ]
12
(6) 363
1205900 = [1
119873sum (119874119899 minus )119873119899=1 ]
12
(7) 364
where M and O denote distribution function and observed variables The RED 365
expression is shown below 366
119877119864119863 = [(minus)
]2
+ [(120590119872minus120590119874)
120590119900]2
+ (1 minus 119903)212
( 8 ) 367
Equation (8) indicates that RED considers all the components of mean bias variations 368
and correlations in a dimensionless way the distribution function performance 369
degrades as RED increases from the perfect agreement with RED=0 370
18
In the Taylor diagrams shown in Fig 6 the cosine of azimuthal angle of each point 371
gives the r between the function-calculated and observed data The distance between 372
individual point and the reference point ldquoObsrdquo represents the RMSE normalized by the 373
amplitude of the observationally based variations As this distance approaches to zero 374
the function-calculated K and S approach to the observations Clearly the values of r 375
are around 097 for Gamma and Weibull r for Lognormal function is slightly smaller 376
(095) The normalized σ are much different for Lognormal Gamma and Weibull 377
distributions with averaged value being 057 0895 and 0785 respectively Therefore 378
the Lognormal distribution exhibits the worst performance for describing HSDs and 379
Gamma and Weibull distributions appear to perform much better (Fig 6a) 380
Noticing that S and K of Gamma and Weibull distributions are equal at the point of S 381
= 2 and K = 6 and have positive relationship (If S lt 2 then K lt 6 and if S gt 2 then k gt 6) In 382
this part we further separately examine the group of data with S lt 2 and K lt 6 (Fig 6b) 383
and compare its result with those of total data The averaged normalized σ are 103 and 384
109 and r are 091 and 090 for Weibull and Gamma distributions respectively 385
suggesting that Weibull distribution performs slightly better than Gamma distribution 386
for the four HSD types in the data group of S lt 2 and K lt 6 whereas the opposite is true 387
for all data This conclusion is further substantiated by comparison of RED values for the 388
four type of precipitation (Fig7) which shows that Lognormal has the largest RED 389
Gamma the smallest and Weibull in between for four types of precipitations in all data 390
whereas Weibull (Lognormal) has smallest (largest) RED values when S lt 2 and K lt 6 It 391
can be inferred for data group of S gt 2 and k gt 6 Gamma distribution performs better 392
19
Further comparison between different precipitation types shows these functions all 393
performs better for raindrop size distributions and mixed-phase than graupel and 394
snowflake size distributions The RED for snowflakes is largest among the four types 395
The performance of Gamma is better for describing solid HSDs of all data but Weibull 396
distribution is better when S lt 2 and K lt 6 397
5 Conclusion 398
The combined measurements collected during a field experiment conducted at the 399
Haituo Mountain site using PARSIVEL disdrometer millimeter wavelength cloud radar 400
and microscope photography are analyzed to classify the precipitation hydrometeor 401
types examine the dependence of fall velocity on hydrometeor size for different 402
hydrometeor types and determine the best distribution functions to describe the 403
hydrometeor size distributions of different types 404
Analysis of the PARSIVEL-measured fall velocities show that on average the 405
dependence of fall velocity on hydrometeor size largely follow their corresponding 406
terminal velocity curves for raindrops graupels and snowflakes respectively suggesting 407
that such measurements are useful to identify the hydrometeor types The associated 408
microscope photos and cloud radar observations support the classification of 409
hydrometeor types based on the PARSIVEL-observed fall velocities Furthermore there 410
are velocity spreads in fall velocity across hydrometeor sizes for all hydrometeors and 411
the spreads for the solid hydrometeors could cause by hydrometeor type turbulence or 412
updraftdowndraft and instrument measured principle The coexistence of various 413
types of hydrometeors likely induces additional spread of fall velocity for given 414
20
hydrometeor sizes such as mixed precipitation Meanwhile complex microphysical 415
processes in cold precipitation such as riming aggregation breakup and collision and 416
coalescence influence fall velocity which likely induce larger spread of fall velocity Last 417
but not the least the disdrometer may suffer from instrumental errors due to the 418
internally assumed relationship between horizontal and vertical particle dimensions 419
Comparison of the type-averaged hydrometeor size distributions shows that the 420
mixed precipitation has more small hydrometeors with D lt 15 mm than others 421
whereas the snowflake precipitation has the least number of small hydrometeors 422
among the four types On the contrary the snowflake precipitation has more large 423
hydrometeors with D between 3 mm and 11 mm 424
The commonly used size distribution functions (Gamma Weibull and Lognormal) 425
are further examined to determine the most adequate function to describe the size 426
distribution measurements for all the hydrometeor types by use of an approach based 427
on the relationship between skewness (S) and kurtosis (K) Taylor diagram and RED are 428
further introduced to assess the performance of different size distribution functions 429
against measurements It is shown that the HSDs for the four types can all be well 430
described statistically by the Gamma and Weibull distribution but Lognormal 431
Exponential and Gaussian are not fit to describe HSDs Gamma and Weibull distribution 432
describe raindrop and mixed-phase size distribution better than snowflake and graupel 433
size distribution and their performances are worst for snowflake It may due to graupel 434
and snowflake precipitation have more big particles When S less than 2 and K less than 435
6 Weibull distribution performs better than Gamma distribution to describe HSDs but 436
21
Gamma distribution performs better for total data 437
A few points are noteworthy First although this study demonstrates the great 438
potential of combining simultaneous disdrometer measurements of particle fall velocity 439
and size distributions microscopic photography and cloud radar to address the 440
challenges facing solid precipitation the data are limited More research is needed to 441
discern such effects on the results presented here Second as the observations show 442
that in addition to sizes there are many other factors (eg hydrometeor type 443
microphysical processes turbulence and measuring principle) that can potentially 444
influence particle fall velocity as well More comprehensive research is needed to 445
further discern and separate these factors Finally the combined use of S-K diagram 446
Taylor diagram and relative Euclidean distance appears to be a powerful tool for 447
identifying the best function used to describe the HSDs and quantify the differences 448
between different precipitation types More research is in order along this direction 449
Acknowledgements 450
This study is mainly supported by the Chinese National Science Foundation under Grant 451
No 41675138 and National Key RampD Program of China (2017YFC0209604) It is partly 452
supported by Beijing National Science Foundation (8172023) the US Department 453
Energys Atmospheric System Research (ASR) Program (Liu and Jia at BNL) Lu is 454
supported by the Natural Science Foundation of Jiangsu Province (BK20160041) The 455
observation data are archived at a specialized supercomputer at Beijing Meteorology 456
Information Center (ftp10224592) which are available from the corresponding 457
author upon request The authors also thank Beijing weather modification office for 458
their support during the field experiment 459
Reference 460
22
Agosta CC Fettweis XX Datta RR 2015 Evaluation of the CMIP5 models in the 461
aim of regional modelling of the Antarctic surface mass balance Cryosphere 9 2311ndash462
2321 httpdxdoiorg105194tc-9-2311-2015 463
Barthazy E and R Schefold 2006 Fall velocity of snowflakes of different riming degree 464
and crystal types Atmos Res 82(1) 391-398 httpsdoiorg101016jatmosres 465
200512009 466
Battaglia A Rustemeier E Tokay A et al 2010 PARSIVEL snow observations a critical 467
assessment J Atmos Oceanic Technol 27(2) 333-344 doi 1011752009jtecha13321 468
Boumlhm H P 1989 A General Equation for the Terminal Fall Speed of Solid Hydrometeors 469
J Atmos Sci 46(15) 2419-2427 httpsdoiorg1011751520-0469(1989)046 lt2419A 470
GEFTTgt20CO2 471
Boudala F S G A Isaac et al 2014 Comparisons of Snowfall Measurements in 472
Complex Terrain Made During the 2010 Winter Olympics in Vancouver Pure and 473
Applied Geophysics 171(1) 113-127 474
Chen B W Hu and J Pu 2011 Characteristics of the raindrop size distribution for 475
freezing precipitation observed in southern China J Geophys Res 116 D06201 476
doi1010292010JD015305 477
Chen B Z Hu L Liu and G Zhang (2017) Raindrop Size Distribution Measurements at 478
4500m on the Tibetan Plateau during TIPEX-III J Geophys Res 122 11092-11106 479
doiorg10100 22017JD027233 480
23
Cugerone K and C De Michele 2017 Investigating raindrop size distributions in the 481
(L-)skewness-(L-)kurtosis plane Quart J Roy Meteor Soc 143(704) 1303-1312 482
httpsdoiorg101002qj3005 483
Donnadieu G 1980 Comparison of results obtained with the VIDIAZ spectro 484
pluviometer and the JossndashWaldvogel rainfall disdrometer in a ldquorain of a thundery typerdquo 485
J Appl Meteor 19 593ndash597 486
Feingold G and Levin Z 1986 The lognormal fit to raindrop spectra from frontal 487
convective clouds in Israel J Clim Appl Meteorol 25 1346ndash1363 488
httpsdoiorg1011751520-0450(1986)025lt1346tlftrsgt20CO2 489
Field P R A J Heymsfield and A Bansemer 2007 Snow Size Distribution 490
Parameterization for Midlatitude and Tropical Ice Clouds J Atmos Sci 64(12) 491
4346-4365 httpsdoiorg1011752007JAS23441 492
Garrett T J and S E Yuter 2014 Observed influence of riming temperature and 493
turbulence on the fallspeed of solid precipitation Geophysical Research Letters 41(18) 494
6515ndash6522 495
Geresdi I N Sarkadi and G Thompson 2014 Effect of the accretion by water drops 496
on the melting of snowflakes Atmos Res 149 96-110 497
Gunn R and G D Kinzer 1949 The terminal velocity of fall for water drops in stagnant 498
air J Meteor 6 243-248 httpsdoiorg1011751520-0469(1949)006lt0243TTVOFFgt 499
20CO2 500
24
Heymsfield A J and C D Westbrook 2010 Advances in the Estimation of Ice Particle 501
Fall Speeds Using Laboratory and Field Measurements J Atmos Sci 67(8) 2469-2482 502
httpsdoiorg1011752010JAS33791 503
Huang G-J C Kleinkort V N Bringi and B M Notaroš 2017 Winter precipitation 504
particle size distribution measurement by Multi-Angle Snowflake Camera Atmos Res 505
198 81-96 506
Intergovernmental Panel on Climate Change (IPCC) 2001 Climate Change 2001 The 507
Scientific Basis Contribution of Working Group I to the Third Assessment Report of the 508
Intergovernmental Panel on Climate Change edited by J T Houghton et al 881 pp 509
Cambridge Univ Press New York 510
Ishizaka M H Motoyoshi S Nakai T Shiina T Kumakura and K-i Muramoto 2013 A 511
New Method for Identifying the Main Type of Solid Hydrometeors Contributing to 512
Snowfall from Measured Size-Fall Speed Relationship Journal of the Meteorological 513
Society of Japan Ser II 91(6) 747-762 httpsdoiorg102151jmsj2013-602 514
Khvorostyanov V 2005 Fall Velocities of Hydrometeors in the Atmosphere 515
Refinements to a Continuous Analytical Power Law J Atmos Sci 62 4343-4357 516
httpsdoiorg101175JAS36221 517
Kikuchi K T Kameda K Higuchi and A Yamashita 2013 A global classification of 518
snow crystals ice crystals and solid precipitation based on observations from middle 519
latitudes to polar regions Atmos Res 132-133 460-472 520
Kneifel S A von Lerber J Tiira D Moisseev P Kollias and J Leinonen 2015 521
Observed relations between snowfall microphysics and triple-frequency radar 522
25
measurements J Geophys Res Atmos 120(12) 6034-6055 523
httpsdoi1010022015JD023156 524
Kubicek A and P K Wang 2012 A numerical study of the flow fields around a typical 525
conical graupel falling at various inclination angles Atmos Res 118 15ndash26 526
httpsdoi101016jatmosres201206001 527
Larsen M L A B Kostinski and A R Jameson (2014) Further evidence for 528
superterminal raindrops Geophys Res Lett 41(19) 6914-6918 529
Lee JE SH Jung H M Park S Kwon P L Lin and G W Lee 2015 Classification of 530
Precipitation Types Using Fall Velocity Diameter Relationships from 2D-Video 531
Distrometer Measurements Advances in Atmospheric Sciences (09) 532
Lin Y L J Donner and B A Colle 2010 Parameterization of riming intensity and its 533
impact on ice fall speed using arm data Mon Weather Rev 139(3) 1036ndash1047 534
httpsdoi1011752010MWR32991 535
Liu Y G 1992 Skewness and kurtosis of measured raindrop size distributions Atmos 536
Environ 26A 2713-2716 httpsdoiorg1010160960-1686(92)90005-6 537
Liu Y G 1993 Statistical theory of the Marshall-Parmer distribution of raindrops 538
Atmos Environ 27A 15-19 httpsdoiorg1010160960-1686(93)90066-8 539
Liu Y G and F Liu 1994 On the description of aerosol particle size distribution Atmos 540
Res 31(1-3) 187-198 httpsdoiorg1010160169-8095(94)90043-4 541
Liu Y G L You W Yang F Liu 1995 On the size distribution of cloud droplets Atmos 542
Res 35 (2-4) 201-216 httpsdoiorg1010160169-8095(94)00019-A 543
Locatelli J D and P V Hobbs 1974 Fall speeds and masses of solid precipitation 544
26
particles J Geophys Res 79(15) 2185-2197 httpsdoi101029JC079i015p02185 545
Loumlffler-Mang M and J Joss 2000 An optical disdrometer for measuring size and 546
velocity of hydrometeors J Atmos Oceanic Technol 17 130-139 547
httpsdoiorg1011751520-0426(2000)017lt0130AODFMSgt20CO2 548
Loumlffler-Mang M and U Blahak 2001 Estimation of the Equivalent Radar Reflectivity 549
Factor from Measured Snow Size Spectra J Clim Appl Meteorol 40(4) 843-849 550
httpsdoiorg1011751520-0450(2001)040lt0843EOTERRgt20CO2 551
Matrosov S Y 2007 Modeling Backscatter Properties of Snowfall at Millimeter 552
Wavelengths J Atmos Sci 64(5) 1727-1736 httpsdoiorg101175JAS39041 553
Mitchell D L 1996 Use of mass- and area-dimensional power laws for determining 554
precipitation particle terminal velocities J Atmos Sci 53 1710-1723 555
httpsdoiorg1011751520-0469(1996)053lt1710UOMAADgt20CO2 556
Montero-Martiacutenez G A B Kostinski R A Shaw and F Garciacutea-Garciacutea 2009 Do all 557
raindrops fall at terminal speed Geophys Res Lett 36 L11818 558
httpsdoiorg1010292008GL037111 559
Niu S X Jia J Sang X Liu C Lu and Y Liu 2010 Distributions of raindrop sizes and 560
fall velocities in a semiarid plateau climate Convective vs stratiform rains J Appl 561
Meteorol Climatol 49 632ndash645 httpsdoi1011752009JAMC22081 562
Nurzyńska K M Kubo and K-i Muramoto 2012 Texture operator for snow particle 563
classification into snowflake and graupel Atmos Res 118 121-132 564
Oue M M R Kumjian Y Lu J Verlinde K Aydin and E E Clothiaux 2015 Linear 565
27
Depolarization Ratios of columnar ice crystals in a deep precipitating system over the 566
Arctic observed by Zenith-Pointing Ka-Band Doppler radar J Clim Appl Meteorol 567
54(5) 1060-1068 httpsdoiorg101175JAMC-D-15-00121 568
Pruppacher H R and J D Klett 1998 Microphysics of clouds and precipitation Kluwer 569
Academic 954 pp 570
Rasmussen R B Baker et al 2012 How well are we measuring snow the 571
NOAAFAANCAR winter precipitation test bed Bull Amer Meteor Soc 93(6) 811-829 572
httpsdoiorg101175BAMS-D-11-000521 573
Reisner J R M Rasmussen and R T Bruintjes 1998 Explicit forecasting of 574
supercooled liquid water in winter storms using the MM5 mesoscale model Q J R 575
Meteorol Soc 124 1071ndash1107 httpsdoi101256smsqj54803 576
Rosenfeld D and Ulbrich C W 2003 Cloud microphysical properties processes and 577
rainfall estimation opportunities Meteorol Monogr 30 237-237 578
httpsdoiorg101175 0065-9401(2003)030lt0237cmppargt20CO2 579
Schaefer V J 1956 The preparation of snow crystal replicas-VI Weatherwsie 9 580
132-135 581
Souverijns N A Gossart S Lhermitte I V Gorodetskaya S Kneifel M Maahn F L 582
Bliven and N P M van Lipzig (2017) Estimating radar reflectivity - Snowfall rate 583
relationships and their uncertainties over Antarctica by combining disdrometer and 584
radar observations Atmos Res 196 211-223 585
Taylor K E 2001 Summarizing multiple aspects of model performance in a single 586
diagram J Geophys Res 106 7183ndash7192 httpsdoi1010292000JD900719 587
28
Tokay A and D A Short 1996 Evidence from tropical raindrop spectra of the origin of 588
rain from stratiform versus convective clouds J Appl Meteor 35 355ndash371 589
Tokay A and D Atlas 1999 Rainfall microphysics and radar properties analysis 590
methods for drop size spectra J Appl Meteor 37 912-923 591
httpsdoiorg1011751520-0450(1998)037lt0912RMARPAgt20CO2 592
Tokay A D B Wolff et al 2014 Evaluation of the New version of the laser-optical 593
disdrometer OTT Parsivel2 J Atmos Oceanic Technol 31(6) 1276-1288 594
httpsdoiorg101175JTECH-D-13-001741 595
Ulbrich C W 1983 Natural variations in the analytical form of the raindrop size 596
distribution J Appl Meteor 5 1764-1775 597
Wen G H Xiao H Yang Y Bi and W Xu 2017 Characteristics of summer and winter 598
precipitation over northern China Atmos Res 197 390-406 599
Wu W Y Liu and A K Betts 2012 Observationally based evaluation of NWP 600
reanalyses in modeling cloud properties over the Southern Great Plains J Geophys 601
Res 117 D12202 httpsdoi1010292011JD016971 602
Yuter S E D E Kingsmill L B Nance and M Loumlffler-Mang 2006 Observations of 603
precipitation size and fall velocity characteristics within coexisting rain and wet snow J 604
Appl Meteor Climatol 45 1450ndash1464 doi httpsdoiorg101175JAM24061 605
Zhang P C and B Y Du 2000 Radar Meteorology China Meteorological Press 511pp 606
(in Chinese) 607
608
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
18
In the Taylor diagrams shown in Fig 6 the cosine of azimuthal angle of each point 371
gives the r between the function-calculated and observed data The distance between 372
individual point and the reference point ldquoObsrdquo represents the RMSE normalized by the 373
amplitude of the observationally based variations As this distance approaches to zero 374
the function-calculated K and S approach to the observations Clearly the values of r 375
are around 097 for Gamma and Weibull r for Lognormal function is slightly smaller 376
(095) The normalized σ are much different for Lognormal Gamma and Weibull 377
distributions with averaged value being 057 0895 and 0785 respectively Therefore 378
the Lognormal distribution exhibits the worst performance for describing HSDs and 379
Gamma and Weibull distributions appear to perform much better (Fig 6a) 380
Noticing that S and K of Gamma and Weibull distributions are equal at the point of S 381
= 2 and K = 6 and have positive relationship (If S lt 2 then K lt 6 and if S gt 2 then k gt 6) In 382
this part we further separately examine the group of data with S lt 2 and K lt 6 (Fig 6b) 383
and compare its result with those of total data The averaged normalized σ are 103 and 384
109 and r are 091 and 090 for Weibull and Gamma distributions respectively 385
suggesting that Weibull distribution performs slightly better than Gamma distribution 386
for the four HSD types in the data group of S lt 2 and K lt 6 whereas the opposite is true 387
for all data This conclusion is further substantiated by comparison of RED values for the 388
four type of precipitation (Fig7) which shows that Lognormal has the largest RED 389
Gamma the smallest and Weibull in between for four types of precipitations in all data 390
whereas Weibull (Lognormal) has smallest (largest) RED values when S lt 2 and K lt 6 It 391
can be inferred for data group of S gt 2 and k gt 6 Gamma distribution performs better 392
19
Further comparison between different precipitation types shows these functions all 393
performs better for raindrop size distributions and mixed-phase than graupel and 394
snowflake size distributions The RED for snowflakes is largest among the four types 395
The performance of Gamma is better for describing solid HSDs of all data but Weibull 396
distribution is better when S lt 2 and K lt 6 397
5 Conclusion 398
The combined measurements collected during a field experiment conducted at the 399
Haituo Mountain site using PARSIVEL disdrometer millimeter wavelength cloud radar 400
and microscope photography are analyzed to classify the precipitation hydrometeor 401
types examine the dependence of fall velocity on hydrometeor size for different 402
hydrometeor types and determine the best distribution functions to describe the 403
hydrometeor size distributions of different types 404
Analysis of the PARSIVEL-measured fall velocities show that on average the 405
dependence of fall velocity on hydrometeor size largely follow their corresponding 406
terminal velocity curves for raindrops graupels and snowflakes respectively suggesting 407
that such measurements are useful to identify the hydrometeor types The associated 408
microscope photos and cloud radar observations support the classification of 409
hydrometeor types based on the PARSIVEL-observed fall velocities Furthermore there 410
are velocity spreads in fall velocity across hydrometeor sizes for all hydrometeors and 411
the spreads for the solid hydrometeors could cause by hydrometeor type turbulence or 412
updraftdowndraft and instrument measured principle The coexistence of various 413
types of hydrometeors likely induces additional spread of fall velocity for given 414
20
hydrometeor sizes such as mixed precipitation Meanwhile complex microphysical 415
processes in cold precipitation such as riming aggregation breakup and collision and 416
coalescence influence fall velocity which likely induce larger spread of fall velocity Last 417
but not the least the disdrometer may suffer from instrumental errors due to the 418
internally assumed relationship between horizontal and vertical particle dimensions 419
Comparison of the type-averaged hydrometeor size distributions shows that the 420
mixed precipitation has more small hydrometeors with D lt 15 mm than others 421
whereas the snowflake precipitation has the least number of small hydrometeors 422
among the four types On the contrary the snowflake precipitation has more large 423
hydrometeors with D between 3 mm and 11 mm 424
The commonly used size distribution functions (Gamma Weibull and Lognormal) 425
are further examined to determine the most adequate function to describe the size 426
distribution measurements for all the hydrometeor types by use of an approach based 427
on the relationship between skewness (S) and kurtosis (K) Taylor diagram and RED are 428
further introduced to assess the performance of different size distribution functions 429
against measurements It is shown that the HSDs for the four types can all be well 430
described statistically by the Gamma and Weibull distribution but Lognormal 431
Exponential and Gaussian are not fit to describe HSDs Gamma and Weibull distribution 432
describe raindrop and mixed-phase size distribution better than snowflake and graupel 433
size distribution and their performances are worst for snowflake It may due to graupel 434
and snowflake precipitation have more big particles When S less than 2 and K less than 435
6 Weibull distribution performs better than Gamma distribution to describe HSDs but 436
21
Gamma distribution performs better for total data 437
A few points are noteworthy First although this study demonstrates the great 438
potential of combining simultaneous disdrometer measurements of particle fall velocity 439
and size distributions microscopic photography and cloud radar to address the 440
challenges facing solid precipitation the data are limited More research is needed to 441
discern such effects on the results presented here Second as the observations show 442
that in addition to sizes there are many other factors (eg hydrometeor type 443
microphysical processes turbulence and measuring principle) that can potentially 444
influence particle fall velocity as well More comprehensive research is needed to 445
further discern and separate these factors Finally the combined use of S-K diagram 446
Taylor diagram and relative Euclidean distance appears to be a powerful tool for 447
identifying the best function used to describe the HSDs and quantify the differences 448
between different precipitation types More research is in order along this direction 449
Acknowledgements 450
This study is mainly supported by the Chinese National Science Foundation under Grant 451
No 41675138 and National Key RampD Program of China (2017YFC0209604) It is partly 452
supported by Beijing National Science Foundation (8172023) the US Department 453
Energys Atmospheric System Research (ASR) Program (Liu and Jia at BNL) Lu is 454
supported by the Natural Science Foundation of Jiangsu Province (BK20160041) The 455
observation data are archived at a specialized supercomputer at Beijing Meteorology 456
Information Center (ftp10224592) which are available from the corresponding 457
author upon request The authors also thank Beijing weather modification office for 458
their support during the field experiment 459
Reference 460
22
Agosta CC Fettweis XX Datta RR 2015 Evaluation of the CMIP5 models in the 461
aim of regional modelling of the Antarctic surface mass balance Cryosphere 9 2311ndash462
2321 httpdxdoiorg105194tc-9-2311-2015 463
Barthazy E and R Schefold 2006 Fall velocity of snowflakes of different riming degree 464
and crystal types Atmos Res 82(1) 391-398 httpsdoiorg101016jatmosres 465
200512009 466
Battaglia A Rustemeier E Tokay A et al 2010 PARSIVEL snow observations a critical 467
assessment J Atmos Oceanic Technol 27(2) 333-344 doi 1011752009jtecha13321 468
Boumlhm H P 1989 A General Equation for the Terminal Fall Speed of Solid Hydrometeors 469
J Atmos Sci 46(15) 2419-2427 httpsdoiorg1011751520-0469(1989)046 lt2419A 470
GEFTTgt20CO2 471
Boudala F S G A Isaac et al 2014 Comparisons of Snowfall Measurements in 472
Complex Terrain Made During the 2010 Winter Olympics in Vancouver Pure and 473
Applied Geophysics 171(1) 113-127 474
Chen B W Hu and J Pu 2011 Characteristics of the raindrop size distribution for 475
freezing precipitation observed in southern China J Geophys Res 116 D06201 476
doi1010292010JD015305 477
Chen B Z Hu L Liu and G Zhang (2017) Raindrop Size Distribution Measurements at 478
4500m on the Tibetan Plateau during TIPEX-III J Geophys Res 122 11092-11106 479
doiorg10100 22017JD027233 480
23
Cugerone K and C De Michele 2017 Investigating raindrop size distributions in the 481
(L-)skewness-(L-)kurtosis plane Quart J Roy Meteor Soc 143(704) 1303-1312 482
httpsdoiorg101002qj3005 483
Donnadieu G 1980 Comparison of results obtained with the VIDIAZ spectro 484
pluviometer and the JossndashWaldvogel rainfall disdrometer in a ldquorain of a thundery typerdquo 485
J Appl Meteor 19 593ndash597 486
Feingold G and Levin Z 1986 The lognormal fit to raindrop spectra from frontal 487
convective clouds in Israel J Clim Appl Meteorol 25 1346ndash1363 488
httpsdoiorg1011751520-0450(1986)025lt1346tlftrsgt20CO2 489
Field P R A J Heymsfield and A Bansemer 2007 Snow Size Distribution 490
Parameterization for Midlatitude and Tropical Ice Clouds J Atmos Sci 64(12) 491
4346-4365 httpsdoiorg1011752007JAS23441 492
Garrett T J and S E Yuter 2014 Observed influence of riming temperature and 493
turbulence on the fallspeed of solid precipitation Geophysical Research Letters 41(18) 494
6515ndash6522 495
Geresdi I N Sarkadi and G Thompson 2014 Effect of the accretion by water drops 496
on the melting of snowflakes Atmos Res 149 96-110 497
Gunn R and G D Kinzer 1949 The terminal velocity of fall for water drops in stagnant 498
air J Meteor 6 243-248 httpsdoiorg1011751520-0469(1949)006lt0243TTVOFFgt 499
20CO2 500
24
Heymsfield A J and C D Westbrook 2010 Advances in the Estimation of Ice Particle 501
Fall Speeds Using Laboratory and Field Measurements J Atmos Sci 67(8) 2469-2482 502
httpsdoiorg1011752010JAS33791 503
Huang G-J C Kleinkort V N Bringi and B M Notaroš 2017 Winter precipitation 504
particle size distribution measurement by Multi-Angle Snowflake Camera Atmos Res 505
198 81-96 506
Intergovernmental Panel on Climate Change (IPCC) 2001 Climate Change 2001 The 507
Scientific Basis Contribution of Working Group I to the Third Assessment Report of the 508
Intergovernmental Panel on Climate Change edited by J T Houghton et al 881 pp 509
Cambridge Univ Press New York 510
Ishizaka M H Motoyoshi S Nakai T Shiina T Kumakura and K-i Muramoto 2013 A 511
New Method for Identifying the Main Type of Solid Hydrometeors Contributing to 512
Snowfall from Measured Size-Fall Speed Relationship Journal of the Meteorological 513
Society of Japan Ser II 91(6) 747-762 httpsdoiorg102151jmsj2013-602 514
Khvorostyanov V 2005 Fall Velocities of Hydrometeors in the Atmosphere 515
Refinements to a Continuous Analytical Power Law J Atmos Sci 62 4343-4357 516
httpsdoiorg101175JAS36221 517
Kikuchi K T Kameda K Higuchi and A Yamashita 2013 A global classification of 518
snow crystals ice crystals and solid precipitation based on observations from middle 519
latitudes to polar regions Atmos Res 132-133 460-472 520
Kneifel S A von Lerber J Tiira D Moisseev P Kollias and J Leinonen 2015 521
Observed relations between snowfall microphysics and triple-frequency radar 522
25
measurements J Geophys Res Atmos 120(12) 6034-6055 523
httpsdoi1010022015JD023156 524
Kubicek A and P K Wang 2012 A numerical study of the flow fields around a typical 525
conical graupel falling at various inclination angles Atmos Res 118 15ndash26 526
httpsdoi101016jatmosres201206001 527
Larsen M L A B Kostinski and A R Jameson (2014) Further evidence for 528
superterminal raindrops Geophys Res Lett 41(19) 6914-6918 529
Lee JE SH Jung H M Park S Kwon P L Lin and G W Lee 2015 Classification of 530
Precipitation Types Using Fall Velocity Diameter Relationships from 2D-Video 531
Distrometer Measurements Advances in Atmospheric Sciences (09) 532
Lin Y L J Donner and B A Colle 2010 Parameterization of riming intensity and its 533
impact on ice fall speed using arm data Mon Weather Rev 139(3) 1036ndash1047 534
httpsdoi1011752010MWR32991 535
Liu Y G 1992 Skewness and kurtosis of measured raindrop size distributions Atmos 536
Environ 26A 2713-2716 httpsdoiorg1010160960-1686(92)90005-6 537
Liu Y G 1993 Statistical theory of the Marshall-Parmer distribution of raindrops 538
Atmos Environ 27A 15-19 httpsdoiorg1010160960-1686(93)90066-8 539
Liu Y G and F Liu 1994 On the description of aerosol particle size distribution Atmos 540
Res 31(1-3) 187-198 httpsdoiorg1010160169-8095(94)90043-4 541
Liu Y G L You W Yang F Liu 1995 On the size distribution of cloud droplets Atmos 542
Res 35 (2-4) 201-216 httpsdoiorg1010160169-8095(94)00019-A 543
Locatelli J D and P V Hobbs 1974 Fall speeds and masses of solid precipitation 544
26
particles J Geophys Res 79(15) 2185-2197 httpsdoi101029JC079i015p02185 545
Loumlffler-Mang M and J Joss 2000 An optical disdrometer for measuring size and 546
velocity of hydrometeors J Atmos Oceanic Technol 17 130-139 547
httpsdoiorg1011751520-0426(2000)017lt0130AODFMSgt20CO2 548
Loumlffler-Mang M and U Blahak 2001 Estimation of the Equivalent Radar Reflectivity 549
Factor from Measured Snow Size Spectra J Clim Appl Meteorol 40(4) 843-849 550
httpsdoiorg1011751520-0450(2001)040lt0843EOTERRgt20CO2 551
Matrosov S Y 2007 Modeling Backscatter Properties of Snowfall at Millimeter 552
Wavelengths J Atmos Sci 64(5) 1727-1736 httpsdoiorg101175JAS39041 553
Mitchell D L 1996 Use of mass- and area-dimensional power laws for determining 554
precipitation particle terminal velocities J Atmos Sci 53 1710-1723 555
httpsdoiorg1011751520-0469(1996)053lt1710UOMAADgt20CO2 556
Montero-Martiacutenez G A B Kostinski R A Shaw and F Garciacutea-Garciacutea 2009 Do all 557
raindrops fall at terminal speed Geophys Res Lett 36 L11818 558
httpsdoiorg1010292008GL037111 559
Niu S X Jia J Sang X Liu C Lu and Y Liu 2010 Distributions of raindrop sizes and 560
fall velocities in a semiarid plateau climate Convective vs stratiform rains J Appl 561
Meteorol Climatol 49 632ndash645 httpsdoi1011752009JAMC22081 562
Nurzyńska K M Kubo and K-i Muramoto 2012 Texture operator for snow particle 563
classification into snowflake and graupel Atmos Res 118 121-132 564
Oue M M R Kumjian Y Lu J Verlinde K Aydin and E E Clothiaux 2015 Linear 565
27
Depolarization Ratios of columnar ice crystals in a deep precipitating system over the 566
Arctic observed by Zenith-Pointing Ka-Band Doppler radar J Clim Appl Meteorol 567
54(5) 1060-1068 httpsdoiorg101175JAMC-D-15-00121 568
Pruppacher H R and J D Klett 1998 Microphysics of clouds and precipitation Kluwer 569
Academic 954 pp 570
Rasmussen R B Baker et al 2012 How well are we measuring snow the 571
NOAAFAANCAR winter precipitation test bed Bull Amer Meteor Soc 93(6) 811-829 572
httpsdoiorg101175BAMS-D-11-000521 573
Reisner J R M Rasmussen and R T Bruintjes 1998 Explicit forecasting of 574
supercooled liquid water in winter storms using the MM5 mesoscale model Q J R 575
Meteorol Soc 124 1071ndash1107 httpsdoi101256smsqj54803 576
Rosenfeld D and Ulbrich C W 2003 Cloud microphysical properties processes and 577
rainfall estimation opportunities Meteorol Monogr 30 237-237 578
httpsdoiorg101175 0065-9401(2003)030lt0237cmppargt20CO2 579
Schaefer V J 1956 The preparation of snow crystal replicas-VI Weatherwsie 9 580
132-135 581
Souverijns N A Gossart S Lhermitte I V Gorodetskaya S Kneifel M Maahn F L 582
Bliven and N P M van Lipzig (2017) Estimating radar reflectivity - Snowfall rate 583
relationships and their uncertainties over Antarctica by combining disdrometer and 584
radar observations Atmos Res 196 211-223 585
Taylor K E 2001 Summarizing multiple aspects of model performance in a single 586
diagram J Geophys Res 106 7183ndash7192 httpsdoi1010292000JD900719 587
28
Tokay A and D A Short 1996 Evidence from tropical raindrop spectra of the origin of 588
rain from stratiform versus convective clouds J Appl Meteor 35 355ndash371 589
Tokay A and D Atlas 1999 Rainfall microphysics and radar properties analysis 590
methods for drop size spectra J Appl Meteor 37 912-923 591
httpsdoiorg1011751520-0450(1998)037lt0912RMARPAgt20CO2 592
Tokay A D B Wolff et al 2014 Evaluation of the New version of the laser-optical 593
disdrometer OTT Parsivel2 J Atmos Oceanic Technol 31(6) 1276-1288 594
httpsdoiorg101175JTECH-D-13-001741 595
Ulbrich C W 1983 Natural variations in the analytical form of the raindrop size 596
distribution J Appl Meteor 5 1764-1775 597
Wen G H Xiao H Yang Y Bi and W Xu 2017 Characteristics of summer and winter 598
precipitation over northern China Atmos Res 197 390-406 599
Wu W Y Liu and A K Betts 2012 Observationally based evaluation of NWP 600
reanalyses in modeling cloud properties over the Southern Great Plains J Geophys 601
Res 117 D12202 httpsdoi1010292011JD016971 602
Yuter S E D E Kingsmill L B Nance and M Loumlffler-Mang 2006 Observations of 603
precipitation size and fall velocity characteristics within coexisting rain and wet snow J 604
Appl Meteor Climatol 45 1450ndash1464 doi httpsdoiorg101175JAM24061 605
Zhang P C and B Y Du 2000 Radar Meteorology China Meteorological Press 511pp 606
(in Chinese) 607
608
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
19
Further comparison between different precipitation types shows these functions all 393
performs better for raindrop size distributions and mixed-phase than graupel and 394
snowflake size distributions The RED for snowflakes is largest among the four types 395
The performance of Gamma is better for describing solid HSDs of all data but Weibull 396
distribution is better when S lt 2 and K lt 6 397
5 Conclusion 398
The combined measurements collected during a field experiment conducted at the 399
Haituo Mountain site using PARSIVEL disdrometer millimeter wavelength cloud radar 400
and microscope photography are analyzed to classify the precipitation hydrometeor 401
types examine the dependence of fall velocity on hydrometeor size for different 402
hydrometeor types and determine the best distribution functions to describe the 403
hydrometeor size distributions of different types 404
Analysis of the PARSIVEL-measured fall velocities show that on average the 405
dependence of fall velocity on hydrometeor size largely follow their corresponding 406
terminal velocity curves for raindrops graupels and snowflakes respectively suggesting 407
that such measurements are useful to identify the hydrometeor types The associated 408
microscope photos and cloud radar observations support the classification of 409
hydrometeor types based on the PARSIVEL-observed fall velocities Furthermore there 410
are velocity spreads in fall velocity across hydrometeor sizes for all hydrometeors and 411
the spreads for the solid hydrometeors could cause by hydrometeor type turbulence or 412
updraftdowndraft and instrument measured principle The coexistence of various 413
types of hydrometeors likely induces additional spread of fall velocity for given 414
20
hydrometeor sizes such as mixed precipitation Meanwhile complex microphysical 415
processes in cold precipitation such as riming aggregation breakup and collision and 416
coalescence influence fall velocity which likely induce larger spread of fall velocity Last 417
but not the least the disdrometer may suffer from instrumental errors due to the 418
internally assumed relationship between horizontal and vertical particle dimensions 419
Comparison of the type-averaged hydrometeor size distributions shows that the 420
mixed precipitation has more small hydrometeors with D lt 15 mm than others 421
whereas the snowflake precipitation has the least number of small hydrometeors 422
among the four types On the contrary the snowflake precipitation has more large 423
hydrometeors with D between 3 mm and 11 mm 424
The commonly used size distribution functions (Gamma Weibull and Lognormal) 425
are further examined to determine the most adequate function to describe the size 426
distribution measurements for all the hydrometeor types by use of an approach based 427
on the relationship between skewness (S) and kurtosis (K) Taylor diagram and RED are 428
further introduced to assess the performance of different size distribution functions 429
against measurements It is shown that the HSDs for the four types can all be well 430
described statistically by the Gamma and Weibull distribution but Lognormal 431
Exponential and Gaussian are not fit to describe HSDs Gamma and Weibull distribution 432
describe raindrop and mixed-phase size distribution better than snowflake and graupel 433
size distribution and their performances are worst for snowflake It may due to graupel 434
and snowflake precipitation have more big particles When S less than 2 and K less than 435
6 Weibull distribution performs better than Gamma distribution to describe HSDs but 436
21
Gamma distribution performs better for total data 437
A few points are noteworthy First although this study demonstrates the great 438
potential of combining simultaneous disdrometer measurements of particle fall velocity 439
and size distributions microscopic photography and cloud radar to address the 440
challenges facing solid precipitation the data are limited More research is needed to 441
discern such effects on the results presented here Second as the observations show 442
that in addition to sizes there are many other factors (eg hydrometeor type 443
microphysical processes turbulence and measuring principle) that can potentially 444
influence particle fall velocity as well More comprehensive research is needed to 445
further discern and separate these factors Finally the combined use of S-K diagram 446
Taylor diagram and relative Euclidean distance appears to be a powerful tool for 447
identifying the best function used to describe the HSDs and quantify the differences 448
between different precipitation types More research is in order along this direction 449
Acknowledgements 450
This study is mainly supported by the Chinese National Science Foundation under Grant 451
No 41675138 and National Key RampD Program of China (2017YFC0209604) It is partly 452
supported by Beijing National Science Foundation (8172023) the US Department 453
Energys Atmospheric System Research (ASR) Program (Liu and Jia at BNL) Lu is 454
supported by the Natural Science Foundation of Jiangsu Province (BK20160041) The 455
observation data are archived at a specialized supercomputer at Beijing Meteorology 456
Information Center (ftp10224592) which are available from the corresponding 457
author upon request The authors also thank Beijing weather modification office for 458
their support during the field experiment 459
Reference 460
22
Agosta CC Fettweis XX Datta RR 2015 Evaluation of the CMIP5 models in the 461
aim of regional modelling of the Antarctic surface mass balance Cryosphere 9 2311ndash462
2321 httpdxdoiorg105194tc-9-2311-2015 463
Barthazy E and R Schefold 2006 Fall velocity of snowflakes of different riming degree 464
and crystal types Atmos Res 82(1) 391-398 httpsdoiorg101016jatmosres 465
200512009 466
Battaglia A Rustemeier E Tokay A et al 2010 PARSIVEL snow observations a critical 467
assessment J Atmos Oceanic Technol 27(2) 333-344 doi 1011752009jtecha13321 468
Boumlhm H P 1989 A General Equation for the Terminal Fall Speed of Solid Hydrometeors 469
J Atmos Sci 46(15) 2419-2427 httpsdoiorg1011751520-0469(1989)046 lt2419A 470
GEFTTgt20CO2 471
Boudala F S G A Isaac et al 2014 Comparisons of Snowfall Measurements in 472
Complex Terrain Made During the 2010 Winter Olympics in Vancouver Pure and 473
Applied Geophysics 171(1) 113-127 474
Chen B W Hu and J Pu 2011 Characteristics of the raindrop size distribution for 475
freezing precipitation observed in southern China J Geophys Res 116 D06201 476
doi1010292010JD015305 477
Chen B Z Hu L Liu and G Zhang (2017) Raindrop Size Distribution Measurements at 478
4500m on the Tibetan Plateau during TIPEX-III J Geophys Res 122 11092-11106 479
doiorg10100 22017JD027233 480
23
Cugerone K and C De Michele 2017 Investigating raindrop size distributions in the 481
(L-)skewness-(L-)kurtosis plane Quart J Roy Meteor Soc 143(704) 1303-1312 482
httpsdoiorg101002qj3005 483
Donnadieu G 1980 Comparison of results obtained with the VIDIAZ spectro 484
pluviometer and the JossndashWaldvogel rainfall disdrometer in a ldquorain of a thundery typerdquo 485
J Appl Meteor 19 593ndash597 486
Feingold G and Levin Z 1986 The lognormal fit to raindrop spectra from frontal 487
convective clouds in Israel J Clim Appl Meteorol 25 1346ndash1363 488
httpsdoiorg1011751520-0450(1986)025lt1346tlftrsgt20CO2 489
Field P R A J Heymsfield and A Bansemer 2007 Snow Size Distribution 490
Parameterization for Midlatitude and Tropical Ice Clouds J Atmos Sci 64(12) 491
4346-4365 httpsdoiorg1011752007JAS23441 492
Garrett T J and S E Yuter 2014 Observed influence of riming temperature and 493
turbulence on the fallspeed of solid precipitation Geophysical Research Letters 41(18) 494
6515ndash6522 495
Geresdi I N Sarkadi and G Thompson 2014 Effect of the accretion by water drops 496
on the melting of snowflakes Atmos Res 149 96-110 497
Gunn R and G D Kinzer 1949 The terminal velocity of fall for water drops in stagnant 498
air J Meteor 6 243-248 httpsdoiorg1011751520-0469(1949)006lt0243TTVOFFgt 499
20CO2 500
24
Heymsfield A J and C D Westbrook 2010 Advances in the Estimation of Ice Particle 501
Fall Speeds Using Laboratory and Field Measurements J Atmos Sci 67(8) 2469-2482 502
httpsdoiorg1011752010JAS33791 503
Huang G-J C Kleinkort V N Bringi and B M Notaroš 2017 Winter precipitation 504
particle size distribution measurement by Multi-Angle Snowflake Camera Atmos Res 505
198 81-96 506
Intergovernmental Panel on Climate Change (IPCC) 2001 Climate Change 2001 The 507
Scientific Basis Contribution of Working Group I to the Third Assessment Report of the 508
Intergovernmental Panel on Climate Change edited by J T Houghton et al 881 pp 509
Cambridge Univ Press New York 510
Ishizaka M H Motoyoshi S Nakai T Shiina T Kumakura and K-i Muramoto 2013 A 511
New Method for Identifying the Main Type of Solid Hydrometeors Contributing to 512
Snowfall from Measured Size-Fall Speed Relationship Journal of the Meteorological 513
Society of Japan Ser II 91(6) 747-762 httpsdoiorg102151jmsj2013-602 514
Khvorostyanov V 2005 Fall Velocities of Hydrometeors in the Atmosphere 515
Refinements to a Continuous Analytical Power Law J Atmos Sci 62 4343-4357 516
httpsdoiorg101175JAS36221 517
Kikuchi K T Kameda K Higuchi and A Yamashita 2013 A global classification of 518
snow crystals ice crystals and solid precipitation based on observations from middle 519
latitudes to polar regions Atmos Res 132-133 460-472 520
Kneifel S A von Lerber J Tiira D Moisseev P Kollias and J Leinonen 2015 521
Observed relations between snowfall microphysics and triple-frequency radar 522
25
measurements J Geophys Res Atmos 120(12) 6034-6055 523
httpsdoi1010022015JD023156 524
Kubicek A and P K Wang 2012 A numerical study of the flow fields around a typical 525
conical graupel falling at various inclination angles Atmos Res 118 15ndash26 526
httpsdoi101016jatmosres201206001 527
Larsen M L A B Kostinski and A R Jameson (2014) Further evidence for 528
superterminal raindrops Geophys Res Lett 41(19) 6914-6918 529
Lee JE SH Jung H M Park S Kwon P L Lin and G W Lee 2015 Classification of 530
Precipitation Types Using Fall Velocity Diameter Relationships from 2D-Video 531
Distrometer Measurements Advances in Atmospheric Sciences (09) 532
Lin Y L J Donner and B A Colle 2010 Parameterization of riming intensity and its 533
impact on ice fall speed using arm data Mon Weather Rev 139(3) 1036ndash1047 534
httpsdoi1011752010MWR32991 535
Liu Y G 1992 Skewness and kurtosis of measured raindrop size distributions Atmos 536
Environ 26A 2713-2716 httpsdoiorg1010160960-1686(92)90005-6 537
Liu Y G 1993 Statistical theory of the Marshall-Parmer distribution of raindrops 538
Atmos Environ 27A 15-19 httpsdoiorg1010160960-1686(93)90066-8 539
Liu Y G and F Liu 1994 On the description of aerosol particle size distribution Atmos 540
Res 31(1-3) 187-198 httpsdoiorg1010160169-8095(94)90043-4 541
Liu Y G L You W Yang F Liu 1995 On the size distribution of cloud droplets Atmos 542
Res 35 (2-4) 201-216 httpsdoiorg1010160169-8095(94)00019-A 543
Locatelli J D and P V Hobbs 1974 Fall speeds and masses of solid precipitation 544
26
particles J Geophys Res 79(15) 2185-2197 httpsdoi101029JC079i015p02185 545
Loumlffler-Mang M and J Joss 2000 An optical disdrometer for measuring size and 546
velocity of hydrometeors J Atmos Oceanic Technol 17 130-139 547
httpsdoiorg1011751520-0426(2000)017lt0130AODFMSgt20CO2 548
Loumlffler-Mang M and U Blahak 2001 Estimation of the Equivalent Radar Reflectivity 549
Factor from Measured Snow Size Spectra J Clim Appl Meteorol 40(4) 843-849 550
httpsdoiorg1011751520-0450(2001)040lt0843EOTERRgt20CO2 551
Matrosov S Y 2007 Modeling Backscatter Properties of Snowfall at Millimeter 552
Wavelengths J Atmos Sci 64(5) 1727-1736 httpsdoiorg101175JAS39041 553
Mitchell D L 1996 Use of mass- and area-dimensional power laws for determining 554
precipitation particle terminal velocities J Atmos Sci 53 1710-1723 555
httpsdoiorg1011751520-0469(1996)053lt1710UOMAADgt20CO2 556
Montero-Martiacutenez G A B Kostinski R A Shaw and F Garciacutea-Garciacutea 2009 Do all 557
raindrops fall at terminal speed Geophys Res Lett 36 L11818 558
httpsdoiorg1010292008GL037111 559
Niu S X Jia J Sang X Liu C Lu and Y Liu 2010 Distributions of raindrop sizes and 560
fall velocities in a semiarid plateau climate Convective vs stratiform rains J Appl 561
Meteorol Climatol 49 632ndash645 httpsdoi1011752009JAMC22081 562
Nurzyńska K M Kubo and K-i Muramoto 2012 Texture operator for snow particle 563
classification into snowflake and graupel Atmos Res 118 121-132 564
Oue M M R Kumjian Y Lu J Verlinde K Aydin and E E Clothiaux 2015 Linear 565
27
Depolarization Ratios of columnar ice crystals in a deep precipitating system over the 566
Arctic observed by Zenith-Pointing Ka-Band Doppler radar J Clim Appl Meteorol 567
54(5) 1060-1068 httpsdoiorg101175JAMC-D-15-00121 568
Pruppacher H R and J D Klett 1998 Microphysics of clouds and precipitation Kluwer 569
Academic 954 pp 570
Rasmussen R B Baker et al 2012 How well are we measuring snow the 571
NOAAFAANCAR winter precipitation test bed Bull Amer Meteor Soc 93(6) 811-829 572
httpsdoiorg101175BAMS-D-11-000521 573
Reisner J R M Rasmussen and R T Bruintjes 1998 Explicit forecasting of 574
supercooled liquid water in winter storms using the MM5 mesoscale model Q J R 575
Meteorol Soc 124 1071ndash1107 httpsdoi101256smsqj54803 576
Rosenfeld D and Ulbrich C W 2003 Cloud microphysical properties processes and 577
rainfall estimation opportunities Meteorol Monogr 30 237-237 578
httpsdoiorg101175 0065-9401(2003)030lt0237cmppargt20CO2 579
Schaefer V J 1956 The preparation of snow crystal replicas-VI Weatherwsie 9 580
132-135 581
Souverijns N A Gossart S Lhermitte I V Gorodetskaya S Kneifel M Maahn F L 582
Bliven and N P M van Lipzig (2017) Estimating radar reflectivity - Snowfall rate 583
relationships and their uncertainties over Antarctica by combining disdrometer and 584
radar observations Atmos Res 196 211-223 585
Taylor K E 2001 Summarizing multiple aspects of model performance in a single 586
diagram J Geophys Res 106 7183ndash7192 httpsdoi1010292000JD900719 587
28
Tokay A and D A Short 1996 Evidence from tropical raindrop spectra of the origin of 588
rain from stratiform versus convective clouds J Appl Meteor 35 355ndash371 589
Tokay A and D Atlas 1999 Rainfall microphysics and radar properties analysis 590
methods for drop size spectra J Appl Meteor 37 912-923 591
httpsdoiorg1011751520-0450(1998)037lt0912RMARPAgt20CO2 592
Tokay A D B Wolff et al 2014 Evaluation of the New version of the laser-optical 593
disdrometer OTT Parsivel2 J Atmos Oceanic Technol 31(6) 1276-1288 594
httpsdoiorg101175JTECH-D-13-001741 595
Ulbrich C W 1983 Natural variations in the analytical form of the raindrop size 596
distribution J Appl Meteor 5 1764-1775 597
Wen G H Xiao H Yang Y Bi and W Xu 2017 Characteristics of summer and winter 598
precipitation over northern China Atmos Res 197 390-406 599
Wu W Y Liu and A K Betts 2012 Observationally based evaluation of NWP 600
reanalyses in modeling cloud properties over the Southern Great Plains J Geophys 601
Res 117 D12202 httpsdoi1010292011JD016971 602
Yuter S E D E Kingsmill L B Nance and M Loumlffler-Mang 2006 Observations of 603
precipitation size and fall velocity characteristics within coexisting rain and wet snow J 604
Appl Meteor Climatol 45 1450ndash1464 doi httpsdoiorg101175JAM24061 605
Zhang P C and B Y Du 2000 Radar Meteorology China Meteorological Press 511pp 606
(in Chinese) 607
608
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
20
hydrometeor sizes such as mixed precipitation Meanwhile complex microphysical 415
processes in cold precipitation such as riming aggregation breakup and collision and 416
coalescence influence fall velocity which likely induce larger spread of fall velocity Last 417
but not the least the disdrometer may suffer from instrumental errors due to the 418
internally assumed relationship between horizontal and vertical particle dimensions 419
Comparison of the type-averaged hydrometeor size distributions shows that the 420
mixed precipitation has more small hydrometeors with D lt 15 mm than others 421
whereas the snowflake precipitation has the least number of small hydrometeors 422
among the four types On the contrary the snowflake precipitation has more large 423
hydrometeors with D between 3 mm and 11 mm 424
The commonly used size distribution functions (Gamma Weibull and Lognormal) 425
are further examined to determine the most adequate function to describe the size 426
distribution measurements for all the hydrometeor types by use of an approach based 427
on the relationship between skewness (S) and kurtosis (K) Taylor diagram and RED are 428
further introduced to assess the performance of different size distribution functions 429
against measurements It is shown that the HSDs for the four types can all be well 430
described statistically by the Gamma and Weibull distribution but Lognormal 431
Exponential and Gaussian are not fit to describe HSDs Gamma and Weibull distribution 432
describe raindrop and mixed-phase size distribution better than snowflake and graupel 433
size distribution and their performances are worst for snowflake It may due to graupel 434
and snowflake precipitation have more big particles When S less than 2 and K less than 435
6 Weibull distribution performs better than Gamma distribution to describe HSDs but 436
21
Gamma distribution performs better for total data 437
A few points are noteworthy First although this study demonstrates the great 438
potential of combining simultaneous disdrometer measurements of particle fall velocity 439
and size distributions microscopic photography and cloud radar to address the 440
challenges facing solid precipitation the data are limited More research is needed to 441
discern such effects on the results presented here Second as the observations show 442
that in addition to sizes there are many other factors (eg hydrometeor type 443
microphysical processes turbulence and measuring principle) that can potentially 444
influence particle fall velocity as well More comprehensive research is needed to 445
further discern and separate these factors Finally the combined use of S-K diagram 446
Taylor diagram and relative Euclidean distance appears to be a powerful tool for 447
identifying the best function used to describe the HSDs and quantify the differences 448
between different precipitation types More research is in order along this direction 449
Acknowledgements 450
This study is mainly supported by the Chinese National Science Foundation under Grant 451
No 41675138 and National Key RampD Program of China (2017YFC0209604) It is partly 452
supported by Beijing National Science Foundation (8172023) the US Department 453
Energys Atmospheric System Research (ASR) Program (Liu and Jia at BNL) Lu is 454
supported by the Natural Science Foundation of Jiangsu Province (BK20160041) The 455
observation data are archived at a specialized supercomputer at Beijing Meteorology 456
Information Center (ftp10224592) which are available from the corresponding 457
author upon request The authors also thank Beijing weather modification office for 458
their support during the field experiment 459
Reference 460
22
Agosta CC Fettweis XX Datta RR 2015 Evaluation of the CMIP5 models in the 461
aim of regional modelling of the Antarctic surface mass balance Cryosphere 9 2311ndash462
2321 httpdxdoiorg105194tc-9-2311-2015 463
Barthazy E and R Schefold 2006 Fall velocity of snowflakes of different riming degree 464
and crystal types Atmos Res 82(1) 391-398 httpsdoiorg101016jatmosres 465
200512009 466
Battaglia A Rustemeier E Tokay A et al 2010 PARSIVEL snow observations a critical 467
assessment J Atmos Oceanic Technol 27(2) 333-344 doi 1011752009jtecha13321 468
Boumlhm H P 1989 A General Equation for the Terminal Fall Speed of Solid Hydrometeors 469
J Atmos Sci 46(15) 2419-2427 httpsdoiorg1011751520-0469(1989)046 lt2419A 470
GEFTTgt20CO2 471
Boudala F S G A Isaac et al 2014 Comparisons of Snowfall Measurements in 472
Complex Terrain Made During the 2010 Winter Olympics in Vancouver Pure and 473
Applied Geophysics 171(1) 113-127 474
Chen B W Hu and J Pu 2011 Characteristics of the raindrop size distribution for 475
freezing precipitation observed in southern China J Geophys Res 116 D06201 476
doi1010292010JD015305 477
Chen B Z Hu L Liu and G Zhang (2017) Raindrop Size Distribution Measurements at 478
4500m on the Tibetan Plateau during TIPEX-III J Geophys Res 122 11092-11106 479
doiorg10100 22017JD027233 480
23
Cugerone K and C De Michele 2017 Investigating raindrop size distributions in the 481
(L-)skewness-(L-)kurtosis plane Quart J Roy Meteor Soc 143(704) 1303-1312 482
httpsdoiorg101002qj3005 483
Donnadieu G 1980 Comparison of results obtained with the VIDIAZ spectro 484
pluviometer and the JossndashWaldvogel rainfall disdrometer in a ldquorain of a thundery typerdquo 485
J Appl Meteor 19 593ndash597 486
Feingold G and Levin Z 1986 The lognormal fit to raindrop spectra from frontal 487
convective clouds in Israel J Clim Appl Meteorol 25 1346ndash1363 488
httpsdoiorg1011751520-0450(1986)025lt1346tlftrsgt20CO2 489
Field P R A J Heymsfield and A Bansemer 2007 Snow Size Distribution 490
Parameterization for Midlatitude and Tropical Ice Clouds J Atmos Sci 64(12) 491
4346-4365 httpsdoiorg1011752007JAS23441 492
Garrett T J and S E Yuter 2014 Observed influence of riming temperature and 493
turbulence on the fallspeed of solid precipitation Geophysical Research Letters 41(18) 494
6515ndash6522 495
Geresdi I N Sarkadi and G Thompson 2014 Effect of the accretion by water drops 496
on the melting of snowflakes Atmos Res 149 96-110 497
Gunn R and G D Kinzer 1949 The terminal velocity of fall for water drops in stagnant 498
air J Meteor 6 243-248 httpsdoiorg1011751520-0469(1949)006lt0243TTVOFFgt 499
20CO2 500
24
Heymsfield A J and C D Westbrook 2010 Advances in the Estimation of Ice Particle 501
Fall Speeds Using Laboratory and Field Measurements J Atmos Sci 67(8) 2469-2482 502
httpsdoiorg1011752010JAS33791 503
Huang G-J C Kleinkort V N Bringi and B M Notaroš 2017 Winter precipitation 504
particle size distribution measurement by Multi-Angle Snowflake Camera Atmos Res 505
198 81-96 506
Intergovernmental Panel on Climate Change (IPCC) 2001 Climate Change 2001 The 507
Scientific Basis Contribution of Working Group I to the Third Assessment Report of the 508
Intergovernmental Panel on Climate Change edited by J T Houghton et al 881 pp 509
Cambridge Univ Press New York 510
Ishizaka M H Motoyoshi S Nakai T Shiina T Kumakura and K-i Muramoto 2013 A 511
New Method for Identifying the Main Type of Solid Hydrometeors Contributing to 512
Snowfall from Measured Size-Fall Speed Relationship Journal of the Meteorological 513
Society of Japan Ser II 91(6) 747-762 httpsdoiorg102151jmsj2013-602 514
Khvorostyanov V 2005 Fall Velocities of Hydrometeors in the Atmosphere 515
Refinements to a Continuous Analytical Power Law J Atmos Sci 62 4343-4357 516
httpsdoiorg101175JAS36221 517
Kikuchi K T Kameda K Higuchi and A Yamashita 2013 A global classification of 518
snow crystals ice crystals and solid precipitation based on observations from middle 519
latitudes to polar regions Atmos Res 132-133 460-472 520
Kneifel S A von Lerber J Tiira D Moisseev P Kollias and J Leinonen 2015 521
Observed relations between snowfall microphysics and triple-frequency radar 522
25
measurements J Geophys Res Atmos 120(12) 6034-6055 523
httpsdoi1010022015JD023156 524
Kubicek A and P K Wang 2012 A numerical study of the flow fields around a typical 525
conical graupel falling at various inclination angles Atmos Res 118 15ndash26 526
httpsdoi101016jatmosres201206001 527
Larsen M L A B Kostinski and A R Jameson (2014) Further evidence for 528
superterminal raindrops Geophys Res Lett 41(19) 6914-6918 529
Lee JE SH Jung H M Park S Kwon P L Lin and G W Lee 2015 Classification of 530
Precipitation Types Using Fall Velocity Diameter Relationships from 2D-Video 531
Distrometer Measurements Advances in Atmospheric Sciences (09) 532
Lin Y L J Donner and B A Colle 2010 Parameterization of riming intensity and its 533
impact on ice fall speed using arm data Mon Weather Rev 139(3) 1036ndash1047 534
httpsdoi1011752010MWR32991 535
Liu Y G 1992 Skewness and kurtosis of measured raindrop size distributions Atmos 536
Environ 26A 2713-2716 httpsdoiorg1010160960-1686(92)90005-6 537
Liu Y G 1993 Statistical theory of the Marshall-Parmer distribution of raindrops 538
Atmos Environ 27A 15-19 httpsdoiorg1010160960-1686(93)90066-8 539
Liu Y G and F Liu 1994 On the description of aerosol particle size distribution Atmos 540
Res 31(1-3) 187-198 httpsdoiorg1010160169-8095(94)90043-4 541
Liu Y G L You W Yang F Liu 1995 On the size distribution of cloud droplets Atmos 542
Res 35 (2-4) 201-216 httpsdoiorg1010160169-8095(94)00019-A 543
Locatelli J D and P V Hobbs 1974 Fall speeds and masses of solid precipitation 544
26
particles J Geophys Res 79(15) 2185-2197 httpsdoi101029JC079i015p02185 545
Loumlffler-Mang M and J Joss 2000 An optical disdrometer for measuring size and 546
velocity of hydrometeors J Atmos Oceanic Technol 17 130-139 547
httpsdoiorg1011751520-0426(2000)017lt0130AODFMSgt20CO2 548
Loumlffler-Mang M and U Blahak 2001 Estimation of the Equivalent Radar Reflectivity 549
Factor from Measured Snow Size Spectra J Clim Appl Meteorol 40(4) 843-849 550
httpsdoiorg1011751520-0450(2001)040lt0843EOTERRgt20CO2 551
Matrosov S Y 2007 Modeling Backscatter Properties of Snowfall at Millimeter 552
Wavelengths J Atmos Sci 64(5) 1727-1736 httpsdoiorg101175JAS39041 553
Mitchell D L 1996 Use of mass- and area-dimensional power laws for determining 554
precipitation particle terminal velocities J Atmos Sci 53 1710-1723 555
httpsdoiorg1011751520-0469(1996)053lt1710UOMAADgt20CO2 556
Montero-Martiacutenez G A B Kostinski R A Shaw and F Garciacutea-Garciacutea 2009 Do all 557
raindrops fall at terminal speed Geophys Res Lett 36 L11818 558
httpsdoiorg1010292008GL037111 559
Niu S X Jia J Sang X Liu C Lu and Y Liu 2010 Distributions of raindrop sizes and 560
fall velocities in a semiarid plateau climate Convective vs stratiform rains J Appl 561
Meteorol Climatol 49 632ndash645 httpsdoi1011752009JAMC22081 562
Nurzyńska K M Kubo and K-i Muramoto 2012 Texture operator for snow particle 563
classification into snowflake and graupel Atmos Res 118 121-132 564
Oue M M R Kumjian Y Lu J Verlinde K Aydin and E E Clothiaux 2015 Linear 565
27
Depolarization Ratios of columnar ice crystals in a deep precipitating system over the 566
Arctic observed by Zenith-Pointing Ka-Band Doppler radar J Clim Appl Meteorol 567
54(5) 1060-1068 httpsdoiorg101175JAMC-D-15-00121 568
Pruppacher H R and J D Klett 1998 Microphysics of clouds and precipitation Kluwer 569
Academic 954 pp 570
Rasmussen R B Baker et al 2012 How well are we measuring snow the 571
NOAAFAANCAR winter precipitation test bed Bull Amer Meteor Soc 93(6) 811-829 572
httpsdoiorg101175BAMS-D-11-000521 573
Reisner J R M Rasmussen and R T Bruintjes 1998 Explicit forecasting of 574
supercooled liquid water in winter storms using the MM5 mesoscale model Q J R 575
Meteorol Soc 124 1071ndash1107 httpsdoi101256smsqj54803 576
Rosenfeld D and Ulbrich C W 2003 Cloud microphysical properties processes and 577
rainfall estimation opportunities Meteorol Monogr 30 237-237 578
httpsdoiorg101175 0065-9401(2003)030lt0237cmppargt20CO2 579
Schaefer V J 1956 The preparation of snow crystal replicas-VI Weatherwsie 9 580
132-135 581
Souverijns N A Gossart S Lhermitte I V Gorodetskaya S Kneifel M Maahn F L 582
Bliven and N P M van Lipzig (2017) Estimating radar reflectivity - Snowfall rate 583
relationships and their uncertainties over Antarctica by combining disdrometer and 584
radar observations Atmos Res 196 211-223 585
Taylor K E 2001 Summarizing multiple aspects of model performance in a single 586
diagram J Geophys Res 106 7183ndash7192 httpsdoi1010292000JD900719 587
28
Tokay A and D A Short 1996 Evidence from tropical raindrop spectra of the origin of 588
rain from stratiform versus convective clouds J Appl Meteor 35 355ndash371 589
Tokay A and D Atlas 1999 Rainfall microphysics and radar properties analysis 590
methods for drop size spectra J Appl Meteor 37 912-923 591
httpsdoiorg1011751520-0450(1998)037lt0912RMARPAgt20CO2 592
Tokay A D B Wolff et al 2014 Evaluation of the New version of the laser-optical 593
disdrometer OTT Parsivel2 J Atmos Oceanic Technol 31(6) 1276-1288 594
httpsdoiorg101175JTECH-D-13-001741 595
Ulbrich C W 1983 Natural variations in the analytical form of the raindrop size 596
distribution J Appl Meteor 5 1764-1775 597
Wen G H Xiao H Yang Y Bi and W Xu 2017 Characteristics of summer and winter 598
precipitation over northern China Atmos Res 197 390-406 599
Wu W Y Liu and A K Betts 2012 Observationally based evaluation of NWP 600
reanalyses in modeling cloud properties over the Southern Great Plains J Geophys 601
Res 117 D12202 httpsdoi1010292011JD016971 602
Yuter S E D E Kingsmill L B Nance and M Loumlffler-Mang 2006 Observations of 603
precipitation size and fall velocity characteristics within coexisting rain and wet snow J 604
Appl Meteor Climatol 45 1450ndash1464 doi httpsdoiorg101175JAM24061 605
Zhang P C and B Y Du 2000 Radar Meteorology China Meteorological Press 511pp 606
(in Chinese) 607
608
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
21
Gamma distribution performs better for total data 437
A few points are noteworthy First although this study demonstrates the great 438
potential of combining simultaneous disdrometer measurements of particle fall velocity 439
and size distributions microscopic photography and cloud radar to address the 440
challenges facing solid precipitation the data are limited More research is needed to 441
discern such effects on the results presented here Second as the observations show 442
that in addition to sizes there are many other factors (eg hydrometeor type 443
microphysical processes turbulence and measuring principle) that can potentially 444
influence particle fall velocity as well More comprehensive research is needed to 445
further discern and separate these factors Finally the combined use of S-K diagram 446
Taylor diagram and relative Euclidean distance appears to be a powerful tool for 447
identifying the best function used to describe the HSDs and quantify the differences 448
between different precipitation types More research is in order along this direction 449
Acknowledgements 450
This study is mainly supported by the Chinese National Science Foundation under Grant 451
No 41675138 and National Key RampD Program of China (2017YFC0209604) It is partly 452
supported by Beijing National Science Foundation (8172023) the US Department 453
Energys Atmospheric System Research (ASR) Program (Liu and Jia at BNL) Lu is 454
supported by the Natural Science Foundation of Jiangsu Province (BK20160041) The 455
observation data are archived at a specialized supercomputer at Beijing Meteorology 456
Information Center (ftp10224592) which are available from the corresponding 457
author upon request The authors also thank Beijing weather modification office for 458
their support during the field experiment 459
Reference 460
22
Agosta CC Fettweis XX Datta RR 2015 Evaluation of the CMIP5 models in the 461
aim of regional modelling of the Antarctic surface mass balance Cryosphere 9 2311ndash462
2321 httpdxdoiorg105194tc-9-2311-2015 463
Barthazy E and R Schefold 2006 Fall velocity of snowflakes of different riming degree 464
and crystal types Atmos Res 82(1) 391-398 httpsdoiorg101016jatmosres 465
200512009 466
Battaglia A Rustemeier E Tokay A et al 2010 PARSIVEL snow observations a critical 467
assessment J Atmos Oceanic Technol 27(2) 333-344 doi 1011752009jtecha13321 468
Boumlhm H P 1989 A General Equation for the Terminal Fall Speed of Solid Hydrometeors 469
J Atmos Sci 46(15) 2419-2427 httpsdoiorg1011751520-0469(1989)046 lt2419A 470
GEFTTgt20CO2 471
Boudala F S G A Isaac et al 2014 Comparisons of Snowfall Measurements in 472
Complex Terrain Made During the 2010 Winter Olympics in Vancouver Pure and 473
Applied Geophysics 171(1) 113-127 474
Chen B W Hu and J Pu 2011 Characteristics of the raindrop size distribution for 475
freezing precipitation observed in southern China J Geophys Res 116 D06201 476
doi1010292010JD015305 477
Chen B Z Hu L Liu and G Zhang (2017) Raindrop Size Distribution Measurements at 478
4500m on the Tibetan Plateau during TIPEX-III J Geophys Res 122 11092-11106 479
doiorg10100 22017JD027233 480
23
Cugerone K and C De Michele 2017 Investigating raindrop size distributions in the 481
(L-)skewness-(L-)kurtosis plane Quart J Roy Meteor Soc 143(704) 1303-1312 482
httpsdoiorg101002qj3005 483
Donnadieu G 1980 Comparison of results obtained with the VIDIAZ spectro 484
pluviometer and the JossndashWaldvogel rainfall disdrometer in a ldquorain of a thundery typerdquo 485
J Appl Meteor 19 593ndash597 486
Feingold G and Levin Z 1986 The lognormal fit to raindrop spectra from frontal 487
convective clouds in Israel J Clim Appl Meteorol 25 1346ndash1363 488
httpsdoiorg1011751520-0450(1986)025lt1346tlftrsgt20CO2 489
Field P R A J Heymsfield and A Bansemer 2007 Snow Size Distribution 490
Parameterization for Midlatitude and Tropical Ice Clouds J Atmos Sci 64(12) 491
4346-4365 httpsdoiorg1011752007JAS23441 492
Garrett T J and S E Yuter 2014 Observed influence of riming temperature and 493
turbulence on the fallspeed of solid precipitation Geophysical Research Letters 41(18) 494
6515ndash6522 495
Geresdi I N Sarkadi and G Thompson 2014 Effect of the accretion by water drops 496
on the melting of snowflakes Atmos Res 149 96-110 497
Gunn R and G D Kinzer 1949 The terminal velocity of fall for water drops in stagnant 498
air J Meteor 6 243-248 httpsdoiorg1011751520-0469(1949)006lt0243TTVOFFgt 499
20CO2 500
24
Heymsfield A J and C D Westbrook 2010 Advances in the Estimation of Ice Particle 501
Fall Speeds Using Laboratory and Field Measurements J Atmos Sci 67(8) 2469-2482 502
httpsdoiorg1011752010JAS33791 503
Huang G-J C Kleinkort V N Bringi and B M Notaroš 2017 Winter precipitation 504
particle size distribution measurement by Multi-Angle Snowflake Camera Atmos Res 505
198 81-96 506
Intergovernmental Panel on Climate Change (IPCC) 2001 Climate Change 2001 The 507
Scientific Basis Contribution of Working Group I to the Third Assessment Report of the 508
Intergovernmental Panel on Climate Change edited by J T Houghton et al 881 pp 509
Cambridge Univ Press New York 510
Ishizaka M H Motoyoshi S Nakai T Shiina T Kumakura and K-i Muramoto 2013 A 511
New Method for Identifying the Main Type of Solid Hydrometeors Contributing to 512
Snowfall from Measured Size-Fall Speed Relationship Journal of the Meteorological 513
Society of Japan Ser II 91(6) 747-762 httpsdoiorg102151jmsj2013-602 514
Khvorostyanov V 2005 Fall Velocities of Hydrometeors in the Atmosphere 515
Refinements to a Continuous Analytical Power Law J Atmos Sci 62 4343-4357 516
httpsdoiorg101175JAS36221 517
Kikuchi K T Kameda K Higuchi and A Yamashita 2013 A global classification of 518
snow crystals ice crystals and solid precipitation based on observations from middle 519
latitudes to polar regions Atmos Res 132-133 460-472 520
Kneifel S A von Lerber J Tiira D Moisseev P Kollias and J Leinonen 2015 521
Observed relations between snowfall microphysics and triple-frequency radar 522
25
measurements J Geophys Res Atmos 120(12) 6034-6055 523
httpsdoi1010022015JD023156 524
Kubicek A and P K Wang 2012 A numerical study of the flow fields around a typical 525
conical graupel falling at various inclination angles Atmos Res 118 15ndash26 526
httpsdoi101016jatmosres201206001 527
Larsen M L A B Kostinski and A R Jameson (2014) Further evidence for 528
superterminal raindrops Geophys Res Lett 41(19) 6914-6918 529
Lee JE SH Jung H M Park S Kwon P L Lin and G W Lee 2015 Classification of 530
Precipitation Types Using Fall Velocity Diameter Relationships from 2D-Video 531
Distrometer Measurements Advances in Atmospheric Sciences (09) 532
Lin Y L J Donner and B A Colle 2010 Parameterization of riming intensity and its 533
impact on ice fall speed using arm data Mon Weather Rev 139(3) 1036ndash1047 534
httpsdoi1011752010MWR32991 535
Liu Y G 1992 Skewness and kurtosis of measured raindrop size distributions Atmos 536
Environ 26A 2713-2716 httpsdoiorg1010160960-1686(92)90005-6 537
Liu Y G 1993 Statistical theory of the Marshall-Parmer distribution of raindrops 538
Atmos Environ 27A 15-19 httpsdoiorg1010160960-1686(93)90066-8 539
Liu Y G and F Liu 1994 On the description of aerosol particle size distribution Atmos 540
Res 31(1-3) 187-198 httpsdoiorg1010160169-8095(94)90043-4 541
Liu Y G L You W Yang F Liu 1995 On the size distribution of cloud droplets Atmos 542
Res 35 (2-4) 201-216 httpsdoiorg1010160169-8095(94)00019-A 543
Locatelli J D and P V Hobbs 1974 Fall speeds and masses of solid precipitation 544
26
particles J Geophys Res 79(15) 2185-2197 httpsdoi101029JC079i015p02185 545
Loumlffler-Mang M and J Joss 2000 An optical disdrometer for measuring size and 546
velocity of hydrometeors J Atmos Oceanic Technol 17 130-139 547
httpsdoiorg1011751520-0426(2000)017lt0130AODFMSgt20CO2 548
Loumlffler-Mang M and U Blahak 2001 Estimation of the Equivalent Radar Reflectivity 549
Factor from Measured Snow Size Spectra J Clim Appl Meteorol 40(4) 843-849 550
httpsdoiorg1011751520-0450(2001)040lt0843EOTERRgt20CO2 551
Matrosov S Y 2007 Modeling Backscatter Properties of Snowfall at Millimeter 552
Wavelengths J Atmos Sci 64(5) 1727-1736 httpsdoiorg101175JAS39041 553
Mitchell D L 1996 Use of mass- and area-dimensional power laws for determining 554
precipitation particle terminal velocities J Atmos Sci 53 1710-1723 555
httpsdoiorg1011751520-0469(1996)053lt1710UOMAADgt20CO2 556
Montero-Martiacutenez G A B Kostinski R A Shaw and F Garciacutea-Garciacutea 2009 Do all 557
raindrops fall at terminal speed Geophys Res Lett 36 L11818 558
httpsdoiorg1010292008GL037111 559
Niu S X Jia J Sang X Liu C Lu and Y Liu 2010 Distributions of raindrop sizes and 560
fall velocities in a semiarid plateau climate Convective vs stratiform rains J Appl 561
Meteorol Climatol 49 632ndash645 httpsdoi1011752009JAMC22081 562
Nurzyńska K M Kubo and K-i Muramoto 2012 Texture operator for snow particle 563
classification into snowflake and graupel Atmos Res 118 121-132 564
Oue M M R Kumjian Y Lu J Verlinde K Aydin and E E Clothiaux 2015 Linear 565
27
Depolarization Ratios of columnar ice crystals in a deep precipitating system over the 566
Arctic observed by Zenith-Pointing Ka-Band Doppler radar J Clim Appl Meteorol 567
54(5) 1060-1068 httpsdoiorg101175JAMC-D-15-00121 568
Pruppacher H R and J D Klett 1998 Microphysics of clouds and precipitation Kluwer 569
Academic 954 pp 570
Rasmussen R B Baker et al 2012 How well are we measuring snow the 571
NOAAFAANCAR winter precipitation test bed Bull Amer Meteor Soc 93(6) 811-829 572
httpsdoiorg101175BAMS-D-11-000521 573
Reisner J R M Rasmussen and R T Bruintjes 1998 Explicit forecasting of 574
supercooled liquid water in winter storms using the MM5 mesoscale model Q J R 575
Meteorol Soc 124 1071ndash1107 httpsdoi101256smsqj54803 576
Rosenfeld D and Ulbrich C W 2003 Cloud microphysical properties processes and 577
rainfall estimation opportunities Meteorol Monogr 30 237-237 578
httpsdoiorg101175 0065-9401(2003)030lt0237cmppargt20CO2 579
Schaefer V J 1956 The preparation of snow crystal replicas-VI Weatherwsie 9 580
132-135 581
Souverijns N A Gossart S Lhermitte I V Gorodetskaya S Kneifel M Maahn F L 582
Bliven and N P M van Lipzig (2017) Estimating radar reflectivity - Snowfall rate 583
relationships and their uncertainties over Antarctica by combining disdrometer and 584
radar observations Atmos Res 196 211-223 585
Taylor K E 2001 Summarizing multiple aspects of model performance in a single 586
diagram J Geophys Res 106 7183ndash7192 httpsdoi1010292000JD900719 587
28
Tokay A and D A Short 1996 Evidence from tropical raindrop spectra of the origin of 588
rain from stratiform versus convective clouds J Appl Meteor 35 355ndash371 589
Tokay A and D Atlas 1999 Rainfall microphysics and radar properties analysis 590
methods for drop size spectra J Appl Meteor 37 912-923 591
httpsdoiorg1011751520-0450(1998)037lt0912RMARPAgt20CO2 592
Tokay A D B Wolff et al 2014 Evaluation of the New version of the laser-optical 593
disdrometer OTT Parsivel2 J Atmos Oceanic Technol 31(6) 1276-1288 594
httpsdoiorg101175JTECH-D-13-001741 595
Ulbrich C W 1983 Natural variations in the analytical form of the raindrop size 596
distribution J Appl Meteor 5 1764-1775 597
Wen G H Xiao H Yang Y Bi and W Xu 2017 Characteristics of summer and winter 598
precipitation over northern China Atmos Res 197 390-406 599
Wu W Y Liu and A K Betts 2012 Observationally based evaluation of NWP 600
reanalyses in modeling cloud properties over the Southern Great Plains J Geophys 601
Res 117 D12202 httpsdoi1010292011JD016971 602
Yuter S E D E Kingsmill L B Nance and M Loumlffler-Mang 2006 Observations of 603
precipitation size and fall velocity characteristics within coexisting rain and wet snow J 604
Appl Meteor Climatol 45 1450ndash1464 doi httpsdoiorg101175JAM24061 605
Zhang P C and B Y Du 2000 Radar Meteorology China Meteorological Press 511pp 606
(in Chinese) 607
608
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
22
Agosta CC Fettweis XX Datta RR 2015 Evaluation of the CMIP5 models in the 461
aim of regional modelling of the Antarctic surface mass balance Cryosphere 9 2311ndash462
2321 httpdxdoiorg105194tc-9-2311-2015 463
Barthazy E and R Schefold 2006 Fall velocity of snowflakes of different riming degree 464
and crystal types Atmos Res 82(1) 391-398 httpsdoiorg101016jatmosres 465
200512009 466
Battaglia A Rustemeier E Tokay A et al 2010 PARSIVEL snow observations a critical 467
assessment J Atmos Oceanic Technol 27(2) 333-344 doi 1011752009jtecha13321 468
Boumlhm H P 1989 A General Equation for the Terminal Fall Speed of Solid Hydrometeors 469
J Atmos Sci 46(15) 2419-2427 httpsdoiorg1011751520-0469(1989)046 lt2419A 470
GEFTTgt20CO2 471
Boudala F S G A Isaac et al 2014 Comparisons of Snowfall Measurements in 472
Complex Terrain Made During the 2010 Winter Olympics in Vancouver Pure and 473
Applied Geophysics 171(1) 113-127 474
Chen B W Hu and J Pu 2011 Characteristics of the raindrop size distribution for 475
freezing precipitation observed in southern China J Geophys Res 116 D06201 476
doi1010292010JD015305 477
Chen B Z Hu L Liu and G Zhang (2017) Raindrop Size Distribution Measurements at 478
4500m on the Tibetan Plateau during TIPEX-III J Geophys Res 122 11092-11106 479
doiorg10100 22017JD027233 480
23
Cugerone K and C De Michele 2017 Investigating raindrop size distributions in the 481
(L-)skewness-(L-)kurtosis plane Quart J Roy Meteor Soc 143(704) 1303-1312 482
httpsdoiorg101002qj3005 483
Donnadieu G 1980 Comparison of results obtained with the VIDIAZ spectro 484
pluviometer and the JossndashWaldvogel rainfall disdrometer in a ldquorain of a thundery typerdquo 485
J Appl Meteor 19 593ndash597 486
Feingold G and Levin Z 1986 The lognormal fit to raindrop spectra from frontal 487
convective clouds in Israel J Clim Appl Meteorol 25 1346ndash1363 488
httpsdoiorg1011751520-0450(1986)025lt1346tlftrsgt20CO2 489
Field P R A J Heymsfield and A Bansemer 2007 Snow Size Distribution 490
Parameterization for Midlatitude and Tropical Ice Clouds J Atmos Sci 64(12) 491
4346-4365 httpsdoiorg1011752007JAS23441 492
Garrett T J and S E Yuter 2014 Observed influence of riming temperature and 493
turbulence on the fallspeed of solid precipitation Geophysical Research Letters 41(18) 494
6515ndash6522 495
Geresdi I N Sarkadi and G Thompson 2014 Effect of the accretion by water drops 496
on the melting of snowflakes Atmos Res 149 96-110 497
Gunn R and G D Kinzer 1949 The terminal velocity of fall for water drops in stagnant 498
air J Meteor 6 243-248 httpsdoiorg1011751520-0469(1949)006lt0243TTVOFFgt 499
20CO2 500
24
Heymsfield A J and C D Westbrook 2010 Advances in the Estimation of Ice Particle 501
Fall Speeds Using Laboratory and Field Measurements J Atmos Sci 67(8) 2469-2482 502
httpsdoiorg1011752010JAS33791 503
Huang G-J C Kleinkort V N Bringi and B M Notaroš 2017 Winter precipitation 504
particle size distribution measurement by Multi-Angle Snowflake Camera Atmos Res 505
198 81-96 506
Intergovernmental Panel on Climate Change (IPCC) 2001 Climate Change 2001 The 507
Scientific Basis Contribution of Working Group I to the Third Assessment Report of the 508
Intergovernmental Panel on Climate Change edited by J T Houghton et al 881 pp 509
Cambridge Univ Press New York 510
Ishizaka M H Motoyoshi S Nakai T Shiina T Kumakura and K-i Muramoto 2013 A 511
New Method for Identifying the Main Type of Solid Hydrometeors Contributing to 512
Snowfall from Measured Size-Fall Speed Relationship Journal of the Meteorological 513
Society of Japan Ser II 91(6) 747-762 httpsdoiorg102151jmsj2013-602 514
Khvorostyanov V 2005 Fall Velocities of Hydrometeors in the Atmosphere 515
Refinements to a Continuous Analytical Power Law J Atmos Sci 62 4343-4357 516
httpsdoiorg101175JAS36221 517
Kikuchi K T Kameda K Higuchi and A Yamashita 2013 A global classification of 518
snow crystals ice crystals and solid precipitation based on observations from middle 519
latitudes to polar regions Atmos Res 132-133 460-472 520
Kneifel S A von Lerber J Tiira D Moisseev P Kollias and J Leinonen 2015 521
Observed relations between snowfall microphysics and triple-frequency radar 522
25
measurements J Geophys Res Atmos 120(12) 6034-6055 523
httpsdoi1010022015JD023156 524
Kubicek A and P K Wang 2012 A numerical study of the flow fields around a typical 525
conical graupel falling at various inclination angles Atmos Res 118 15ndash26 526
httpsdoi101016jatmosres201206001 527
Larsen M L A B Kostinski and A R Jameson (2014) Further evidence for 528
superterminal raindrops Geophys Res Lett 41(19) 6914-6918 529
Lee JE SH Jung H M Park S Kwon P L Lin and G W Lee 2015 Classification of 530
Precipitation Types Using Fall Velocity Diameter Relationships from 2D-Video 531
Distrometer Measurements Advances in Atmospheric Sciences (09) 532
Lin Y L J Donner and B A Colle 2010 Parameterization of riming intensity and its 533
impact on ice fall speed using arm data Mon Weather Rev 139(3) 1036ndash1047 534
httpsdoi1011752010MWR32991 535
Liu Y G 1992 Skewness and kurtosis of measured raindrop size distributions Atmos 536
Environ 26A 2713-2716 httpsdoiorg1010160960-1686(92)90005-6 537
Liu Y G 1993 Statistical theory of the Marshall-Parmer distribution of raindrops 538
Atmos Environ 27A 15-19 httpsdoiorg1010160960-1686(93)90066-8 539
Liu Y G and F Liu 1994 On the description of aerosol particle size distribution Atmos 540
Res 31(1-3) 187-198 httpsdoiorg1010160169-8095(94)90043-4 541
Liu Y G L You W Yang F Liu 1995 On the size distribution of cloud droplets Atmos 542
Res 35 (2-4) 201-216 httpsdoiorg1010160169-8095(94)00019-A 543
Locatelli J D and P V Hobbs 1974 Fall speeds and masses of solid precipitation 544
26
particles J Geophys Res 79(15) 2185-2197 httpsdoi101029JC079i015p02185 545
Loumlffler-Mang M and J Joss 2000 An optical disdrometer for measuring size and 546
velocity of hydrometeors J Atmos Oceanic Technol 17 130-139 547
httpsdoiorg1011751520-0426(2000)017lt0130AODFMSgt20CO2 548
Loumlffler-Mang M and U Blahak 2001 Estimation of the Equivalent Radar Reflectivity 549
Factor from Measured Snow Size Spectra J Clim Appl Meteorol 40(4) 843-849 550
httpsdoiorg1011751520-0450(2001)040lt0843EOTERRgt20CO2 551
Matrosov S Y 2007 Modeling Backscatter Properties of Snowfall at Millimeter 552
Wavelengths J Atmos Sci 64(5) 1727-1736 httpsdoiorg101175JAS39041 553
Mitchell D L 1996 Use of mass- and area-dimensional power laws for determining 554
precipitation particle terminal velocities J Atmos Sci 53 1710-1723 555
httpsdoiorg1011751520-0469(1996)053lt1710UOMAADgt20CO2 556
Montero-Martiacutenez G A B Kostinski R A Shaw and F Garciacutea-Garciacutea 2009 Do all 557
raindrops fall at terminal speed Geophys Res Lett 36 L11818 558
httpsdoiorg1010292008GL037111 559
Niu S X Jia J Sang X Liu C Lu and Y Liu 2010 Distributions of raindrop sizes and 560
fall velocities in a semiarid plateau climate Convective vs stratiform rains J Appl 561
Meteorol Climatol 49 632ndash645 httpsdoi1011752009JAMC22081 562
Nurzyńska K M Kubo and K-i Muramoto 2012 Texture operator for snow particle 563
classification into snowflake and graupel Atmos Res 118 121-132 564
Oue M M R Kumjian Y Lu J Verlinde K Aydin and E E Clothiaux 2015 Linear 565
27
Depolarization Ratios of columnar ice crystals in a deep precipitating system over the 566
Arctic observed by Zenith-Pointing Ka-Band Doppler radar J Clim Appl Meteorol 567
54(5) 1060-1068 httpsdoiorg101175JAMC-D-15-00121 568
Pruppacher H R and J D Klett 1998 Microphysics of clouds and precipitation Kluwer 569
Academic 954 pp 570
Rasmussen R B Baker et al 2012 How well are we measuring snow the 571
NOAAFAANCAR winter precipitation test bed Bull Amer Meteor Soc 93(6) 811-829 572
httpsdoiorg101175BAMS-D-11-000521 573
Reisner J R M Rasmussen and R T Bruintjes 1998 Explicit forecasting of 574
supercooled liquid water in winter storms using the MM5 mesoscale model Q J R 575
Meteorol Soc 124 1071ndash1107 httpsdoi101256smsqj54803 576
Rosenfeld D and Ulbrich C W 2003 Cloud microphysical properties processes and 577
rainfall estimation opportunities Meteorol Monogr 30 237-237 578
httpsdoiorg101175 0065-9401(2003)030lt0237cmppargt20CO2 579
Schaefer V J 1956 The preparation of snow crystal replicas-VI Weatherwsie 9 580
132-135 581
Souverijns N A Gossart S Lhermitte I V Gorodetskaya S Kneifel M Maahn F L 582
Bliven and N P M van Lipzig (2017) Estimating radar reflectivity - Snowfall rate 583
relationships and their uncertainties over Antarctica by combining disdrometer and 584
radar observations Atmos Res 196 211-223 585
Taylor K E 2001 Summarizing multiple aspects of model performance in a single 586
diagram J Geophys Res 106 7183ndash7192 httpsdoi1010292000JD900719 587
28
Tokay A and D A Short 1996 Evidence from tropical raindrop spectra of the origin of 588
rain from stratiform versus convective clouds J Appl Meteor 35 355ndash371 589
Tokay A and D Atlas 1999 Rainfall microphysics and radar properties analysis 590
methods for drop size spectra J Appl Meteor 37 912-923 591
httpsdoiorg1011751520-0450(1998)037lt0912RMARPAgt20CO2 592
Tokay A D B Wolff et al 2014 Evaluation of the New version of the laser-optical 593
disdrometer OTT Parsivel2 J Atmos Oceanic Technol 31(6) 1276-1288 594
httpsdoiorg101175JTECH-D-13-001741 595
Ulbrich C W 1983 Natural variations in the analytical form of the raindrop size 596
distribution J Appl Meteor 5 1764-1775 597
Wen G H Xiao H Yang Y Bi and W Xu 2017 Characteristics of summer and winter 598
precipitation over northern China Atmos Res 197 390-406 599
Wu W Y Liu and A K Betts 2012 Observationally based evaluation of NWP 600
reanalyses in modeling cloud properties over the Southern Great Plains J Geophys 601
Res 117 D12202 httpsdoi1010292011JD016971 602
Yuter S E D E Kingsmill L B Nance and M Loumlffler-Mang 2006 Observations of 603
precipitation size and fall velocity characteristics within coexisting rain and wet snow J 604
Appl Meteor Climatol 45 1450ndash1464 doi httpsdoiorg101175JAM24061 605
Zhang P C and B Y Du 2000 Radar Meteorology China Meteorological Press 511pp 606
(in Chinese) 607
608
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
23
Cugerone K and C De Michele 2017 Investigating raindrop size distributions in the 481
(L-)skewness-(L-)kurtosis plane Quart J Roy Meteor Soc 143(704) 1303-1312 482
httpsdoiorg101002qj3005 483
Donnadieu G 1980 Comparison of results obtained with the VIDIAZ spectro 484
pluviometer and the JossndashWaldvogel rainfall disdrometer in a ldquorain of a thundery typerdquo 485
J Appl Meteor 19 593ndash597 486
Feingold G and Levin Z 1986 The lognormal fit to raindrop spectra from frontal 487
convective clouds in Israel J Clim Appl Meteorol 25 1346ndash1363 488
httpsdoiorg1011751520-0450(1986)025lt1346tlftrsgt20CO2 489
Field P R A J Heymsfield and A Bansemer 2007 Snow Size Distribution 490
Parameterization for Midlatitude and Tropical Ice Clouds J Atmos Sci 64(12) 491
4346-4365 httpsdoiorg1011752007JAS23441 492
Garrett T J and S E Yuter 2014 Observed influence of riming temperature and 493
turbulence on the fallspeed of solid precipitation Geophysical Research Letters 41(18) 494
6515ndash6522 495
Geresdi I N Sarkadi and G Thompson 2014 Effect of the accretion by water drops 496
on the melting of snowflakes Atmos Res 149 96-110 497
Gunn R and G D Kinzer 1949 The terminal velocity of fall for water drops in stagnant 498
air J Meteor 6 243-248 httpsdoiorg1011751520-0469(1949)006lt0243TTVOFFgt 499
20CO2 500
24
Heymsfield A J and C D Westbrook 2010 Advances in the Estimation of Ice Particle 501
Fall Speeds Using Laboratory and Field Measurements J Atmos Sci 67(8) 2469-2482 502
httpsdoiorg1011752010JAS33791 503
Huang G-J C Kleinkort V N Bringi and B M Notaroš 2017 Winter precipitation 504
particle size distribution measurement by Multi-Angle Snowflake Camera Atmos Res 505
198 81-96 506
Intergovernmental Panel on Climate Change (IPCC) 2001 Climate Change 2001 The 507
Scientific Basis Contribution of Working Group I to the Third Assessment Report of the 508
Intergovernmental Panel on Climate Change edited by J T Houghton et al 881 pp 509
Cambridge Univ Press New York 510
Ishizaka M H Motoyoshi S Nakai T Shiina T Kumakura and K-i Muramoto 2013 A 511
New Method for Identifying the Main Type of Solid Hydrometeors Contributing to 512
Snowfall from Measured Size-Fall Speed Relationship Journal of the Meteorological 513
Society of Japan Ser II 91(6) 747-762 httpsdoiorg102151jmsj2013-602 514
Khvorostyanov V 2005 Fall Velocities of Hydrometeors in the Atmosphere 515
Refinements to a Continuous Analytical Power Law J Atmos Sci 62 4343-4357 516
httpsdoiorg101175JAS36221 517
Kikuchi K T Kameda K Higuchi and A Yamashita 2013 A global classification of 518
snow crystals ice crystals and solid precipitation based on observations from middle 519
latitudes to polar regions Atmos Res 132-133 460-472 520
Kneifel S A von Lerber J Tiira D Moisseev P Kollias and J Leinonen 2015 521
Observed relations between snowfall microphysics and triple-frequency radar 522
25
measurements J Geophys Res Atmos 120(12) 6034-6055 523
httpsdoi1010022015JD023156 524
Kubicek A and P K Wang 2012 A numerical study of the flow fields around a typical 525
conical graupel falling at various inclination angles Atmos Res 118 15ndash26 526
httpsdoi101016jatmosres201206001 527
Larsen M L A B Kostinski and A R Jameson (2014) Further evidence for 528
superterminal raindrops Geophys Res Lett 41(19) 6914-6918 529
Lee JE SH Jung H M Park S Kwon P L Lin and G W Lee 2015 Classification of 530
Precipitation Types Using Fall Velocity Diameter Relationships from 2D-Video 531
Distrometer Measurements Advances in Atmospheric Sciences (09) 532
Lin Y L J Donner and B A Colle 2010 Parameterization of riming intensity and its 533
impact on ice fall speed using arm data Mon Weather Rev 139(3) 1036ndash1047 534
httpsdoi1011752010MWR32991 535
Liu Y G 1992 Skewness and kurtosis of measured raindrop size distributions Atmos 536
Environ 26A 2713-2716 httpsdoiorg1010160960-1686(92)90005-6 537
Liu Y G 1993 Statistical theory of the Marshall-Parmer distribution of raindrops 538
Atmos Environ 27A 15-19 httpsdoiorg1010160960-1686(93)90066-8 539
Liu Y G and F Liu 1994 On the description of aerosol particle size distribution Atmos 540
Res 31(1-3) 187-198 httpsdoiorg1010160169-8095(94)90043-4 541
Liu Y G L You W Yang F Liu 1995 On the size distribution of cloud droplets Atmos 542
Res 35 (2-4) 201-216 httpsdoiorg1010160169-8095(94)00019-A 543
Locatelli J D and P V Hobbs 1974 Fall speeds and masses of solid precipitation 544
26
particles J Geophys Res 79(15) 2185-2197 httpsdoi101029JC079i015p02185 545
Loumlffler-Mang M and J Joss 2000 An optical disdrometer for measuring size and 546
velocity of hydrometeors J Atmos Oceanic Technol 17 130-139 547
httpsdoiorg1011751520-0426(2000)017lt0130AODFMSgt20CO2 548
Loumlffler-Mang M and U Blahak 2001 Estimation of the Equivalent Radar Reflectivity 549
Factor from Measured Snow Size Spectra J Clim Appl Meteorol 40(4) 843-849 550
httpsdoiorg1011751520-0450(2001)040lt0843EOTERRgt20CO2 551
Matrosov S Y 2007 Modeling Backscatter Properties of Snowfall at Millimeter 552
Wavelengths J Atmos Sci 64(5) 1727-1736 httpsdoiorg101175JAS39041 553
Mitchell D L 1996 Use of mass- and area-dimensional power laws for determining 554
precipitation particle terminal velocities J Atmos Sci 53 1710-1723 555
httpsdoiorg1011751520-0469(1996)053lt1710UOMAADgt20CO2 556
Montero-Martiacutenez G A B Kostinski R A Shaw and F Garciacutea-Garciacutea 2009 Do all 557
raindrops fall at terminal speed Geophys Res Lett 36 L11818 558
httpsdoiorg1010292008GL037111 559
Niu S X Jia J Sang X Liu C Lu and Y Liu 2010 Distributions of raindrop sizes and 560
fall velocities in a semiarid plateau climate Convective vs stratiform rains J Appl 561
Meteorol Climatol 49 632ndash645 httpsdoi1011752009JAMC22081 562
Nurzyńska K M Kubo and K-i Muramoto 2012 Texture operator for snow particle 563
classification into snowflake and graupel Atmos Res 118 121-132 564
Oue M M R Kumjian Y Lu J Verlinde K Aydin and E E Clothiaux 2015 Linear 565
27
Depolarization Ratios of columnar ice crystals in a deep precipitating system over the 566
Arctic observed by Zenith-Pointing Ka-Band Doppler radar J Clim Appl Meteorol 567
54(5) 1060-1068 httpsdoiorg101175JAMC-D-15-00121 568
Pruppacher H R and J D Klett 1998 Microphysics of clouds and precipitation Kluwer 569
Academic 954 pp 570
Rasmussen R B Baker et al 2012 How well are we measuring snow the 571
NOAAFAANCAR winter precipitation test bed Bull Amer Meteor Soc 93(6) 811-829 572
httpsdoiorg101175BAMS-D-11-000521 573
Reisner J R M Rasmussen and R T Bruintjes 1998 Explicit forecasting of 574
supercooled liquid water in winter storms using the MM5 mesoscale model Q J R 575
Meteorol Soc 124 1071ndash1107 httpsdoi101256smsqj54803 576
Rosenfeld D and Ulbrich C W 2003 Cloud microphysical properties processes and 577
rainfall estimation opportunities Meteorol Monogr 30 237-237 578
httpsdoiorg101175 0065-9401(2003)030lt0237cmppargt20CO2 579
Schaefer V J 1956 The preparation of snow crystal replicas-VI Weatherwsie 9 580
132-135 581
Souverijns N A Gossart S Lhermitte I V Gorodetskaya S Kneifel M Maahn F L 582
Bliven and N P M van Lipzig (2017) Estimating radar reflectivity - Snowfall rate 583
relationships and their uncertainties over Antarctica by combining disdrometer and 584
radar observations Atmos Res 196 211-223 585
Taylor K E 2001 Summarizing multiple aspects of model performance in a single 586
diagram J Geophys Res 106 7183ndash7192 httpsdoi1010292000JD900719 587
28
Tokay A and D A Short 1996 Evidence from tropical raindrop spectra of the origin of 588
rain from stratiform versus convective clouds J Appl Meteor 35 355ndash371 589
Tokay A and D Atlas 1999 Rainfall microphysics and radar properties analysis 590
methods for drop size spectra J Appl Meteor 37 912-923 591
httpsdoiorg1011751520-0450(1998)037lt0912RMARPAgt20CO2 592
Tokay A D B Wolff et al 2014 Evaluation of the New version of the laser-optical 593
disdrometer OTT Parsivel2 J Atmos Oceanic Technol 31(6) 1276-1288 594
httpsdoiorg101175JTECH-D-13-001741 595
Ulbrich C W 1983 Natural variations in the analytical form of the raindrop size 596
distribution J Appl Meteor 5 1764-1775 597
Wen G H Xiao H Yang Y Bi and W Xu 2017 Characteristics of summer and winter 598
precipitation over northern China Atmos Res 197 390-406 599
Wu W Y Liu and A K Betts 2012 Observationally based evaluation of NWP 600
reanalyses in modeling cloud properties over the Southern Great Plains J Geophys 601
Res 117 D12202 httpsdoi1010292011JD016971 602
Yuter S E D E Kingsmill L B Nance and M Loumlffler-Mang 2006 Observations of 603
precipitation size and fall velocity characteristics within coexisting rain and wet snow J 604
Appl Meteor Climatol 45 1450ndash1464 doi httpsdoiorg101175JAM24061 605
Zhang P C and B Y Du 2000 Radar Meteorology China Meteorological Press 511pp 606
(in Chinese) 607
608
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
24
Heymsfield A J and C D Westbrook 2010 Advances in the Estimation of Ice Particle 501
Fall Speeds Using Laboratory and Field Measurements J Atmos Sci 67(8) 2469-2482 502
httpsdoiorg1011752010JAS33791 503
Huang G-J C Kleinkort V N Bringi and B M Notaroš 2017 Winter precipitation 504
particle size distribution measurement by Multi-Angle Snowflake Camera Atmos Res 505
198 81-96 506
Intergovernmental Panel on Climate Change (IPCC) 2001 Climate Change 2001 The 507
Scientific Basis Contribution of Working Group I to the Third Assessment Report of the 508
Intergovernmental Panel on Climate Change edited by J T Houghton et al 881 pp 509
Cambridge Univ Press New York 510
Ishizaka M H Motoyoshi S Nakai T Shiina T Kumakura and K-i Muramoto 2013 A 511
New Method for Identifying the Main Type of Solid Hydrometeors Contributing to 512
Snowfall from Measured Size-Fall Speed Relationship Journal of the Meteorological 513
Society of Japan Ser II 91(6) 747-762 httpsdoiorg102151jmsj2013-602 514
Khvorostyanov V 2005 Fall Velocities of Hydrometeors in the Atmosphere 515
Refinements to a Continuous Analytical Power Law J Atmos Sci 62 4343-4357 516
httpsdoiorg101175JAS36221 517
Kikuchi K T Kameda K Higuchi and A Yamashita 2013 A global classification of 518
snow crystals ice crystals and solid precipitation based on observations from middle 519
latitudes to polar regions Atmos Res 132-133 460-472 520
Kneifel S A von Lerber J Tiira D Moisseev P Kollias and J Leinonen 2015 521
Observed relations between snowfall microphysics and triple-frequency radar 522
25
measurements J Geophys Res Atmos 120(12) 6034-6055 523
httpsdoi1010022015JD023156 524
Kubicek A and P K Wang 2012 A numerical study of the flow fields around a typical 525
conical graupel falling at various inclination angles Atmos Res 118 15ndash26 526
httpsdoi101016jatmosres201206001 527
Larsen M L A B Kostinski and A R Jameson (2014) Further evidence for 528
superterminal raindrops Geophys Res Lett 41(19) 6914-6918 529
Lee JE SH Jung H M Park S Kwon P L Lin and G W Lee 2015 Classification of 530
Precipitation Types Using Fall Velocity Diameter Relationships from 2D-Video 531
Distrometer Measurements Advances in Atmospheric Sciences (09) 532
Lin Y L J Donner and B A Colle 2010 Parameterization of riming intensity and its 533
impact on ice fall speed using arm data Mon Weather Rev 139(3) 1036ndash1047 534
httpsdoi1011752010MWR32991 535
Liu Y G 1992 Skewness and kurtosis of measured raindrop size distributions Atmos 536
Environ 26A 2713-2716 httpsdoiorg1010160960-1686(92)90005-6 537
Liu Y G 1993 Statistical theory of the Marshall-Parmer distribution of raindrops 538
Atmos Environ 27A 15-19 httpsdoiorg1010160960-1686(93)90066-8 539
Liu Y G and F Liu 1994 On the description of aerosol particle size distribution Atmos 540
Res 31(1-3) 187-198 httpsdoiorg1010160169-8095(94)90043-4 541
Liu Y G L You W Yang F Liu 1995 On the size distribution of cloud droplets Atmos 542
Res 35 (2-4) 201-216 httpsdoiorg1010160169-8095(94)00019-A 543
Locatelli J D and P V Hobbs 1974 Fall speeds and masses of solid precipitation 544
26
particles J Geophys Res 79(15) 2185-2197 httpsdoi101029JC079i015p02185 545
Loumlffler-Mang M and J Joss 2000 An optical disdrometer for measuring size and 546
velocity of hydrometeors J Atmos Oceanic Technol 17 130-139 547
httpsdoiorg1011751520-0426(2000)017lt0130AODFMSgt20CO2 548
Loumlffler-Mang M and U Blahak 2001 Estimation of the Equivalent Radar Reflectivity 549
Factor from Measured Snow Size Spectra J Clim Appl Meteorol 40(4) 843-849 550
httpsdoiorg1011751520-0450(2001)040lt0843EOTERRgt20CO2 551
Matrosov S Y 2007 Modeling Backscatter Properties of Snowfall at Millimeter 552
Wavelengths J Atmos Sci 64(5) 1727-1736 httpsdoiorg101175JAS39041 553
Mitchell D L 1996 Use of mass- and area-dimensional power laws for determining 554
precipitation particle terminal velocities J Atmos Sci 53 1710-1723 555
httpsdoiorg1011751520-0469(1996)053lt1710UOMAADgt20CO2 556
Montero-Martiacutenez G A B Kostinski R A Shaw and F Garciacutea-Garciacutea 2009 Do all 557
raindrops fall at terminal speed Geophys Res Lett 36 L11818 558
httpsdoiorg1010292008GL037111 559
Niu S X Jia J Sang X Liu C Lu and Y Liu 2010 Distributions of raindrop sizes and 560
fall velocities in a semiarid plateau climate Convective vs stratiform rains J Appl 561
Meteorol Climatol 49 632ndash645 httpsdoi1011752009JAMC22081 562
Nurzyńska K M Kubo and K-i Muramoto 2012 Texture operator for snow particle 563
classification into snowflake and graupel Atmos Res 118 121-132 564
Oue M M R Kumjian Y Lu J Verlinde K Aydin and E E Clothiaux 2015 Linear 565
27
Depolarization Ratios of columnar ice crystals in a deep precipitating system over the 566
Arctic observed by Zenith-Pointing Ka-Band Doppler radar J Clim Appl Meteorol 567
54(5) 1060-1068 httpsdoiorg101175JAMC-D-15-00121 568
Pruppacher H R and J D Klett 1998 Microphysics of clouds and precipitation Kluwer 569
Academic 954 pp 570
Rasmussen R B Baker et al 2012 How well are we measuring snow the 571
NOAAFAANCAR winter precipitation test bed Bull Amer Meteor Soc 93(6) 811-829 572
httpsdoiorg101175BAMS-D-11-000521 573
Reisner J R M Rasmussen and R T Bruintjes 1998 Explicit forecasting of 574
supercooled liquid water in winter storms using the MM5 mesoscale model Q J R 575
Meteorol Soc 124 1071ndash1107 httpsdoi101256smsqj54803 576
Rosenfeld D and Ulbrich C W 2003 Cloud microphysical properties processes and 577
rainfall estimation opportunities Meteorol Monogr 30 237-237 578
httpsdoiorg101175 0065-9401(2003)030lt0237cmppargt20CO2 579
Schaefer V J 1956 The preparation of snow crystal replicas-VI Weatherwsie 9 580
132-135 581
Souverijns N A Gossart S Lhermitte I V Gorodetskaya S Kneifel M Maahn F L 582
Bliven and N P M van Lipzig (2017) Estimating radar reflectivity - Snowfall rate 583
relationships and their uncertainties over Antarctica by combining disdrometer and 584
radar observations Atmos Res 196 211-223 585
Taylor K E 2001 Summarizing multiple aspects of model performance in a single 586
diagram J Geophys Res 106 7183ndash7192 httpsdoi1010292000JD900719 587
28
Tokay A and D A Short 1996 Evidence from tropical raindrop spectra of the origin of 588
rain from stratiform versus convective clouds J Appl Meteor 35 355ndash371 589
Tokay A and D Atlas 1999 Rainfall microphysics and radar properties analysis 590
methods for drop size spectra J Appl Meteor 37 912-923 591
httpsdoiorg1011751520-0450(1998)037lt0912RMARPAgt20CO2 592
Tokay A D B Wolff et al 2014 Evaluation of the New version of the laser-optical 593
disdrometer OTT Parsivel2 J Atmos Oceanic Technol 31(6) 1276-1288 594
httpsdoiorg101175JTECH-D-13-001741 595
Ulbrich C W 1983 Natural variations in the analytical form of the raindrop size 596
distribution J Appl Meteor 5 1764-1775 597
Wen G H Xiao H Yang Y Bi and W Xu 2017 Characteristics of summer and winter 598
precipitation over northern China Atmos Res 197 390-406 599
Wu W Y Liu and A K Betts 2012 Observationally based evaluation of NWP 600
reanalyses in modeling cloud properties over the Southern Great Plains J Geophys 601
Res 117 D12202 httpsdoi1010292011JD016971 602
Yuter S E D E Kingsmill L B Nance and M Loumlffler-Mang 2006 Observations of 603
precipitation size and fall velocity characteristics within coexisting rain and wet snow J 604
Appl Meteor Climatol 45 1450ndash1464 doi httpsdoiorg101175JAM24061 605
Zhang P C and B Y Du 2000 Radar Meteorology China Meteorological Press 511pp 606
(in Chinese) 607
608
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
25
measurements J Geophys Res Atmos 120(12) 6034-6055 523
httpsdoi1010022015JD023156 524
Kubicek A and P K Wang 2012 A numerical study of the flow fields around a typical 525
conical graupel falling at various inclination angles Atmos Res 118 15ndash26 526
httpsdoi101016jatmosres201206001 527
Larsen M L A B Kostinski and A R Jameson (2014) Further evidence for 528
superterminal raindrops Geophys Res Lett 41(19) 6914-6918 529
Lee JE SH Jung H M Park S Kwon P L Lin and G W Lee 2015 Classification of 530
Precipitation Types Using Fall Velocity Diameter Relationships from 2D-Video 531
Distrometer Measurements Advances in Atmospheric Sciences (09) 532
Lin Y L J Donner and B A Colle 2010 Parameterization of riming intensity and its 533
impact on ice fall speed using arm data Mon Weather Rev 139(3) 1036ndash1047 534
httpsdoi1011752010MWR32991 535
Liu Y G 1992 Skewness and kurtosis of measured raindrop size distributions Atmos 536
Environ 26A 2713-2716 httpsdoiorg1010160960-1686(92)90005-6 537
Liu Y G 1993 Statistical theory of the Marshall-Parmer distribution of raindrops 538
Atmos Environ 27A 15-19 httpsdoiorg1010160960-1686(93)90066-8 539
Liu Y G and F Liu 1994 On the description of aerosol particle size distribution Atmos 540
Res 31(1-3) 187-198 httpsdoiorg1010160169-8095(94)90043-4 541
Liu Y G L You W Yang F Liu 1995 On the size distribution of cloud droplets Atmos 542
Res 35 (2-4) 201-216 httpsdoiorg1010160169-8095(94)00019-A 543
Locatelli J D and P V Hobbs 1974 Fall speeds and masses of solid precipitation 544
26
particles J Geophys Res 79(15) 2185-2197 httpsdoi101029JC079i015p02185 545
Loumlffler-Mang M and J Joss 2000 An optical disdrometer for measuring size and 546
velocity of hydrometeors J Atmos Oceanic Technol 17 130-139 547
httpsdoiorg1011751520-0426(2000)017lt0130AODFMSgt20CO2 548
Loumlffler-Mang M and U Blahak 2001 Estimation of the Equivalent Radar Reflectivity 549
Factor from Measured Snow Size Spectra J Clim Appl Meteorol 40(4) 843-849 550
httpsdoiorg1011751520-0450(2001)040lt0843EOTERRgt20CO2 551
Matrosov S Y 2007 Modeling Backscatter Properties of Snowfall at Millimeter 552
Wavelengths J Atmos Sci 64(5) 1727-1736 httpsdoiorg101175JAS39041 553
Mitchell D L 1996 Use of mass- and area-dimensional power laws for determining 554
precipitation particle terminal velocities J Atmos Sci 53 1710-1723 555
httpsdoiorg1011751520-0469(1996)053lt1710UOMAADgt20CO2 556
Montero-Martiacutenez G A B Kostinski R A Shaw and F Garciacutea-Garciacutea 2009 Do all 557
raindrops fall at terminal speed Geophys Res Lett 36 L11818 558
httpsdoiorg1010292008GL037111 559
Niu S X Jia J Sang X Liu C Lu and Y Liu 2010 Distributions of raindrop sizes and 560
fall velocities in a semiarid plateau climate Convective vs stratiform rains J Appl 561
Meteorol Climatol 49 632ndash645 httpsdoi1011752009JAMC22081 562
Nurzyńska K M Kubo and K-i Muramoto 2012 Texture operator for snow particle 563
classification into snowflake and graupel Atmos Res 118 121-132 564
Oue M M R Kumjian Y Lu J Verlinde K Aydin and E E Clothiaux 2015 Linear 565
27
Depolarization Ratios of columnar ice crystals in a deep precipitating system over the 566
Arctic observed by Zenith-Pointing Ka-Band Doppler radar J Clim Appl Meteorol 567
54(5) 1060-1068 httpsdoiorg101175JAMC-D-15-00121 568
Pruppacher H R and J D Klett 1998 Microphysics of clouds and precipitation Kluwer 569
Academic 954 pp 570
Rasmussen R B Baker et al 2012 How well are we measuring snow the 571
NOAAFAANCAR winter precipitation test bed Bull Amer Meteor Soc 93(6) 811-829 572
httpsdoiorg101175BAMS-D-11-000521 573
Reisner J R M Rasmussen and R T Bruintjes 1998 Explicit forecasting of 574
supercooled liquid water in winter storms using the MM5 mesoscale model Q J R 575
Meteorol Soc 124 1071ndash1107 httpsdoi101256smsqj54803 576
Rosenfeld D and Ulbrich C W 2003 Cloud microphysical properties processes and 577
rainfall estimation opportunities Meteorol Monogr 30 237-237 578
httpsdoiorg101175 0065-9401(2003)030lt0237cmppargt20CO2 579
Schaefer V J 1956 The preparation of snow crystal replicas-VI Weatherwsie 9 580
132-135 581
Souverijns N A Gossart S Lhermitte I V Gorodetskaya S Kneifel M Maahn F L 582
Bliven and N P M van Lipzig (2017) Estimating radar reflectivity - Snowfall rate 583
relationships and their uncertainties over Antarctica by combining disdrometer and 584
radar observations Atmos Res 196 211-223 585
Taylor K E 2001 Summarizing multiple aspects of model performance in a single 586
diagram J Geophys Res 106 7183ndash7192 httpsdoi1010292000JD900719 587
28
Tokay A and D A Short 1996 Evidence from tropical raindrop spectra of the origin of 588
rain from stratiform versus convective clouds J Appl Meteor 35 355ndash371 589
Tokay A and D Atlas 1999 Rainfall microphysics and radar properties analysis 590
methods for drop size spectra J Appl Meteor 37 912-923 591
httpsdoiorg1011751520-0450(1998)037lt0912RMARPAgt20CO2 592
Tokay A D B Wolff et al 2014 Evaluation of the New version of the laser-optical 593
disdrometer OTT Parsivel2 J Atmos Oceanic Technol 31(6) 1276-1288 594
httpsdoiorg101175JTECH-D-13-001741 595
Ulbrich C W 1983 Natural variations in the analytical form of the raindrop size 596
distribution J Appl Meteor 5 1764-1775 597
Wen G H Xiao H Yang Y Bi and W Xu 2017 Characteristics of summer and winter 598
precipitation over northern China Atmos Res 197 390-406 599
Wu W Y Liu and A K Betts 2012 Observationally based evaluation of NWP 600
reanalyses in modeling cloud properties over the Southern Great Plains J Geophys 601
Res 117 D12202 httpsdoi1010292011JD016971 602
Yuter S E D E Kingsmill L B Nance and M Loumlffler-Mang 2006 Observations of 603
precipitation size and fall velocity characteristics within coexisting rain and wet snow J 604
Appl Meteor Climatol 45 1450ndash1464 doi httpsdoiorg101175JAM24061 605
Zhang P C and B Y Du 2000 Radar Meteorology China Meteorological Press 511pp 606
(in Chinese) 607
608
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
26
particles J Geophys Res 79(15) 2185-2197 httpsdoi101029JC079i015p02185 545
Loumlffler-Mang M and J Joss 2000 An optical disdrometer for measuring size and 546
velocity of hydrometeors J Atmos Oceanic Technol 17 130-139 547
httpsdoiorg1011751520-0426(2000)017lt0130AODFMSgt20CO2 548
Loumlffler-Mang M and U Blahak 2001 Estimation of the Equivalent Radar Reflectivity 549
Factor from Measured Snow Size Spectra J Clim Appl Meteorol 40(4) 843-849 550
httpsdoiorg1011751520-0450(2001)040lt0843EOTERRgt20CO2 551
Matrosov S Y 2007 Modeling Backscatter Properties of Snowfall at Millimeter 552
Wavelengths J Atmos Sci 64(5) 1727-1736 httpsdoiorg101175JAS39041 553
Mitchell D L 1996 Use of mass- and area-dimensional power laws for determining 554
precipitation particle terminal velocities J Atmos Sci 53 1710-1723 555
httpsdoiorg1011751520-0469(1996)053lt1710UOMAADgt20CO2 556
Montero-Martiacutenez G A B Kostinski R A Shaw and F Garciacutea-Garciacutea 2009 Do all 557
raindrops fall at terminal speed Geophys Res Lett 36 L11818 558
httpsdoiorg1010292008GL037111 559
Niu S X Jia J Sang X Liu C Lu and Y Liu 2010 Distributions of raindrop sizes and 560
fall velocities in a semiarid plateau climate Convective vs stratiform rains J Appl 561
Meteorol Climatol 49 632ndash645 httpsdoi1011752009JAMC22081 562
Nurzyńska K M Kubo and K-i Muramoto 2012 Texture operator for snow particle 563
classification into snowflake and graupel Atmos Res 118 121-132 564
Oue M M R Kumjian Y Lu J Verlinde K Aydin and E E Clothiaux 2015 Linear 565
27
Depolarization Ratios of columnar ice crystals in a deep precipitating system over the 566
Arctic observed by Zenith-Pointing Ka-Band Doppler radar J Clim Appl Meteorol 567
54(5) 1060-1068 httpsdoiorg101175JAMC-D-15-00121 568
Pruppacher H R and J D Klett 1998 Microphysics of clouds and precipitation Kluwer 569
Academic 954 pp 570
Rasmussen R B Baker et al 2012 How well are we measuring snow the 571
NOAAFAANCAR winter precipitation test bed Bull Amer Meteor Soc 93(6) 811-829 572
httpsdoiorg101175BAMS-D-11-000521 573
Reisner J R M Rasmussen and R T Bruintjes 1998 Explicit forecasting of 574
supercooled liquid water in winter storms using the MM5 mesoscale model Q J R 575
Meteorol Soc 124 1071ndash1107 httpsdoi101256smsqj54803 576
Rosenfeld D and Ulbrich C W 2003 Cloud microphysical properties processes and 577
rainfall estimation opportunities Meteorol Monogr 30 237-237 578
httpsdoiorg101175 0065-9401(2003)030lt0237cmppargt20CO2 579
Schaefer V J 1956 The preparation of snow crystal replicas-VI Weatherwsie 9 580
132-135 581
Souverijns N A Gossart S Lhermitte I V Gorodetskaya S Kneifel M Maahn F L 582
Bliven and N P M van Lipzig (2017) Estimating radar reflectivity - Snowfall rate 583
relationships and their uncertainties over Antarctica by combining disdrometer and 584
radar observations Atmos Res 196 211-223 585
Taylor K E 2001 Summarizing multiple aspects of model performance in a single 586
diagram J Geophys Res 106 7183ndash7192 httpsdoi1010292000JD900719 587
28
Tokay A and D A Short 1996 Evidence from tropical raindrop spectra of the origin of 588
rain from stratiform versus convective clouds J Appl Meteor 35 355ndash371 589
Tokay A and D Atlas 1999 Rainfall microphysics and radar properties analysis 590
methods for drop size spectra J Appl Meteor 37 912-923 591
httpsdoiorg1011751520-0450(1998)037lt0912RMARPAgt20CO2 592
Tokay A D B Wolff et al 2014 Evaluation of the New version of the laser-optical 593
disdrometer OTT Parsivel2 J Atmos Oceanic Technol 31(6) 1276-1288 594
httpsdoiorg101175JTECH-D-13-001741 595
Ulbrich C W 1983 Natural variations in the analytical form of the raindrop size 596
distribution J Appl Meteor 5 1764-1775 597
Wen G H Xiao H Yang Y Bi and W Xu 2017 Characteristics of summer and winter 598
precipitation over northern China Atmos Res 197 390-406 599
Wu W Y Liu and A K Betts 2012 Observationally based evaluation of NWP 600
reanalyses in modeling cloud properties over the Southern Great Plains J Geophys 601
Res 117 D12202 httpsdoi1010292011JD016971 602
Yuter S E D E Kingsmill L B Nance and M Loumlffler-Mang 2006 Observations of 603
precipitation size and fall velocity characteristics within coexisting rain and wet snow J 604
Appl Meteor Climatol 45 1450ndash1464 doi httpsdoiorg101175JAM24061 605
Zhang P C and B Y Du 2000 Radar Meteorology China Meteorological Press 511pp 606
(in Chinese) 607
608
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
27
Depolarization Ratios of columnar ice crystals in a deep precipitating system over the 566
Arctic observed by Zenith-Pointing Ka-Band Doppler radar J Clim Appl Meteorol 567
54(5) 1060-1068 httpsdoiorg101175JAMC-D-15-00121 568
Pruppacher H R and J D Klett 1998 Microphysics of clouds and precipitation Kluwer 569
Academic 954 pp 570
Rasmussen R B Baker et al 2012 How well are we measuring snow the 571
NOAAFAANCAR winter precipitation test bed Bull Amer Meteor Soc 93(6) 811-829 572
httpsdoiorg101175BAMS-D-11-000521 573
Reisner J R M Rasmussen and R T Bruintjes 1998 Explicit forecasting of 574
supercooled liquid water in winter storms using the MM5 mesoscale model Q J R 575
Meteorol Soc 124 1071ndash1107 httpsdoi101256smsqj54803 576
Rosenfeld D and Ulbrich C W 2003 Cloud microphysical properties processes and 577
rainfall estimation opportunities Meteorol Monogr 30 237-237 578
httpsdoiorg101175 0065-9401(2003)030lt0237cmppargt20CO2 579
Schaefer V J 1956 The preparation of snow crystal replicas-VI Weatherwsie 9 580
132-135 581
Souverijns N A Gossart S Lhermitte I V Gorodetskaya S Kneifel M Maahn F L 582
Bliven and N P M van Lipzig (2017) Estimating radar reflectivity - Snowfall rate 583
relationships and their uncertainties over Antarctica by combining disdrometer and 584
radar observations Atmos Res 196 211-223 585
Taylor K E 2001 Summarizing multiple aspects of model performance in a single 586
diagram J Geophys Res 106 7183ndash7192 httpsdoi1010292000JD900719 587
28
Tokay A and D A Short 1996 Evidence from tropical raindrop spectra of the origin of 588
rain from stratiform versus convective clouds J Appl Meteor 35 355ndash371 589
Tokay A and D Atlas 1999 Rainfall microphysics and radar properties analysis 590
methods for drop size spectra J Appl Meteor 37 912-923 591
httpsdoiorg1011751520-0450(1998)037lt0912RMARPAgt20CO2 592
Tokay A D B Wolff et al 2014 Evaluation of the New version of the laser-optical 593
disdrometer OTT Parsivel2 J Atmos Oceanic Technol 31(6) 1276-1288 594
httpsdoiorg101175JTECH-D-13-001741 595
Ulbrich C W 1983 Natural variations in the analytical form of the raindrop size 596
distribution J Appl Meteor 5 1764-1775 597
Wen G H Xiao H Yang Y Bi and W Xu 2017 Characteristics of summer and winter 598
precipitation over northern China Atmos Res 197 390-406 599
Wu W Y Liu and A K Betts 2012 Observationally based evaluation of NWP 600
reanalyses in modeling cloud properties over the Southern Great Plains J Geophys 601
Res 117 D12202 httpsdoi1010292011JD016971 602
Yuter S E D E Kingsmill L B Nance and M Loumlffler-Mang 2006 Observations of 603
precipitation size and fall velocity characteristics within coexisting rain and wet snow J 604
Appl Meteor Climatol 45 1450ndash1464 doi httpsdoiorg101175JAM24061 605
Zhang P C and B Y Du 2000 Radar Meteorology China Meteorological Press 511pp 606
(in Chinese) 607
608
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
28
Tokay A and D A Short 1996 Evidence from tropical raindrop spectra of the origin of 588
rain from stratiform versus convective clouds J Appl Meteor 35 355ndash371 589
Tokay A and D Atlas 1999 Rainfall microphysics and radar properties analysis 590
methods for drop size spectra J Appl Meteor 37 912-923 591
httpsdoiorg1011751520-0450(1998)037lt0912RMARPAgt20CO2 592
Tokay A D B Wolff et al 2014 Evaluation of the New version of the laser-optical 593
disdrometer OTT Parsivel2 J Atmos Oceanic Technol 31(6) 1276-1288 594
httpsdoiorg101175JTECH-D-13-001741 595
Ulbrich C W 1983 Natural variations in the analytical form of the raindrop size 596
distribution J Appl Meteor 5 1764-1775 597
Wen G H Xiao H Yang Y Bi and W Xu 2017 Characteristics of summer and winter 598
precipitation over northern China Atmos Res 197 390-406 599
Wu W Y Liu and A K Betts 2012 Observationally based evaluation of NWP 600
reanalyses in modeling cloud properties over the Southern Great Plains J Geophys 601
Res 117 D12202 httpsdoi1010292011JD016971 602
Yuter S E D E Kingsmill L B Nance and M Loumlffler-Mang 2006 Observations of 603
precipitation size and fall velocity characteristics within coexisting rain and wet snow J 604
Appl Meteor Climatol 45 1450ndash1464 doi httpsdoiorg101175JAM24061 605
Zhang P C and B Y Du 2000 Radar Meteorology China Meteorological Press 511pp 606
(in Chinese) 607
608
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
29
Table 1 Summary of observed precipitation events in winter 609
Events Duration
(BJT)
Number of
samples
Dominant
hydrometeor
type
Surface
temperature
()
Precipitation
rate (mmh)
2016116 1739-2359 1793 Snowflake -88 09
2016116 2010-2359 797
Raindrop
(2010-2200)
and snowflake
-091 04
2016117 0000-0104 280 Snowflake 043 054
20161110 0717-1145 1232 Snowflake -163 068
20161120 1820-2319 1350 Graupel -49 051
20161121 0005-0049
0247-1005 2062
Graupel
(0005-0049)
and mixed
-106 071
20161129 1510-1805 878 Snowflake -627 061
20161130 0000-0302 780 Snowflake -518 096
2016125 0421-0642 718 Mixed -545 05
20161225 2024-2359 317 Snowflake -305 028
20161226 0000-0015
0113-0243 112 Mixed -678 022
201717 0537-1500 726 Snowflake -421 029
610
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
30
611
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
31
Table 2 Averaged information for each HSD 612
HSD type Sample
number
Mean maximum
dimension (mm)
Number
concentration (m-3)
Raindrop 378 101 7635
Graupel 1608 109 6508
Snowflake 6785 126 4488
Mixed 2634 076 16942
613
614
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
32
615
Table 3 Relationships between max dimension and terminal velocity for different types of 616
hydrometeors (Gunn and Kinzer 1949 Locatelli and Hobbs 1974) calibrated by air density in Haituo 617
Mountain 618
Hydrometeor types Terminal velocity
Raindrop 119881119905 = 11405(965 minus 103119890minus06119863)
Graupel 119881119905 = 11405(13119863066)
Aggregates of unrimed radiating assemblages of
plates bullets and columns 119881119905 = 11405(069119863041)
Graupel like snow of hexagonal type 119881119905 = 11405(086119863025)
Aggregates of densely rimed radiating assemblages
of dendrites 119881119905 = 11405(079119863027)
Densely rimed dendrites 119881119905 = 11405(062119863033)
Aggregates of unrimed radiating assemblages of
dendrites 119881119905 = 11405(08119863016)
619
620
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
33
Table 4 Functions used to fit HSD 621
Name Function Parameters
Gamma 119899(119863) = 1198730119863120583119890119909119901(minus120582119863) No λ μ
Lognormal
119873 =119873119879
radic2120587119897119900119892120590
1
119863exp(minus
1198971199001198922(119863119863119898
)
21198971199001198922120590)
NT σ Dm
Weibull 119873 = 1198730119863119902minus1119890119909119901(minus120582119863119902) No λ q
Exponential 119899(119863) = 1198730119890119909119901(minus120582119863) No λ
Gaussian 119873 =119873119879
120590radic2120587
1
119863exp(minus
(119863 minus 119863119898)2
21205902) NT σ Dm
622
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
34
623
624
Figure 1 Topographic distribution of the experiment site The elevation of the site is 625
1310 m 626
627
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
35
628
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
36
Figure 2 Fall velocity as a function of particle maximum dimension (maximum diameter) for the four 629
hydrometeor types of (a) supercool raindrop (b) graupel (c) snowflake and (d) mixed The color 630
scheme denotes the particle number concentration The solid red curve denotes the typical 631
expression of terminal velocity of raindrops The black curve represents the terminal velocity of 632
lump graupels The blue curve represents the typical terminal velocity of aggregates of densely 633
rimed planes bullets and columns The light blue yellow green and orange curves represent 634
terminal velocities of hexagonal aggregates of densely rimed dendrites densely rimed dendrites 635
and aggregates of unrimed dendrites The dash lines provide the estimate of possible range of 636
instrumental errors for graupels and snowflakes (averaged velocity of these types) estimated by the 637
empirical terminal velocity plusmn20 The representative microscope photographs of the corresponding 638
different precipitation types observed during the same period are shown on the left panel 639
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
37
640
Figure 3 Height-time distribution of cloud radar parameters of graupel precipitation (a b) snowflake 641
precipitation (c d) mixed-phase (e f) reflectivity (dBz) (a c e) linear depolarization ratio (LDR) 642
under 08 km (dB) (b d f) 643
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
38
644
645
Figure 4 Averaged hydrometeor size distributions for the raindrop graupel snowflake 646
mixed-phase precipitations 647
648
0 1 2 3 4 5 6 7 8 9 10 11001
01
1
10
100
1000 raindrop
graupel
snowflake
mixed
N (m
-3m
m-1
)
Max dimension(mm)
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
39
649
650
Figure 5 S-K diagram comparing the relationships between observations (dots) and the 651
commonly used size distribution functions (solid lines) for raindrop (a) graupel (b) 652
snowflake (c) mixed-phase precipitation (d) The blue red and green lines represent 653
S-K relationships of Gamma Lognormal and Weibull distribution respectively The S 654
and K of Exponential and Gaussian distributions are the point (2 6) and (0 0) 655
respectively 656
657
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
-1 0 1 2 3 4 5 6
0
10
20
30
40
50
Raindrop
K
S
Gamma
Lognormal
Weibull
Graupel
K
S
Snowflake
K
S
MixedK
S
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
40
658
659
Figure 6 Taylor diagrams of K from (left) all the data and (right) data with S less than 2 660
and K less than 6 The numbers ldquo1rdquo ldquo2rdquo and ldquo3rdquo denote ldquoGammardquo ldquoLognormalrdquo and 661
ldquoWeibullrdquo distributions respectively 662
663
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
41
664
Figure 7 RED for all data (left) and data with S less than 2 and K less than 6 (right) The 665
shorter the distance the better distribution function performance is 666
raindrop graupel snowflake mixed00
05
10
15
20
25
30
35R
ela
tive
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull
raindrop graupel snowflake mixed0
1
2
3
4
5
6
Re
lative
Eu
clid
ea
n D
ista
nce
Gamma
Lognormal
Weibull