Experimental study on severe convection forecast in Ningxia by non-linear retrieval and variational assimilation using satellite

data

HU Wen-dong1,2 SHEN Tong-li3

DING Jian-jun1 YANG You-lin1 LIU Jian-jun1 CHEN Xiao-juan2WANG Chenwei3

(1Key Laboratory of Meteorological Disaster Preventing and Reducing in Ningxia, 2Ningxia Meteorological Observatory, Yinchuan China, 750002, 3Nanjing Institute

of Meteorology, Nanjing China, 210044)

1.      Introduction

• The application of satellite data is mainly confined to the synoptic, satellite meteorological conception model, and subjective, qualitative explanation in provincial meteorological agency.

• The numerical weather prediction (NWP) models are getting more and more perfected, their products have become one of the indispensable parts for modern meteorology and. But the problem of initial field remains unsolved, thus the meso-scale NWP cannot work efficiently.

• The characteristics of meteorological satellite data make themselves play a very important role on data assimilation.

• The hardware performance, technical staff in provincial meteorological services are not good enough to support the operational implement of complicated retrieval and assimilation system.

• Simplicity and easy-going should be the basic features in provincial meteorological branch.

2. Satellite data and derived elements • The Geostationary Meteorological Satellite infrared data

of 1999, 2000, and 2001 from May 1st to Sept. 30 each year were used ， the total samples is 6839.

• The gray-level data at every meteorological station in Ningxia were read correspondingly.

• The gray-level temporal change in a certain position was calculated as it did in the reference [1].

• Vk,i,j=Ck,i,j- Ck-1,i,j (1)• Here C is gray-level, k is time (hour), and i,j means the coordinate of the station,

or geographic position. This element indicates the change range of gray-level in a certain temporal interval, and reflects the stability of weather system.

• In the same data file, the spatial gradient was calculated as:

• Gi,j= (2)2

1,1,2

,1,1 )()( jijijiji cccc

• This element reflects the consistency degree of the cloud. A small gradient means more similar near the taken pixel, and the weather tendency of cloud there is not obvious, vice versa.

• The bright temperature was calculated and both the change rate and gradient were derived.

• The hourly precipitations of 21 meteorological stations during that period were collected.

• The fields of relative humidity on surface and at different levels of atmosphere were calculated for the study using the surface observation and sonde data.

3. Retrieval of meteorological satellite data • 3.1 Assimilation and satellite data retrieved humidity

• Chou[2], Charney[3] conducted experiment using satellite data. Kou[4] indicated that the precipitation forecast is very sensitive to the initial humidity. Because of the wide change of humidity both in space and time, and the sparsely location of meteorological observation, it is hard to describe the detail of moisture distribution and it is impossible to meet the need of NWP on initial condition. Shen[5] studied the assimilation with limited area model using satellite data and improvement of precipitation was achieved. Cui[6] adjusted the humidity at 850 ～ 400hPa and found the ability of rainfall prediction was elevated. Lin[7], Zhu[8] researched the torrent rain NWP with satellite data retrieved humidity and obtained satisfactory results.

• In the light of the studies above, humidity retrieval using satellite was carried out to provide good initial field for NWP in Ningxia.

• 3.2 Non-linear retrieval and optimal fitting• Because of the non linear essential of atmosphere

movement, the linear process is only an approximate approach under certain conditions.

• It is hard to acquire ideal effect based on this relation. Retrieval with satellite data is a complex issue and a nonlinear model is more reasonable.

• Regression: mature technology and easy to be applied but linear only.

• If the very relation is nonlinear, the nonlinear regression can be done with special process. Here below are the cases of nonlinear regression.

• 1. fit with polynomial. Take x,x2,x3…xn as linear independent factors.

• 2. Transforming with some functions to linear regression, such as Gagin’s[9], Bocchieri’s work [10].

• 3. Normalize the variable as Bocchieri[11] did with mathematic model and then to set up regression model.

• The method in this paper is, try to find out more precise relations between the independent and dependent variables with suitable mathematic model developed by fitting on the samples. The linear relations can be established for regression after transform, and the further study can be conducted.

• In this case, the key to the problem is to find out the non linear relation.

• In fact, because of the widely scattering of the sample, it may not be a strict linear relation after the transform, but the linear degree will be improved and it’s beneficial for the quality of regression.

• Xie[12], Chu[13] adopted the fitting method on meteorological use, however it is quite rare.

• The works [9-13] mentioned above assumed the fixed function and try to get the parameters only. It is limited and the function chosen may not an optimal one.

• In this paper, we try to find out a cluster of mathematic functions to meet the physics demands, and get the parameters. So the optimal function can be found out in a certain extent.

• Considering the shape of variables distribution, 48 functions were designed to fit the samples.

• The functions chosen were sorted by the fitting effect, or residual error. The best 2 functions were listed in table 1.

21 dxcx

bxay

21 dxcx

bxay

cbxay

1

Items (number of passed functions)

1the best 2the second

A. Relative humidityand gray-level (33)

a = 0.3343302b = -0.43019449c = -1.6622662d = 0.48286566

a = 0.32236575b = 0.27838399c = -0.55497431d = 0.93163654e = -0.45718758

B. Relative humidityAnd temporal change of gray-level (30)

y=a+b.cos(cx+d)a = 0.49123164b = 0.097777643c = 9.1731609d = -4.1514746

a = 0.15391716b = 0.44475178c = -2.5936814d = 3.7911048

… … …

F. Relative humidityAnd special gradient of bright temperature (12)

a = 0.65758276b = 4373.3971c = 8078.6531d = 8998.4372

a = 1.5260107b = 0.70485075c = 0.15384818

Table 1. The fitted functions

• 3.3 Over fitting • The coefficients were improved with the best functions. All the

absolute coefficients of others were elevated more than 0.1.

• But overfitting phenomenon appeared for gray-level. Because the function pursued the fitness too much, indulged special details and the particular non typical samples, the fit function is too sensitive and caused violent vibration. (Runge phenomenon [14,15]. )

• In order to keep the stability and avoid the overfitting, the 2nd function was taken for gray-level.

• The linearity improvement of bright temperature is the most remarked, the absolute correlation increased 0.135, and the others increased more than 0.1 except temporal change of bright temperature which increased 0.084.

• Generally speaking, the correlation improved to a better level. The lowest is 0.148 and the highest is 0.367.

• 3.4 Nonlinear regression• The regression can be conducted after the transform to set up the

relation between humidity and the IR data of geostationary meteorological satellite. For concision, let:

• V1=gray-level

• V2=temporal change of gray-level

• V3=spatial gradient of gray-level

• V4=bright temperature

• V5=temporal change of bright temperature

• V6=spatial gradient of bright temperature

• V7=relative humidity

• Then • V7 ＝ a1Ψ1(V1)+a2Ψ2(V2)+a3Ψ3(V3)+a4Ψ4(V4)+a5Ψ5(V5)+a6Ψ6(V6)+b (7)

• Here ai, b are coefficient of regression and Ψi() are the nonlinear

functions selected above and i=1 ， 2 ， 3 …， 6.

 Total

deviation

Correlation

Order of the factorsStandard

errorResidual F

Before 19.864 .312V6, V5, V1, V3, V2,

V4.1928 184.192 89.027

After 46.662 .478V6, V4, V2, V1, V3,

V5.1783 157.394 244.733

Table 2. effect of regression before and after transform.

•The regression with independent fitting transform is obviously better than the original one. The correlation enhanced 53.2% from 0.312 to 0.478, the standard error decreased from 0.1928 to 0.1783 and the residual decreased 27.189, from 184.192 to 157.394.The f was employed to examine the significance of the regression ：

(8)

Here n: number of samples and p: number of factors

The bigger the correlation, the bigger the f, and the better the regression. The f of transformed regression is 2.75 times of that of original one. Take degree of freedom as 6 and the number of samples ∞, α ＝ 0.05, then F0 ＝ 2.22 。Both fs of the 2 regressions developed are bigger than F0, so the

regression models are acceptable or significant, and the nonlinear regression is better.

)1()1( 2

2

pnr

pr

f

Table 3. Regression parameters, A: original, B: fitting transformed.

 

Non-normalized coefficients

Standard error normalized coefficients

t

A B A B A B A B

Intercept -5.025 -.347 1.067 .067     -4.709 -5.203

V1 11.918 .135 1.986 .028 1.759 .106 6.000 4.786

V2 -.912 1.614 .227 .258 -.341 .290 -4.011 6.256

V3 .588 -.289 .407 .054 .059 -.165 1.444 -5.348

V4 2.691 .825 .540 .051 1.460 .326 4.983 16.025

V5 -.572 -.431 .233 .318 -.209 -.064 -2.460 -1.356

V6 -1.306 -0.036 .290 .061 -.189 -.018 -4.510 -.589

• BP Network to retrieve

• Generally 4 layers are enough to form a difficult network, and we think that the forecast is a difficult problem and a 4-layer network is needed.

• 　 Experiment was conducted to find the optimal structure, and the best is that has 6 nodes in each hide layer, and the network to retrieve was built by training

No. Nodes in 1st hide layer

Nodes in 2nd hide layer

error

1 6 6 0.051363

2 5 4 0.051472

3 4 4 0.051505

4 3 3 0.051599

5 2 4 0.051649

6 3 4 0.051656

7 7 2 0.051665

8 7 6 0.051668

… … … …

49 1 6 0.054079

• 3.5 Retrieval of satellite data for heavy precipitation

• Geographically, Ningxia located in the northwest China, far inside the mainland and with an arid climate. Take Yinhcuan city, the capital as an example; the annual precipitation is only about 200mm. Heavy rainfall must go with severe convection. Without abundant moisture, even though the convection happens, lack of enough energy supply of latent heat of condensation provided by moisture, the convection will hardly develop, and the heavy rainfall will not occur.

• After all, heavy rainfall in Ningxia must accompany with severe convection and, the severe convection must be supported by plentiful moisture.

• For the torrent rainfall, moisture is the key condition. 990 samples were selected taking relative humidity as threshold and the criterion was set as 75% experimentally. With the nonlinear approach employed, the relative humidity retrieval models at different levels of atmosphere were developed and the accuracy was further improved.

4. Brief summary of experiment

• Using the models developed above, relative humidity retrieval can be processed easily with satellite data, and it can satisfy the requirement of provincial meteorological department.

• After the retrieval using the approach in this paper and neutral network, variational assimilation were conducted as reference [16] did.

• Relative humidity quality control. In space, no introduction here.• Then the retrieved humidity was put into MM5V3 with other initial

fields of T213 output, for a sudden occurred heavy rainfall in northern Ningxia on July 21 2003, which caused a flood.

• The results show that the precipitation region forecast with retrieved humidity is highly consistent with observation, and the precipitation products are helpful to the operational forecast, and spin up was improved 25%. While the forecast without retrieved data failed in this experiment.

• 　　 Satellite data: July 21 2003, 08:00 am, FY － 2 IR

• 　　 The grid is 60km west and 80km south to the actual position in the images. The information was read directly from satellite data after geographic calibration, in stead of from the images above.

• 　　 Retrieved relative humidity after quality control and originals at 400 and 500hPa. Dot line(blue): humidity of T213, solid line(red): retrieved after quality control.

• 　　 It is clear that the retrieved relative humidity after quality control is consistent with the original in macroscale, so it is beneficial for the model to run stable.

• 　　 On the other hand, the mesoscale systems retrieved are much more obvious compared with the T213s.

• A case of heavy rainfall• 　　 a convective torrential rain was observed at 14:00-15:00, July 21 2003in north

part of Ningxia. Maximum hourly precipitation reported 22.3mm, with 3.2, 1.6, 1.8 and 0.1mm in some other stations and the hour next.

• Spatial and temporal distribution of precipitation

• MM5V3 precipitation without satellite data. The convective precipitation only, with a very tiny value 0.2128mm at the south end of Ningxia (hundreds km away) the maximum forecasted 4h later than the observation (spin-up)

• The MM5 can not indicate this convective rainfall at all without the assimilation.

• 　　 The satellite data at different levels were retrieved and quality controlled (The relative humidity fields above), then they were put into the MM5v3.

• 14:00, 15:00, 16:00 July 21,2003

• 17:00 18:00 precipitation (mm)　• The precipitation got enhanced greatly, the convective rainfall was forecasted in

north part of Ningxia since 14:00, the exact area of observed, and middle part also, maybe false, without observation evidence. 15:00 north: stronger 0.2mm, middle: disappear. North only. 16:00: 0.8. 17:00 1.1 mm, 18:00 0.5mm and the area shrinking. 19:00 stopped.

5. Conclusion and discussion

• With optimal fitting, the mathematical relations between the relative humidity and meteorological satellite data were found out and, all of the relations are nonlinear.

• After the transform with these nonlinear functions, nonlinear regression was achieved, and the effect of regression was enhanced.

• For the heavy rainfall, the capability of retrieval improved further. Comparing with the traditional regression, it is not only much more reasonable, but achieved a rather high precision also.

• The primary experiment indicated the NWP forecast made a distinct advance with retrieved data for a sudden occurred severe convection with an intensive precipitation and caused a flood, meanwhile the NWP without assimilation failed to forecast.

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thanks for your attention谢谢merci

胡文东宁夏气象防灾减害重点实验室，宁夏银川， 750002,

HU 　 Wendong

Key Laboratory of Meteorological Disaster Preventing and Reducing in Ningxia, Yinchuan China, 750002,

hu.wendong@163.com, 86-951-5043015