university of hawai'1 library
TRANSCRIPT
UNIVERSITY OF HAWAI'1 LIBRARY
ENVIRONMENTAL STEERING FLOW ANALYSIS FOR
CENTRAL NORTH PACIFIC TROPICAL CYCLONES BASED ON
NCEPINCARREANALYSIS DATA
A THESIS SUBMITTED TO THE GRADUATE DIVISION OF THE UNIVERSITYOF HAWAII IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
IN
METEOROLOGY
AUGUST 2003
By
Anthony Reynes
Thesis Conunittee
Duane Stevens, ChairGary Barnes
YuqingWang
ACKNOWLEDGMENTS
I wish to deeply thank the following people for their invaluable contributions: my
advisor Dr. Duane Stevens for his dedicated guidance and encouragement throughout the
preparation of this thesis, Dr. Gary Barnes and Dr. Yuqing Wang for all their helpful
revisions and suggestions. Thanks to Mr. Samuel H. Houston for his revisions and
collaboration through the NWS/COMET program which provided the funding to make
this project possible. I also want to thank Dr. Frank Marks~ and Dr. Chris Landsea for
their suggestions. A big thank you to Miss Mary Ann Esteban for her mathematical
expertise and unconditional support~ Mr. Hideki Okajima for his computer expertise, and
Mr. Bo Yang for his helpful discussions. Also~ Mr. Qinghua Ding~ Yongxin Zhang (Fred),
Yang Yang (Edward), Christopher Chambers~ and LOOin Pan for their technical
assistance.
This thesis is dedicated to the loving memory of my mother Angelica Figueroa
Alverio. Your love, wisdom~ and spirit will forever live in my heart.
iii
ABSTRACT
An environmental steering flow analysis for central north Pacific tropical
cyclones was made utilizing model wind data from the NCEPINCAR Reanalysis project,
since no aircraft or rawinsonde data are readily available in this region. The results are
compared with previous work performed in other hurricane basins. Tropical cyclone best
track data were obtained from the Central North Pacific Hurricane Center. Most of the
cyclonic activity analyzed in this project was observed at latitudes below 20~, where
most tropical cyclones followed a general west to northwestward track. Environmental
steering was defined as a 50_1' annulus around the cyclone center.
On average, tropical cyclones were observed to move faster than the
environmental steering flow, moving to the right of the environmental flow at the mid
lower tropospheric levels between 850 and 600 mb, and to the left at higher levels. These
results show agreement with previous work for the north Atlantic basin, and disagree
with most previous results for the north-west Pacific (where most cyclones show
movement to the left of the environmental steering flow at all levels). Out of36 candidate
steering layers, two were identified as the recommended steering layers for different
cyclone intensities: 850-400 mb for tropical storms and depressions, and 850-300 mb for
hurricanes. The differences between these steering layers and tropical cyclone motion are
smaller south of20~, especially southeast of the Hawaiian islands.
The possibility of a direct relationship between wind shear and the environmental
steering flow was also investigated, but no correlation between these two variables was
found.
iv
TABLE OF CONTENTS
ACKNOWLEDGMENTS iii
ABSTRACT " iv
LIST OF TABLES viii
LIST OF FIGURES ix
LIST OF ABBREVIATIONS AND SYMBOLS xi
CHAPTER 1. INTRODUCTION 1
1.1 Backgro'Ulld "' 1
1.2 Previous work M 2
1.2.1 Environmental steering layer and deep layer means 2
1.2.2 Translational speed and angle differences 4
1.2.3 Radius of influence ofthe tropical cyclone circulation 5
1.2.4 Stratification oftropical cyclone data 6
1.2.5 Correlation between steering and tropical cycloneIntensIty 8
1.2.6 Vertical wind shear and steering : 8
1.2.7 Be1:a effect " , 9
1.3 Scientific objectives 10
CHAPTER 2. DATA AND METHODOLOGy 12
2.. 1 Dam ...............•, ' ' , 12
2.1.1 Global wind data 12
2.1.2 Tropical cyclone best track data 12
2..2 Database criteria ' 13
v
2.2.1 Central north Pacific domain 13
2.2.2 Database period 13
2.2.3 Selection oftropical cyclone cases 14
2.3 Calculating environmental steering from NCEPINCAR
ReaIlalysis dam 15
2.3.1 Candidate steering layers and levels 15
2.3.2 The u and v components for the environmental steering
layer " <11 ••••• " •• f!' ••••••••••••••••••••••• 16
2.4 Tropical cyclone motion vector 16
2.5 Calculating environmental steering layer u and v components 17
2.6 Vertical 'Wind. shear 19
CHAPTER 3. CLIMATOLOGY ANALVIS 20
3.1 Composite ofwinds in the central north Pacific 20
3.2 Tropical cyclone climatology 21
3.2.1 Intensity " " 21
3.2.2 Direction .., , ,.., 21
3.2.3 Speed 23
CHAPTER 4: Sl'EERING ANALYSIS 24
4.1 All tropical cyclone cases 24
4.2 Vertical variation analysis 26
4.2.1 Tropical storms and depressions 26
4.2.2 Hurrican.es ~ 28
4.2.3 Direction and speed stratifications 29
VI
4.3 Environmental steering layer analysis 30
4.3.1 Absolute angle difference analysis for tropical
stonns and depressions 31
4.3.2 Absolute angle difference analysis for hurricanes 33
4.3.3 Absolute speed difference layer analysis 35
4.4 Central north Pacific domain analysis 36
4.5 Wind shear and steering 38
CHAPTER 5: SUMMARY 40
5.1 Conclusions and discussion 40
5.2 Future work , , 43
APPENDIX A: FORMULAS 45
APPENDIX B: DATA TABLES AND SIGNIFICANCE TESTS 47
REFERENCES 89
vii
TABLfJ
LIST OF TABLES
PAGE
1. Stratification oftropical cyclone cases by motion direction and speed 22
2. Level analysis for all tropical cyclones 25
3. Significance test for angle mean difference 26
4. Level analysis for tropical stonns and depressions 27
5. Level analysis for hurricanes 28
6. ESL analysis for tropical stonns and depressions 32
7. ESL analysis for hurricanes 34
8. Significance test for absolute angle mean difference; quadrant
comparison an.alysis 37
viii
FIGURE
LIST OF FIGURES
PAGE
2.1 Central north Pacific domain 58
2.2 Tropical cyclone database yearly distribution 59,
2.3 Environmental steering layer definition diagram 60
2.4 Polar plane for angle calculations 61
2.5 Steering annulus diagram 62
3.1 Twenty six year wind composite: 850 mb 63
3.2 Twenty six year wind composite: 500 mb 64
3.3 Twenty six year wind composite: 200 mb 65
3.4 Tropical cyclone best track chart: 1975-2000 66
3.5 Tropical cyclone monthly distribution 67
3.6 Tropical cyclone intensity distribution 68
3.7 Tropical cyclone direction and speed stratification 69
4.1 Angle vs. speed difference scatter plot for mid-lower levels 70
4.2 Angle vs. speed difference scatter plot for higher levels 71
4.3 Normal probability plot for the 850 mb pressure level 72
4.4 Normal probability plot for the 250 mb pressure level 73
4.5 Histogram ofangle difference for the levels of 850 and 250 mb 74
4.6 Vertical variation analysis difference for the intensity categories 75
4.7 Vertical variation analysis ofangle difference for the translational
direction and speed categories 76
IX
4.8 Vertical variation analysis ofspeed difference for the translational
direction and speed categories 77
4.9 Angle vs. standard deviation scatter plot for tropical storms and
depressions f/ ••••••••••••••••••••• 78
4.10 Angle vs. standard deviation scatter plot for hurricanes 79
4.11 Significance test ofabsolute angle difference: tropical storms
an.d depressions 11\ "' ·80
4.12 Significance test ofabsolute angle difference: hurricanes 81
4.13 Speed vs. standard deviation scatter plot 82
4.14 Significance test ofabsolute speed difference 83
4.15 Quadrant analysis for selected layers 84
4.16 Vertical wind shear vs. absolute angle difference: tropical storms
an.d depressions " _ , "85
4.17 Vertical wind shear vs. absolute angle difference for hurricanes 86
4.18 Vertical wind shear vs. absolute speed difference for tropical storms
an.d depressions , 87
4.19 Vertical wind shear vs. absolute speed difference for hurricanes 88
x
LIST OF ABBREVIATIONS AND SYMBOLS
A8.d absolute angle mean difference
3d angle mean difference
ASd absolute speed mean difference
CNP central north Pacific
DLM deep layer mean
ESL environmental steering layer
h hour
Ian kilometers
kts knots
m s-1 meters per second
mb millibars
n mi nautical miles
NA north Atlantic
NNR NCEPINCAR Reanalysis
~ degrees north
Ow de~~swem
Sd speed mean difference
SESL environmental steering layer wind speed
SP south Pacific
Src tropical cyclone propagation speed
std, a standard deviation ~ sigma
u u wind component
.Xl
UTe
UTC, vTC
v
NWP
wsh
environmental steering layer U and v components
coordinated universal time
tropical cyclone U and v components
v wind component
north west Pacific
vertical wind shear
xii
CHAPTER ONE
INTRODUCTION
1.1 Background
For the past 20 years there has been an increasing interest in hurricane research in
the central north Pacific (CNP) basin, particularly due to the risk of a direct hit on the
Hawaiian Islands. Thereforet it is critical to improve current knowledge on tropical
cyclone motion for this region. Hurricane Iniki in 1992 and its associated cost provided
the best example ofthe vulnerability ofthe islands, as it made a direct hit on the island of
Kauai on September 11, 1992.
Figure 2.1 shows the domain of the CNP basin. It is defined as the area between
1400W and I800W' (the dateline), and extending northward from the equator. The
Hawaiian Islands are located around the middle region of the domain between I8~ and
22~. A well-known problem when attempting hurricane research in Hawaii is the
paucity of tropical cyclone events in the CNP (Clark and Chu I999)t especially when
compared to other more active basins like the north Atlantic, eastem and western north
Pacific. By looking into previous work done on these basins we can determine the best
way to approach the initial objectives for this project. An important aspect to consider is
the need to understand the relation between the tropical cyclone motion and the
environmental wind (synoptic flow) surrounding it. For this initial phase of the work
CNP tropical cyclone tracks are investigated, with an emphasis on the satellite era. Ifwe
better understand the relation between the environmental wind and the motion of tropical
1
cyclones over the Hawaiian regioI4 this knowledge could hopefully be applied in
seasonal and short tenn outlooks. The recent availability of the NCEPINCAR Reanalysis
database has provided an alternative source of satellite derived meteorological data for
the CNP, where surface measurements other than on the islands themselves, sparse ship
reports, or routine aircraft missions during a tropical cyclone event are not available.
1.2 Previous work
1.2.1 Environmental steering layers and deep layer means
The two primary aspects when analyzing tropical cyclone track relations with the
environmental steering flow are differences in speed and direction (i.e., vector velocity
differences) between them. Previous work has been performed for the more active
tropical cyclone basins of the north Atlantic (NA), north west Pacific (NWP) and the
south Pacific (SP). Kasahara (1957) showed that it is possible to obtain valuable
information regarding the relations between environmental steering flow and tropical
cyclone track by directly comparing the winds surrounding the core of a storm, at
different atmospheric levels, with its track data. Kasahara (1959), Ballenzweig (1959),
and George and Gray (1976) showed early results in which they describe the winds at the
500 and 700 mb levels as the principal data levels for tropical cyclone steering. Although
the techniques of defining and describing the environmental steering flow vary
considerably from author to author, the most common one utilizes wind data from two or
more atmospheric levels and calculates the vertical mass-weighted average wind.
2
Therefore the environmental steering flow is then described in tenns of layer means or
environmental steering layers (ESL), a concept that has been widely embraced as a good
approach to define tropical cyclone steering (Kasahara 1960, Jones 1961, Jones 1964,
Sanders et. al 1975, Chan et. al 1980, Chan and Gray 1982, Holland 1983, Shapiro and
Neumann 1984, Dong 1986, Lajoie 1986, Carr and Elsberry 1990). The top and bottom
of these vertically av~ged ESLs also varies depending on the criteria. applications and
needs of each particular author. Section 3.2.1 will explain in more detail the approach
chosen for this project.
Kasahara (1960) performed one of the earliest techniques of defining deep layer
means (DLM) for numerical prediction analysis utilizing a two-level baroclinic model,
with a first vertically averaged layer of 1000-700 mb, and a second one of 500-200 mb.
Holland (1984) neglects the upper and lower atmospheric layers by citing a significant
distortion of the basic steering current in question due to the presence of asymmetric
inflow (outflow) circulations in the lowest (highest) atmospheric layers toward (away
from) the stonn. He ignored the layers between 800 mb and the surface, as well as the
layers above 300 mb, thus defining (by assumption) a basic steering current as a DLM of
800..300 mb. Therefore, the information contained in these upper and lower regions and
their possible contribution to tropical cyclone motion should be studied separately. Jones
(1961) indicated that none of the individual wind levels of 1000, 700, 500, or 200 mb
adequately represented the steering of hurricane Audrey in 1957, but their weighted
average did. He identified the ESLs of900-300 mb and 800400 mb as showing the best
correlation with the track of Audrey. His later numerical forecast scheme for hurricane
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trajectories by the steering method (Jones, 1964) utilized a single deep layer mean of
850-200 mb. Chan and Gray (1982) recommend the layer of 700-500 mb, which
describes the middle tropospheric winds, if rawinsonde data in the area of the cyclone is
available. Pike (1985) also describes the mid-tropospheric layer of 700-500 mb, and the
DLM of 1000-100 mb as better predictors for NA tropical cyclone motion compared to
single atmospheric levels. Carr et. al (1990) discard the use of individual levels and used
strictly DLM as predictors of tropical cyclone propagation. They also argue that for
statistical work of this nature it is better to use "composite" data rather than each case
separately, since the variability in direction and speed can be very large from case to
case. Wu and Kurihara (1996) favor a DLM of 850-300 mb for their numerical studies of
tropical cyclone motion relative to the environment (see appendix B.l).
1.2.2 Translational speed and angle differences
Two of the most significant findings of previous research in the NA, NWP, and
the SP basins address directional deviations (angle differences) and translational speed
differences between tropical cyclone motion and the environmental steering flow. George
and Gray (1976) showed that in most NWP tropical cyclones there is a left bias of their
tracks when compared to the environmental steering flow with angle differences ofup to
16° (in other words, storms tend to move to the left of the environmental steering flow).
Also, most cyclones moved faster than the steering flow by about 1 m S·l. They
specifically identified the level of 500 mb as best representative of steering, and 700 mb
for speed. Holland (1984) also reported cyclones in the SP (Australian) basin moving
4
faster than a deep layer mean (DLM) of 850-300 mb~ but with an angle mean difference
to the right of the DLM. Earlier, Dunn and Miller (1964) also suggested tropical cyclone
movement generally faster and to the left of the environmental steering flow for NA
cyclones, but indicated that stratification of the data might show different results
depending on the geographical region where the tropical cyclone is actually moving.
Dong and Newmann (1986), and Dong (1988) reported similar results for NA and NWP
tropical cyclones, but with a greater emphasis on the need for data stratification.
1.2.3 Radius of influence ofthe tropical cyclone circulation
When a cyclonic vortex is embedded on a surrounding flow one of the most
difficult tasks to date is to determine the proper radius of influence on which the
surrounding flow is distorted by the vortex circulation. In order to determine this radius
of influence a wide range ofdistances from the tropical cyclone center have been studied,
but no single technique has been universally adopted. Kasahara (1957) proposed to
consider all the information inside a 300 Ion radius or less from the center in his early
attempts of numerical prediction models. Fujiwara (1962) made symmetric hurricane
vortex simulations with an imposed radius of influence which equals one third the
observed physical radius of the cyclone. Sanders et. al (1975) utilized a radius of 300 n
mi (555 kIn) from the cyclone center, which was determined mostly from aircraft and
rawinsonde data, when available. for storms in the NA.
Perhaps one of the most referenced representations of the winds surrounding the
inner core of the storm and the immediate surrounding wind was given by George and
5
Gray (1976). They defined a composite circular grid with eight annular zones extending
outward from 1° to ISo from the estimated tropical cyclone center. Using this technique
Chan and Gray (1982) concluded that the best correlation between the tropical cyclone
motion and its environmental steering, determined by rawinsonde and aircraft data, was
found in the annulus with radius of about SO-7' from the center regardless ofthe physical
size ofthe cyclone.
1.2.4 Stratification oftropical cyclone data
One of the most comprehensive studies on tropical cyclone steering was
performed by Chan and Gray (1982) for the three main hurricane basins. Their primary
objective was to stratify the tropical cyclone data in several categories, searching for
dependency relations between the environmental steering flow and the Properties
defining each category. The early results describing cyclones having an average
movement to the left and slightly faster than the ESL were probably underestimating the
dependence on geographical position, intensity, and direction. To expose such
dependencies, they stratified their tropical cyclone database into 6 categories and 21 sub
categories. This wide scope of stratification was possible due to the relatively large
abundance of tropical cyclone data available in the NWP, NA, and to a lesser extent the
SP (Australian) basin. In fact, the NWP and the SP basins have many scattered islands,
and therefore networks of rawinsonde stations scattered around their oceanic domains
(over 20 stations). In the NA basin, routine aircraft reconnaissance missions are flown in
order to collect dropsonde data from selected cyclones and their environment.
6
For angle mean difference calculations the first category in Chan and Gray (1982)
classified the cyclones by "latitude", separating cyclones moving either north or south of
20~. The reason for this is to investigate how the main synoptic wind patterns within
each sub-domain may affect tropical cyclone motion. South of 20~ there is a more
dominant presence ofeasterly winds in the lower levels ofthe atmosphere, while north of
20~ the synoptic patterns tend to have a greater influence ofwesterly winds.
The speed category separated the cyclones as slow, moderate, and fast movers,
with specific criteria for each basin. The movement category separated cyclones moving
westward, northward or eastward as described by a polar coordinate system with pure
northward movement as 0°. The intensity category separates tropical storms from
hurricanes. Some further stratification for intensities was made for the NWP only, as well
as several sub-categories for size and intensity changes. In their analysis most tropical
cyclones show a movement to the left ofthe environmental steering flow for the northern
hemisphere and to the right in the southern hemisphere. The mid·low level tropospheric
winds (between 700 and 500 mb) seem to show a better correlation with steering than
higher levels, particularly above 300 mb. An important exception to these general
findings is observed for cyclones moving south of 20~ in the NWP and the NA. The
leftward deviation appears not only to be reduced for lower latitudes, but cyclones can
actually move to the right of the environmental steering flow. This particular group of
cyclones generally move in a synoptic environment dominated by low and mid level
easterly winds. Previously, Brand et. al. (1981) reported NWP tropical cyclones moving
to the left of the environmental steering flow at latitudes north of 20~. For the lower
7
latitudes (south of 18~ cyclones moved more to the right of the environmental steering
flow. Dunn and Miller (1964) also observed that westward moving cyclones tend to move
more to the right of the environmental steering flow while northwest and northward
movers tend to move to the left. Further analysis by Dong and Newmann (1986) also
support these generalizations for cyclones in the NA.
1.2.5. Correlation between steering and tropical cyclone intensity
The importance of considering the analysis of mid-tropospheric layer means in
order to determine relationships between tropical cyclone intensity and the environmental
steering flow was discussed by Newmann (1981). Dong and Newmann (1986) reported
that the depth of the steering layer increases in proportion to the tropical cyclone
intensity. Chan and Gray (1982), and Wang and Holland (1996) also suggest the possible
dependence of DLM depth on tropical cyclone size and intensity. Again, the top and
bottom of the DLM varies depending on the assumptions, initial conditions and
objectives of each experiment. But the general findings suggest that hurricanes interact
with a deeper steering layer than tropical storms or depressions.
1.2.6. Vertical wind shear and steering
Wind shear has been analyzed in several studies in order to establish a definite
role on tropical cyclone steering. Many involve complex model analysis using baroclinic
and dynamical schemes, such as potential vorticity fields in the inner most part of the
tropical cyclone core, and Coriolis (beta effect) parameterizations (Wu and Emanuel
8
1993, Marks 1992, Franklin et. al 1993, Wang and Holland 1996). Although such
analyses are outside the scope of this project, it is worth mentioning that in general a
clear correlation between wind shear and steering has not yet been established. Marks
(1992) and Franklin et at. (1993) describe the role of vertical shear on intensification and
structure ofhurricanes Norbert and Gloria, but with no conclusive evidence on the role of
wind shear in steering. Dr. Frank Marks (personal communication, 2002) has stated that
wind shear and steering are not related.
1.2.7. Beta effect
Environmental steering has been identified as the most important influence on
cyclone movement, up to 70 to 90010 of the total cyclone motion (Newmann, 1992). The
other important influence has been identified as the latitudinal variation of the Coriolis
parameter, or the so-called beta effect (drift). For this project, however, the tropical
cyclone data do not provide enough information regarding wind structure in the cyclone
vortex, which is crucial in obtaining key parameters to properly calculate the beta effect
(Smith et al., 1997). Nevertheless, the following general theoretical results regarding beta
drift impact on cyclone motion are relevant for this project.
For the northern hemisphere, the beta effect will deviate a tropical cyclone
towards the northwest, especially when the environmental steering flow is weak or absent
(DeMaria, 1985; Chan and Williams, 1987 and 1994; Fiorino and Elsberry, 1989; Wang
and Li, 1994; Jones, 1995; Smith et al., 1997). Also, if a cyclone is embedded in the
easterly flow south ofthe subtropical ridge, the beta effect will cause the cyclone to move
9
to the right and faster than the steering flow, while for northeastward moving cyclones
the beta effect will cause a motion to the left and slightly slower than the steering flow
(Elsberry et al., 1987). DeMaria (1987) suggests that the beta effect can have a greater
impact on the motion of larger and intense cyclones. On the other hand, if the
environmental steering flow is strong (e.g., between 7 and 8 mls), the impact of the beta
effect and other small scale internal influences on cyclone motion can be masked out
especially for the smaller cyclones.
1.3 Scientific objectives
As an initial objective I will utilize model NCEPINCAR Reanalysis wind data to
empirically identify the steering layers that might show the best correlation with tropical
cyclone motion in this region. Since there is no previous work which could provide an
initial guidance regarding the nature and definition of steering for the CNP, I will explore
different combinations of eight atmospheric pressure levels in order to fmd a suitable
ESL for tropical cyclones in the CNP. The technique of defining steering as an annulus
5°--,0 from the cyclone center will be utilized (see section 2.5). Sensitivity analysis of the
ESL dependence on tropical cyclone intensity will be performed by stratifying the
tropical storms and depressions from the hurricanes. Speed and angle mean differences
between ESL and tropical cyclone motion will be calculated for both categories. Since
the number of cases available for this project is considerably smaller compared to the
abundant tropical cyclone data in the NWP and the NA, I am limiting the stratification of
10
the data to six other categories: three for tropical cyclone direction (westward, northward,
south/east), and three for speed (slow, moderate, and fast moving). The analysis for the
intensity categories is the main focus ofthis project.
Tropical cyclone speed and angle differences relative to steering flow at eight
different pressure levels will be analyzed following a procedure similar to Chan and Gray
(1982), and George and Gray (1976). The results could then be compared with the other
hurricane basins. Also, I will address the question of the possible dependence of steering
on vertical wind shear for both tropical stonns and hurricanes by analyzing the ESLs that
show the best results (smallest differences) for each category.
1t is the ultimate goal of this work to provide the first comprehensive analysis of
tropical cyclone motion and the relation with its environmental steering flow for the CNP
as defined from NCEPINCAR Reanalysis model wind data.
11
CHAPTER TWO
DATA AND METHODOLOGY
2.1 Data
2.1.1 Global wind data
Historically, data sources for research in the domain of the CNP have been very
limited since the only areas with adequate data collection platforms are within the
Hawaiian Islands and their immediate coastal waters. The development of the
NCEPINCAR Reanalysis Project has provided an alternative source of meteorological
data for the CNP (Kalnay et al., 1996). Pressure level wind data were obtained from the
National Centers for Environmental Prediction and their NCEPINCAR Reanalysis
Project database (hereafter NNR). The variables chosen are the u and v wind
components computed as averages of instantaneous values at the reference times 0000,
0600, 1200, and 1800 UTC. The resolution is 2.5 degrees latitude by 2.5 degrees
longitude on a global grid. For these variables there ate seventeen levels available
between 1000 mb and 10mb. Kalnay et. al (1996) describes the main features of the
reanalysis system, quality control and the properties ofthe data products it generates.
2.1.2 Tropical cyclone best track data
Best track and tropical cyclone intensity data were provided by the Central
Pacific Hurricane Center, collocated with the National Weather Service Forecast Office
at Honolulu, Hawaii. The tropical cyclone positions are reported daily at 0000, 0600,
12
1200 and 1800 UTC respectively, along with the estimated wind intensity in knots. The
best track is a subjectively "smoothed" path used to represent the movement of the
tropical cyclone based on satellite estimating techniques when no other forms of in-situ
measurements are available.
2.2 Database criteria
2.2.1 Central north Pacific domain
The official National Weather Service domain of the CNP is shown in Figure 2.1.
Since all of the tropical cyclone activity relevant to this project is observed equatorward
of35'W, the northern boundary bas been set at 40~. Also, the eastern boundary bas been
extended to 1300W in order to include the region of the eastern north Pacific from where
tropical cyclones move into the CNP.
2.2.2 Database period
The databases used in this project depend mostly on satellite derived information
for the analysis of both tropical cyclone best track and NNR wind data. Therefore it is
reasonable to select a temporal coverage that emphasizes the satellite era. The
implementation of routine, satellite-derived data was fIrst established in the mid-1960's
with the development of the TIROS Satellite Program. Due to the novelty of satellite
technology in those days, data images were generally inferior in quality and resolution.
13
The establishment ofmore advanced remote sensing programs like ERTS (Earth
Resources Technology Satellites) and LANDSAT (Land Satellite Program) in the early
and mid-1970's provided the technology for acquiring and processing satellite data with
better quality and reliability (Lillesand, 1994). Therefore the database for this project will
cover the years from 1975 to 2000.
2.2.3 Selection oftropical cyclone cases
A selection of a tropical cyclone required satisfaction of at least one of the
following:
1. cyclone that crossed 1400W from the northeast Pacific with at least tropical
depression intensity, and further intensified into a tropical storm while moving in
the CNP domain.
2. cyclones that approached the 1400W degree longitude from the eastern north
Pacific and persisted with an intensity of at least tropical depression for at least 24
hours while moving between 1300W and 1400W before dissipating.
3. cyclones for which genesis took place in the CNP domain and intensified into
tropical storms.
Additionally, all selected cyclones must be moving (Le. speed> 0 m S·I), and have no
inconsistencies or errors in the data file.
Figure 2.2 shows the distribution of the tropical cyclone cases, a total of 65 that
were selected for the period. Hurricane Dot in 1959, and tropical storm Sarah in 1967
14
were also included due to their historical impact on the Hawaiian Islands. Dot
made landfall on the island ofKauai in August 1959. Sarah moved south of the islands
for several days without considerable weakening, keeping local surveillance on high
alert. There are two other years in which a tropical cyclone also affected Kauai; 1982
(Iwa), and 1992 (Iniki). Some additional climatology ofthe tropical cyclone database will
be shown in section 3.2.
2.3 Calculating environmental steering from NCEPINCAR Reanalysis data
2.3.1 Candidate steering layers and levels
Most previous work demonstrates that low to middle level tropospheric steering
shows the best correlation with tropical cyclone motion. From section 1.2.1, I followed
Chan and Gray (1982), and Holland (1984) regarding the exclusion of the highest upper
tropospheric winds (above 200 mb), as well as the winds near the surface. These levels
might contribute significant distortions when analyzing the environmental steering of
tropical cyclones, due to the presence of both the cyclonic and anticyclonic inflow and
outflow circulations ofthe storm. Eight standard pressure levels (850, 700, 600, 500, 400,
300, 250, and 200 mb) from NNR are selected to create a group of36 candidate steering
layers for this project. Figure 2.3 is a schematic diagram ofthese ESLs. The eight original
NNR levels are shown in the vertical axis arranged from bottom (850 mb) to top (200
rob).
15
2.3.2 The u and v wind components for the environmental steering layer
A layer "mean average wind" was calculated for each ESL. For the individual
pressure levels the values ofthe u and v components were taken from the NNR files. For
the steering layers a weighted average vertical integration was performed:
where
Layer Mean =
Ubot + UtopU= ----
2
fOP.tot U dp
Cdp
dp == (pbot - PlOp)
(2.1)
where u (or v) are the wind component values from the NNR data, and dp is the pressure
difference between layer bottom and top. The wind components for each ESL will be
referred as UESL and VESL hereafter. The method for interpolation of layer components
(UESLand VESt) is explained in section 2.5.
2.4 Tropical cyclone motion vector
The displacement ofthe cyclones was calculated from the best track data points in
intervals of 6 hours. The UTe and VTC components were obtained by calculating the
distance between points A to B over a great circle path on a sphere with the following
formula (Snyder~ 1987):
16
Dist (A,B) = Orr) cos·j [sin f/JA sin th + cos f/JA cos th COS(OA-8B) ] (2.2)180
where
r = radius ofearth in /an or m,
f/JA = latitude ofA,
th = latitude ofB,
OA = longitude ofA,
fk = longitude ofB.
The tropical cyclone angle of direction determined by UTC and VTC was calculated using
the polar plane shown in Figure 2.4. Appendix A provides detailed formulae for this
section.
2.5 Calculating environmental steering layer u and v components
The previously discussed absence of tropical cyclone data in the CNP compared
to the other basins imposes strong constraints when attempting to define the inner core of
the cyclones. Similarly, qualitative analysis of satellite images to determine the tropical
cyclone physical properties of the inner structure can be misleading if aircraft or
rawinsonde are not available for comparison. Neither source is widely available for this
project. The NNR model generated data are available on a 2.5° X 2.50 global grid
resolution, which is coarser than the one degree resolution used in most previous work
17
based on rawinsonde or aircraft data. Resolving the extent ofthe influence ofthe cyclone
circulation on the background wind field is more difficult to achieve with the resolution
ofthe NNR data.
To determine the ESL vector a similar approach from the generally accepted
method was taken. An annulus around the cyc1(>ne center was defmed with an inner
radius of 550 km, and an outer radius of 800 km as shown in Figure 2.5. This range is in
agreement with the 5°-7° steering annulus. The data points lying within the annulus are
then selected and averaged for a particular time. The UESL and VESL values for any 6 hour
period are simply the average between the initial and final time (see Appendix A for
formulas). The ESL angle is determined using the polar plane from Figure 2.4. The basic
relationship between the environmental steering flow and the tropical cyclone motion
vectors are also shown in Figure 2.4. With cyclone motion as reference, the speed
difference Set between them is determined as follows:
Sd = SESL - STC (2.3)
where a negative (positive) value of Set means that the tropical cyclone is moving faster
(slower) than the ESL wind. The difference between the tropical cyclone direction (aTe)
and ESL wind direction (&Est> is given by:
(2.4)
18
The criterion followed is to assign a negative (positive) value to 3d when the cyclone is
moving to the right (left) of the ESL.
2.6 Wind Shear
The vertical wind shear was determined by calculating the difference between the
winds at 200 rob and 850 rob, using the conventional expression for wind shear:
(2.5)
Five categories for wsh are defined, utilizing intervals of 5 m S·l, starting with the values
between 0 and 5 m S·l, and so on until 25 m S·l. A plot ofwsh vs. 3d (8<1) can be created in
order to explore the possible correlation between wsh and steering.
19
CHAPTER 3
CLIMATOLOGY ANALYSIS
3.1 Composite ofwinds in the central north Pacific
A well known feature in the area of the Hawaiian Islands is the presence of east~
northeast trade winds year round. This phenomenon is caused by the presence of a semi
permanent high pressure cell in the north Pacific, and its associated ridge could extend to
the vicinity of the Hawaiian Islands. Figures 3.1 to 3.3 show the monthly averaged winds
for the hurricane season, which runs from June to November.
The 26 years studied in this project (1975-2000) are averaged at three
representative levels: 850, 500, and 200 mb. The presence of this trade wind regime is
observed at the lower 850 mb winds. Easterly wind at this level is found over most of the
southern CNP (Figure 3.1). At 500 mb and higher the wind becomes more westerly
(Figures 3.2 and 3.3). It is clear that the extent of the high pressure cell east-northeast of
Hawaii is observed well into the southern CNP in the middle and lower tropospheric
levels.
The regional climatology of the lower and middle troposphere is dominated by
persistent easterly winds, with an average speed between 5 and 10 m S·l, particularly in
the southeast portion of the defined CNP working domain.
20
3.2 Tropical cyclone climatology
Figure 3.4 shows a track chart with all the sixty five best tracks of the CNP
tropical cyclone cases selected for this project~ with the Hawaiian Islands indicated by the
red circle. There are a total of 991 observations each representing a six hour displacement
of the cyclone. The monthly distribution of the selected tropical cyclones for the
hurricane season~ which runs from June to November, is shown in Figure 3.5. The peak
ofthe cyclonic activity is observed from mid July to August.
3.2.1 Intensity
The tropical cyclones were stratified in two main intensity categories: tropical
storms and depressions~ with maximum sustained winds below 64 kts, and hurricanes,
with maximum sustained winds equal or greater than 64 kts. Figure 3.6 shows the
distribution for each category. Nearly 60% of the data belong to tropical stOtnlS and
depressions.
3.2.2 Direction
Two obvious characteristics are inferred from Figure 3.4: most of the CNP
cyclones move on a west to west-northwest track~ and they primarily occur south of
20~, particularly in the southeast quadrant Figure 3.7a shows a stratification of the
tropical cyclones by their direction of motion following Chan and Gray (1982).
Table la shows the definitions of each category and the corresponding number of
21
a.
Category Criteria All 'T. Storms Hurrieanesanddep.
Westward 2250 < TCdir ~315° 868 548 320
Northward 3160 < TCdir ~45° llO 35 75
Other 460 < TCdir $2240 13 9 4
Slow TCspeed < 4 m S·l 161 95 66
Moderate 4 m S·l < TCspd ~8 m S·l 615 361 254
Fast 8 m S·l < TCspd 215 134 81
Table 1. Stratification oftropical cyclone observations by motion direction (a), and speed (b)
observations. The great majority of cyclones, especially those of lesser strength, moved
in a westward or west-northwest direction.
Ofparticular note is the fact that hurricanes make up nearly 70% of the northward
movers while contributing only 40% of the total observations (see Figure 3.6). Figures
3.2 to 3.3 indicated only very small regions of southerly seasonal flow, generally light
and on the west side of the subtropical high. Hence, if environmental steering flow of
these northward moving hurricanes toward the latitude of Hawaii is an important
mechanism, then it preferentially affects the strongest cyclones, and it must involve
transient synoptic-scale systems.
22
3.2.3 Speed
Figure 3.7b shows the stratification by speed, following the categories from Chan
and Gray (1982) for the NA. Table lb describes the definitions of each category (slow,
moderate, and fast movers). In general the majority of the cyclones analyzed on this
project are moderate moving cyclones with speeds between 4 and 8 m st.
23
CHAPTER 4
STEERING ANALYSIS
4.1 All tropical cyclone cases
The first analysis was performed for all tropical cyclone observations prior to
stratification. Figures 4.1 and 4.2 show scatter plots of angle diffrence (3d) vs. speed
difference (Sd) for the eight individual tropospheric levels. The middle and lower
tropospheric levels~ 850~ 700, 600~ and 500 mb are shown in Figure 4.1, and the higher
levels~ 400, 300~ 250~ and 200 mb in Figure 4.2. It is evident that the mean differences in
speed and angle have a correlation with height. The clustering of data in the lower levels
is more pronounced towards the origin (zero difference), while in ·the highest levels a
more dispersed pattern is observed. This is most evident when comparing the 850 mb
with the 200 mb plot. The standard deviation (spread) of the differences is also greater at
the higher levels (see Table 2). At 300~ 250 and 200 mb it is clear that there is a negative
bias on 3d. This first result is in agreement with previous findings for the NWP~NA, and
SP basins~ where middle and lower tropospheric steering has a better correlation with
tropical cyclone motion than the higher tropospheric levels (Chan and Holland 1982~
Chan 1984~ George and Gray 1976).
Figures 4.3 and 4.4 show normal probability plots of 3d and Sd for levels 850 and
250 mb. At the 850 mb and 500 mb (not shown) levels, the data approximately follows a
normal distribution having a good agreement with the linear normal fit (dashed line)
24
between the 25th and the 75th percentiles. In addition, the histogram of·8d at 250 mb in
Figure 4.5 shows that the data at these levels appear less normally distributed. The
spread of the data on the higher levels is also evident on Figure 4.5. Table 2 shows the
mean and standard deviation of Sd and 8d at each level. The values of both the means and
standard deviations are in good agreement to those reported by Chan and Gray (1982),
and Chan (1985).
Since the upper level data might deviate from normality, two different
significance tests were performed: a parametric student t-test, and a non..parametric sign
test (Wilks 1995, Weiss and Hassett 1991) for a null hypothesis of similarity of means
and population distribution at a 5% rejection level. Both tests showed virtually identical
results. Table 3 shows the results of the significance test for 8d. The results verify that the
differences between the middle and lower and the higher levels are significant (see
appendix B.2 for the Sd analysis).
Level Sd (J 8d 0
(ms"l) (ms'l) (deg.) (deg.)
200 -0.2 4.1 8.7 92.7250 ...().9 3.9 13.4 82.8300 -1.5 3.4 11.0 71.1400 ..1.8 2.6 6.4 47.2500 -1.1 2.2 0.7 27.8600 -0.5 1.9 -1.8 22.7700 -0.2 2.2 -5.5 25.3850 -0.4 2.2 -8.0 25.6
.Table 2. Level analySIS for all tropIcal cyclones. Pressure levels areshown from top to bottom. The standard deviation is shown on thesigma (0) columns.
25
200 1 1 1 1 0 0 00.00 0.00 0.00 0.00 0.63 0.71 0.16
250 1 1 1 1 0 0 .0.00 0.00 0.00 0.00 0.06 0.55
300 1 1 1 1 0 .0.00 0.00 0.00 0.01 0.15
400 1 1 1 1 -0.00 0.00 0.02 0.04
500 1 1 0 .0.03 0.00 0.08
600 1 0 -0.00 0.11
700 H=O .p=0.07
850 .850 700 600 500 400 300 250
Table 3. Signifi~ance test (student test) ofangle mean difference 3d for a null hypothesis flo ofsimilar means and population distribution at the 5% rejection level (H=1 ifthe hypothesis isrejected). The p value is the probability ofthe null hypothesis being accepted. Significantdifferences are found between the mid-lower and higher levels.
4.2 Vertical variation analysis
A vertical variation analysis was made for each of the categories, plotting the
average speed and angle differences vs. the individual pressure levels. Figure 4.6 shows
the analysis for both intensity categories. The dashed zero lines represent the tropical
cyclone movement and the solid curves the environmental steering flow deviation from
the cyclone motion (slower/leftward for positive seY3d values, faster/rightward for
negative values). The lower panels indicate the standard deviation for each level.
4.2.1 Tropical storms and depressions
The vertical.analysis for Sd and 3d is shown in Figures 4.6a, and 4.6c. It is found
that for tropical storms and depressions movement was slightly faster, and to the right of
26
the envirolUl1ental steering flow in the lower levels of850 and 700 mb, and to the left at
600 mb and above. The maximum rightward difference is at 850 mb (approx. 8 degrees),
and the leftward at 250 mb (approx. 15 degrees). The Sd profile is in good agreement with
the results reported by Chan and Gray (1982), and George and Gray (1976), with most
cyclones moving faster than the environment in the NWP with a difference ofaround 1 to
1.5 m S·l (except for fast and eastward movers). The ~ profile does not match their
results for WNP tropical storms in the lowest levels, where cyclone movement was to the
left of the environmental steering flow. It is in good agreement with tropical storms in the
NA, both in magnitude and shape. The standard deviation for both ~ and Sd are smaller at
the lower levels and increasing with height (see Table 4). For the corresponding
significance test table see appendix B.3. A z-test was performed to determine if the mean
values for Sd and ~ are significantly different from zero (dashed line) at the 95%
Level Stt 0 ztst P 3d 0 ztst P(ms·i ) (ms·i ) (deg.) (deg.)
200 -0.3 4.3 0 0.09 10.2 99.88 1 0.01250 -1.1 3.9 1 0.00 16.3 89.52 1 0.00300 -1.8 3.5 1 0.00 12.9 76.07 1 0.00400 -2.1 2.9 1 0.00 8.6 51.60 I 0.00500 -1.7 2.6 1 0.00 3.9 29.44 1 0.00600 -0.7 2.4 1 0.00 0.3 20.63 0 0.39700 -0.5 2.5 1 0.00 -3.1 23.19 1 0.00850 -0.5 2.3 1 0.00 -5.4 21.83 1 0.00
Table 4. Level analysis for tropical storms and depressions. The ztst and p columnsshow the results for a z-test with a null hypothesis ofa mean value of0 at a 5% rejectionlevel. The hypothesis is rejected (ztst=1) ifthe mean 54 or 8d ofa level show significantdifferences from O.
27
confidence level. The p-values of the z-test demonstrate that most of the Sd and ~ values
are significantly different from zero.
4.2.2 IItUTi~es
The vertical analysis for htUTicanes is shown in Figure 4.6b and 4.6d. Similar to
the tropical storms, Sd shows a faster movement or coincidental with the individual
environmental level winds. The ~ results indicate hurricanes moving to the right of the
middle and lower levels, and to the left at 400 mb and above (see Table 5). This profile
does not match the reports by George and Gray (1976) or any of the ca~gories from
Chan and Gray (1982) for the NWP. However, it is in good agreement with several of
their results for categories in the NA, sPeCifically profiles from Chan and Gray (1982)
for tropical cyclones moving in region 1 of the NA (equatorward of 18~ in the
Caribbean and west Atlantic), slow movers, hurricanes, and tropical storms as well. The
Level Sd 0 ztst P 3d 0 ztst P(ms·1) (ms1
) (deg.) (deg.)
200 0.0 3.9 0 0.89 6.6 80.9 1 0.04250 -0.6 3.7 1 0.00 9.3 71.5 1 0.01300 -1.1 3.2 1 0.00 8.2 62.6 1 0.01400 -1.4 2.1 1 0.00 3.1 39.6 0 0.11500 -0.9 1.6 1 0.00 -3.9 24.0 1 0.00600 -0.3 1.5 1 0.00 -5.4 25.0 1 0.00700 0.2 1.7 1 0.00 -9.1 27.7 1 0.00850 -0.4 1.9 1 0.00 -11.8 29.9 1 0.00
Table 5. Level analysis for hurricanes. Same format as Table 4
28
rightward bias in the lower levels on these NA categories is shallower, becoming leftward
around 600 mb.
The analysis on Figure 4.6d does not match the Chan and Gray (1982) results for
the NWP, where a consistent general tropical cyclone motion to the left of the steering
flow was observed, regardless of categories. The mean Sd profile (4.6b) is in good
agreement with most of Chan and Gray (1982) profiles in the NA for hurricanes and
. tropical storms, where cyclones are moving faster than the steering flow at all levels. For
the NWP, most cyclones move slightly faster than or coincidental with the steering flow.
See appendix B.4 for the corresponding significance test table. As before, the z-test
indicates that most mean values of Sd and 3d are significantly different from zero.
4.2.3 Direction and speed stratifications
Figure 4.7 shows that the 3d profiles for the direction and speed categories are in
general similar to the intensity categories: cyclone motion to the right of the
environmental steering flow at the lower levels, close to zero at 500 mb, and to the left
above 500 mb. The category for cyclone direction other than westward or northward is
not included in this analysis since the number ofobservations is too small (see Table 1).
Westward moving cyclones have mean angle differences of less than ten degrees,
while northward movers show mean differences of nearly fifty degrees at the higher
levels. For the speed categories, slow moving cyclones have the bigger values of8d (up to
20 degrees) while fast movers show the lowest values (4 degrees or coincidental from
29
850 up to 400 mb). The profile for the moderate movers profile is very similar to the
westward movers.
The Sd profiles are shown in Figure 4.8. For westward movers, a speed
coincidental or slightly faster than the steering at all levels (similar to moderate movers)
is observed. Fast movers show a cyclone motion faster than the environment of up to 5 m
S·l at the higher levels, while slow movers have a speed slower than the steering flow at
all levels. Northward movers show motion coincidental or slightly faster than the
environment, becoming slower at the higher levels. In general, these results are in good
agreement with Chan and Gray (1982), and Chan (1984). where most of their NWP
categories indicate cyclones moving faster than the environment at the middle and lower
levels. Their intensity, speed, direction, and region categories all show cyclone
movement faster or coincidental with the steering flow. Tables of level analysis and
significance test (between levels and z-test) for each of the categories discussed in this
section are shown in appendix B.S. As before, greater values of standard deviation are
observed in the upper troposphere than lower troposphere (e.g., for westward movers is
up to five times greater). The z·test also indicates that the above statements about angle
and speed differences from zero are statistically significant in most cases.
4.3 Environmental steering layer analysis
The previous sections presented the results of the vertical analysis technique on
tropospheric pressure levels to generally describe the average correlation between
30
tropical cyclone motion and the environmental steering flow. The main reason why I
followed this technique was to produce a set of results comparable with previous work in
the other hurricane basins.
The approach taken for the analysis on the environmental steering layers (ESLs)
defined in section 2.3.1 is somewhat different. A careful look into the results of Table 5,
for example, indicates that the values of 3d and Sd could be very close to zero in the
middle and lower levels, and still relatively small at 400 mb and higher. However, the
standard deviation values (0) may indicate that two mean differences which are similar
and close to zero at two pressure levels can have significant variability. An alternative to
this problem is to calculate the absolute value of the difference for each level and layer
instead. By doing this, not only means are compared but also deviations. Therefore,
candidate ESLs for tropical stonns and depressions, and hurricanes could be identified as
having the smallest mean values for the magnitudes (absolute values) of3d, Sd, and also a.
The mean absolute differences are identified as A8d for absolute angle difference
and ASd for absolute speed difference (see appendix A for formulas).
4.3.1 Angle difference analysis for tropical storms and depressions
Table 6 contains the results of the ESL analysis for tropical stonns and
depressions (column I shows the depth ofeach layer, and columns 2 through 5 the values
for As~ Aae and their respective a values). The scatter plot for Aae vs. a is shown in
Figure 4.9. The layers above the dotted line correspond to the upper troposphere layer
group from Figure 2.3, with the largest values for absolute mean differences and a. The
31
LAYER ASd 0 Altd 0 Sd 0 ltd 0IDS-I ms'l deg. deg. ms'l IDS'I (leg. deg.
200-200 3.2 2.7 86.8 50.2 -0.2 4.2 10.1 99.8250-200 3.1 2.6 82.6 50.0 -0.7 4.0 12.5 95.8250-250 3.1 2.5 76.8 48.6 -1.0 3.9 16.2 89.5300-200 3.1 2.5 77.0 49.1 -1.2 3.8 14.6 90.2300-250 3.1 2.4 69.0 47.3 -1.5 3.7 11.7 82.9300-300 3.1 2.4 61.3 46.7 -1.7 3.5 12.9 76.0400-200 3.0 2.4 62.9 46.7 -1.8 3.4 9.5 77.9400-250 3.0 2.3 55.0 45.2 -2.0 3.3 11.8 70.3400-300 3.0 2.3 48.0 43.0 -2.1 3.1 10.7 63.6400400 2.8 2.2 36.6 37.2 -2.1 2.9 8.5 51.6500-200 3.0 2.3 49.8 43.5 -2.1 3.1 10.8 65.3500-250 2.9 2.2 41.6 39.5 -2.1 2.9 11.1 56.4500-300 2.8 2.1 34.7 35.4 -2.1 2.8 8.7 48.8500400 2.5 2.0 24.0 26.6 -1.8 2.6 7.0 35.1500-500 2.2 1.8 19.7 22.2 -1.2 2.5 3.8 29.4600-200 2.8 2.2 37.2 36.7 -2.1 2.8 10.0 51.3600-250 2.7 2.1 29.9 31.1 -2.0 2.7 8.8 42.2600-300 2.5 2.0 24.2 26.8 -1.9 2.6 6.2 35.7600-400 2.2 1.8 17.9 20.3 -1.4 2.5 3.6 26.8600-500 2.0 1.7 14.8 17.3 -1.0 2.4 1.8 22.8600..600 1.8 1.6 13.3 15.7 -0.6 2.4 0.7 20.6700-200 2.6 2.0 28.1 29.3 -2.0 2.6 7.4 39.9700-250 2.5 1.9 22.2 25.1 -1.9 2.5 5.6 33.0700-300 2.3 1.8 18.0 20.9 -1.7 2.5 4.2 27.3700400 2.0 1.7 14.0 15.1 -1.2 2.3 1.6 20.6700-500 1.8 1.6 12.8 14.4 -0.8 2.3 0.5 19.2700-600 1.8 1.6 13.6 14.5 -0.6 2.3 -0.8 19.9700-700 1.8 1.7 16.0 17.0 -0.4 2.4 -3.0 23.1850-200 2.4 1.9 19.5 21.7 -1.9 2.4 4.1 28.9850-250 2.2 1.8 15.7 18.3 -1.7 2.3 2.4 24.0850-300 2.1 1.7 13.2 14.7 -1.4 2.3 0.8 19.8850400 1.8 1.6 11.8 13.3 -1.0 2.2 -0.4 17.8850-500 1.7 1.6 12.3 13.5 -0.7 2.2 -1.4 18.2850-600 1.7 1.6 13.4 14.0 -0.5 2.2 -2.5 19.2850-700 1.7 1.5 14.0 14.6 -0.5 2.2 4.0 19.8850-850 1.7 1.6 15.7 16.1 -0.4 2.2 -5.4 21.8
1 2 3 4 5 6 7 8 9
Table 6. ESL analysis for tropical storms and depressions. Column 1shows the "bottom-top" pair for each layer. The averaged absolute valuesfor speed and angle differences are shown in columns 2 and 4, withcorresponding standard deviations in columns 3 and 5. The mean Sd and ltdare in columns 6 and 8, with standard deviations in columns 7 and 9.
32
cluster of ESLs with lowest absolute mean differences is dominated by deep
intennmediate (yellow) and low..level shallow (green) layers. The leading ESLs are the
deep-intermediate 850400 mb, and 850-500 mb, closely followed by a group of shallow
layers. The 850-400 mb ESL is one of the deep layer means previously mentioned by
several authors.
To determine if the leading candidates are significantly different from the
remaining 34 layers a significance test was performed. Both a one-sided student test and
a non-parametric sign test were utilized with the same results for a null hypothesis of
similarity of means and population distribution (see appendix B.6 for corresponding
tables). Figure 4.11 shows the A8d significance test results for the two leading ESL
candidates of tropical storms and depressions. The 850400 mb and 850-500 mb layers
have significant differences from thirty of the remaining layers. Four shallow low level
layers and the 850-300 mb deep layer show no significant differences at the 95%
confidence level. The separation between low and high levels is again observed.
4.3.2. Angle difference analysis for hurricanes
Figure 4.10 show the ESL analysis scatter plot for hurricanes (see also Table 7).
The scaling has been preserved in order to facilitate comparison with the tropical storms
analysis. From Figure 4.10 it is clear that for the more intense cyclones the cluster of
layers with the lowest absolute mean differences is now dominated by deepest and deep
intermediate layers. The leading ESLs are 850-300, and 850..250 mb. The absolute angle
33
Layer ASd 0 A8d 0 Sd 0 8d 0ms·\ ms.t deg. deg. ms·\ ms·\ deg. deg.
200-200 3.0 2.3 64.9 48.5 -0.0 3.8 6.6 80.9250-200 3.0 2.2 60.9 46.2 -OJ 3.7 9.3 75.9250-250 3.0 2.1 56.4 44.7 -0.5 3.7 9.2 71.5300-200 2.9 2.1 56.1 44.3 -0.7 3.6 10.4 70.8300-250 2.8 2.1 51.2 42.3 -0.9 3.4 7.9 65.9300-300 2.6 2.0 47.6 41.4 -1.1 3.1 8.2 62.6400-200 2.6 1.9 44.8 38.8 -1.1 3.0 7.2 58.9400-250 2.4 1.8 40.9 36.8 -1.3 2.8 7.4 54.5400-300 2.3 1.7 36.9 33.9 -1.4 2.5 6.7 49.7400-400 2.0 1.5 28.4 27.6 -1.4 2.1 3.1 39.6500-200 2.2 1.7 35.2 33.0 -1.3 2.5 6.7 47.8500-250 2.1 1.6 31.8 30.3 -1.4 2.2 5.5 43.7500-300 1.9 1.5 27.7 27.4 ..1.4 2.0 4.7 38.7500-400 1.7 1.2 20.7 20.8 -1.2 1.7 .0.7 29.4500-500 1.5 1.0 17.3 17.7 .o.S 1.6 -3.9 24.5600-200 1.9 1.5 27.5 27.1 -1.4 2.0 4.9 38.4600-250 1.8 1.4 23.8 24.2 -1.3 1.8 3.8 33.8600-300 1.7 1.2 20.5 20.9 -1.3 1.7 0.6 29.36()()..400 1.4 1.0 16.0 16.6 -1.0 1.5 -3.6 22.8600-500 1.2 0.9 15.2 18.3 -0.6 1.4 -5.5 23.1600-600 1.2 0.9 16.1 19.8 -0.2 1.4 -5.4 25.0700-200 1.7 1.3 21.0 21.6 -1.3 1.7 2.0 30.1700-250 1.6 1.1 18.2 18.8 -1.2 1.6 0.0 26.2700-300 1.5 1.0 15.7 16.5 -1.1 1.5 -2.5 22.770Q.400 1.2 0.9 14.5 16.8 .0.7 1.3 -6.0 21.4700-500 1.1 0.8 15.6 19.1 .0.3 1.4 -5.5 24.0700-600 1.2 0.9 17.1 19.6 .0.0 1.5 -7.1 25.0700-700 1.3 1.0 19.5 21.6 0.2 1.7 -9.0 27.7850-200 1.5 1.1 15.6 17.2 -1.2 1.5 -1.6 23.2850-250 1.4 1.0 13.8 14.7 -1.0 1.4 -3.1 20.0850-300 1.2 0.9 13.5 14.7 .0.9 1.3 -5.1 19.3850-400 1.1 0.8 15.1 18.7 .o.S 1.3 -6.0 23.3850-500 1.1 0.9 16.7 19.4 -0.2 1.4 -7.4 24.5850..600 1.2 1.0 18.5 21.0 -0.1 1.6 -9.0 26.5850-700 1.3 1.1 19.6 22.4 .oJ 1.7 -10.2 28.0850-850 1.6 1.3 21.7 23.6 .0.4 2.0 -11.8 29.9
1 2 3 4 ? 6 7 8 9
Table 7. ESL analysis for hurricanes. Column format is the same asin Table 6.
34
difference magnitudes are similar as for tropical storms and depression. Figures 4.12
shows the significance test results for A8d on the candidate layers of 850-300 and 850
250 mb (see appendix B.7 for tables). Again the null hypothesis for most of the
remaining ESLs is rejected. No significant differences are now observed between the
deepest (red), two deep intermediate (yellow), and only one shallow layer. These results
suggest that CNP hurricanes may be interacting with deeper layers compared to the
tropical storms and depressions. This supports previous reports by Dong and Newman
(1986) ofa positive correlation between tropical cyclone intensity and ESL depth.
4.3.3. Speed differences layer analysis
Figure 4.13 shows the scattergram for ASd vs. a for tropical storms and
hurricanes (see also Tables 6 and 7). For both categories there is a group of shallow and
deep intermediate layers with lowest difference values. The leading candidates are 850
700 mb for tropical storms, and 850400 for hurricanes. Tables 6 and 7 also indicate that
several layers (shallow and deep) have similar values for ASd and standard deviation.
Figure 4.14 is the corresponding significance test (see appendix B.6 and B.7 for tables). It
is clear that there is a greater range of layers with no significant differences from the
candidate ESLs. Unlike the absolute angle difference analysis, the values for absolute
speed differences among layers, along with the significance test results, makes it more
difficult to identify a specific candidate layer for speed.
35
4.4 Central north Pacific domain analysis
In the previous section candidate ESLs for absolute angle differences were
identified for the intensity categories. Since it has been discussed in previous work that
tropical cyclone motion might be dependent on the geographical area in which they
occur, it is worth investigating the possibility of steering layer dependence on a specific
area in the CNP. The working domain from Figure 2.1 is divided in 4 geographic
quadrants as shown in Figure 4.14, with the quadrants identified with capital roman
numerals in a clockwise direction starting with the northeast quadrant. The analysis was
performed on the quadrants where either a tropical storm formed (genesis), or moved into
the CNP and its track posed a threat to the islands ofHawaii on the previously mentioned
candidate layers of 850-400 mb, 850-300 mb, and 850-250 mb.
Most cyclones were born in quadrants II and III or moved from the eastern north
Pacific into quadrant II. Tropical cyclones moving on quadrant III pose the threat of
recurving northward toward Hawaii. Cyclones moving in quadrant I can also (although
more infrequently) approach Hawaii on a westward track. For quadrant IV none of these
criteria were observed as all the cyclones were moving away from Hawaii, and no
cyclogenesis took place. Therefore quadrant IV was not included in this analysis. From
Figure 4.l5a, cyclones moving in quadrant II show the lowest values for A8d, followed
by quadrant III. It is seen that quadrant I show the bigger values of A8d. The
corresponding significance test results between quadrants for each layer is presented in
Table 8. Significant differences are found between quadrant I and the other quadrants for
36
all three candidate layers. Quadrants II and III do not show significant differences among
their Alld values. The low Alld values in quadrant II coincide with tropical cyclones that
are in general westward movers (see Figure 4.7) below20~.
It has been established from section 4.1 that the influence of the easterly wind
flow penetrates well into the lower latitudes south of Hawaii, which are precisely the
areas ofquadrants II and III. From the seasonal analysis of section 3.1 we can see that the
area in quadrants II and III are under the influence ofthe edge of the high pressure ridge
throughout the months of the CNP hurricane season, especially quadrant II. The observed
tropical cyclone motion in this quadrant is overwhelmingly to the west-northwest (Figure
3.4). These results tend to support the fmdings of Chan (1984), and Chan and Gray
(1982) that west-norhtwestward moving tropical cyclones have a better correlation with
ESL
Quadrant 8S0-4oomb SSO-3OOmb 8SQ..2S0mbco
.n
110= 1 1 1quad I - quad II p=O.OI 1.8 e-03 3.1 e-06
1 1 1quad I - quad III 0.02 3e...()4 0.03
0 0 0quad II - quad III 0.18 0.09 0.23
.Table 8. Slgmficance test for absolute angle mean error quadrant mter-companson, allcyclone cases included. Quadrant I show significant differences from II and III. The samefor absolute speed (appendix B) show no significant difference among any ofthequadrants.
37
the ESL than cyclones moving in other directions. Figure 4.15b shows the same analysis
for AScI. Except for one layer mean value, no significant differences are found among any
ofthe values of AScI from all quadrants (see appendix B.8 for table).
In general it was found that southeast and southwest of Hawaii the three selected
ESLs for absolute angle differences show the best correlation with tropical cyclone
motion, while the worst correlation is observed northeast of the islands.
4.5 Wind shear and Steering
The possibility of relating wind shear with steering is explored utilizing the ESLs
identified in previous sections. The vertical wind shear (wsh) is calculated following
formula 3.18. The values of A~ and AScI are then classified according to each wsh
category. Then the average ESL difference corresponding to the wsh category is
computed. Figure 4.16 shows the results of wsh vs. A3d for tropical storms and
depressions (the candidate deep ESLs 850-400 mb,the previous shallower 85()..500 mb,
and the following deeper 850-300 mb are shown for comparison). It is evident from
Figure 4.16 that none of the three ESLs show a good correlation (positive or negative) of
A3d with increasing wsh. Also, there are no significant differences on any ofthe values of
A~, except between the 0-5 and 5-10 m S·l categories. Hurricanes, as shown in Figure
4.17, do not show a good correlation either. The only significant differences are between
the 0-5 and 1()"15 m S·l wsh categories, and the strong variability for the wsh categories
show that from this data set it is difficult to establish a correlation. The same analysis for
38
A8(t is shown in Figures 4.18 and 4.19. Significance tests (see appendix B.8) indicated no
significant differences were found between any ofthe values for the wsh categories.
In general, these analyses show that from the tropical cyclone data set analyzed in
this project, no substantive correlation has been established between steering and vertical
wind shear. This supports previous claims of a lack of correlation between these two
variables.
39
CHAPTERS
SUMMARY
5.1 Conclusions and discussion
The relationship between tropical cyclone motion and its surrounding
environmental steering flow was studied for the region of the central north Pacific and
Hawaii utilizing model data from the NCEPINCAR Reanalysis project as an alternative
to the lack ofrawinsonde and aircraft data. The tropical cyclone data set available for this
project is small compared with the other more active north Atlantic and north west
Pacific regions. It was found that most analyzed tropical cyclones move in a west~
northwest track, and south of20'N. This tropical cyclone activity, concentrated southeast
and southwest of Hawaii, coincides with a prevailing easterly wind flow at the middle
and lower tropospheric levels with an average speed between 5 and 10m S-I. The
influence of these easterlies is observed at all the levels of the middle and lower
troposphere (from 850 to 500 mb) during the hurricane season. Most tropical cyclones
were observed to move with a forward speed between 4 and 8 m S-I.
It was found that middle and lower tropospheric steering shows a berter
correlation with tropical cyclone motion than the higher levels. This is in agreement with
most previous work in other basins. No direct evidence was found to support the reports
of George and Gray (1976) regarding the 700 mb level as best descriptor of tropical
40
cyclone speed, although low levels (850, 700 and 600 mb) have lower speed differences
than levels above 600 mb.
Vertical variation analysis for tropical storms and depressions indicate a mean
tropical cyclone motion to the right of the environmental steering flow, up to five
degrees, and very close or slightly faster (less than 1 m S·1) than the middle and lower
tropospheric winds at 850, 700, and 600 mb. Above these levels, tropical storms and
depressions move to the left (up to 10 degrees), and also faster. Hurricanes show similar
profiles, with angle differences of up to 12 degrees at 850 mb, and moving to the right
above 500 mb. The speed profile looks virtually identical to that of tropical storms and
depressions.
The observation ofcyclones moving to the right of the steering flow at the middle
and lower troposphere is in good agreement with results reported by Brand (1981), and
Chan (l984) of a general rightward bias in tropical cyclone motion south of20~. This
supports the findings of beta effect impact on cyclones embedded in easterly flow, which
causes motion to be faster and to the right of the environmental steering flow. Also, the
fact that hurricanes show a slightly bigger deviation to the right of the steering flow
suggests that the beta effect might be more significant in the stronger cyclones (DeMaria,
1985).
Westward~ moderate and fast moving cyclones show a better correlation with the
environmental steering flow than northward and slow moving cyclones. This is also in
good agreement with most previous findings in other regions of the world (Chan 1984~
Chan and Gray 1982).
41
The vertical variation analyses for tropical cyclone motion vs. environmental
steering flow presented here have more similarities with previous work on NA cyclones,
and differ from most ofthe results for NWP tropical cyclones in general.
From the DLM analysis, an important finding in this work is the observatiort of a
positive correlation between tropical cyclone intensity and the depth ofthe ESL. The
analysis for angle differences shows that hurricanes have a better correlation with deeper
layers than tropical storms and depressions. This supports the reports of Dong and
Newmann (1986) ofa positive correlation between intensity and DLM depth.
It is concluded that the layer from 850-400 mb is the recommended steering layer
for tropical stonns and depressions, with stonn motion having an absolute mean angle
difference of 11.8°, and a speed mean difference of 1.8 m 8.1• For hurricanes the steering
layers of 850-300, and 850-250 mb are recommended with an absolute angle difference
of 13.5°, and a speed mean difference of 1.2 m S·I. These values provide an estimate of
typical error associated with the steering layer concept (Chan 1985). The above DLMs
have been mentioned in previous work by Holland (1983), Wu and Kurihara (1986), Carr
and Elsberry (1990), and others as the best predictors for tropical cyclone motion. The
angle differences parameter A8d was chosen as the criteria for ESL selection due to the
lack ofsignificant differences between layers in the speed analysis.
As mentioned in most previous work, the DLM approach proved to be very useful
for steering analyses. As an example, in the hurricane analysis, the DLM of 850-400 mb
has an absolute angle difference of 120., and an absolutes~ difference of 1.8 m S·I. The
500mb steering level on the other hand, identified in the literature as a good descriptor of
42
tropical cyclone motion, has an absolute angle difference of 19°, and an absolute speed
difference of 2.2 m S·l. Therefore, it is useful to consider not only the mean values of the
differences, but the error (standard deviation) as well.
Is vertical wind shear related to steering? Contrary to my expectations, the results
for the shear vs. DLM differences analyses do not show a correlation. The fact that the
amount of data is small compared to other basins might present a problem when
stratifying for the wind shear categories.
This project has shown that by utilizing NNR model wind data for steering
analyses it is possible to obtain results that are in good agreement with most previous
work based on rawinsonde and aircraft data, which were available for other regions.
5.2 Future work
Additional work may include analyses of tropical cyclone stage for intensifying
VS. weakening. Since it was observed that the vertical variation profiles in the CNP have
more similarities with the NA than with other regions, the same studies developed in this
project can be performed in the NA hurricane basin for comparison.
The analyses and results in this thesis summarize the effort of applying model
wind data for finding a suitable tropical cyclone steering tool for the CNP. Since much of
the cyclonic activity is related to tropical cyclones that move into the area from the north
eastern Pacific, it will also be very useful to understand under what conditions tropical
cyclones have a better chance of being advected into the CNP by the steering flow arid
43
eventually become a threat to the Hawaiian Islands. Backward and forward trajectories
from and toward Hawaii can then be calculated from the NCEPINCAR Reanalysis
project and numerical weather prediction forecasting models, which might provide an
additional tool to improve seasonal and short tenn outlooks for tropical cyclone activity
in the central north Pacific.
44
APPENDIX A
The tropical cyclone displacement was determined with a time interval
At=6*3600 seconds. The direction is calculated by plotting the u and v components
against the polar plane from Figure 3.4, and determining the quadrant on which u and v
are operating:
OTC = arctan( vTC) •
UTC
By adding (subtracting) the proper angle, depending on the quadrant, the storm direction
is calculated; as shown in Figure 3.4. For example ifu and v are operating on quadrant 1,
the TC direction is given by
dir rc =90 -Ore
The environmental steering flow direction and speed were calculated by:
x,+Xz+ ••• +X. 1
U'I=-------n
Same formulas for VESL.
XI + Xz +,., + X. ()/ 2U,z =: , UESL = U,l+ UI2 •n
The ESL direction is calculated following the same procedure for tropical cyclone
direction:
45
(VeSL )(JESL == arctan - ,UESL
e.g. quadrant 1: dirESt. == 90 • (JE3L •
To calculate mean absolute differences:
N
1:l aelnA.a = ..:.n=..."l:....-__
e N
N
1: I Se InAs == .;.;.n=-'l'--__
e N ,
where N is the total amoWlt ofdata points evaluated on each layer.
46
APPENDIX B
B.ISltfi
Summary ofrelevant preVIOUS work on tropIcal cyclone motion and envlfomnental steering flowfor the west north and south Pacific, and the north Atlantic hurricane basins.
e erence umtnary
George & Gray, 1976 TC motion to the left and faster (around 1.16 mls) than ESF for most cases.500 mb level: best directional correlation with TC motion.700 mb level: best speed correlation with TC motion.
Brand et aI, 1981 TC moving at or higher than latitude 20~: generally to the leftand faster than ESF.TC moving lower than latitude 20~: generally less to the left or theright, and faster than ESF.
Chan & Holland, 1982 DLM of900-200 mb for TC steering when only satellite derived data isavailable. Use of individual atmospheric levels to determine general trends ofcyclone motion vs. environmental flow.
Upper tropospheric winds show the worst correlation with TC motion.
NWP~ TC motion to the left ofESL north of20~, less leftwarddeviation or close to zero south of20~. Storms generally move faster than theESF.
NA: TC motion slightly to the right ofthe ESL at the lowest levels(900-700) and to the left for the mid-higher levels. Leftwarddeviation is smaller south of 18o:N. Westward moving TC show arelative smaller leftward deviation than northward movers.Storms generally mow slightly faster or coincidental with the ESF. Westwardmoving TC show a better correlation with the ESF than Northward movingcyclones.
Chan, 1984 Westward moving TC tend to move to the right and slightly faster than theESF.
Holland, 1984 DLM of8()()'300 mb for TC steering.
Dong & Neumann 1986 Westward moving hurricanes tend to move the right ofeasterly mid-tropospheric winds.
Northward moving hurricanes tend to move the left ofwesterly mid-tropospheric winds.
Depth ofDLM dependent on Intensity. Hurricanes interact with deeper layermeans than Tropical Storms.
Carr & Elsberry, 1990 Discard the use of individual atmospheric levels. TC Motion predictorsdescribed in terms ofDLM only.
Wu & Kurihara, 1996 DLM of 850-300 mb. as best descriptor ofTC motion. . . . .
47
B.2
Significance t-test ofSd for the eIght indlVldual pressure levels. with a null hypothesIS ofsmularitiesofmean and population distrIbution.
200 0 0 1 1 1 0 10.08 0.08 0.02 0.00 0.00 0.14 0.04
250 1 1 1 0 1 1 .0.03 0.00 0.01 0.10 0.00 0.00
300 1 1 1 1 0 -0.00 0.00 0.00 0.01 0.05
400 1 1 1 1 .0.00 0.00 0.02 0.04
500 1 1 1 -0.03 0.00 0.00
600 0 0 .0.08 0.71
700 H=O -p=0.39
850 .850 700 600 500 400 300 250. .. . .
B.3
200 0 0 0 1 1 1 10.35 0.45 0.05 0.00 0.00 0.00 0.00
250 1 I 1 0 1 1 -0.00 0.00 0.04 0.35 0.00 0.00
300 1 1 1 1 0 -0.00 0.00 0.00 0.01 0.09
400 1 1 1 1 -0.00 0.00 0.00 0.00
500 1 1 1 -0.00 0.00 0.00
600 0 0 -0.12 0.09
700 H=O -0=0.81
850 -
850 700 600 500 400 300 250Slgmficance test of Sd for tropical stonns and depreSSIOns.
48
200 1 1 1 0 0 0 00.00 0.00 0.02 0.014 0.72 0.60 0.27
250 1 1 1 1 0 0 ·0.00 0.00 0.00 0.03 0.07 0.49
300 1 1 1 1 0 -0.00 0.00 0.00 0.00 0.25
400 1 1 1 0 ·0.00 0.00 0.02 0.06
500 1 1 1 .0.00 0.00 0.03
600 1 1 ·0.00 0.00
700 H-O .I> =-0.07
850 -850 700 600 500 400 300 250
SIgnIficance test of3d for tropical storms and depressIOns.
B.4
SIgnIficance test of Sd for humcanes.
200 0 0 0 1 1 1 10.10 0.15 0.22 0.00 0.00 0.00 0.04
250 0 1 0 0 1 1 ·0.35 0.00 0.12 0.13 0.00 0.02
300 1 1 1 0 0 -0.00 0.00 0.00 0.17 0.17
400 1 1 1 1 ·0.00 0.00 0.00 0.00
sao 1 1 1 -0.00 0.00 0.00
600 0 I ·0.39 0.01
700 H-l -I> =- 0.00
850 .
850 700 600 sao 400 300 250. .
200 1 1 1 I 0 0 00.00 0.00 0.01 0.01 0.44 0.75 0.62
250 1 I 1 1 0 0 ·0.00 0.00 0.00 0.03 0.13 0.83
300 1 1 I I 0 .0.00 0.00 0.00 0.00 0.17
400 I I 1 I ·0.00 0.00 0.02 0.00
500 I I 0 .0.00 0.01 0.40
600 1 1 ·0.00 0.04
700 H-O .1>=-0.18
850 .
850 700 600 500 400 300 250SIgnIficance test of3d for huncanes.
49
B.5
WESTWARD:
speed differences Angle differences
Sd (J ztst P 8d (J ztst P
200 -0.8 3.6 1 0.00 4.9 95.6 1 0.04250 -1.5 3.4 1 0.00 10.5 85.2 1 0.00300 -2.0 3.0 1 0.00 8.0 72.5 1 0.00400 -2.1 2.5 1 0.00 3.2 45.5 1 0.04500 -1.2 2.2 1 0.00 0.7 24.6 0 0.42600 -0.6 2.1 1 O~OO -0.8 16.8 0 0.16700 -0.2 2.3 1 0.01 -3.3 19.0 1 0.00850 -0.5 2.1 1 0.00 4.9 17.3 1 0.00
200 1 1 1 1 1 1 10.02 0.00 0.00 0.01 0.00 0.00 0.01
250 1 1 1 1 1 1 -0.00 0.00 0.00 0.03 0.02 0.01
300 1 1 1 1 0 -0.00 0.00 0.00 0.00 0.71
400 1 1 1 1 -0.00 0.00 0.02 0.00
500 1 1 1 -0.00 0.00 0.00
600 0 1 .0.37 0.00
700 H=1 -D=O.OO
850 -850 700 600 500 400 300 250
SignIficance test of Sd for westward movmg cyclones.
200 1 1 1 0 0 0 00.00 0.01 0.03 0.12 0.63 0.45 0.20
250 1 1 1 1 1 0 -0.00 0.00 0.00 0.00 0.03 0.50
300 1 1 1 1 0 .0.00 0.00 0.00 0.00 0.10
400 1 1 1 0 -0.00 0.00 0.01 0.14
500 1 1 0 -0.00 0.00 0.14
600 1 1 .0.00 0.00
700 H=O -p=0.07
850 .850 700 600 500 400 300 250
SIgnificance test of8d for westward moving cyclones.
50
NORTHWARD:
Speed differences Angle differences-----_.._-_. ._...._---Sd (J ztst P 8cJ (J ztst P
200 3.8 4.1 1 0.00 42.3 58.4 1 0.00250 2.9 3.7 1 0.00 40.3 55.4 1 0.00300 1.4 3.2 1 0.00 37.0 52.3 1 0.00400 -0.5 2.5 1 0.03 30.9 50.9 1 0.00500 -0.8 1.3 1 0.00 ~1.3 38.5 0 0.73600 -0.2 1.9 0 0.23 -13.1 40.2 1 0.00700 0.1 2.1 0 0.46 -26.6 42.8 I 0.008S0 0.0 2.1 0 0.93 -33.6 45.3 1 O~OO
Slgmficance test of Sci for northward movers.
200 1 1 1 1 1 1 00.00 0.00 0.00 0.00 0.00 0.00 0.09
250 1 1 1 1 1 1 .0.00 0.00 0.00 0.00 0.00 0.01
300 1 1 1 1 1 .0.00 0.00 0.00 0.00 0.00
400 0 1 0 0 .0.09 0.04 0.34 0.37
500 1 1 1 .0.01 0.00 0.03
600 0 0 -0.37 0.17
700 H=O .0=0.65
850 .
850 700 600 500 400 300 250.
200 1 1 1 1 0 0 00.00 0.00 0.00 0.00 0.12 0.47 0.79
250 1 1 1 1 0 0 -0.00 0.00 0.00 0.00 0.19 0.65
300 1 1 1 1 0 .0.00 0.00 0.00 0.00 0.38
400 1 1 1 1 -0.00 0.00 0.00 0.00
500 1 1 1 .0.00 0.00 0.03
600 1 1 .0.01 0.02
700 H=O .0=0.24
850 .850 700 600 500 400 300 250
Significance test of 8cJ for northward movers.
51
SLOW:
Speed differences Angle differences._-_.-_...._-- ---_._---_....
8d (J ztst P 8tt (J ztst P
200 3.2 3.4 1 0.00 23.6 92.3 1 0.00250 2.3 3.2 1 0.00 11.3 91.9 0 0.12300 1.4 2.7 1 0.00 4.4 86.0 0 0.52400 0.3 2.1 0 0.12 9.2 69.0 1 0.04500 0.6 2.0 1 0.00 -4.4 50.2 0 0.26600 0.9 1.9 1 0.00 -5.1 44.5 0 0.15700 1.3 1.9 1 0.00 -13.6 45.9 1 0.00850 1.6 1.6 1 0.00 -18.8 45.3 1 0.00
200 1 1 1 1 1 1 10.00 0.00 0.00 0.00 0.00 0.00 0.02
250 1 1 1 1 1 1 -0.01 0.00 0.00 0.00 0.00 0.01
300 0 0 0 1 1 -0.33 0.65 0.09 0.01 0.00
400 1 1 1 1 -0.00 0.00 0.00 0.16
500 1 1 0 .0.00 0.00 0.12
600 1 0 .0.01 0.11
700 H-O -Il =0.06
850 -850 700 600 500 400 300 250
Stgntficance test of Sd for slow movers.
200 1 1 1 1 0 0 00.00 0.00 0.00 0.00 0.11 0.06 0.23
250 1 1 1 1 0 0 .0.00 0.00 0.04 0.03 0.81 0.59
300 1 1 0 0 0 -0.00 0.02 0.21 0.26 0.58
400 1 1 1 1 .0.00 0.00 0.03 0.04
500 I 0 0 -0.01 0.08 0.90
600 1 1 -0.01 0.09
700 H=O -.,=0.30
850 -850 700 600 500 400 300 250
Significance test of8tt for slow movers.
52
MODERATE:
Speed differences Angle differences
-------- -_._.~....-..__.._..Sd (J ztst P a.s (J ztst P
200 -0.1 3.3 0 0.47 8.5 95.2 1 0.03250 -0.8 3.0 1 0.00 16.3 84.2 1 0.00300 -1.5 2.6 1 0.00 13.6 72.0 1 0.00400 -1.8 2.0 1 0.00 7.5 44.6 1 0.00500 -1.0 1.8 1 0.00 2.2 22.1 1 0.01600 -0.4 1.6 1 0.00 -1.4 15.8 1 0.03700 0.1 1.8 0 0.50 4.4 19.6 1 0.00850 -0.3 1.6 1 0.00 -6.7 20.3 I 0.00
SIgnIficance test of Sd for moderate movers.
200 0 0 0 1 1 1 10.10 0.33 0.08 0.00 0.00 0.00 0.00
250 1 1 1 0 1 1 .0.01 0.00 0.00 0.11 0.00 0.00
300 0 1 1 1 1 .0.33 0.00 0.00 0.00 0.01
400 1 1 1 1 .0.00 0.00 0.00 0.00
500 1 1 1 .0.00 0.00 0.00
600 0 1 .0.89 0.00
700 H"'1 -0=0.00
850 .8S0 700 600 500 400 300 250.
200 1 1 1 0 0 0 00.00 0.00 0.00 0.11 0.82 0.29 0.13
250 1 1 1 1 1 0 -0.00 0.00 0.00 0.00 0.02 0.55
300 1 1 1 1 0 .0.00 0.00 0.00 0.01 0.08
400 1 1 1 1 -0.00 0.00 0.00 0.01
500 1 1 1 .0.00 0.00 0.00
600 1 0 -0.00 0.00
700 H=1 -0=0.04
8S0 -850 700 600 SOO 400 300 250
Significance test ofa.s for moderate movers.
53
FAST:
Speed differences Angle differences_....---...._ .._-_....__.._-Sd 0' ztst P Pel 0' ztst P
200 -3.0 4.7 1 0.00 1.7 83.7 0 0.77250 -3.5 4.4 1 0.00 7.0 70.3 1 0.04300 ~3.9 4.1 1 0.00 8.8 53.2 1 0.02400 -3.5 3.4 1 0.00 0.9 31.6 0 0.68500 -2.7 2.7 1 0.00 0.4 16.5 0 0.71600 -2.1 2.4 1 0.00 -0.4 13.4 0 0.66700 -1.8 2.6 1 0.00 -2.7 14.9 1 0.01850 -2.3 2.3 1 0.00 -3.6 14.1 1 0.00
200 1 1 1 0 0 1 00.04 0.00 0.01 0.33 0.24 0.04 0.22
250 1 1 1 1 0 0 -0.00 0.00 0.00 0.01 0.85 0.42
300 1 1 1 1 0 .0.00 0.00 0.00 0.00 0.27
400 1 1 1 1 .0.00 0.00 0.00 0.01
500 0 1 1 .0.13 0.00 0.03
600 0 0 .0.42 0.19
700 H=1 .0""0.04
850 .
850 700 600 500 400 300 250SIgnIficance test ofSd for fast movers.
200 0 0 0 0 0 0 00.74 0.87 0.82 0.72 0.67 0.12 0.24
250 1 1 0 0 0 0 -0.03 0.04 0.13 0.18 0.24 0.77
300 1 1 1 1 0 .0.00 0.01 0.01 0.03 0.06
400 1 0 0 0 -0.04 0.14 0.58 0.8$
500 1 1 0 -0.01 0.04 0.58
600 1 0 -0.01 0.10
700 H=O -0=0.50
850 -850 700 600 500 400 300 250
SIgnIficance test of 8cI for filst movers.
54
B.6
8SO-400mb 8SO - 500 mb
AScI Aad AScI AadLayer
He P He P He P Ho P
850-850 a 0.07 1 0.00 a 0.61 1 0.00850-700 a 0.05 1 0.01 0 0.50 1 0.04850-600 a 0.12 a 0.06 0 0.73 0 0.19850-500 0 0.20 a 0.57 0 1.00 0 1.00850-400 0 1.00 0 1.00 0 0.20 0 0.S7850-300 1 0.01 0 0.09 1 0.00 0 0.268S0-2S0 1 0.00 1 0.00 1 0.00 1 0.00850-200 1 0.00 1 0.00 1 0.00 1 0.00700-700 0 0.84 1 0.00 a 0.29 1 0.00700-600 0 0.70 1 0.04 a 0.37 a 0.12700-500 a 0.93 a 0.25 a 0.17 a 0.S6700-400 1 0.04 1 0.01 1 0.00 1 0.04700-300 1 0.00 1 0.00 1 0.00 1 0.00700-250 1 0.00 1 0.00 1 0.00 1 0.00700-200 1 0.00 1 0.00 1 0.00 1 0.00600-600 a 0.77 0 0.08 a 0.11 a 0.21600-S00 a 0.17 1 0.00 0 O.OS 1 0.00600-400 1 0.00 1 0.00 1 0.00 1 0.00600-300 1 0.00 1 0.00 1 0.00 1 0.00600-250 1 0.00 1 0.00 1 0.00 1 0.00600-200 1 0.00 1 0.00 1 0.00 1 0.00500-500 1 0.00 1 0.00 1 0.00 1 0.00SOO-400 1 0.00 1 0.00 1 0.00 1 0.00500-300 1 0.00 1 0.00 1 0.00 1 0.00500-250 1 0.00 1 0.00 1 0.00 1 0.00SOO-200 1 0.00 1 0.00 1 0.00 1 0.00400-400 1 0.00 1 0.00 1 0.00 1 0.00400-300 1 0.00 1 0.00 1 0.00 1 0.00400-250 1 0.00 1 0.00 1 0.00 1 0.00400-200 1 0.00 1 0.00 1 0.00 1 0.00300-300 1 0.00 1 0.00 1 0.00 1 0.00300-250 1 0.00 1 0.00 1 0.00 1 0.00300-200 1 0.00 1 0.00 1 0.00 1 0.00250-250 1 0.00 1 0.00 1 0.00 1 0.00250-200 1 0.00 1 0.00 1 0.00 1 0.00200-200 1 0.00 1 0.00 1 0.00 1 0.00
Significance test ofthe candidate ESLs for tropical storms and depression.
55
B.7
8SO-300mb SSO·2SOmb
ASd A8d ASd A8dLayer
Ho P Ho P Ho P Ho P
850-850 1 0.00 1 0.00 0 0.11 1 0.00850-700 0 0.80 1 0.01 0 0.08 1 0.04850-600 0 0.16 1 0.00 1 0.00 1 0.19850-500 1 0.00 1 0.01 1 0.00 1 0.02850-400 1 0.01 0 0.16 1 0.00 0 0.27850-300 0 1.00 0 1.00 0 0.08 0 0.73850-250 0 0.08 0 0.73 0 1.00 0 1.00850-200 1 0.00 0 0.07 0 0.12 0 0.12700-700 0 0.61 1 0.00 0 0.25 1 0.00700-600 0 0.08 1 0.00 1 0.00 1 0.01700-500 1 0.02 1 0.03 1 0.00 1 0.04700-400 0 0.44 0 0.34 1 0.01 0 0.53700-300 1 0.03 1 0.04 0 0.32 1 0,03700-250 1 0.00 1 0.00 1 0.01 1 0.00700-200 1 0.00 1 0.00 1 0.00 1 0.00600-600 0 0.10 1 0.03 1 0.00 1 0.03600-500 0 0.51 a 0.15 1 0.02 0 0.26600-400 1 0.03 1 0.02 0 0.70 1 0.04600-300 1 0.00 1 0.00 1 0.00 1 0.00600-250 1 0.00 1 0.00 1 0.00 1 0.00600-200 1 0.00 1 0.00 1 0.00 1 0.00500-500 1 0.02 1 0,00 0 0.52 1 0.00500-400 1 0.00 1 0.00 1 0.00 1 0.00500-300 1 0.00 1 0.00 1 0.00 1 0.00500-250 1 0.00 1 0.00 1 0.00 1 0.00500-200 1 0.00 1 0.00 1 0.00 1 0.00400-400 1 0.00 1 0.00 1 0.00 1 0.00400-300 1 0.00 1 0.00 1 0.00 1 0.00400-250 1 0.00 1 0.00 1 0.00 1 0.00400-200 1 0.00 1 0.00 1 0.00 1 0.00300-300 1 0.00 1 0.00 1 0.00 1 0.00300-250 1 0.00 1 0.00 1 0.00 1 0.00300-200 1 0.00 1 0.00 1 0.00 1 0.00250-250 1 0.00 1 0.00 1 0.00 1 0.00250-200 1 0.00 1 0.00 1 0.00 1 0.00200-200 1 0.00 1 0.00 1 0.00 1 0.00
Significance test ofthe candidate ESLs for hUtticanes.
56
B.8
ESL
Quadrant 850400mb 8S0-3OOmb 8So-250mb
Sigmticance test for SImIlarities ofmeans and populationdistribution of Sd for the selected ESL candidates.
comoanson
Ho=O 0 1quad I - quad II p=0.77 0.47 0.02
0 0 0quad I - quad m 0.23 0.84 0.32
0 0 0quad II - quad m 0.18 0.90 0.56
. . ..
B.9
Significance tests for vertical wind shear categories showed that no significant
differences were found between the absolute average differences of the tested ESLs,
except for the following categories:
Aact: Layer <mbl WSHgtegoa
T. Storms: 850-300
Hunicanes: 850-400
850·300
850-250
0-5, and 20-25
0-5, and to-15
0-5, and 10..15
0-5, and to-150-5, and 15-20
T. Storms: 850·300 0-5, and 15-20
Hurricanes: n/a
57
: :
. ~........... . ;.......... . .
CENTRAL NORTH PACIFIC DOMAIN
~~f"
40N
5ONH" .
•••••• t..--~--~---IIIIt---~--"'t----~-~-----~------iII
•I30N ,.......... . ·······t
I
I20N :•.~.~ ..~'"". I••• ••• ••• ••••••• ••••• •••••••••••••••••••••••••• '" ••••• ,.. • H ..
! H~waiian Island, I~ 1ONH'H"'" ,. .. ....., ...........: .
EO ------!----!-.-- .I l !
108
20S ............11. . .308'-__'- '-- '-- '-- '-- '--_---'__---'
170E 1eJJW 170W 160W 150W 140W 130W 120W 110W
longitude
Figure 2.1. Offieial NWS domain of the central north Pacific,which covers the area between 140 and 180 west of Greenwich,and northward from the equator (solid line). For this project, theworking domain was set between 0 and 40N , and extended to13OW, the area where tropical cyclones cross into the centralnorth Pacific (dashed line).
58
TC DISTRIBUTION PER YEAR8..------,-----....-----.....----...,.--------r-'--,
7
6
CJ) 5w
ffiIf 4:::>
8g 3
2
1
o1975 1980
Ii....!
1985 1990
YEAR
1995 2000
Figure 2.2 . Yearly distribution of the tropical cyclone database ofselected cases for the time period from 1975 to 2000 (the satelliteera). Not shown in the figure are hurricanes Dot from 1959 andtropical storm Sarah from 1967. Dot, twa and Iniki are cyclones thataffected or made landfall in Hawaii.
59
200
I250
I300
I400
----- I1500 - --------
600
I700
I850mb
•DEEPEST
6-8 levels
•DEEP..INTERMMEDIATE
4-5 levels
•SHALLOW1-3 levels
Figure 2.3. Diagram for the definition of each ESL. The depth of eachlayer is described by the height of a vertical bar from bottom to top. Thethree categories are identified by the color code, and the horizontaldashed line marks the 500 mb level, which divides the Shallow categoryinto two groups: Shallow Low and Shallow High (layer basesbelow/above 500 mb).
60
-u 2700
v0°
Sd \\...
----h=-- :::i ad \
1--""-----""-------1 ._---------f 900 u
1800
-v
Figure 2.4. Polar plane. The angle difference 8cl in degrees betweenthe tropical cyclone and the ESL vectors is calculated. The value ofad results in a positive value when the cyclone is moving to the rightof the ESL, or a negative value if the cyclone is moving to the left ofit.
61
800km
x
x x
Figure 2.5. 5°·7° annulus. Wind from points lying inside the550-800 km ring from the cyclone center position are selectedand averaged.
62
25 YEAR WIND COMPOSITE: 850 MB LEVEL
a. June-August«lNIT.::l'''i:::::l''~~;:;>'''i::>''''l:'''''''''''''-'''''''-~--:':--:--:::-::'"~-::-I: : : : : -....;\\rrrrr
,/"..,...,/"..,...,/v.."..,.".....-~, ' , t [3DN /)"I'(r\-,:'j:XX;;;;i
\ :-.. ,.-..,.-,;-.--.:-., , , , .,-'""t:~-..,:~~~~_......:.....~~~~/(:I-,:~ T, • '. ,--.:.......~....,_:__,.r!"/"~~~~~~~~~_~~/c
-., .: ..,.....i~ ...: ,....;r".-:.-,.-,;.-,~__~ .......~r20M '-';--.--i\+~": t,-.-i_~~"""I~\~~~~-~-~~~~~15N§:\ ;"\'" -Mi ~ ~....,--:-. rli .......: ....-<:~
'~-il-f-l~-'~--.r~
10M r--1i~~~~--1--r1-i""':-" -.: .. -.: ....,~.....-"~-'-,;-'~:"","""":-"-,,,,,;""'-.....;"" ': . ': ' ': '
5N '-~"'-:~--';C""""':~\1-C"'f'"'T""r'i"""\, , , • , , , , 1
-''->;-'--':-'"""''';''~ ~ \ ~ \ ~ \ ~,
.,. 10 m S·1
b. September-November-'---~-~-----'--"I:'"""""",,,,,,,",......::,..,. .......-~----,
~~~~~;-~-~~,~\L:. : , : : : : _ ;" 'r '(- : I !- "-"-""'"":~v;.;."'"",,;,;---,":~,_:'<__ L,~' : : : : ://I/rI
; -~.-:_...-:_......-:/ /:/ /: : :/ / ' ' , , ':-.":/.~/' iD---:'-- . :.-.",\:-:\.",~,;-..;,.;~ ': ,... :....
-~~-~-.~~ ~....,-~~r/"~_~.....-.~~~~~ ~~~c~-.~-.~-.~~~~ ~.-,~~r
, ; ; I ~. , • • •
• , , , lio, , • • •
~-~-,.-r;r1:!>...., '; , ,:., ....:~~---~~~~-..~-.~~-.~-~~
, , . . , , , ,."""':-._.....-.:""i-..;;.:~-r-<'~ i ....--r-<'~
.-...;.:,.,~""'i ""'r:-;-..:-.-r:....,-.,.;.....,-r-t~-.:
~-..~-..~-.~-.~-..~-.~-.-.~~-., .
,.-r:,.,~..,-;t'""""':-.--:-'"'"":- ""'1': ..........:~-:-. . , ,
Figure 3.1. Twenty five year wind composite (1975-2000) at 850 mb: the firsthalf of the hurricane season Jun..August (a), and the second halfSeptember-November (b). In general, wind speed averages between 5 and10m S·1 are observed south of 25 oN
63
25 YEAR WIND COMPOSITE: 500 MB LEVEL
a. June-Augusta __----~--------___:-----,
145'1 144W Il!I5W 13QW
", I"""I;~--'. , .( .. i .... ~~--.
1M 17IlW '6!WI ,_ IMW ,
-.,-.,.:-,. I, ' ~ .......~--.--t;-"4--'4'-'~.-ot:-<I , , , I , • , •
~~~~~~~~~~,~,~~
:!-.-;,."'-i'""";-,,~,.~~~,ol.,,..;,......:.- .\ / /:; / / /:__/ 1/ I\,~ :.A""~.r~~.~~_~:..c/.:!--;;.;.:;;:...
-"I__........:......_-~---;----:.-.-\I·/ j' I I: : : : : : : : / :
25M .~-~~~'\ \ fTIIT'\\'\':'\'----;--..1 / / /.~/. /:/ ~ -;--:--:-r"'~\' j"r i··j··i'··\"et'--~~(7T"'"'-:' '",:........ -::-.-<...--<.......:---.-,4
,lIN ..~"'.;,-.:..,-.:-....,; , I:.....,~-~-.:~
--,-..;-,. "T: ( ': \--.:.....,--'.-e4--<~-<~~--':
~~~~~~~~~~~~~. . .
b. September-NovemberG1,..--'7--:-~~- -~~~__.____,
" j.. ~ " \) \~,.. &~ ~~~ ~_ LS-l&. Ii ... 'Ii. L\..." ~\- :.
l.....'-'-L\ \ \ i .. :, , :, ~&,.,.;l..-4",,;'. . ., '"
lOll ~J.,..;,<~_:._~_:._~J"..~.l,.,.,,a,..,,,;.:'..,,.<J,.....
\~,~,~~~,~,~........~-~~~I I f I : : : : : : :
25M ....•.: ....~.\~-.~,~-'.,....,,~~........;....../'/ /'/ /: :.......",....... : : :
; ; /;--~tr ~; ; --;-;---~~20Il ~L/:~ .......\: .... :,~.,.""",-:.-~......~.:r
.-J_") :'" \ I. ":_/ I L '--:' ':': :---,,:....... -:: : : I I I I \
Il1N :--.:-......:-.-.f-,.-:-......:-......, ,:00,.;,: ... ... .
~~~~~~~~~~~~~~~-
ION. .
-r~~~~~~~~~~~~~~:~~
5N ..-.:......-r."""t~-.:--.--.:--:-~-.-.,;-.I • , • •• • ,
Figure 3.2. Same as Fig 3.1 ; for the 500 mb level.
64
25 YEAR WIND COMPOSITE: 200 MB LEVEL
tIN '
a. June-August4ON..-----:--...,..----------~
~~~,\,~,~,~~~~~~~
lllM \'. \ ,\.\. .L.\J.\'~~....i-~"""""~~Ar r rrrr r\---i.- ;
!ON .lL t rJ\ _. ,~"""""""",""",..-"\..-"~-<../1
rr\,,~'~"""""",,~~~.......v"'v-'<......v-12Sll '\.~I",.;~-\.-.l~~~~~ ..................~A/
r--............~...1I-'~._'lj,.,.... ...........,.,--...............~..........,,_,,/:,.,/, 1>,
2011 ' , . ;l-""',?;;' ..
: ; ,~~--~/, : : ~\~I...":/'"\"""
~ , .... .....,;1....""'-.; ....... "" , ....-"': : : I j: : : : :.....
10N .... , :-~~ '\'H :-,./.('~~--:-~ ....//>/> ......>.......;...-./"/"/":.r .......;...""'.-:-.-:......
, • j j • • , , ,
5N ,A~""",:-",:~~/,,'/,/."~/.:/<""":/,/,~~>.
~...........~.-A/'~/'~ /";..... /')- /" j /')- /'/ /'
b. September-November«lit .
~'-.J -If.J. ~ 1bJi. .. 'Ii \\ Ii. 'Ljhli-L.J....-"-J:IIlM ,~ ~'-~i J ~ w....~'-\...."-~
lL....l... ~~l-~'-'--'-"--i..-'-L...L..i....:_' ...Jl..-I, l ,,' , , , , , ,
lOll'"':>,;.. _,~l...-\,..'-.l,.,.,~l,.,..\....J,_\-W'--i-·~...lL..-l" ~"- ~l.." L.".l-'-l-L..l-l......~,~: "'-M-"-"""-"""'--i
25M :\.~~.~L....l.-L.\.-Uj~~~~1-\.~,~l...~G: : :
2011 ' \,..j ;' .. 1> '
Figure 3.3. Same as Fig. 3.1 for the 200 mb level.
65
SELECTED CENTRAL NORTHPACIFIC BEST TRACKS
1975-2000
· .. I. .~ : ~ : : ~ : : ~ ~ .· . . . . . . . .· . . . . . , . .· . . " . . " . .
" . . , . . . . .· . . . .. .I • • • I' •
• I • I • I • t
3QH ••••••• :............. ..: ••••••• :. • .•••. : •.••••• : ••••••• : ••••••..~ •..•••• : .•••.••• I ••••••· "".,,..· ."."..· ." ..• • I ••
• •• I'· .. ..2SIt •.
1011 : : : : .• • I' "-= :: ::-:i: : . : : . :\: ;~ : : : ~ ~ ~
5H •.•••.• ~ .•••.••._ ~ .••.••..:. •...••• : .
E~ 0 175W 170W 165W 1eow ISDW 146W ,.OW 135W 130.
Figure 3.4. Best track chart of the tropical cyclones selected foranalysis. The Hawaiian Islands are indicated by the red circle.The tracks of hurricanes Dot (1959) and Sarah (1967) are alsoincluded.
66
TO OBSERVAnONS MONTHLY DlSTRISUTION
350
300
5 250
J200'5
I 150z
100
50
o
-
I I
JUN JUL AUG SEP OCT NOV DEC
Figure 3.5 . Monthly distribution of the number of 6 hourlyobservations of tropical cyclones in the central north Pacific.
67
TC INTENSITY OISTRIBUTION PIE CHART
60% T. Stams andDepressions
<64kts
Hunicanes>- 64kts
40%
Figure 3.6 . Tropical cyclone intensity distribution. A total of 991observations are divided into tropical storms or depressions, andhurricanes. The number of observations in each category is shownby the boxed number.
68
TC DIRECTION CAlCOORIESa.600.-----,---------,----------,------------,
500
CD
ti 400
~ffi~300LLoffilQ
~200z
100
b.
lOT. Stoml8 -oep·1DH~
Ncrlhwtrd
TC DIRECTION
TC TRAN8LA11ONAL.SPEED CoI.TEGOAIE8
350
300
CD
~F250~ffiIII 200o~
ffi 150~:::>z
100
o
- ICJ T. S1oona-Dep. Io HLrriCllne8
-
-- I---
~
FlIIl
Figure 3.7. Tropical cyclone direction (a> and speedstratification (b) following Chan and Gray (1982). Westwardmoving tropical cyclOnes have a motion direction between 225-315°, and northward moving cyclones between 316-45°. Slowmovers have a speed below 4 mls. moderate between 4 and 8mis, and fast moving cyclones higher than 8 mIs.
69
Middle and lower tropospheric levels
850mb 700mb
200100
.. '
_151....-_......-4---.....I-._-,--_.....J-200 -100 0
15..---~---,----~--.,
10
5
o ----'-~--~--'
-5
-10
200100o-100
10
-10
15..---~---,----~--.,.:• I
II
.1 '
I :----------~.i:-~-:--"0 ,' ... :"_'~':'
III -5 . ··<l\!.·· '.I. ,IIII
:_151....--......-4---.....I-._-,--_.....J-200
600mb 500mb15..---~---,----..------,
200100oad (deg.)
-100
10I·I
• II
• .' ~I
:e--_·--~-.~~~i~:~~ __ ~-~·_~-.. ,_.~:
.. J" ...." .. t:-.! ...:5 -..),1: ,
- • 1 .'
• IIII
:_151....-_......-4---.....I-.--,--_.....J-200
-10
Figure 4.1. Sci vs. Sd scatter.plots for the middle and lowertropospheric levels of 850, 700, 600 and 500 mb.
70
Higher tropospheric levels
400mb15r-----..----,----.------,
300mb15r---~-----r---...---__,
200100o-100-15 '-------'----"-----'-----'-200200100o-100
-15 '-----'-----'----'-----'-200
250mb 200mb15 r----.....----,----.-----, 15r---~----,----.---___,
Figure 4.2. Same as Figure 4.1 for the higher tropospheric levels of 400,300, 250 and 200 mb.
71
NORMAL PROBABILIlY PLOT FOR THE 850 MB LEVELANGLE AND SPEED DIFFERENCES
0.999
0.997
0.990.98
0.95
0.90
0.75
~i 0.50~Q.
0.25
0.10
0.05
0.020.01
0.003
0.001
/ +i .j.. +I iI .j..
",
,
.;j:.f
T++
0.999
0.997
0.990.98
0.95
0.90
0.75
0.50
0.25
0.10
0.05
0.020.01
0.003
0.001
I
//E~+
A .. " ...... " ...
JIII
~
I,JI1
+.'
-10 10
Figure 4.3. Normal probability plot to identify normal distributionproperties on ad and Sd. The dashed line represents the theoretical valuefor the perfect linear fit. especially between the 25th and the 75th
percentiles.
72
NORMAL PROBABIUTY PLOT FOR THE 250 MB LEVELANGLE AND SPEED DIFFERENCES
.If0.0031-+ ·, ·..· · ·,· · · .., ·..· ·.,
0.0011+.... · , · ·· ..: · ·....,· · -1
±fp't ....l
IIf
I~r
I/
J I
+ I
0.50
0.75
0.25
0.999
0.997
0.990.98
0.95
0.90
0.10
0.05
0.020.01
0.003
0.001
-15 -10 -5 0 5100o-100
0.25
0.10
0.05 .
0.020.01
0.999 :....... . - .. I
~:Tri,l0.95
0.90 ..
0.75 ., ~ ,.
~
~~ 0.50
Q.
Figure 4.4. Same as figure 4.3 for the 250 mb level.
73
200100o
1 250mb I
-,.....c-- -c--
c- -c-f-
I nno-200 -100
400
50
200
100
150
250
300
350
200100o
HISTOGRAM COMPARISON OF ad BETWEEN 850 AND 250 MB LEVELS
450
1850mb I .-
f-
fo-
S ho-200 -100
50
400
450
100
350
i 300
i 250
15 200
Iz 150
Figure 4.5. Histogram comparison of angle difference between thelevels 850 mb and 250 mb. Following Panosky and Brier (1958),the total classes are calculated as 5 log 10(n) =15 (for n=991).
74
Vertical Variation analysis for the Intensity stratification categories
T.STORMS-DEP. HURR.100
C d200
300
400I
500 :I~00
600l!!
Q..
700
800
900-10 0 10 -10 0 10
ad (deg.)
T.STOFIMS-OEP. HUPIFI.100
200
300
400
500
600
700
800
900_100 0 100 -100 0 100
5o5 -5
Sd (mls)
o
T.STOFIMS-DEP. HUFIFI100~---r-~~r-~--,.---'---'
: :a I b I
I II II iIIII II II II II II II II II II II II II II II II II II II II II II II IIIIIIIIIIIIIIIIII II I
: :
BOO
200
900-5
600
500
700
T.STORMS-DEP. HURR100
300
1400
l
I
Figure 4.6. Vertical variation analysis stratifying by intensity: tropicalsrorms-depressions (a,e), and hurricanes (b,d). The lower panels showthe error bar plots of the standard deviation of each category
75
Vertical Variation analysis for the direction and speedstratification categories
ANGLE MeAN DIFFERENCE
westward NOI1hWard Slow Fast
200
300
700
800
900 -10 o 10 -50 o 50 -20 o 20 -10 0 10 -10 0 10
Fill!
100 -100 0 100 -100 0 100 -100 0 100 -100 0 100
-d(deg·)
We8IWlI"ll
IIIII
II
II
IIIII
I-- --l
f- f-,
H-i
f-H
rhI
~100 0
700
800
200
300
100
Figure 4.7 . ad analysis for the categories of direction of motion,and translational speed.
76
Vertical Variation analysis for the direction and speedstratification categories
SPEED MEAN DIFFERENCE
FastSlowNorthward
0 5 -5 0 5 -5 0 5 -5 0 5 -5 0 5
sd (mla)
Westw8d NOI'IhWanI Slew MocIer8Ia Fll8t100
200
300
1400
!sooisoo
700
800
900-6 0 5 -6 0 5 -6 0 5 -6 0 5 -5 0 5
8. (lnIe) .
Figure 4.8. Same as Figure 4.7 for Sd'
Westward
: : : : T
I I I I, I I II I I II I I II , I II I II I I II I I II I , II I I I, I I I, I I II , , ,, I , I
I III
I II II ,I II II II I, II II II I II II I
I II
IIII,IIIIIII III I II I I
: : i : :900
-5
200
700
100
300
1300
!4001- 500;I0. 600
77
Tropical Stanns and Dep. «64 Ids.)
30
25
20
15
• •,•• •
•••
~----------------------lr-----------------------------------,•
0
•l;>
•i'
•..• 850-400 mb~ 850-500 mb
1010 20 30 60 60 70 80 90
ABSOLUTE ANGLE DIFFERENCE Aac. (deg.)
Figure 4.9. Absolute angle difference '1$. standard deviationscattergram for tropical storms and depressions. Deepintennediate (yeUow) and shallow (green) layers show the lowestvalues for~ vs. std.
78
Hurricanes (~ 64 Ids)
50
•
25
20
45
••
35 •o
30 0
.0.:
~.<JA.
850-300 mb15 • __---..850-250 mb
• •, •
908070605040302010l-_........I...-_-..Il.-_--L-_-..I__--.l.-_--l__....l.-_------I
10
ABSOLUTE ANGLE DIFFERENCE~ (deg.)
Figure 4.10. Absolute angle difference va. standard deviationscattergram for .hurricanes. The deepest (red) and deepintermediate (yellow) layers show the lowest values for ScI va. Std.
79
Layertop
Layertop
Significance test for ADd : Tropical storms and dep.
850-400mb
200 1 1 I I 1 1 1 1250 1 1 I I 1 1 1 -300 I 1 1 1 - -~ 1 1 1 - - -500 1 1 - - - -600 1 - - - - -700 1 1 - - - - - -850 1 - - - - - - -
850 700 600 500 400 300 250 200-850-500mb
200 1 1 1 I 1 1 1 1
250 1 1 I I 1 1 1 -300 I I 1 1 1 - -400 I 1 1 1 - - -500 1 1 - - - -600 - - - - -700 1 1 - - - - - -850 1 - - - - - - -
IS 700 600 500 400 300 250 200
Layer bottom
Fipre 4.11. Absolute angle difference ADd significance test on thetwo candidate ESLs for tropical storms 850-400, and 850-500 mb.The x axis indicates the "layer bottom", and the y axis the "layertops" or depth. The test assigns either a 1 (reject null hypothesis)or a zero (null hypothesis not rejected) to the rest ofthe layers thatare compared to the candidate ESLs.
80
Layertop
Layertop
Significance test for Aact : Hurricanes
8So-3OOmb
200 ) 1 1 1 1 1 1 1
250 1 t 1 1 1 ..
• I t 1 1 1 .. ..400 1 1 1 .. .. ..500 I 1 ) 1 .. .. .. ..600 1 1 1 .. .. .. .. ..700 1 1 .. .. - - .. ..850 1 .. .. .. .. .. - ..
• 700 600 500 400 300 250 200
8So-2S0mb
200 1 t I 1 1 1 1
~ 0 1 I I 1 1 1 ..300 0 I t 1 1 1 .. ..400 1 1 1 .. - ..500 I 1 1 .. .. .. ..600 1 1 1 .. .. - .. ..700 I 1 .. .. .. .. .. ..850 1 .. .. .. .. .. .. ..
19 700 600 500 400 300 250 200
Figure 4.12 Same format as Figure 4.11 for hwricanes.
81
82
Layertop
Layertop
Significance test for ASd :
T. STORMS: 850-500 mb
200 1 1 I 1 1 1 1
250 1 1 I 1 1 1 -300 1 I I 1 1 1 - -400 I 1 1 1 - - -~ 1 - - - -600 - - - - -700 - - - - - -850 - - - - - - -
BS 700 600 500 400 300 250 200
HURRICANES: 850400 mb
200 1 1 I 1 1 1 1250 1 1 J 1 1 1 1 -300 I I 1 1 1 - -~ 1 1 1 - - -500 1 - - - -600 - - - - -700 1 - - - - - -850 1 - - - - . . -
~ 700 600 500 400 300 250 200
Layer bottom
Figure 4.14 Same format as Figure 4.11 for speed analysis.
83
Absolute angle and speed mean difference analysis byquadrant for the candidate ESLs
ql"=' .. ••• ••••• ~ ••''''''-~''-'' - .. ~.
~«l,==-,----r---r----r---.-------,----r---.-------,-----,
qlV
30
iI
___ . .1. :N I A·····t··· ~ .850-400 rnb 17.3
............. ""''' """!nb 19.0
850-250~ 25.4
25 ' ' --, .. _ ••• _~•••••••••• - ••••• 0 ; •••••••••••••••••
qll
I~_.
850-400m> 12.5
85Q-3OOn'tl 12.6
85O-25Omb n.7
5 --,'. ..
qlll !
15 ..... .;.~_---,_...._.. --....,..--.•..,...,------ .....--!--........850-400 ITil lot.1
,85~1Til .. 14.0
8SO-25Q1Til 15.7
10
; 20f-- .......:.__....-_~'o_...____,'bN--___,------.;...----__i
I~.
i
I~
O'---_-L-_----'-__..L-_~__'---_..J__-..l.__""--_--'-_---'
-180 -175 -170 -165 -180 -155 -150 -145 -140 -135 -130
L.or91ude
ql
<IO.-----,---,---,.----.---.--------..-------r---r---,-----,qlV
n'O 2.3
ntL 2.1~/A
30
i 2Ol--'------;-----=------(j---'--;-----:---------l~
III
10
llllO-4OO j1CI 1.4
~~ ...l.6
el5O-*lftI 1.8
qlll •
Sao -1711
1• qH
-170 -1I111 -leo -165 -11lO -I<4l1 -1<10 -135 -130
l.aVIUdf
Figure ,4.15. Absolute angle (a) and speed (b) mean differencequadrant analysis. No analysis was made on quadrant IV since TCare moving away from Hawaii in this quadrant.
84
WIND SHEAR va. ANGLE DIFFERENCET. STORMS AND DEP.
22r-------.--------r--------,,-----,---------,
20 [ffiJ850-400-$0-850-500
850-300
••
12
252010 15VERTICAL WIND SHEAR (mIs)
5
10 '-- -'-- ---'-- ---J'-- -'-- --'
o
FigU", 4.16. Absolute angle mean difference vs. increasing windshear for tropical stonns and depl'888ions. The analysis was made onthe 850-400 mb ESL (solid line-circl8s). The next deeper ESL of 850300 (dashed line-diamonds) and the previous shallower 850·500 mb(dotted line-asteriks) are included for comparison.
85
WIND SHEAR VS. ANGLE DIFFERENCEHURRICANES
22,..-------,-------,---------,r------,--------,f\-
_20D'l
!~ 18ffia:wIt 16ow-'(!) 14~~3 12
mc( 10
... 850-300mb-+- 850-250 mb...... 850-400mb
.'
.-li
..\. '.
\. ".\. ",
\. ". .,1;)\. '. .," ". ",,"
\. .... "" . .,""({J'
'.'.
25205 10 15
VERTICAL WIND SHEAR (mls)
8'----....L--------'---------l-----'--------Jo
Figure 4.17. Absolute angle mean error (Aae) VS. increasing windshear for hurricanes. The analysis was made for the 850-300·mb ESL(solid line-circles).The previous shallower 850.-400 mb (dashed linetriangles) and the following deeper 85()"25O mb (dotted line-asterisks)are also included for comparison.
86
WIND SHEAR~. ABSOWTE SPEED DIFFERENCET. STORMS AND DEP.
3r-------,---------,-----.----------,------,
..
..'.'
...•........
.....'........,...~
2520151051.5L.------L..-------..J-----L-------I.-------J
oVERTICAL WIND SHEAR (1M)
Figure 4.18. Same as figure 4.16 for absolute speed meandifferenCe (Asc.).
87
WINO SHEAR va. ABSOLUTE SPEED DIFFERENCEHURRICANES
3.----------.--------r---------,-----,---------,
...., , .."""" .
' .... '.
•
~------------&----....~--..". -------- ...., "
~-- "",~~' ...........
.......... "0
0.5
10 15VERllCAl WIND SHEAR OM)
20 25
Figure 4.19. Same as figure 4.17 for absolute speed meandifference (AsJ.
88
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