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

3

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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