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THE RELATIONSHIP BETWEEN SYNOPTIC FACTORS AND INTENSITY CHANGES OF TYPHOONS OVER THE WESTERN NORTH PACIFIC OCEAN DURING ENSO AND NON-ENSO EVENTS

DISSERTATION

Presented in Partial Fulfillment of the Requirements for

the Degree Doctor of Philosophy in the

Graduate School of The Ohio State University

By

Ke-Mao Wu, M. S.

*****

The Ohio State University 2000

Dissertation Committee: Approved by Professor Jay Hobgood, Adviser

Professor Jeffery Rogers ^ ______

Professor John Rayner Atmospheric Sciences Graduate Program UMI Number 9971663

UMI

UMI Microform9971663 Copyright 2000 by Bell & Howell Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code.

Bell & Howell Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 ABSTRACT

Tlie purpose of this study is to find the relationship between synoptic factors and intensity changes of typhoons over the western North Pacific Ocean during ENSO (El Nino /Southern

Oscillation) and non-ENSO events. An empirical equation between climatological sea surface temperature (SST) and maximum potential intensity (MPI) of typhoon is derived by- using 27 years (1965 - 1991) of data from the Joint Typhoon Warning Center and

Comprehensive Ocean-Atmosphere Data Set. This equation is provided as a capping function for a given SST and its related typhoon intensity. Six years (1992 - 1997) of data were used to test the derived equation and there was no typhoon intensity exceeding the MPI.

This empirical equation is used to as a measure of intensification potential (POT), one of the six synoptic variables used to relate the intensity changes of typhoons during ENSO and non-ENSO events. The other variables are vertical wind shear (SHEAR), time tendency of the shear (DSHEAR), relative and planetary eddy angular momentum flux convergence

(REFC and PEFC), and relative angular momentum (RAM). These six synoptic variables are the independent variables and the intensity change of typhoons is the dependent variable.

The standard multiple linear regression is used to relate the synoptic variables and intensity changes at 12, 24, 36,48, 60, and 72 hours during ENSO and non-ENSO events.

ii The results of this study reveal that each variable has a different pattern of significance at various time periods. POT is not significant on the intensity changes of typhoon at any time period during ENSO and non-ENSO events. This may result from the rather uniform SSTs in the region where typhoons develop. SHEAR and DSHEAR are significant at most time periods with negative correlation with intensity changes which indicate that they are good predictors. RAM is significant at most time period of non-ENSO events (1996 and 1998) and not significant at all during ENSO (1997). REFC is not significant on 1996 but is significant on 1997 and 1998. The change of pattern of large-scale environment circulation induced by

ENSO may affect the performance of these variables.

Ill Dedicated to my mother and father

IV ACKNOWLEDGMENTS

I would like to thank my advisor. Dr. Jay S. Hobhood. to his guidance through my graduate studies. I am grateful to Dr. Hobgood for providing the opportunity to learn through research. Thanks also to Dr. John Rayner, Dr. Jeff Rogers. Dr. Ellen Mosley-Thompson and

Dr. Mark Lander for their comments and suggestions during this study. I acknowledge Dr.

Derek West and Dr. Kevin Petty for providing information and data used in this study.

Special thanks also to all my beloved friends for their friendships. Finally, I wish to express my gratitude to my parents and family members for their support and encouragement. VITA

December 1 L 1966 ...... Bom — Taipei. Taiwan, Republic of China

1989 B.S. Meteorology. The Chinese Culture University. Taipei. Taiwan. R. O. C.

1989-1991 Graduate Fellow, The Chinese Culture University. Taipei, Taiwan, R. O. C.

1991-1993 ...... Researcher, Dept, of Geography, National Taiwan University, Taipei, Taiwan. R. O. C.

1993-2000 ...... Graduate Research Associate. The Ohio State University. Columbus, Ohio, U. S. A.

FIELD OF STUDY

Major Field: Atmospheric Science

VI TABLES OF CONTENTS

Page

Abstract ...... ii

Dedication ...... iv

Acknowledgments ...... v

Vita...... vi

List of Tables ...... ix

List of Figures ...... xi

Chapters:

1. Introduction ...... 1

2. Literature Review...... 4

2.1 Climatology of the North Pacific Basin ...... 4 2.2 El Nino and the Southern Oscillation ...... 13 2.3 Typhoons ...... 22 2.4 Sea Surface Temperature ...... 29 2.5 Vertical Wind Shear ...... 46 2.6 Eddy Angular Momentum Flux ...... 54

3. Data and Methodology ...... 58

3.1 Data...... 61 3.1.1 Western North Pacific Best Track Data ...... 61 3.1.2 Climatological Sea Surface Temperature Data ...... 62 3.1.3 Daily Wind Field Data ...... 63

VII 3.2 Calculation of Synoptic Variables ...... 64 3.2.1 Vertical Wind Shear ...... 64 3.2.2 Angular Momentum Variables ...... 65

3.3 Translation Speed ...... 70 3.4 Statistical Analysis ...... 72

4. .A.nalysis and Results ...... 79 4.1 Climatological SST versus Typhoon Intensity ...... 79 4.1.1 Empirical Equation for SST and Typhoon Intensity ...... 79 4.1.2 Case Study of the Empirical Maximum Potential Intensity Function ...... 90 4.2 The Relationship between the Synoptic Variables and Typhoon Intensity Changes during ENSO and Non-ENSO Events ...... 109 4.2.1 The Results of Study for 1996 (before ENSO) ...... 110 4.2.2 The Results of Study for 1997 (ENSO) ...... 113 4.2.3 The Results of Study for 1998 (ENSO) ...... 115 4.2.4 Comparison with Previous Studies ...... 118 4.2.5 The Influence of ENSO on the Synoptic Variables 122

5. Summary and Conclusions ...... 135

Appendix A: SPSS Statistical Output for 1997 ...... 139 .A.ppendi.x B: SPSS Statistical Output for 1998 ...... 152 .A.ppendi.x C: SPSS Statistical Output for 1999 ...... 165

List of Reference ...... 178

Vlll LIST OF TABLES

Table Page

2.1 Properties of the SST groups (from DeMaria and Kaplan. 1994a) ...... 41

2.2 Normalized regression coefficients for the combined climatological. persistence, and synoptic predictors. The coefficients that are significant at the 95% level are in bold: r' is the percent of the total variance explained by the regression (from DeMaria and Kaplan. 1994b) ...... 51

2.3 The horizontal convergence of relative angular momentum per unit area (-V-Vm). A positive entr>' denotes a gain of angular momentum. Units are 10^ kg s*“ (from McBride. 1981) ...... 55

4.1 SST group properties ...... 83

4.2 SST Intensity percentiles ...... 84

4.3 Western North Pacific typhoons containing the maximum intensity data point 87

4.4 The regression output ...... 88

4.5 The number of cases and percentage of tvphoons to reach their 50% and 80% MPI...... ' ...... 99

4.6 Synoptic variables included in the multiply regression analysis ...... 109

4.7 Normalized regression coefficient for residual variables after backward regression for 1996. The statistically significant at the 90% level are presented ...... 112

4.8 Normalized regression coefficient for residual variables after backward regression fori 997. The statistically significant at the 90% level are presented ...... 114

4.9 Normalized regression coefficient for residual variables after backward regression for 1998. The statistically significant at the 90% level are presented ...... 117

IX 4.10 Normalized regression coefficients for the combined climatological. persistence, and synoptic predictors. The coefïicients that are significant at the 95% level are in bold: r" is the percent of the total variance explained by the regression (from DeMaria and Kaplan. 1994b) ...... 119

4.11 Normalized regression coefficients for the combined climatological and persistence predictors. The coefficients that are significant at the 95% level are in bold (from Petty. 1997) ...... 119

4.12 Normalized regression coefficients for the combined climatological. persistence, and synoptic predictors included in the model. The coefficients that are significant at the 95% level are in bold (from Petty. 1997) ...... 120

4.13 Tlie frequency of typhoons in the westem North Pacific basin during ENSO and non- ENSO events (the numbers in the bracket are the frequency of super typhoons).. 123

4.14 The frequency of typhoons in the Atlantic basin during ENSO and non-ENSO events ...... 123 LIST OF FIGURES

Figure Page

2.1 Mean surface level streamline analyses over the Pacific for January (from Sandler. 1975) ...... !...... 6

7 7 Mean surface level streamline analyses over the Pacific for July (from Sandler. 1975) ...... !...... 7

The position of the Equatorial Trough (Intertropical Convergence Zone or Intertropical Front in some sectors) in February and August (after Saha 1973. Riehl 1954 and Yoshino 1969) (from Barry and Chorley 1987) ...... 8

2.4 Mean surface wind field and velocity divergence for February. Units of isotachs are m s“^:units of divergence 10'^ s“^ (solid lines positive, dashed lines negative) (From P.asmusson and Carpenter 1982) ...... 9

2.5 Mean surface wind field and velocity divergence for August. Units as in Fig. 2.4 (From Rasmusson and Carpenter 1982)...... 10

2.6 Time-longitude sections of sea-surface temperature (SST). The sections follow the equator to 95°W and then follow the climatological cold axis to its intersection with South American coast at 85°S. ( top ) Mean climatology, (middle) Composite El Nino anomalies. The El Nino year is year 0. (bottom) Anomalies from 1981 to 1983. Note the larger contour interval (from Cane 1986) ...... 11

2.7 Sea-surface temperature anomalies (in °C) during a typical ENSO event obtained by averaging data for the events between 1950 and 1973. a, March, April and May after the onset; b, the following August. September and October; c, the following December. January and February; d. May, June and July, more than a year after the onset (from Philander 1983) ...... 14

XI 2.8 The solid line gives sea-surface temperature anomalies at Puerto Chicama, Peru, an index of El Nino. The dashed line is the difference in sea-level pressure between Darwin, Australia, and Tahiti, an index of Southern Oscillation. Both are normalized by their long-term standard deviations. Major El Nino events are shaded (from Rasmusson 1985) ...... 18

2.9 (a) Time series of the Southern Oscillation index and of anomalous SST in the eastern Pacific (Puerto Chicama, Peru) (redrawn after Oceanus 1984). (b) Same as in (a) but derived from the extended-range integration with the coupled ocean-atmosphere GCM (Latif et al. 1992). The model SOI is defined as the anomalous pressure difference between an average over the eastern Pacific and the Indian Ocean. SST anomalies have been averaged over the Nino-3 region, which is an average over the eastern equatorial Pacific. All time series are normalized by their long-term standard deviation (from Latif 1993) ...... 19

2.10 Time series of SST anomalies at Puerto Chicama, Peru (smoothed with a 3-month running mean), and the Southern Oscillation Index (smoothed with an 11 -month recursive filter). SST anomalies above one standard deviation are shaded in black. Small flags attached to the SOI curve single the beginning (staff) and duration (flag) of the SST shading for each El Nino event. Solid (hatched) flags refer to S an VS (W and M) events from the compilation of Quinn et al. (1987) (from Enfield. 1989) ..... 20

2.11 Frequency of hurricane genesis (numbered isopleths) for a 20-year period. The principal hurricane tracks and the areas of sea surface having water temperatures greater than 27°C in the warmest month are also shown (after Palmén 1948 and Gray 1979)(from Barry and Chorley 1987) ...... 24

2.12 Schematic view of a typical tropical cyclone. Arrows denote the mean circulation (from Frank 1977) ...... 25

2.13 A model of the areal (above) and vertical (below) structure of a hurricane. Cloud is stippled and areas of precipitation are shown in the vertical section. The streamlines symbols refer to the upper diagram (from Berry and Chorley 1984)...... 27

2.14 Annual frequency of tropical cyclones for the eastern, westem North Pacific and North Atlantic Ocean. The numbers include tropical storms and hurricanes and typhoons ...... 28

xn 2.15 Typical hurricane paths originating over regions where the SST is generally greater than 26°C during the warmest season (Palmén, 1948) ...... 30

2.16 Change in central pressure versus sea surface temperature for Hurricane Esther (Perlroth. 1962) ...... 30

2.17 Miller's (1958) relationship between sea surface temperature and maximum potential intensity of tropical cyclones (from Elsberry et al.. 1987) ...... 32

2.18 Scatter diagram of maximum sustained wind speed (MSW) corrected for storm motion versus climatological SST for a 12-year sample of Atlantic tropical cyclones. The curve drawn against the data represents the SST capping function based on the 99'*' percentile (from Merrill, 1987) ...... 34

2.19 Maximum attainable central surface pressure (mb) as a function of surface air temperature (Tg) and weighted mean outflow temperature (T^^J assuming an ambient surface pressure of 1015 mb, ambient surface relative humidity of 80%, f evaluated at 20 degree latitude, and rg = 500 km (from Emanuel. 1986) ...... 37

2.20 Minimum attainable surface central pressure (mb) in September (a) for .Atlantic and Indian Ocean and (b) for Pacific Ocean (from Emanuel. 1986) ...... 38

2.21 The maximum storm intensity and the 99'*’. 95'*’. 90'*’. and 50'*’ intensity percentiles for each 1°C SST group. The X coordinate is the midpoint of each SST group and the storm translational speed was subtracted from all intensities ( from DeMaria and Kaplan, 1994a) ...... 42

2.22 The observed maximum storm intensity for each 1°C SST group and least-squares function fit for the 31-year Atlantic sample (from DeMaria and kaplan, 1994a)...42

2.23 Comparison between the eastern North Pacific MPI and Atlantic MPI function (Whitney and Hobgood, 1997)...... 45

2.24 Climatological average for August of the zonal vertical wind shear between 200 mb and 850mb. Positive values indicate the zonal wind at 200 mb is stronger from the west or weaker from the east than the zonal wind at 850 mb (from Gray, 1968).. .47

2.25 Plan views of zonal shear, Ujoomb “ UgoQ^b (m s" ^ ) for the northwest Pacific (from McBride and Zehr, 1981) ...... 49

2.26 Plan views of meridional shear, Ujoomb ~ Ugoomb s"^) for the northwest Pacific (from McBride and Zehr, 1981) ...... 50

xiii 2.27 Schematics of the 200 - 850 mb wind shear arising from (a) a low-latitude system with upper-tropospheric winds concentrated in a shallow layer versus (b) linearly distributed over a deep layer as might exist in a midlatitude trough (from Elsberry and Jeffries. 1996) ...... 53

3.1 Examples of positive and negative relationships. Beer sales are positively related to temperature, and coffee sales are negatively related to temperature (from Gravetter and Wallnau, 1992)...... 74

3.2 The distance between the actual data point (Y) and the predicted point on line (Ÿ) is defined as Y - Ÿ. The goal of regression is find to the equation for the line that minimizes these distance (From Gravetter and Wallnau. 1992) ...... 74

3.3 Graph of a multiple sample regression line based o data for the variables Y, X,, and X, (From Hamburg, 1985) ...... 77

4.1 Scatter diagram indicates the typhoon intensities and SSTs of all 12089 observations in the 27-year sample (1965 - 1991) ...... 80

4.2 Scatter diagram with the typhoon intensity and SSTs of all 11062 observations in the31 -year sample (1963 - 1993). Intensities are corrected for storm translational speed ( From Whitney and Hobgood, 1997) ...... 81

4.3 The maximum typhoon intensity and the 99th. 95th, 90th, and 50th intensity percentiles associated with 1 °C SST group ...... 85

4.4 The observed maximum typhoon intensity associated with 1°C SST group and the least squares function fit ...... 89

4.5 Annual average motion of tropical cyclones (> 17 m s ') in various basins during specified time periods (Neumann, 1993) ...... 91

4.6 The observed intensities of typhoon Elsie and its associated maximum potential intensity (MPI) ...... 93

4.7 The track of typhoon Elsie ...... 93

4.8 The observed intensities of typhoon Gay and its associated maximum potential intensity (MPI) ...... 94

4.9 The track of typhoon Gay ...... 94

XIV 4.10 The observed intensities of typhoon Zelda and its associated maximum potential intensity (MPI) ...... 95

4.11 The track of typhoon Zelda ...... 95

4.12 The observed intensities of typhoon Yates and its associated maximum potential intensity (MPI) ...... 96

4.13 The track of typhoon Yates ...... 96

4.14 Areas where typhoons intensified rapidly during summer and early fall (20 June - 16 October)-number of occurrence (1956 - 76) ( From Holliday and Thompson. 1979) ...... 97

4.15 The observed intensities of typhoon Joan and its associated maximum potential intensity (MPI) ...... 100

4.16 The track of typhoon Joan ...... 100

4.17 The observed intensities of typhoon Paka and its associated maximum potential intensity (MPI) ...... 101

4.18 The track of typhoon Paka ...... 101

4.19 The observed intensities of typhoon Ward and its associated maximum potential intensity (MPI) ...... 102

4.20 The track of typhoon Ward ...... 102

4.21 The observed intensities of typhoon Wilda and its associated maximum potential intensity (MPI) ...... 103

4.22 The track of typhoon Wilda ...... 103

4.23 The observed intensities of typhoon Page and its associated maximum potential intensity (MPI) ...... 104

4.24 The track of typhoon Page ...... 104

4.25 The observed intensities of typhoon Dale and its associated maximum potential intensity (MPI) ...... 105

4.26 The track of typhoon Dale ...... 105

XV 4.27 The observed intensities of typhoon Orson and its associated maximum potential intensity (MPI) ...... 106

4.28 The track of typhoon Orson ...... 106

4.29 The observed intensities of typhoon Hunt and its associated maximum potential intensity (MPI) ...... 107

4.30 The track of typhoon Hunt ...... 107

4.31 The observed intensities of typhoon Keith and its associated maximum potential intensity (MPI) ...... 108

4.32 The track of typhoon Keith ...... 108

4.33 The tracks of tropical cyclones for westem North Pacific Ocean of 1996 ...... 126

4.34 The tracks of tropical cyclones for westem North Pacific Ocean of 1997 ...... 126

4.35 The tracks of tropical cyclones for westem North Pacific Ocean of 1998 ...... 127

4.36 The distribution of sea surface temperature in the North Pacific Ocean on June and July of 1996 ...... 128

4.37 The distribution of sea surface temperature in the North Pacific Ocean on August and September of 1996 ...... 129

4.38 The distribution of sea surface temperature in the North Pacific Ocean on June and July of 1997 ...... 130

4.39 The distribution of sea surface temperature in the North Pacific Ocean on August and September of 1997 ...... 131

4.40 The distribution of sea surface temperature in the North Pacific Ocean on June and July of 1998 ...... 132

4.41 The distribution of sea surface temperature in the North Pacific Ocean on August and September of 1998 ...... 133

4.42 The low-level circulation during the summer in tropics of the westem North Pacific: (a) The long-term average, and (b) a schematic example of the low-level circulation associated with a reverse-oriented monsoon trough. Bold zig-zag lines indicate ridge axes, and bold dashed line indicates the axis of the monsoon trough (from Lander, 1996) ...... 134 xvi CH APTER 1

INTRODUCTION

A typhoon is a warm-core tropical cyclone in which the maximum sustained surface wind speed (1-min mean) is 64 knots (33 m s ' )or more (OFCM, 1997). In westem North Pacific

Ocean, the term typhoon is used to describe this kind of violent tropical storm. The intensity of typhoon is defined as the maximum sustained surface wind. Strongest typhoons have intensities which exceed 160 knots (81.6 m s ') and produce serious destruction. An understanding of what causes the intensity and intensity changes of typhoons is very' important in forecasting the activity of typhoons. Some meteorological factors that influence the intensity have been studied for many years. Sea surface temperature (SST) is one of the important variables related to the typhoon intensity and its variations.

The SST is a significant factor which influences the formation and intensification of tropical cyclones (Palmén. 1948; Miller, 1958). Although SST alone is not a sufficient predictor of tropical cyclone intensity, Evans (1993), Miller (1958) and Merrill (1987) concluded that SST can provided an upper bound on the maximum potential intensity of tropical cyclones. The empirical relationship between climatological SST and the maximum intensity of tropical cyclones for North Atlantic and Eastern North Pacific Ocean has been developed by

DeMaria and Kaplan ( 1994a) and Whitney and Hobgood (1997) respectively. The purpose of this study is to establish a similar relationship for westem North Pacific Ocean. Once the empirical maximum potential intensity (MPI) function is derived, it can be compared with the actual typhoon intensities to investigate how close the intensity of a typhoon is to the

MPI.

The derived MPI can be used as a measure of intensification potential (POT). POT is the magnitude of the difference between the maximum potential intensity and the current intensity of a typhoon. It is believed that POT has an effect on typhoon intensity and intensity change. Some other factors, such as vertical shear of the horizontal wind (SHEAR), time tendency of the vertical shear (DSHEAR). relative and planetar}' angular momentum flux convergence (REFC and PEFC), relative angular momentum (RAM), are also included in this study to relate the intensity changes of typhoon.

In previous studies, these synoptic factors were used as predictors in a statistical model to predict the intensity of tropical cyclones (DeMaria and Kaplan, 1994a; Petty. 1997). In this study, these variables are not used to establish a model, but to find out which variable has a significant influence on typhoon intensity during El Nino and Southern Oscillation

(ENSO) and non-ENSO events. An important interaction between atmosphere and ocean.

ENSO, is considered to affect the intensity changes of typhoons. During the ENSO event, the frequency and intensity of hurricanes in the Atlantic Ocean were reduced by the unfavorable environment attributed to ENSO (Gray, 1984). Although the effects of ENSO are different in westem North Pacific Ocean, examination of significantly synoptic variables and intensity changes is still useful in understanding the nature of the intensification of a typhoon.

Chapter 2 introduces the westem North Pacific typhoons, briefly discusses ENSO and presents the relationship between these factors and intensity changes. Chapter 3 presents the data and methodology used in this study. The results of the statistical analyses are presented in chapter 4. The summary and conclusions from this research are presented in chapter 5. CHAPTER 2

LITERATURE REVIEW

2.1 Climatology of the North Pacific Basin

Over equatorial waters, the air is warm and rises upward. The rising air reaches the tropopause and moves laterally toward the poles. The Coriolis force deflects the poleward moving air toward the right hand side in the Northern Hemisphere and forms the westerly winds at the upper level near 30° latitudes. As the p»oleward moving air approaches the middle latitudes, it begins to cool and converges. The convergence of air aloft produces high pressure systems that are called subtropical highs. Then the air descends to the surface and moves back toward the equator to complete a thermally direct circulation called the Hadley cell in the meridional direction (Ahrens. 1991).

The air moving back to the equator is deflected by the Coriolis force. It causes the northeast winds called trade winds in the Northern Hemisphere. The northeast trade winds converge with the southeast trade winds along a boundary near the equator that is called the intertropical convergence zone (ITCZ). Figures 2.1 and 2.2 present the mean surface level streamline analyses over the Pacific Ocean for January and July, respectively. The averaged

position of ITCZ is located near 5°N over the North Pacific in January and it shifts toward

the north in July. Figure 2.3 also shows the Equatorial Trough and ITCZ moving seasonally

away from the equator (Barry and Chorley, 1987). The position of the ITCZ is favorable for

the genesis of tropical storms and typhoons. The semi-permanent pressure system of the

Pacific high that is located over the central Pacific in summer also has a great influence on the direction of movement of typhoons (cf. Fig. 2.2).

The seasonal cycle of surface winds in the tropical Pacific is presented in Figure 2.4 and

2.5. The northeast trade winds extend from eastern to westem North Pacific and encounter the northeast flow of the Asian Winter Monsoon in February. The maximum wind speeds are about 7-8 m s*^ (Rasmusson and Carpenter, 1982). The ITCZ is associated with the minimum wind speed in the eastern Pacific. In August, the ITCZ and the northeast trade winds move a few degrees northward to 10°N. The northeast trade winds extend westward to west of 160°E and combine with the Asian Summer Monsoon circulation (cf. Fig. 2.5).

The sea surface temperature (SST) of the equatorial Pacific Ocean is higher in the west and lower in the east. Figure 2.6 (top) shows the distribution of sea surface temperature plotted with respect to longitude and time. The annual and inter-annual temperature variations are small west of the date line where the warmest SST is situated(Cane, 1986).

The westem tropical Pacific has the largest warm water pool in the world ocean. This pattem occurs despite the northeast trade winds driving the colder ocean current from the eastern

Pacific toward the westem Pacific. The cooler current is heated under the strong tropical sun JANUARY WINDOW

I20E I30E I40E I50E I60E I70E I80E I70W 160* 150* 140* 130* 120* 110* 100* 90* 80* 70*

Figure 2.1 ; Mean surface level streamline analyses over the Pacific for January (from Sandler, 1975). 40N

: 30N

20N

205

305 I20E I30E I40E I50E I60E I70E I6GE I70W I60W I50W I40W I30W I20W HOW lOOW 90W SOW 70W

Figure 2.2: Mean surface level streamline analyses over the Pacific for July (from Sandler, 1975). IflO'w 90' 90' \ 30 '

AUC AUG

FEB

\b‘

- ; 30 * 30

Figure. 2.3; The position of the Equatorial Trough (Intertropical Convergence Zone or Intertropieal Front in some sectors) in February and August (after Saha 1973, Rich! 1954 and Yoshino 1969) (from Barry and Chorlcy 1987). wot ê9i

01 • I z • 01

• 01

• Of irm Trr tm

K—:T

Figure 2.4: Mean surface wind field and velocity divergence for February. Units of isotachs are m s'^ ; units of divergence 10'^ s'* (solid lines positive, dashed lines negative) (from Rasmussen and Carpenter 1982). I ##*! tO(

0> 01

«•I f ■•I

not im

*02

«0(

3^ 1

Figure 2.5; Mean surface wind field and velocity divergence for August. Units as in Fig. 2.4. (from Ra.snui.s.son and Carpenter l ‘>S2) equatorial climatqlogical sst JUL APR JAN OCT JUL APR

JAN OCT JUL COMPOSITE EL NINO SST ANOMALY JUL ( + 1) T APR ( + 1) JAN (•*-! )- OCT ( 0) JUL ( 0) APR ( 0) JAN ( O) OCT(-U JUL (- I) 1981 - 1983 SST ANOMALY JUL (83) APR (83) JAN (83) OCT (82) JUL (82) A P R (82)

JAN (82)' OCT (8 1) JUL (81 I40E 180 140 W 100 W

Figure 2.6: 'l imc-longiludc scellons ofsea-surlaee leniperniure (SST). Tlie scellons tbilow llie equaior lo 95°W and ihen follow the cilmaiologleai cold axis to Its Intersection with South American coast at 85=S. (top) Mean climatology, (middle) Composite El Nino anomalies. The El Nino year Is year 0. (bottom) Anomalies from 1981 to 1983. Note the larger contour Interval (Ifom Cane 1986). and warms by the time it reaches western Pacific (Cane, 1986).

The relatively cold water of surface flow in the equatorial eastern Pacific south of the equator is from the Peru (Humbolt) Current, which flows along the coast of south

America. Another source for the cold water in this region is coastal and equatorial upwelling

(Cane. 1986). The wind is southerly along the south American coast and the Coriolis force deflects the surface water to the left (Southern Hemisphere) at right angles to the wind.

So the surface waters are driven away from the coast and replaced by the colder waters underneath. The rising cold water is called upwelling (Cane, 1986). The area of cold surface water extending from eastern to central Pacific is called the cold tongue.

Tlie annual variations of the cold tongue in the eastern equatorial Pacific begins in the late autumn. The Sun is overhead in the Northern Hemisphere in July and moves southward to

Southern Hemisphere in January. The intertropieal convergence zone moves equatorward with the moving Sun. Thus, during the latter part of the year the weakening of southeast trade winds results in the decreasing of coastal and equatorial upwelling and reduces the deeper layer of cold water into the surface layer. Since the sources of colder water diminish, the surface waters become warmer by the heating of Sun.

The variation of sea surface temperature is very important in this study due to the interaction between the ocean and atmosphere. The climatology of North Pacific is influenced by the distribution of sea surface temperature very much. In the next section, an important phenomenon, El Nino and Southern Oscillation, that is associated with the interaction of air and sea is introduced.

1 2 2.2 El Nino and the Southern Oscillation

El Nino is an anomalous ocean warming which occurs along the coast of Peru and

Ecuador and extends to the central tropical Pacific (Gill, 1982). Originally it was thought to be a local and short-term phenomenon. The cool Peru Current flows northward along the western coast of South America. Above the current, the southerly winds combine with the

Coriolis effect to transport coast surface water away from the coast (Enfield, 1989).

Upwelling promoted by the winds keeps the surface water cold. Around the end of year, a warm current flows southward to replace the cold surface water. Because this condition often appears immediately after Christmas, local Peruvians called it El Nino (Spanish for boy child), referring to the Child Jesus (Ahrens, 1991).

In most years, the warming continues only for a couple of weeks then the oceanic pattern returns to normal conditions. If El Nino lasts for several months or longer and the anomalous warming extends from coast of Peru and Ecuador to the central Pacific, this extremely warm period is call a major El Nino event (Ahrens, 1991). Figure 2.7 shows the distribution of sea surface temperature anomalies during the average major El Nino events.

The varying intervals of El Nino events are 2 to 10 years (Enfield, 1989). Quinn et al.

(1978) classified El Nino as very strong (VS), strong (S), moderate (M), and weak (W) according to the intensity and duration of environmental anomalies. The average interval for

El Nino events is 3 - 4 years. The strong events appeared at intervals above 6 - 7 years. The very strong events occurred at intervals no less than 20 years.

13 b AH|uii«0(tobcr

too E 1:0 140 160 E 110 160 W 140 1:0 too 10 w

Fig. 2.7: Sea-surface temperature anomalies (in °C) during a typical ENSO event obtained by averaging data for the events between 1950 and 1973. a, March, April and May after the onset; b. the following August, September and October; c, the following December, January and February; d. May. June and July, more than a year after the onset (from Philander 1983).

14 The influence of El Nino is not only on the tropical Pacific Ocean, but also on the global scale by its atmospheric counterpart, the Southern Oscillation (SO). Normally, the pressure distribution over the tropical Paciflc Ocean is high pressure with descending air and dry conditions located in the region of eastern Pacific, and low pressure accompanied by rising air and precipitation centered over Indonesia. The trade winds blow westward fi-om eastern

Pacific to western Pacific, ascend in the western Pacific, then return at upper tropospheric levels and descend in the eastern Pacific, to complete a zonal cell named Walker Circulation

(Bjerknes, 1969).

This zonal surface pressure distribution in the equatorial Pacific (high in the east and low in the west) is not permanent. Every few years, air pressure rises in the western Pacific and falls in the eastern Pacific. The direction of the pressure gradient reverses. The easterly trade winds are weakened and replaced by westerly winds. The reversal of atmospheric pressure at opposite ends of the Pacific Ocean which can last 1 - 2 years is called Southern Oscillation

(Ahrens. 1991). Walker (1924) was the first one who used the term "Southern Oscillation" to describe the oscillation of surface pressure departure from the long-term average over the both ends of Pacific. The Southern Oscillation Index (SOI) is defined as the difference between the sea surface pressure at Tahiti (17.5°S, 149.6°W) in the southeast Pacific and

Darwin (12.4°S, 130.9°E) in the northern Australia, whose annual average pressures are correlated at -0.79 (Trenberth, 1984). The SOI is used to express the strength and phase of

Southern Oscillation. A positive SOI means that pressure is higher than average in the southeast Pacific and lower than average in the north of Australia (Newell et al., 1982).

15 The connection between El Nifio and Southern Oscillation and their influence on the large

scale climate has been studied by oceanographers and meteorologists for many years. The

pioneering work began with a study of the failure of the Indian monsoons since 1904 by Sir

Gilbert Walker, the director general of observatories in India. Walker tried to find the

relationship between the monsoon variability and global fluctuations in climate in order to

develop techniques for forecasting monsoons. He was aware of the sea-level pressure swings

from South America to the India-Australia region and named it the "Southern Oscillation".

Walker's studies did not connect the SO and El Nino. He correlated the precipitation in the

central equatorial Pacific and in India, and temperature in southeastern Africa, southeastern

U. S. and southwestern Canada with the Southern Oscillation (Walker, 1924, Walker and

Bliss. 1932). The results were not satisfying owing to the short duration of available records

(Cane, 1986).

The relationship between Southern Oscillation and El Nino was not noticed until the late

1960's. Bjerknes (1966) found that the swings of long term SO could be explained by an

interaction between the ocean and the atmosphere. First, the anomalous zonal and meridional

SST gradients over broad areas were created by an unusually warm equatorial ocean along the zonal direction. Those SST gradients increased the thermal energy going into the

meridional circulation of the atmospheric "Hadley cells", which in turn increased the

poleward flux of angular momentum to the Jet streams on winter hemisphere, and finally enhanced the mid-latitude westerlies. The results of these processes changed weather patterns downstream. The anomalous SST from El Nifio warming and its influences on the climate of regions is a form of "teleconnections" (Enfield, 1989).

16 About the same time, Berlage (1966) linked the SO and El Nino by relating the variation

of inter-annual surface pressure at Djakarta and SST at Puerto Chicama on the Pervian coast.

Figure 2.8 shows the close inverse relationship between these two events and Figure 2.9

indicates that SOI and SST also vary out of phase on inter-annual time scales (Latif et al.,

1993).

Doberitz (1968) found a positive correlation between precipitation and SST in the dry

areas of the equatorial Pacific. The first noticeable synthesis of relationship between the

inter-annual SST fluctuation in the eastern equatorial Pacific and SO was provided by

Bjerknes (1969, 1972). He used 17 years of precipitation data at Canton island (2°48'S,

171°43'W) and the circulation patterns to establish the link between SST variations, the SO

related shift of zonal circulation (the Walker circulation) and the large scale rainfall over the

equatorial Pacific. Bjerknes' work transferred the studies from statistical analysis to

physically oriented diagnostic studies and initiated a more rapid development of a theory for

the modeling ENSO (Rasmusson and Carpenter, 1982).

A significant new development of SO/El Nino theory was provided by Wyrtki (1975,

1979) whose studies switched attention from SST to the zonal slope of sea level in the

tropical Pacific. That is, the fluctuation in SST during ENSO has a relationship to the ocean

dynamics and not to the variation of sea surface heat flux (Cane, 1986). Wyrtki proposed that a long period of strong southeast trade winds (or high SOI) should precede the El Nifio in the

central and eastern Pacific (Fig. 2.10, from Enfield, 1989). The strong trade winds move the

water westward and raise the sea level in the western Pacific. After the trade winds weaken, the unbalanced eastward pressure gradient in the upper ocean drives the water flow back to

17 0

00

—h 2

1935 1980

Figure 2,8; 1 he solid line gives sca-surt’acc temperature anomalies at Puerto Chicama, Peru, an index of El Nino. The dashed lines is the difference in sea-level pressure between Darwin, Australia, and Tahiti, an index of Southern Oscillation. Both are nonnali/ed by their long-lemi standard deviations. Major 01 Nino events are shaded (from Rasmusson 1985). OBSERVED a) C/Î oi < z 2 o

D 0 LU N

2 z cr — — SOI o SST

1957 1962 1967 1972 1977 1982 TIME (year]

SIMULATED b ) LO 3 UJ _J 2 < Z o 1

0 Q LU 1 N _J < 2 z 0: 3 SO o z - 4 0 5 10 15 20 2 5 Tl ME (year)

Figure 2.9: (a) Time series of the Southern Oscillation index and of anomalous SST in the eastern Pacific (Puerto Chicama, Peru) (redrawn after Ocean us 1984). (b) Same as in (a) but derived from the extended-range integration with the coupled ocean-atniosphere GCM (Latil et al 1992). The model SOI is defined as the anomalous pressure difference between an averaee over the eastern Pacific and the Indian Ocean. SST anomalies have been averaged o\.er cite Nino-3 region, which is an average over the eastern equatorial Pacific. .\11 time \crie> are normalized b\ their lone-term standard de\ iation (tV >m l.atil'et aI.l'-^'3)

19 10

Ro Chicama Anomalies 5

CD 0

5

Tahiti - Darwin Index

1840 1950 1960 1970 I960 1990 Years

I ig 2.KJ: l ime scries of SST anomalies ai Puerto Chicama, Peru (smoollied with a 3-month running mean), and the Souliicrn Osciliaiion Index (smoothed with an 11-month recursive the east in tile form of an internal equatorial Kelvin wave filter). SST anomalies above one siandaid deviation are shaded in black. Small (lags attached to the SOI curve single the beginning (staff) and duration (Hag) ol the SST shading for each 121 Nino event. Solid (hatched) flags refer to S an VS (W and .MJ events from the compilation of'Quinn et al. (1987) (from Enfield 1989).

20 the east in the form of internal equatorial Kelvin waves and the thermocline structure is

depressed in the eastern equatorial Pacific. The reason for the anomalously warm SSTs in

the eastern Pacific is due to the depression of thermocline and advection of warmer water

from the warm pool of the western Pacific. Wyrtki's collection and interpretation of sea level

and thermocline depth data in the tropical Pacific supported his theory. The theory also

proved to be supported by the results from numerical models in the 1980's. Wyrtki's work

provided a basis of understanding of the oceanography of El Nino (Cane, 1986).

Suarez and Schopf (1988) proposed a hypothesis called a "delayed action oscillator" to

explain the possible mechanisms causing the irregular oscillatory characteristic of the ENSO

cycle. The basic idea of a delayed action oscillator was that the existence of the coupled

ocean-atmosphere system's "memory" in the ocean’s thermocline state resulted in the

transition from opposite phases of ENSO. Over the western Pacific, an upwelling Kelvin

wave translates eastward with easterly wind anomalies along the equator and contributes to

the reduction of sea surface temperature in the shallow thermocline area of eastern Pacific.

As the Kelvin waves propagate eastward, downwelling Rossby waves begin to develop and

propagate westward in the eastern Pacific. When the Rossby waves arrive at the boundary

of western Pacific, the warm SSTs are not influenced by the Rossby waves due to the deep

thermocline in the warm pool of western Pacific. The Rossby waves are reflected back to the eastern boundary of Pacific Ocean. This time the SST can be changed by the Rossby waves

in the shallow thermocline area of eastern Pacific to initiate a warm phase of ENSO. The

repetition of these events with opposite signs can account for the oscillation of ENSO (Latif

et al., 1998).

2 1 The theory of oscillatory modes of ENSO was supported by Battisti and Sarachik (1995).

They provided the observational evidence and indicated that ENSO can be predicted by considering it as a low fiequency, basin-wide event. However, Latif et al. (1998) pointed out three hypothesized factors, random noise, nonlinear interactions with the annual cycle, and decadal variations of the mean state restrict the predictability of ENSO events. These factors influence the sensitivities of the different types of models and affect their ability to predict the occurrence of ENSO.

Although the extent of ENSO is basin-wide, the influence on weather and climate is global. In this study, an attempt is made to relate the effect of ENSO to the intensity changes of typhoons in the western North Pacific area.

2.3 Typhoons

A t) phoon is a warm-core tropical cyclone in which the maximum sustained surface wind speed is 74 mi/hr (33 m s'^) or more (OFCM, 1997). This kind of violent storm has different names in different regions. In the northern Atlantic and eastern North Pacific, it is called hurricane. The term typhoon is used in the western North Pacific. Since the geographical region for this study is the western pacific, the term typhoon will be used throughout this document.

Certain conditions are necessary for the formation of typhoons. First, the SST must be greater than 26°C (79°F) over a large area to provide enough energy for typhoon. This

2 2 condition is present in summer and autumn over the tropical and subtropical North Pacific and North Atlantic oceans. It is the reason for the occurrence of typhoons from June to

November. Figure 2.11 indicates the distribution of tropical cyclones genesis associated with the higher sea surface temperature (Barry and Chorley, 1987).

For the unorganized thunderstorms of a tropical disturbance to develop into a typhoon, other conditions must be present. Some process must organize the thunderstorms, and vorticity must be generated to initiate rotation. After the thunderstorms are organized, a large mass of water vapor can be transported to higher levels in the atmosphere. The release of latent heat energy during condensation warms the air as it is converted to internal energy in the middle and upper troposphere. This generates the warm core necessary for the development of a tropical cyclone.

The warm core in the upper troposphere generates divergence. The removal of mass at the upper levels reduces the pressure near the Earth surface and air begins to converge in the lower levels. Tins convergence of air spins counterclockwise in the Northern Hemisphere.

Because the Coriolis force is equal to zero at the Equator, typhoons usually form beyond at least 5° to 10°. Otherwise this type of rotation will not develop. The 5° - 20° latitude of western North Pacific area is favorable for the development of typhoons. Weak vertical wind shear is also important for the typhoon's development. Strong vertical wind shears disturb the organized convection pattern and vortex. The energy that is necessary to maintain the warm core and for the intensification of typhoon is also dispersed.

23 IvJ

[ _____ 2 ] SEA SURFACE TEMPERATURE > 2 7 ’c IN WARMEST MONTH

HURRICANE tracks

to FREQUENCY OF HURRICANE GENESIS (20-YEAR PEfliOOl

Fig. 2.11. Frequency of hurricane genesis (numbered isopleths) for a 20-year period. The principal hurricane tracks and the areas of sea surface having water temperatures greater than 27°C in the warmest month are also shown {after Palmén 1948 a n d Cray 1979). (from Barry and Chorley 1987). CIRRUS SHIELD

$ L INNER _ . OUTER OUTER w MOAT > wjRAINBANDS RAINBANDS CIRCULATION 100

200 3 0 0 4 0 0 5 0 0

6 0 0 7 0 0

. 8 0 0 9 0 0 sfc O 2 3 4 5 6 7 8 RADIUS (degrees latitude)

Figure 2.12: Schematic view of a typical tropical cyclone. Arrows denote the mean circulation (from Frank 1977).

25 A vertical structure of a mature typhoon is shown in Figure 2.12. The innermost region of the typhoon is the eye. Adiabatic warming of descending air in the warm core results in the high temperature and broken clouds with light winds. Typically the diameter of eye is from 30 - 50 km (Barry and Chorley, 1987). Adjacent to the eye, the region o f strongest cyclonic wind, intense convection and heaviest precipitation is in the eye wall. The eye wall extends vertically to the height of 15 km and the horizontal width is about 10-20 km (Shea and Gray, 1973). Beyond the eyewall, the cyclonic winds and vertical convection decrease witli radius gradually. A relatively clear or "moat" area with weak convection occurs outside from these strong convective areas (Frank, 1977).

Figure 2.13 shows the plane view of the streamlines of the typical typhoon. In the

Northern Hemisphere, the cyclonic circulation spins counterclockwise in lower level. The convergence brings moist air into the typhoon. The convergence generates rising motion, the moist air flows upward and releases large amount of latent heat as the energy for intensification. The anticyclonic circulation with divergence aloft produces outflow to enhance the low-level inflow and maintain the typhoon.

Figure 2.14 presents the frequency distribution of typhoons in western North Pacific, and hurricanes in eastern North Pacific and in North Atlantic from 1966 - 1998. Since 1966 when satellite observations became available, the numbers of typhoons have been estimated more accurately. It is apparent that the western North Pacific is the most active tropical cyclones region, but the eastern North Pacific contains a small area which produces the largest number of tropical cyclones per unit area (Elsberry et al., 1987). A negative correlation between the annual frequency in eastern North Pacific and North Atlantic is also foimd. The years of

26 1969 and 1995 were the "prolific" years in Atlantic but "meager" years in other basins.

Although they may have contributed to the global pattern of tropical cyclones, the El

Nino/Southem Oscillation (ENSO) and the quasi-biennial oscillation (QBO) are insufficient

to explain the unusual distribution of tropical cyclones during 1995 (Lander and Guard,

1998).

7 ? 9 T

TROPOPAUSE

X «Cu .

X 300 100 O 100 300 Y km s u r f a c e streamlines 200mo streamlines

Fig. 2.13: A model of the areal (above) and vertical (below) structure of a hurricane. Cloud is stippled and areas of precipitation are shown in the vertical section. The streamlines symbols refer to the upper diagram (from Barry and Chorley 1987).

27 Annual Tropical Cyclone Frequency

3- -^W . Pacific Typhoon S 3 E. Pacific T. Cyclone O’ 0> — Atlantic Hurricane

V- N- Year

Figure 2.14: Annual frequency of tropical cyclones for llte eastern, western North Pacific and North Atlantic Ocean. The number includes tropical storms and hurricanes and typhoons.

28 2.4 Sea Surface Temperature

The release of latent heat during condensation is the major source of energy for the development and intensification of tropical cyclones (Miller, 1958). This energy is primarily provided by the ocean through evaporation of water from the sea surface. Since the interaction between ocean and tropical cyclones is so important, the sea surface temperature

(SST) is often chosen as the most representative element of upper ocean layer in studies of these features.

Vertical instability is one of the important factors for the formation of hurricanes.

Palmén's (1948) study revealed that vertical instability in September was greater than it was in February. Ocean waters are also warmer in September than in February. Palmén found that hurricanes developed in regions of SSTs at 26°C or higher. The study also compared vertical instabilities and SSTs in the Atlantic ocean. Figure 2.15 shows that hurricanes form over the oceans where the SST is higher than 26°C (Palmén. 1948).

Fisher (1958) studied eleven Atlantic hurricanes and found a strong positive relationship between intensification of hurricanes and increasing magnitudes of SSTs. The study showed that hurricanes intensify over warmer waters and weaken after they move to regions of relatively colder waters. Perlroth's (1962) case study of hurricane Esther (1961 ) agreed with

Fisher's point of view. Perlroth used Esther’s central pressures as a measure of the hurricane's intensities. The central pressures were related to the SSTs along the track of hurricane Esther.

Figure 2.16 shows that hurricane Esther's central pressure fell (hurricane intensification) when SSTs increased and rose (hurricane weakens) when SSTs decreased. However, not all

29 to 22______no 'Y*_____ no go

Figure 2.15: Typical hurricane paths originating over regions where the SST is generally greater than 26°C during the warmest season (Palmén, 1948).

r I 1 1 1 / / ! 1 / 1 ^ , 1 1 1 d 4 I'm. 1J 1 l\ f / . i 4 I ; ... \ ^ " r t T~‘ I \ 1 t V !-! 1* , 1 1 \ \ L \ > N • J \ n i \ N \ V \ V \ f ^ 1 \ f \ l J V

! 1

Figure 2.16: Change in central pressure versus sea surface temperature for Hurricane Esther (Perlroth. 1962).

30 hurricane's intensities vary exactly with changing SSTs. Perlroth (1962) emphasized that

by assuming the hurricane was not interacting with surrounding systems, such as an extra tropical trough or a front, and was keeping its tropical characteristics, the obvious relationship between intensity and SST could be determined.

Miller (1958) tried to establish a relationship between minimum sea surface pressure which is represented as hurricane's maximum intensity and the following four variables: sea surface temperature (SST), relatively humidity of surface air, the lapse rate in the vicinity of the hurricane and upper level constant pressure distribution. To obtain the minimum sea surface pressure, he used the equation of state and assumed hydrostatic equilibrium to describe the process of rising air moist adiabatically from sea surface to the top of troposphere and then subsiding air dry adiabatically back to the sea level at the center of hurricane. Figure 2.17 shows Miller's results. The intensity of a hurricane is related to SST. but Miller also concluded that this relationship occurred under ideal states. Intensity is not only influenced by SST, but also by the circulation features in the storm's environment.

Malkus and Riehl (1960) used an approach that related changes in air parcels in the tropical cyclone to the balance of available thermodynamic energy and surface momentum losses. Their work assumed surface pressure in the tropical cyclone was the result of adjustment that maintained the hydrostatic balance (Haurwitz, 1935). In the hydrostatic balance a net warming of a column of atmosphere produces the decreasing of the surface pressure (Hirschberg and Fritsch, 1993). However, this warming from the release of latent heat in the convective layer of tropical cyclone can only reduce the surface pressure by

31 980

m S > 9 4 0 -

< P 900 Z LU H* O QL

860 26 28 30 32

SEA TEMPERATURE (©C)

Figure 2.17: Miller's (1958) relationship between sea surface temperature and maximum potential intensity of tropical cyclones (from Elsberry et al., 1987) 20 - 40 mb (Riehl, 1948, 1954). It is not sufficient enough to decrease the surface pressure to reach the pressure observed in the intense tropical cyclone. Additional energy is required to make the surface pressure fall much below 1000 mb. Malkus and Riehl (1960) concluded that near the convective layer in a tropical cyclone the vertical redistribution of moist entropy, as expressed by equivalent potential temperature, could reduce significantly the surface pressure. Under the assumption of 100 mb tropopause height, their relationship between the surface pressure (Pg) change and the equivalent potential temperature (Og) was

5Pg (mb) = c00e(°K)

C = -2.5.

Merrill (1987, 1988a,b) used Atlantic hurricane cases from a 12 year period to compare monthly averaged SSTs with tropical cyclone intensity, represented by maximum sustained winds. He found that the maximum potential intensity increased where the SST increased, but that a tropical cyclone may have different maximum sustained wind speeds over the same

SST (Fig. 2.18). Other environmental factors such as wind shear also affect the maximum sustained winds in tropical cyclones. Thus, there is no single linear relationship between the

SST and actual tropical cyclone intensity. Merrill (1987) concluded that SST was better treated as a capping function on the tropical cyclone intensity rather than as a direct predictor. Only a few hurricanes reached their maximum intensity due to the influence of other atmospheric processes.

33 MSHIR)/5ST SCATTER. 1974-1985 to r t o I 70 w lu t o to t o

60 - oc SO - # 3 tn ê • 20 • # # • • 10 • e

10 \ . 1 1 I I I I I I I I I 10 12 l« 1# It 20 22 2*1 26 26 10 M SST. DEC. C

Figure 2.18: Scalier diagram of maximum susiained wind speed (MSW) corrected for storm molion versus climalologicai SST I'or a 12-\ear sample ol'Ailanlic tropical cyclones. The curve drawn against the data represents the SS 1 capping I'unction based on the 99“' percentile (from Merrill. 1987).

34 The transfer of latent heat from the ocean to the atmosphere is thought to be very important for the development and maintenance of tropical cyclones. Emanuel (1986) tried to show that the maintenance of tropical cyclones in an intense steady state does not need ambient conditional instability. He applied a simple Carnot heat engine system in which the extraction of latent and sensible heat from the ocean occurred at a temperature Tg and the energy was released in the outflow at a temperature therefore the thermodynamic efficiency of the system is

T‘ B - T ‘ out Ts

Multiplication of the efficiency by the oceanic heat source produces the energy available to drive the circulation. The energy is used to overcome frictional dissipation in the boundary layer and drive the outflow to large radii. Intense tropical cyclones occur by increasing the thermodynamic efficiency when the sea surface temperature is higher or when the outflow stratospheric temperature is much lower than at present. Emanuel (1986) also mentioned that when the sea surface temperature is below 26°C, the depth of the conditionally neutral or unstable layer is too shallow to attain a reasonable thermodynamic efficiency. Then the development of tropical cyclones is stopped.

35 Emanuel (1986) expressed the minimum attainable surface pressure in the center of a

tropical cyclone as a function of surface air temperature and outflow temperature. This

relationship is presented in Figure 2.19. The minimum central surface pressure is very

sensitive to surface air temperature, which, in tern, is related to the underlying sea surface

temperature. Usually the surface air temperature is 1°C to 2°C lower than the SST in tropical

cyclones (Riehl, 1954).

The intensity of tropical cyclones at the mature stage depends even more directly on sea

surface temperature. In order to examine the attainable minimum central pressure of tropical

cyclones under normal oceanic and atmospheric conditions, Emanuel (1986) used the

averaged surface and standard level data for September 1979 (from the National

Oceanographic and Atmospheric Administration's Environmental Data and Information

Service) and averaged September SSTs (from Reynolds, 1982). Figure 2.20 shows the results

of Emanuel's calculations. The distribution of minimum attainable surface pressure in the

center of tropical cyclones coincides with observations of tropical cyclones in the month of

September in the regions of the western North Pacific, the East Pacific off Central Mexico,

the Caribbean and Gulf of Mexico, and the Bay of Bengal. Emanuel's work emphasizes that ambient conditional instability plays a secondary role in supporting the development of tropical cyclones while sea surface fluxes may play a more important role.

Emanuel (1988) derived an exact equation for the computation of the maximum possible

pressure drop in steady-state tropical cyclones by applying the Carnot heat engine principle.

This equation included the effects of gaseous and condensed water substance on density and

36 32 AS mo 30

9 2 0 9 3 0 2 8 940 990 (• 9 60

. 26 9 7 0 980

2 4 9 9 0

22 lO O O

-10 -20 0 -5 0 -60 -70-3 •80

Figure 2.19: Maximum attainable central surface pressure (mb) as a function of surface air temperature (Tg) and weighted mean outflow temperature (T^) assuming an ambient surface pressure of 1015 mb, ambient surface relative humidity of 80%, f evaluated at 20 degree latitude, and ro = 500 km (from Emanuel, 1986).

37 lOCw 8C 6 0 4Ç 2QW 0 ______20 E 40 SC 90 lOOC

— SO &

lOOE 120 140 I60E ISO I SOW 140 120 ICC BO SOW

1000

Figure 2.20: Minimum attainable surface central pressure (mb) in September (a) for Atlantic and Indian Ocean and (b) for Pacific Ocean (from Emanuel, 1986).

38 fully reversible thermodynamics. Under some critical conditions, there was no solution for

the minimum central pressure from this equation. Emanuel's work provided a theory about

an upper bound on the intensity of tropical cyclones related to sea surface temperature, the

relative humidity in the boundary layer, and the outflow temperature of the tropical cyclones.

The predicted intensities from the theory were compared to the actual intensities of tropical

cyclones under the same conditions. Emanuel found that most tropical cyclones did not attain

theoretical maximum intensity. Only the most intense tropical cyclones were close to the

upper bound.

Evans' (1993) study of tropical cyclones in five ocean basins (North Atlantic, western

North Pacific, South Pacific-Australian region, north Indian and southwest Indian oceans)

also supported Merrill's (1988b) results and indicated the relative importance of SST in the

process of tropical cyclone development. The data from a 20-year period (1967-1986) were

used to relate the tropical cyclone intensity and SST. The sea surface temperatures were

stratified into 1°C groups. Evans indicated that the most frequent occurrence of the most

intense tropical cyclones was located over the warmer oceans with 28°C SST or higher.

However, Evans (1993) concluded that SST along is not a sufficient predictor of tropical cyclone intensity. The use of SST can not determine the actual tropical cyclone intensity, but

it can provide an upper bound as the maximum potential intensity. This agreed with Merrill’s

(1988b) earlier findings.

39 DeMaria and Kaplan (1994a) used a 31-year sample (1962-1992) to develop an empirical relationship between climatological SSTs and the maximum intensities of North Atlantic tropical cyclones. The maximum sustained surface wind speed was used to represent the intensity due to the fact that wind data were reported for every 6-hour observation whereas the sea level pressure was not always available. Table 2.1 shows that the SST groups from

14.5°C to 30.5°C were assigned to 16 evenly spaced groups ( 1 ®C intervals) and the intensity for each group was plotted against the midpoint of each group (15.0°C to 30.0°C).

Figure 2.21 shows the maximum tropical cyclone intensity and the 99th, 95th, 90th, and 50th intensity percentiles. Only the 50th percentile varies very little with the SST change, the other percentiles are strongly related to the variation of SSTs.

In order to smooth the curves presented in Figure 2.21 DeMaria and Kaplan (1994a) derived a function to fit the maximum intensity observations. An exponential function was considered to fit the pattern of the maximum intensity and 99th percentile that is presented in Figure 2.22. This empirical function is:

V=A +Be (C(r-To))

where V is the maximum wind (m s"^) which is referred to as the maximum possible intensity (MPI), T is the SST (°C), Tq is a specified reference temperature (30.0°C), and constant A, B and C are 28.2 m s'^, 55.8 m s'^ 0.1813°C'^ respectively. The above empirical function indicates that MPI increases with rising SST.

40 SST Midpoint (°C) Number of Average SST (°C) Average Intensity Observations (m s-I) 15.0 20 15.0 17.4 16.0 25 16.0 17.5 17.0 29 17.1 16.1 18.0 43 18.0 19.2 19.0 48 19.0 20.0 20.0 60 20.0 19.2 21.0 92 21.0 21.0 22.0 112 22.0 21.8 23.0 152 23.0 22.3 24.0 261 24.1 21.7 25.0 476 25.1 23.9 26.0 942 26.1 21.1 27.0 1501 27.1 19.7 28.0 2089 28.0 20.7 29.0 1229 28.9 23.9 30.0 31 29.7 19.4

Table 2.1 : Properties of the SST groups (from DeMaria and Kaplan, 1994a).

Emanuel's (1988) theory points out that the maximum intensity of tropical cyclones is a function of SST, outflow temperature and relative humidity o f the ambient boundary layer.

Emanuel (1987) also argued that the ambient relative humidity is nearly constant over the tropical and subtropical oceans. The outflow temperature is controlled by the tropopause temperature which is strongly related to the SST over the tropical and subtropical oceans

(Reid and Gage 1981). So Emanuel thought that, to a first approximation, the maximum intensity was a function only of SST. According to Emanuel's theory, DeMaria and Kaplan assumed the ambient relative humidity as a constant and fixed the relationship between SST and tropopause temp>erature to determine the maximum intensity as a function of SST.

41 I# 72 2 4 2« 2 8 to to MAXIMUM ts % t o r . sor. to - -to

so

- 4 0

X

1 0 - - 10

I t I t M 22 <4 24 S t 3 0 SEA SURFACE TEMPERATURE (C)

Fig. 2.21 : The maximum storm intensity and the 99*, 95*, 90*, and 50* intensity percentiles for each 1°C SST group. The X coordinate is the midpoint of each SST group and the storm translational speed was subtracted from all intensities (from DeMaria and Kaplan, 1994a).

I t It SS S4 S t to to _ MAXIMUM t o - FUNCTION FIT -to

7 0 - - 7 0

to- -to

- 5 0

2 4 0 - - 4 0

- 3 0

10 - - 1 0

I t I t SO S3 34 St 38 30 SEA SURFACE TEMPERATURE (C)

Fig. 2.22; The observed maximum storm intensity for each 1°C SST group and the least- squares function fit for the 31-year Atlantic sample (from DeMaria and Kaplan, 1994a).

42 DeMaria and Kaplan (1994a) defined the relative intensity as the ratio of observed maximum intensity of a actual tropical cyclone to the empirical maximum possible intensity

(MPI) calculated from the above function determined by SST. After the land cases were removed, only 19% of Atlantic tropical cyclones reached 80% or more of their MPI. 58% of storms attained 50% of their MPI. These results proved that the large-scale SST could not

fully control the intensification of tropical cyclones. Other factors such as vertical wind shear may be more responsible for the intensification in most cases. The SST can provide an upper bound for the maximum intensity of tropical cyclones, but can not be used to predict the real­ time intensity due to other influence of atmospheric-oceanic conditions.

DeMaria and Kaplan (1994b) developed the Statistical Hurricane Intensity Prediction

Scheme (SHIPS) model to predict the intensity change of Atlantic tropical cyclones. The maximum possible intensity (MPI) derived from the empirical function was used in the

SHIPS model. They found that the intensification potential (POT), which is defined as the difference between the MPI and the current storm intensity, is better in predicting the intensity change than the SST alone. The SHIPS model improved the forecast of hurricane intensity change and is considered to be more skillful than the Statistical Hurricane Intensity

Forecast (SHIFOR) model used by the National Hurricane Center.

Whitney and Hobgood (1997) derived an empirical relationship between climatological sea surface temperature and maximum intensity of Eastern North Pacific tropical cyclones from 31-year sample (1963-1993). This relationship, represented by a linear function, is:

EPMPl = A + B(SST)

43 where EPMPI (m s"^) is the Eastern Pacific maximum potential intensity and SST (°C) is the sea surface temperature. The constants A and Bare -79.17262 m s”^ and 5.361814

m s" ^ °C* ^. The comparison of the empirical maximum potential intensity function for the

Eastern North Pacific derived from Whitney and Hobgood (1997) and for Atlantic ocean derived from DeMaria and Kaplan (1994a) is shown in Fig. 2.23. The difference between two curves is less than 5 m s’^ over the SST range from 22°C to 29°C. While 19% of

Atlantic tropical cyclones reached 80% of their MPI, only 11% of Eastern North Pacific storms attained 80% of their MPI. The possible reason for the difference between the two empirical relationship is that poleward recurving Atlantic hurricanes experienced cooler SST

(Whitney and Hobgood, 1997).

Holland (1997) provided a thermodynamic approach for estimating the maximum potential intensity (MPI) of tropical cyclones. In his results, MPI is highly sensitive to the surface relative humidity under the eyewall, to the height of the warm core, and to the transient change of SST. The ocean plays a role in establishing a suitable environment for the development of tropical cyclones in the initial stage, and in supplying the additional energy required for intensification. During the colder months sea surface temperatures are lower than 26°C, and the development of tropical cyclones is not likely. As the increased solar radiation causes SSTs to increase during the spring and summer, transfer of energy from the ocean to the atmosphere causes air to warm in the low level of troposphere and cool near the tropopause, but with little change in mid-levels (Holland, 1997). At that time, the thermodynamic efficiency is increased and MPI will increase rapidly by about 30 hpa °C'^.

44 In summary, the relationship between sea surface temperature (SST) and the intensity of tropical cyclones has been observed and studied in recent years. The SST is a significant factor that influences the formation and intensification of tropical cyclones (Palmén, 1948;

Miller, 1958). Although SST alone is not a sufficient predictor of tropical cyclone intensity

(Evans, 1993), SST can provide an upper bound on the maximum potential intensity of tropical cyclones (Miller, 1958; Merrill, 1987; Emanuel, 1988).

E. Pacific MPI vs Atlantic MPI

90 -I r 90

80 - £. Pacific MPI ■ 80 Atlcntic MPI 70 - - 70

'in 60 ■ 60 I 50- 50

tn c 40 - 40 g (U c 30 - 30 Ç

20 - 20

1 7 1 9 21 23 25 27 29 31 Sec Surface Terp.perc'.ure (deg C)

Figure 2.23 : Comparison between the eastern North Pacific MPI and Atlantic MPI function (from Whitney and Hobgood. 1997). 45 2.5 Vertical Wind Shear

Vertical wind shear is one of the environmental factors that determines the potential

development of tropical cyclones (Gray, 1968, 1975). Tropical cyclones develop when the

vertical wind shear is below some threshold value. The vertical wind shear is often

represented by the difference between 200-mb and 850-mb wind. These levels are chosen,

because the tropical data at upper level (200mb) are available from satellite cloud-drift winds

and jet aircraft reports and lower level (850mb) data are obtained from satellite cloud-drift

winds and surface reports extrapolated upward (Elsberry et al., 1996). Other data sources such as rawindsondes are sparsely distributed over the tropical oceans and not always available to depict the vertical wind conditions during the formation and intensification of tropical cyclones on the tropical oceans.

Gray (1968) used the zonal component of winds at 200 and 850-mb pressure levels for the months of January, April, August and October to analyze the climatological averages of vertical wind shear. Figure 2.24 indicates the high negative correlation between the zonal vertical wind shears and the development o f tropical cyclones for the month of August. The areas of zero vertical shear lie on the western, eastern tropical North Pacific and northwest tropical Atlantic which are the genesis regions of tropical cyclones. Higher values of vertical wind shear will prohibit the intensification of tropical cyclones by removing upper level heat during developing stage and making the formation difficult (Gray, 1968). Zehr (1992) estimated a vertical shear threshold value for the development of the western North Pacific

46 Figure 2.24: Climatological average for August of the zonal vertical wind shear between 200 mb and 850mb Positive valus indicate the zonal wind at 200 mb is stronger from the west or weaker from the east than the zonal wind at 850 mb (from Gray, 1968). tropical cyclones by using real-time analyses from the Australian Bureau of Meteorology.

Zelir concluded that tropical cyclones will not develop when the vertical wind shears exceed the threshold value of 12.5 m s"k

McBride and Zehr (1981) studied the dynamic and thermodynamic structure of tropical weather systems and classified the developing and non-developing cloud clusters on the basis of the zonal and meridional vertical wind shears in the Pacific areas. Figures 2.25 and 2.26 show that the zero zonal and meridional vertical shears are located close to the center of developing systems (Dl, D2 and D3), and a large value of vertical shear is over the center of non-developing system (Nl). These results demonstrate very well the theory of the relationship between the vertical shear and intensification of tropical cyclones. However, there are strong shear lobes on either side of the developing system with opposite sign. This situation is still under investigation. It is possible that the minimum vertical wind shear occurs only in a small region sandwiched between regions of large vertical wind shear over the tropical cyclone (McBride, 1995).

DeMaria et al. (1993) calculated the vertical wind shear between 200 and 850mb from real-time objective analyses on a 1° latitude-longitude grid and obtained a negative correlation with the intensity changes for Atlantic tropical cyclones. Table 2.2 indicates the statistical relationships between some predictors in the SHIPS model and the intensity changes in each 12 hours interval. The normalized regression coefficients for the vertical shear (SHEAR) are negative in all intervals and significant at the 95% level. This indicates that shear has a negative impact on intensity.

48 ••ciric N I

•to

■20

■Ï* a » ■>» I ' 1 »

-a

■» » y f - 1' ; ■ # tt

Figure 2.25; Plan views of zonal shear, Ujoomb “ '^goomb s"*) for the northwest Pacific (from McBride and Zehr, 1981).

49 M C :fiC N I -S

-5

-i -a J> j ' *• I* l> M* > > i»n

Fig. 2.26: Plan views of meridional shear, U 2oomb “ ^ 9 oomb(*^ s'^) for the northwest Pacific (from McBride and Zehr, 1981).

50 12h 24h 36h 48h 60h 72h POT +0.32 +0.46 +0.56 +0.63 +0.68 +0.70 SHEAR -0.20 -0.26 -0.31 -0.36 -0.31 -0.25 DVMX +0.40 +0.28 +0.18 +0.16 +0.18 +0.16 REFC +0.03 +0.08 +0.16 +0.22 +0.19 +0.17 PEFC +0.08 +0.12 +0.12 +0.10 +0.10 +0.10 JDATE -0.04 -0.06 -0.07 -0.09 -0.12 -0.13 LONG +0.14 +0.14 +0.08 +0.03 -0.02 -0.09 DTE +0.12 +0.12 +0.09 +0.05 +0.00 -0.09 RAM +0.11 +0.11 +0.09 +0.05 +0.05 +0.03 DSHEAR -0.01 +0.06 +0.13 +0.07 -0.03 -0.11 r (%) 35.7 39.4 44.4 50.4 52.0 53.6

Table 2.2: Normalized regression coefficients for the combined climatological, persistence, and synoptic predictors. The coefficients that are significant at the 95% level are in bold: r is the percent of the total variance explained by the regression (from DeMaria and Kaplan, 1994b).

Jones (1994) used a three dimensional primitive equation model to study the vortices, which were initially barotropic. She found that vertical shear in the environmental flow resulted in the differential advection of potential vorticity. The differential advection tilted the vortex fi’om vertical. After the vortex tilted, a cyclonic circulation developed between the upper and lower level potential vorticity anomalies, that would oppose the strong influence of the vertical shear. The tilting would change the thermal structure of the vortex to keep the flow in a balanced condition. This change in the thermal pattern reduced the convection of the central vortex, and weakened the storm intensity. This mechanism of the shear-induced tilting of the vortex provides one conceptual firamework to explain why vertical shear has a negative relationship with the intensification of tropical cyclones.

51 Elsberry and Jef&ies (1996) calculated the vertical wind shear between 200 and 850mb from operational and special interactive analyses during the Tropical Cyclone Motion (TCM) field experiment. Their results show that 200 mb winds associated with low-latitude circulations, that originally seem to impinge on tropical cyclones, are actually deflected around the convective outflow (Elsberry et al., 1996). Based on their analyses, they assumed that these systems have only small vertical wind shears at lower levels and the vertical shear produced by stronger winds at higher levels are concentrated in a shallow layer below the tropopause (Fig. 2.26a). On the other hand, the vertical wind shear associated with a midlatitude circulation may have a linear distribution in depth (Fig. 2.26b)(Elsberry and

Jeffries, 1996).

The vertical wind shear plays an important role in limiting the intensification of tropical cyclones, although the complete description of the processes involved has not yet been completed. However, the vertical wind shear still can be used in many operational models as a forecast predictor (Dvorak, 1984: DeMaria and Kaplan, 1994b).

52 a 200 MB

p ;

850 MB

Figure 2.27: Schematics of the 200 — 850 mb wind shear arising from (a) a low-latitude system with upper-tropospheric winds concentrated in a shallow layer versus (b) linearly distributed over a deep layer as might exist in a midlatitude trough (from Elsberry and Jeffries, 1996).

53 2.6 Eddy Angular Momentum Flux

The importance of the interaction between tropical cyclones and the surrounding

environmental flow has been noticed for many years. The first one to emphasize this idea

was Pfeffer (1955) who recognized the existence of inward fluxes of momentum in a tropical

cyclone. Subsequent studies also indicated that the environmental flow transferred a certain

amount of angular momentum into the center of a tropical cyclone. This angular momentum

was strongly believed to be responsible for the intensification of tropical cyclones (Palmén

and Riehl. 1957; Frank, 1977; Holland, 1983; Merill, 1988a,b). The results of McBride and

Zehr’s (1981) studies are shown in Table 3. The values of the horizontal convergence of

relative angular momentum are larger in developing systems than in non-developing systems

in both the Pacific and Atlantic basin.

Relative angular momentum is more closely related to intensity changes of tropical cyclones than absolute angular momentum. Merrill (1988b) used five-year hurricane data to relate the upper level environmental flow with the developing and non-developing hurricanes. The results indicated no strong correlation between absolute angular momentum and change of intensity. The importation of relative eddy angular momentum is connected to the interactions of the upper level westerly winds with the tropical cyclones and features such as the outflow jet. It is difficult to clearly identify the specific effects of angular momentum transfers on intensity because the interactions are related to the increasing vertical wind shear. The increased vertical wind shear may offset the positive effect of relative angular momentum on the intensification of tropical cyclones.

54 Latitude Latitude Latitude Data Set 0-4° 0-6° 0-8°

Pacific non-developing N 1 Cloud cluster -1.8 1.6 0.5

Pacific developing D2 pre-typhoon cloud cluster 6.7 8.0 3.7 D3 Intensifying cyclone 11.9 10.3 5.5 D4 Typhoon 22.4 23.0 23.5

Atlantic non-developing Nl Cloud cluster -3.6 3.8 0.5 N2 Wave trough cluster 2.4 2.7 2.9 N3 Non-developing depression 7.5 5.8 7.0

Atlantic developing D1 Pre-hurricane cloud cluster 8.1 10.6 6.7 D2 Pre-hurricane depression 8.5 11.3 7.1 D3 Intensifying cyclone 8.7 19.0 18.3 D4 Hurricane 12.5 11.7 6.7

Table 2.3 ; The horizontal convergence of relative angular momentum per unit area (-V Vm). A positive entry denotes a gain of angular momentum. Units are 10^ kg s'^ (from McBride and Zehr, 1981).

55 According to the theoretical studies of Holland and Merrill ( 1984) and the observational studies of Molinari and Vollaro (1989), the tropical cyclone interacting with the large scale environmental flow may increase the rate of intensiflcation by making the upper-level flow more cyclonic. This interaction of tropical cyclones and environmental flow may occur primarily in the upper levels. At lower levels, the rapid rotation of tropical cyclone's circulation produces large inertial instability and restricts its interaction with the environment

(Holland and Merrill, 1984).

Challa and Pfeffer (1990) studied the relationship between the large scale eddy convergence of angular momentum and the formation of cloud clusters and depressions in

Atlantic areas. They indicated that eddy flux convergence of angular momentum existed in the upper troposphere during the developing tropical disturbances. Momentum transfers into the center of systems extends from 300 to 1000 km. The eddy flux convergence of momentum may exert a stress on the upper troposphere and lower stratosphere to change the balance of the Coriolis, pressure gradient and centrifugal forces. Thus, the development and intensification of cloud clusters and disturbances proceed through interactions between the upper level outflow, low level inflow and tropospheric upwelling.

56 2.7 Summary

The preceding sections depict the background of climatology of the North Pacific, an important phenomenon of interaction between atmosphere and ocean, El Nino and Southern

Oscillation (ENSO), the severe weather system, typhoon, and some important factors that effect the intensities of typhoons. These factors, sea surface temperature (SST), vertical shear of horizontal winds and eddy angular momentum flux, are used in this study to relate the intensity changes of typhoons during ENSO and non-ENSO events. In the next chapter, the data and methodology used in this study will be introduced and discussed. The purpose of this study is to find the differences between the ENSO and non-ENSO events on the intensity changes of typhoons in the western North Pacific Ocean.

57 CHAPTERS

DATA AND METHODOLOGY

The purpose of this study is to correlate the relationship between intensity changes of

typhoons and selected meteorological factors during the ENSO and non-ENSO events in the western North Pacific Ocean. Although the ENSO events are basin-wide, their

influences on climate are not only regional but also worldwide. Gray (1994) found that the number of Atlantic basin hurricanes is reduced by more tropospheric vertical wind shear as a result of stronger than normal westerly winds created by moderate to strong ENSO events, Shapiro (1987) studied the climate fluctuation of hurricanes and the large-scale circulation and found that the number of hurricanes is reduced especially south of 30°N.

During the La Nina event, the easterly 200-mb zonal wind anomalies decrease the vertical shear and cause more favorable conditions for the development and intensification of hurricanes. Sometimes stronger La Ninas created too much easterly vertical shear with height resulting in the opposite effect and inhibiting the genesis of hurricanes (Gray, 1988).

ENSO events are included in Gray’s research as a factor in predicting the activities of

Atlantic hurricanes (Gray, 1993, 1994). To understand the possible impact of ENSO on the intensity changes of western North Pacific typhoon, several analyses have been calculated in this study.

58 The first task of this study is to establish an empirical relationship between

climatological sea surface temperature (SST) and maximum potential intensity (MPI) for

western North Pacific typhoons. The methodology is similar to the work of DeMaria and

Kaplan (1994a) used for Atlantic tropical cyclones. The results of DeMaria and Kaplan

(1994a) were used to be part of the predictors in the SHIPS model for the predicting of

intensity change in Atlantic hurricanes. In this approach the maximum wind speed of a

typhoon is plotted as a function of the SST at the location of the center of the storm. The

observations are divided into groups based on rounding of the SST to the nearest whole

degree Celsius. Then the maximum wind speed for each group is chosen to be

representative of the MPI of that SST. This approach in empirical MPI is based on actual

observations of typhoons. A curve is then fit to these observations and the characteristic

equation is determined. The derived empirical equation relating SST and MPI in this study

is then used as a factor in the next procedure.

The second part of the analysis is to relate the meteorological factors to the intensity changes of typhoons. Several factors are selected to be evaluated in this study. They are:

intensification potential (POT), vertical shear of the horizontal wind (SHEAR), time tendency of the shear (DSHEAR), the 200-mb relative and planetary eddy angular momentum flux convergence (REFC and PEFC), and the relative angular momentum

(RAM). These factors are introduced concisely in the following section:

The intensification potential (POT) is the magnitude of difference between the maximum potential intensity and the current intensity of storm. Since the maximum

59 potential intensity (MPI) is derived from an empirical relationship with SST, POT is also

a function of SST.

Vertical shear of the horizontal wind (SHEAR) is the magnitude of difference between

the 850 and 2(X) mb wind vectors. It is thought to have a negative influence on tropical cyclone intensification (Gray, 1968; Merrill, 1988a,b). The details of its calculation are presented in section 3.2.1.

Time tendency of the vertical shear (DSHEAR) is calculated from the difference between the vertical shear over the current position of the storm and the position 24 hours prior to the current time. If the 24-hour position was not available in the best track, the vertical shear at a 12-hour interval was used for the tendency calculation. This is the same method used by DeMaria and Kaplan (1994b).

The 200-mb relative and planetary eddy angular momentum flux convergence (REFC and

PEFC) account for positive interactions between the tropical cyclone and synoptic-scale systems. According to the studies of Holland and Merrill (1984) and Molinari and Vollaro

(1989), the intensification rate of the storm may be increased as the storm interacts with the large-scale flow that makes the upper-level flow more cyclonic. So the eddy flux convergences provide measures of whether the large-scale flow can increase or decrease the azimuthally averaged tangential wind of the storm (DeMaria and Kaplan, 1994b). The REFC and PEFC are evaluated at 200-mb due to the fact that the interaction of the storm with the environment is more likely to occur in the upper levels (Holland and Merrill, 1984). The integrated relative angular momentum (RAM) is used as a measure of the extent of the outer

60 circulation of the tropical cyclones (DeMaria and Kaplan, 1994b; Petty, 1997). The details of angular momentum calculation are presented in section 3.2.2.

In this study, standard multiple linear regression is used to relate the synoptic variables and intensity changes. The dependent variables are intensities change at 12, 24, 36, 48, 60, and 72-hour during ENSO and non-ENSO events. The independent variables are POT,

REFC, PEFC, RAM, SHEAR, and DSHEAR. These six synoptic variables are calculated at each time period to see whether they are statistically significant for the intensity changes. It is important to understand how these factors are related to the changes of intensities of typhoons during ENSO and non-ENSO events because this may lead to improve prediction of intensity changes.

3.1 Data

3.1.1. Western North Pacific Best Track Data

The data for Western North Pacific typhoons data were obtained from the Annual

Tropical Cyclone Report compiled by the staff of the Joint Typhoon Warning Center

(JTWC). The best track file includes the position (latitude and longitude) and intensities at 6-hour intervals (OOZ, 06Z, 12Z, 18Z) of all Western North Pacific typhoons. A 34-year period (1965-1998) of samples was used in this study.

The maximum 1-minute sustained surface wind was used to represent the intensity of typhoon. Sea surface pressures were not used in this study due to the fact that surface

61 pressure data were not reported as often as the surface wind. The sustained surface wind

was not directly related to the SST in this study. In their study, DeMaria and Kaplan

(1994a) demonstrated that the translational speed of tropical cyclones should be subtracted

from the sustained wind speed to represent the relative wind speed of tropical cyclones.

The reason for using the relative wind speed is that some fast moving tropical cyclones

generate high wind speeds due to their rapid translational movement. To obtain the

translational speed, the distance between two successive positions from the reports of

typhoon record was calculated, and then divided by the observational time interval (6 hours

usually). The details of this calculation are introduced in section 3.3.

In a few cases, negative wind speeds were found after the translational speeds were subtracted from the sustained wind. This indicates that the wind speed was slower than the moving velocity of typhoon. Those cases were removed from the study.

3.1.2. Climatological Sea Surface Temperature Data

Two sets of climatological sea surface temperature (SST) data used in this study were obtained from Columbia University. The first one is from the Comprehensive Ocean-

Atmosphere Data Set (COADS) in which the SSTs were computed for 2 degree latitude x

2 degree longitude boxes for each month of the period from 1854 - 1992. The 27-year

(1965 - 1991) sample was used in this study to relate the SSTs and typhoon intensities, then derive an empirical function.

62 The second set is weekly SST calculated for 1 degree latitude and longitude grid from

Integrated Global Ocean Service System (IGOSS). The SST data were derived from in situ

(ship and buoy) and satellite observations by blended analysis (Reynolds, 1988) and improved by using sea ice data to simulate SSTs in ice-covered regions (Reynolds and

Marsico, 1993). Reynolds and Smith (1994) used optimum interpolation (OI) to analyze in situ and corrected satellite data weekly and daily for bias correction and improving the spatial and temporal resolution of the blend in their study. These SST data were used from

1992 - 1997 for testing the derived empirical function.

3.1.3. Daily Wind Field Data

NOAA NECP-NCAR CDAS-1 (Climate Data Assimilation System 1) Data are used in this study to calculate the synoptic variables. These data contain 1000, 925, 850, 700,

600, 500, 400, 300, 250, 200, 150, 100, 70, 50, 30, 20, and 10 mb pressure levels at a resolution 2.5° x 2.5° of latitude and longitude. Variables included in these data are: absolute vorticity, pressure vertical velocity, geopotential height, specific humidity, relative humidity, temperature, zonal wind and meridional wind. CDAS-1 data are available on a daily basis from 1958 to 1999. After 1 Oct. 1998, the resolution was improved to 1° x 1° .In this smdy, 3 years data (1996 - 1998) of the zonal and meridional wind at 850 and 200 mb were used to compute the synoptic variables.

63 3.2. Calculation of Synoptic Variables

3.2.1 Vertical Wind Shear

The theory that vertical shear of horizontal wind has a negative correlation with the intensification of tropical cyclones is well accepted (Gray, 1968; Merrill, 1988a, b; DeMaria and Kaplan, 1994b). The definition of vertical shear (SHEAR) is the magnitude of the difference between the 200 and 850 mb horizontal wind vectors (DeMaria and Kaplan,

1994b). The reason for selecting these two levels is that most satellite cloud-drift winds data are available at these levels. The horizontal wind components (U and V) are averaged over a circular area with a radius of 1400 km fi-om the center of tropical cyclone at each level

(Petty, 1997). Each point that is less than 139 km (equivalent half distance of the grid spacing (2.5 ° longitude)) from the center of tropical cyclone is eliminated to avoid the core of the tropical cyclone which may be unrepresentative of large scale flow.

To evaluate the vertical shear of horizontal wind, first we calculate the vertical shear at each component by the definition of vertical shear.

^2-. = ^200 - (3.1) and

= ^200 - ^.,0 • (3-2)

The overbar denotes an areal average. Then we combine the zonal (U,.*) and meridional

64 (Vi.g) components to obtain the absolute vertical shear.

The equation is

■ (3 3)

The zonal and meridional components of the wind and the absolute vertical wind shear are

used to compute the synoptic variables used in this study. The previous study indicated that

zero or small vertical shear was related to the developing tropical cyclones (McBride and

Zehr, 1981).

3.2.2 Angular Momentum Variables

To account for the interactions between the intensity changes of typhoon and synoptic scale systems over the western North Pacific area, the angular momentum flux convergences are used in this study. The previous studies indicated that there is a positive correlation between the angular momentum fluxes and intensity changes of tropical cyclone (Holland and Merrill, 1984; Molinari and Vollaro, 1989; DeMaria and Kaplan, 1994b). The relative and planetary angular momentum flux convergence are believed to be associated with the intensity changes in western North Pacific typhoons.

65 Following the work of DeMaria and Kaplan (1994b) and Petty (1997), the relative eddy angular momentum flux convergence (REFC) and planetary eddy angular momentum flux convergence (PEFC) are evaluated by equations

REFC = -r''^— r'^U'v' , (3 .4 ) d r and

PEFC = - f ' u ' . (3 .5 )

These two momentum flux variables are computed only at 200mb due to the greater possibility of the interaction of the storm and it's environment is higher in upper level than in lower level (Holland and Merrill, 1984). In these two equations, U is the radial wind and

V is the tangential wind, f is the Coriolis parameter, and r is the radius from the center of typhoon. The overbar represents an azimuthal average and the prime denotes a deviation from the azimuthal average. The regression tests of DeMaria and Kaplan (1994b) indicated that averaging REFC from 100 to 900km provided the best predictors of intensity. The value of 700km is selected to represent the radius of r in this study.

To evaluate the equation of REFC, first we calculate the deviation of the radial and tangential winds which are expressed in the following forms:

U ' = U - V , (3 .6 ) and

v ' = V - V . (3 .7 )

6 6 where U' and V are the deviation of the radial and tangential wind respectively. The overbar represents an azimuthal average of radial and tangential wind. Azimuthally averaged U and

V are calculated by the following equations:

n HU, J) - (3 8) n

n HV, V = (3 9) n where n is the total number of grid points used for azimuthal average.

After the deviation of radial and tangential wind (U' and V) are obtained. The next step is to calculate the relative eddy flux convergence for the radius of 700 km. The following two equations represent the azimuthal average of U'V within a radius of 700km (Eq. 3.10) and around the annulus between 700 and 1400 km (Eq. 3.11),

n E u 'y '; (3.10) IJ'V' /=! (0-700km) n

HU'V, (3.11) U'V’ 1=1 ^ (700-I400toFi) n

67 Equation 3.10 and 3.11 are multiplied by respectively to give

^ »"(o-7o«.)X350xlO'm)^ (3.12) and

From equation (3.4) to calculate the convergence.

a n'v' - Tj'v' ± r ^ U 'v ' = . ( 3 . 1 4 ) dr TOOxlO^m

Finally, to complete the calculation.

1 II'v' - u'v' = ------—( ------— ------— ) • (3.15) (700x1 O^m)^ 700x10^/»

The steps for computation of planetary eddy flux convergence (PEFC) are simpler. First, the deviation of the Coriolis parameters with all grid points within the radius of 1400km are calculated:

/ ' = / - / . ( 3 . 1 6 )

The deviation of the radial wind components have obtained from the equation (3.6). Then the average of the product of equation (3.6) and (3.16) times (-l)is the PEFC,

68 = -(f-f)iU - U) . ( 3 . 1 7 )

The integrated relative angular momentum (RAM) is included in this study to relate the intensity changes of typhoons to the initial state of the systems. RAM is as a measure of the extent of the outer circulation of the tropical cyclones (DeMaria and Kaplan, 1994b; Petty,

1997). The equation for RAM is

RAM = (\rV)rdr , (3 . 1 8 ) ^r. where V is the tangential wind at 850mb, r, = 400km and r, = 800km. The equation of RAM is rewritten to

RAM = f'\Vr^)dr . ( 3 . 1 9 )

To calculate the average of Vr^ in the annulus area between the radius o f400 and 800km, the

V r overbar is treated as a constant and removed from the integration. Then the equation of

RAM becomes

RAM = Vr^f^dr = yr\r^-r^) = Vr\400km) . ( 3 . 2 0 )

69 3.3 Translation Speed

Translation speed is computed to represent the motion of a typhoon. Since the sustained surface wind includes the translation speed and relative wind speed, the translation speed must be subtracted from the sustained wind to obtain the relative wind speed to represent the intensity of typhoon. Following the work of Petty (1997), the zonal and meridional displacements are calculated first to establish the distance between two positions from typhoon. The following equations are used for this purpose,

ALAT = LAT - LAT..,2 (3.21) and

ALONG = LONG - LONG,.,2 . (3.22)

LAT and LONG are the latitude and longitude of the typhoon position at the start of the forecast period. LAT ,.12 and LONG ,.,2 are the latitude and longitude of the position of typhoon 12 hours earlier than the start of forecast. ALAT and ALONG are the change of latitude and longitude during the 12 hours period. The zonal (x-direction) and meridional

(y-direction) displacements are calculated by the following equation:

CÜC = R{co%iù,LAT X -E_)) X {^cd.ONG x _5_) (3.23) 180 180 and

70 a Y = R(aLAT X -JL) . (3.24) 180

Where R is the radius of the earth (6371 km). AX and AY are the distances in the zonal and meridional directions between two points. The zonal and meridional translation speeds

(in m s ’) can be obtained by using equation (3.23) and (3.24) divided by time (12 hours) respectively,

UTS = ------— ------(3 .2 5 ) 3 6 0 0 X 12 and

VTS = ------— ------. (3 .2 6 ) 3 6 0 0 X 12

UTS is the zonal translation speed and VTS is the meridional translation speed. To obtain the total translation speed (TS):

TS = . (3 .2 7 ) 3 6 0 0 X 12

71 3.4 Statistical Analysis

To derive an empirical equation between SSTs and typhoon intensity, the statistical technique, correlation, is used to measure and describe a relationship between two variables.

In this section, the two variables X and Y are SSTs and typhoon intensity respectively. The relationship is described by three characteristics (Gravetter and Wallnau, 1992): a. Direction. A relation can be either positive or negative. A positive relation means that X and Y vary in the same direction. A negative relation means that X and Y vary in opposite directions. The examples of positive and negative relationships are shown in Fig. 3.1. In this section of studies, a positive relation will be anticipated because typhoon intensity increases with the increasing SSTs. b. Form. The most common form for a relation is a straight line. The other forms are possible. Suppose the relation is this section of studies is a linear form. The Pearson correlation will be used to measure the degree of linear relationship. c. Degree. The magnitude of the correlation measures the degree to which the data points fit the specified form. A correlation of 1.00 (or -1.00) indicates a perfectly consistent relation, and a correlation of 0 indicates there is no degree of fit.

The Pearson correlation is used to measure linear form and is identified by the letter r.

This formula is computed by

SP r=- y/SSxSSy

72 where SP is the sum of products of deviations and is defined by the following formula:

SP=YSX-X)(Y-Y) or

n where n is the number of observation.

SS^ and SSy are the sums of the squared deviations for X and Y respectively,

SSx= Z iX -X f ,

SSy=lXY-ŸŸ .

Overbar means the average of the variable.

Regression is used to determine a linear equation which can represent a general linear relation between two variables X and Y. This equation of regression can predict the Y value corresponding to any known value of X:

Predicted Y value = Ÿ = bX + a .

The least-squares method is used to minimize the error between the predicted Y values and the actual Y values. The best fitting line (Fig. 3.2) is attained when the equation of regression has

SSx

73 (a) Rekition b«twe«n b««r Ml#* (b) Retoilon between coffee Mies and tempetaixjt» and remcerature 6 0 - 6 0-

5 0 - 5 0 - 3 40 — t 4 0 - 1 Z 3 0 - 5 3 0 -

I 2 0 - 1 2 0 - > x

1 0 - 10 —

1------1------1------1------1------r - ^'^1, i A i i 2 0 3 0 4 0 50 60 70 ao T sm p o a tw (In d # g w M F) Temperatue (In d eg rees F)

Fiure. 3.1: Examples of positive and negative relationships. Beer sales are positively related to temperature, and coffee sales are negatively related to temperature (From Gravetter and Wallnau, 1992)

• Distance * v - ?

X. Y d d t o p o in t

Fiure. 3.2: The distance between the actual data point (Y) and the predicted point on line (Ÿ) is defined as V - Ÿ. The goal of regression is to find the equation for the line that minimizes these distance (From Gravetter and Wallnau, 1992)

74 and

a=Ÿ-bX .

The standard error of estimate is used to measure the accuracy of the prediction. That is, the standard distance between the predicted Y value on the equation line and the actual data point. The formula of standard error of estimate is:

SSerror n-2

where = £(Y - Ÿ)- or

SS^, = (1 -r:)SSy .

To relate synoptic variables to intensity changes of a typhoon, two or more independent variables are used to estimate the values of a dependent variable instead of a single independent variable. Multiple regression and correlation analysis are used to achieve this purpose. An example of multiple regression equation is:

Ÿ = a + b,X| + bjXj where Ÿ is the predicted value (dependent value) and X,, Xi are two independent variables, and a, b„ and b? are numerical constants that must be determined from the data in a manner analogous to that of the two-variable case (Hamburg, 1985).

75 In the previous discussion, the least squares is used to obtain the best fitting straight line

for two variables. These two-variable points are plotted in two dimensions along the X and

Y axes. In the present section, the method of least squares is used to obtain the best fitting plane for three variables. These points are plotted in three dimensions, along the X,, X, and

Y axes (Fig. 3.3). By the method of least squares, £(Y - Ÿ)^ is required to be minimum.

Three normal equations must be solved to determine the values of a, b, and b,.

^Y = na + b,EX, + b.EX2

IX , Y = a£X, + b,lX ,: + b,lX,X,

IX,Y = alX , + b.iX.X, + b£X,^

Once the values of a, bl and b2 are obtained, the multiple regression equation is determined.

If there are more than three variables, the general form of the multiple regression equation for k-1 independent variables X,, X,, ...... X^., is

Ÿ = a + b|X, + biXi + ...... + bk_,Xk.,

This linear equation that is fitted to data for four or more variables is referred to as a hyper plane that can not be visualized.

76 Fiure. 3.3: Graph of a multiple sample regression line based on data given for the variables Y, X,, and X; (from Hamburg, 1985).

77 The standard error of estimate is

Ecr- i f n~k

where n is the number of observations and k is the number of constants in the regression equation. The (n-k) represents the number of degrees of freedom.

In this study, standard multiple linear regression is used to relate the synoptic variables to intensity changes. The dependent variables are intensities of change at 12,24,36,48, 60, and

72-hour. The independent variables are POT, REFC, PEFC, RAM, SHEAR, and DSHEAR.

These six synoptic variables are calculated at each time period to see whether they are statistically significant to the intensity changes. Backward regression is appropriate because this method provides a first-step look at each individual variable adjusted against all other independent variables (Neter et al., 1989). Then the insignificant variables are removed from the calculation one by one until all residual variables are statistically significant at the level of 90%. The probability of F-to-remove criterion is set to 0.100 to provide a criterion of judging the significant variables. The statistical package (SPSS) is used to provide necessary information of this study.

78 CHAPTER 4

ANALYSIS AND RESULTS

4.1 Climatological SST versus Typhoon Intensity

In this chapter, the relationship between the maximum potential intensity and SST is derived for 27 years (1965-1991) of data. This result is also tested for the 6 years (1992-

1997) data, which represent an independent sample, to examine whether this empirical equation can provide an upper bound for the typhoon intensity in the western North Pacific

Ocean. Selected synoptic variables are used to relate the intensity changes in the 12, 24, 36,

48, 60. and 72 hours period to check what variables are significant to intensity changes during the ENSO and non-ENSO event.

4.1.1. Empirical equation for SST and Typhoon Intensity

To present the initial relationship between the climatological SST and typhoon intensity in western North Pacific areas. Fig. 4.1 shows a scatter diagram that plots all 12089 cases of intensities associated with SSTs. The result of Whitney and Hobgood (1997) for Eastern

North Pacific regions showed in Fig. 4.2. The linear relationship between these two variables

79 Intensity vs. SST

g

G/)

: . V J < ^

10 20 30 40 Sea Surface Temperature (°)

Figure 4.1: Scatter diagram indicates the typhoon intensities and SSTs of all 12089 observations in the 27-year sample (1965 - 1991).

80 Intensity vs SST (Eastern Pacific Basin 1 963—1 993)

70

60

50 vL 40

30 I Ç 20

10 .. - - M m 0 21 23 25 27 Sea Surface Temperature (deg C)

Figure 4.2: Scatter diagram with the typhoon intensity and SSTs of all 11062 observations in the 31-year sample (1963 - 1993). Intensities are corrected for storm translational speed (from Whitney and Hobgood, 1997).

81 in Fig. 4.1 is not as significant as Fig. 4.2 shows, but the SSTs do have the pattern o f a capping function for the maximum intensities.

The following step was to stratify the SST data from 20.5°C to 31.5°C into 11 evenly spaced groups of 1 °C interval each. Maximum intensities were found after a search of the largest value of wind speed in each SST group. Table 4.1 shows the properties of the SST groups and associated maximum intensities. The SST cases below 20.5°C were not considered due to the fact that each group contained only a few cases. The 21° - 25°C groups contain 4.92% of the cases, and the 26° - 31°C groups contain 95.08% of the cases.

The maximum typhoon intensity and its 99th, 95th, 90th, and 50th intensity percentiles for each group were determined and presented in Table 4.2. The percentiles indicate the percentage of cases in each group under the given value of intensity. For example, the 50th percentile for the 23°C SST group reveals that 50% of the cases in this group exceeded the standard of tropical storm intensity (17 m s '). The 95th percentile for the 31°C SST group indicates that only 5% of the cases reached the intensity of typhoon (33 m s').

Figure 4.3 shows the maximum and percentile intensities associated with SSTs. The curve for the 50th percentile dose not change significantly with SST. This is similar to the results found by DeMaria and Kaplan (1994a) for the Atlantic and Whimey and Hobgood (1997) for the eastern North pacific. The other percentiles and maximum intensity curve suggest a linear relationship between SST and intensity by the range from 21°C to 29°C. The pronounced decrease of intensity in the warmest SST range (30°C and 3 l°C) is interesting.

8 2 SST Midpoint Number of Avg. SST Avg. Intensity Max. Intensity (°C) Observations (°C) (m/s) (m/s)

21.0 44 20.98 22.894 30.41

22.0 62 22.00 25.169 38.60

23.0 105 23.08 25.281 55.52

24.0 140 24.01 28.323 53.39

25.0 230 25.06 28.256 63.49

26.0 456 26.07 30.339 66.84

27.0 1215 27.06 32.262 71.85

28.0 3254 28.06 31.440 81.53

29.0 4864 28.98 24.835 80.00

30.0 1303 29.78 21.185 72.26

31.0 120 30.92 15.259 36.07

Table 4.1 : SST group properties

83 SST Group 99% 95% 90% 50% (°C) (m/s) (m/s) (m/s) (m/s) 21.0 29.41 27.86 25.31 12.56

22.0 38.00 37.10 32.99 15.65

23.0 54.15 37.03 33.85 17.27

24.0 48.29 30.44 25.85 12.59

25.0 48.19 37.99 28.30 12.49

26.0 51.54 41.34 37.26 18.39

27.0 63.62 53.80 48.70 23.75

28.0 68.78 58.58 53.48 22.88

29.0 64.70 51.95 41.75 13.15

30.0 67.08 49.31 38.56 12.06

31.0 35.56 33.52 28.42 10.57

Table 4.2: Intensity Percentiles.

84 Intensity Curves for Western North Pacific Typhoons

90

Maximum -"-99% - * - 9 5 7c I 40 -#-90% : -"-50% ^ 20

21 22 23 24 25 26 27 28 29 30 31 Sea Surface Temperature (Degree C)

Figure 4.3: The maximum typhoon intensity and the 99th, 95th, 90th, and 50th intensity percentiles associated with 1 °C SST group.

85 The possible explanation is that the higher SST (30°C - 31°C) regions are usually concentrated in the area ranging from equator to 20°N, and from 150°E to 170°E. Although typhoons form over the warmest waters their westward or northwestward movement results in most systems attaining their maximum intensity west of 150°E, strongest wind speeds are not observed when the tropical cyclone is over the warmest SSTs..

The maximum intensity data in Table 4.1 were used to derive an empirical frmction for the relationship of maximum intensity and SST in the western North Pacific Ocean. Those data points were from 7 intense typhoons shown in Table 4.3. To smooth the maximum intensity curve in Figure 4.3, the method of least squares was used to fit the maximum intensity cases. According to the shape of maximum intensity and 99th percentile curves, a linear form of function was selected to represent the best fit line:

V = A + B(SST) where V is the maximum wind (m s ') and is referred to as the maximum potential intensity

(MPI) for the western North Pacific typhoons, SST is the sea surface temperature (°C). The two constants A and B are -70.685 m s ' and 5.178 m s ' °C ‘ respectively. The regression output calculated by SPSS is presented in the Table 4.4. Figure 4.4 shows the observed maximum typhoon intensity and its least squares function fit for each 1°C SST group.

The appropriate range of SST for using in the empirical MPI function is from 20.5°C up to 31.5°C. It dose not make sense to have a negative intensity. Most typhoons that move over sea surface with 13°C or cooler are usually in the stage of dissipation. These cases are not relevant to this research project.

86 SST Group Typhoon Year Lat/Lon Max. Intensity (°C) Name (M/s)

21.0 Bess 1965 37.2/150.8 30.41

22.0 Kathy 1966 35.5/172.2 38.60

23.0 Bess 1965 35.3/148.5 55.52

24.0 Carmen 1965 32.0/147.8 53.39

25.0 Carmen 1965 29.1/147.0 63.49

26.0 Carmen 1965 26.6/146.6 66.84

27.0 Carmen 1965 24.9/145.8 71.85

28.0 Tip 1979 16.9/137.2 81.53

29.0 Kit 1968 20.7/130.9 80.00

30.0 Olive 1965 22.2/147.9 72.26

31.0 Pamela 1976 7.6/153.0 36.07

Table 4.3: Western North Pacific typhoons containing the maximum intensity data point.

87 Regression

Model Summary**^

Std. Error Variables Adjusted of the Model Entered Removed R R Square R Square Estimate 1 TEMP*'" .925 .856 .838 6.8322 a. Dependent Variable: MAXSPEEO b. Method: Enter c. Independent Variables: (Constant), TEMP 0. All requested variables entered.

ANOVA* Sum of Mean Model Squares df Square F Sig. 1 degression 2212.223 1 2212.223 47.393 .000® Residual 373.428 8 46.678 Total 2585.651 9 a Dependent Variable: MAXSPEED b Independent Variables: (Constant). TEMP

Coefficients* Standar dized Unstandardized Coeffici Coefficients ents Std. Model B Error Beta t Sig. 1 (Constant) -70.685 19.302 -3.662 006 TEMP 5 178 752 925 6.884 .000 a Dependent Variable: MAXSPEED

Table 4.4: The regression output

88 1 0 0

Maximum Function Fit

21 22 23 24 25 26 27 28 29 30 31 Sea Surface Temperature (Degree C)

Figure 4.4; The observed maximum typhoon intensity associated with 1 °C SST group and the least squares function fit.

89 4.1.2. Case Study of the Empirical Maximum Potential Intensity Function

The monthly SST data of 27-year (1965 - 1991) were used to relate SST to the maximum intensity of typhoons and to derive the regression equation V = -70.685 +5.178(SST). To test the accuracy of this MPI function, it was applied to weekly SST data from 6 years (1992 -

1997) and compared with typhoon records. Typhoon data of the same period were also used, tropical depressions and tropical storms were not selected in this study because it only focused on how close the typhoon intensities could reach their maximum potential intensity

(MPI).

The SSTs associated with the time and position of typhoons were put into the empirical

MPI function, and the maximum potential intensities in the same time and position were obtained, then all the typhoon intensities were compared with their MPI to see how much difference there was between them. Because the motion of western North Pacific typhoons are influenced by the Pacific high pressure system, most typhoons move to the west- northwest then north-northeast to the higher latitudes where the colder waters located (cf.

Fig. 4.5). Cold waters reduce the amount of evaporation and the energy provided for the typhoons is also decreased. The reduction of the available energy results in the weakening of typhoons. The following figures show the actual change of intensities of typhoons associated with their MPI and track motion.

90 w ITM IIM lOM Ma Ma 70a ua Ma «oa Ma Ma laa xp %, aayawygapu^ ^ r y i" i " r r"'iyT''T'"iyr^r'i " p,"|aa, p,,,|,,,,gMn 6 0 f )V •••••• a 4lia W • • • \ É i l £ : -

' ^ • •••

M-M o

/

i w ï r cyclones (> 17 m s ' )in various basins during specified lime periods (Neumann. Figure 4.6 reveals that the intensities of typhoon Elsie decreased as the system moved to

north of 30°N (cf. Fig. 4.7). At its peak intensity typhoon Elsie approached its MPI. During

the dissipation stage, lower SST accompanied by the lower MPI provided an upper bound

on the actual intensity. At no time did the intensity exceed the MPI derived from the

empirical equation. Figure 4.8 indicates that typhoon Gay moved over an area with a

relatively constant SST and never moved north of 30°N (cf. Fig. 4.9) so the variations of

MPI are not significant. The actual maximum intensity is again close to the MPI but never

exceeds it.

Figure 4.10 shows that typhoon Zelda intensified while moving into an area with warmer

SST (cf. Fig. 4.11). The actual intensities approached the MPI closely but were lower than

the MPI. Figure 4.12 is a case of a rapidly intensifying typhoon Yates. Ito ( 1963) found that

the greatest frequency of rapidly deepening (2.0 mb h ' pressure fall or a 50 kt increase in 24-

hour) typhoons occurred over the Philippine sea south of 25°N. and also were associated

with sea surface temperature greater than 28°C. Typhoon Yates intensified rapidly over the

region west of 145°E and south of 25°N (cf. Fig. 4.13). This is a favorable region for rapidly

intensifying typhoons (cf. Fig. 4.14). Warmer SSTs also provided higher bound of MPI in the development and intensification stage. Typhoons that moved northward north of 30°N to the cold waters was the cause of rapidly decreasing intensities and MPI. For the last period, the intensity exceeded the MPI due to the very cold SST predictor, but by that time the typhoon was making a transition from a tropical to an extratropical system.

92 ISO*

LATE JUNE (20th)-MID OCTOBER (I6lh) so* iL _

*0* - r

10* 10*

.0

110* 120*

Figure 4.14: Areas where typhoons intensified rapidly during summer and early fall (20 June -16 October) - number of occurrence (1956 - 76) (from Holliday and Thompson, 1979).

97 Figures 4.15 and 4.17 show that the formation and intensification of typhoons Joan and

Paka over warmer SST (cf. Fig. 4.16,4.18). Smaller variation of SSTs provided a smoother

MPI as an intensity bound during the intensification of these two typhoons. The actual

intensities reached 99% of their MPI but neither was higher than the MPI. This is a

particularly impressive finding when the rapid intensification and extreme intensity of the

two storms are considered. Figure 4.19 reveals that there is a similar pattern and trend for the

actual intensities and their MPIs during the process of intensification and dissipation.

Typhoon Ward was a weaker storm. The MPI decreased gradually with typhoon Ward as it moved northward (cf. Fig. 4.20). It is very apparent that SSTs play a significant role in the development of typhoon Ward. Figures 4.21 — 4.28 display cases of rapid reduction of

MPI during the dissipation of northward moving typhoons. As these typhoons moved northward to cold water regions very fast, the reduction of available energy resulted in the rapid weakening of these systems. Figures 4.29 and 4.31 are two cases of similar trend between actual intensities and MPI during the stage of dissipation. The reason is that typhoon

Hunt and Keith recurved to higher latitude areas over cold water (cf. Fig. 4.30 and 4.32).

In conclusion, none of the typhoons in the independent sample exceeded the MPI during the initial and intensification stage. Only some cases came very close to their MPI (up to

99%) (Fig. 4.6 -4.18). A few cases exceeded the MPI during the dissipation stage (Fig. 4.12,

4.21, and 4.25). This result is due to the movement of typhoons over colder waters and hence the associated MPI were declining faster than the circulation spin down. The pattern of the typhoon intensity is similar to the MPI during the stage of dissipation in some cases

98 (Fig. 4.6, 4.12,4.19 - 4.31). This situation often occurred while typhoons moved northward and experienced cooler and cooler waters.

The number of cases and percentage of typhoons reaching 50% and 80% of the calculated

MPI are shown in Table 4.5. The years 1992 and 1997 were exceptional with very intense typhoons. In those years, almost 60% of cases reached their 50% of MPI, and 11.3% and

27.6% of cases attained 80% of their MPI in 1992 and 1997, respectively. For the total cases,

41.9% of typhoon intensity reached their 50% MPI, 10.7% attained 80% of MPI.

50% of MPI 80% o f MPI Total 1992 270 (59.87%) 51 (11.31%) 451 1993 72 (38.50%) 2 ( 1.07%) 187 1994 200 (30.86%) 32 ( 4.94%) 648 1995 57 (27.54%) 14(6.67%) 207 1996 185 (32.86%) 47 ( 8.53%) 563 1997 265 (59.95%) 122 (27.60%) 442 Total 1049 (41.94%) 268 (10.73%) 2491

Table 4.5: The number of cases and percentage of typhoons to reach their 50% and 80% MPI

99 Typhoon Ward

>< u

MPI Actual Intensity (m/s) 1 S 9 13 17 21 25 2 9 33 37 3 7 11 15 19 23 27 31 35

Sequence number

Figure 4.19: The observed intensities of typhoon Ward and its associated maximum potential intensity (MPI).

Figure 4.20: Tlte track of typhoon Ward.

102 4.2. The Relationship between the Synoptic Variables and Typhoon Intensity Changes during ENSO and non-ENSO Events

In this section, the results of the multiple linear regression analysis for the six synoptic variables and intensity changes over six time intervals during ENSO and non-ENSO years are discussed. A three-year period (1996 - 1998) was selected to represent before-ENSO,

ENSO, and after-ENSO events. The year of 1998 also represents the transition from El Nino to La Nina. The six independent variables are listed in the Table 4.6. Portions of the SPSS statistical outputs are shown in appendix. These results are also compared to the previous study of DeMaria and Kaplan (1994b) for the Atlantic Ocean and Petty (1997) for the eastern

North Pacific Ocean. The possible physical mechanisms are also discussed.

POT Intensification potential

REFC The 200-mb relative eddy angular momentum flux convergence

PEFC The 200-mb planetary eddy angular momentum flux convergence

RAM The 850-mb relative angular momentum

SHEAR Magnitude of 850 — 200-mb vertical shear of the horizontal wind

□SHEAR Time tendency of the vertical shear

Table 4.6: Synoptic variables included in the multiply regression analysis

109 4.2.1. The Results of Study for 1996 (before ENSO)

The results for 1996 of the multiple linear regression analysis from SPSS output are

presented in appendix A. According to the processes of backward regression, all the six

synoptic factors as independent variables were entered into the regression model. After the

calculation, the least significant variable was removed from the model. Then the regression

was repeated and the next insignificant variable removed until all insignificant variables were

removed. The probability of F-to-remove criterion was set to 0.100 to ensure the residual

variables with their coefficients were statistically significant at the 90% level. The output of

SPSS included the unstandardized (non-normalized) and standardized (normalized)

coefficients, the standard error of B, t value for B and significance level of t.

In the regression on the intensity changes over 12 hours, the PEFC was the first variable

to be removed from the model. The smallest absolute value of t (0.088) and the largest value

of significance level of t (0.930) indicate that PEFC was the most insignificant synoptic

variable. SHEAR was the last variable to be left because its significance level of t (0.016) was smaller than the F-to-remove criterion (0.100). The standardized coefficient of SHEAR was -0.389. The negative value meant that SHEAR was negatively related to the intensity change that is consistent with prior research. In this period, SHEAR was the only significant synoptic variable.

In the regression for intensity changes over 24 hours, POT was the first variable to be removed from the model. Once again, SHEAR was the only variable to be left in the final

110 stage of calculation, and SHEAR was again negatively related to intensity change. In the

regression for intensity changes over 36 hours, DSHEAR was the least significant variable

in the model. SHEAR was still the most significant variable and with negative relationship

to the intensity change. In the regression for intensity changes over 48 hours, POT was

removed first, RAM and DSHEAR were the significant synoptic variables with positive and

negative correlations to the intensity change, respectively. These results are also consistent

with prior research. RAM represents the effect of the size o f the systems. Tropical cyclones

that have large circulations in their formative stages often continue to intensify. Conversely, as shear increases over a tropical cyclone, dissipation occurs more rapidly. Although SHEAR was not retained in the final model (the 5* and 6* in the 48-hour period table in Appendix

A), it was the last variable to be removed. In the regression equation for intensity change over 48 hours, the effect of vertical shear was represented by DSHEAR. In the regression for intensity changes over 60 and 72 hours, POT and DSHEAR were the least significant variables, respectively. The same three variables (PEFC, RAM, and SHEAR) were retained in the regression equations for both time periods. RAM and PEFC had positive correlation to the intensity change and the SHEAR had a negative impact on the intensity change. The inclusion of more synoptic variables at longer time periods reflects the greater impacts of changes in the large scale environment on the intensity of tropical cyclones at longer time scales.

Table 4.7 displays a siunmary of the regression analysis. The vertical wind shear

(SHEAR) was significant at most time intervals except at 48 hours. Negative coefficients indicated that vertical wind shear had a negative correlation with intensity changes. Increased

III vertical wind shear resulted in the reduction of typhoon intensity. The increasing magnitude

of the normalized regression coefficients from the 12-hour to 72-hour indicated that SHEAR

might provide a better predictor of intensity at longer forecast periods. The importance of

vertical shear as a predictor was greatest at 60- and 72-hour. This result agrees with the

findings of previous research (e. g. DeMaria, 1996, DeMaria and Kaplan, 1994b). The

relatively angular momentum (RAM) was significant at 48, 60, and 72-hour and was

correlated to intensity changes positively. This indicated that larger and stronger circulations

were likely to continue to intensify over the period from 2 to 3 days into the future. The

planetary eddy angular momentum (PEFC) was only significant at 60 and 72 hours and also

had a positive correlation with intensity changes. For the year of before-ENSO (1996),

SHEAR and RAM had greater influence on typhoon intensity changes than the other variables did. DSHEAR was only significant at 48 hours. POT and REFC were not significant at any interval.

12h 24h 36h 48h 60h 72h POT — ...». ... ------REFC — — ••• ------PEFC —- ••• —- — 0.442 0.489

RAM —- ••• — 0.403 0.389 0.289 SHEAR -0.389 -0.489 -0.448 ... -0.703 -0.762 DSHEAR — "* ------— -0.421 ------••• R- (%) 23.1 34.0 28.6 38.8 40.9 37.7

Table 4.7: Normalized regression coefficient for residual variables after backward regression for 1996. The statistically significant at the 90% level are presented.

112 4.2.2. The Results of Study for 1997 (ENSO)

The results for 1997 of multiple linear regression analysis from SPSS output are presented in appendix B. In the regression for intensity changes over 12 hours, RAM was the first variable to be removed from the model. There was no variable that had a t value of significance level smaller than the probability of F-to-remove criterion. So all variables were removed from the model. This indicated that these variables were not signifrcantly related to the intensity change at 12 hours. This is not a completely unexpected results since prior research has shown that persistence of current trends is sometimes the best predictor at 12 hours. In the regression for intensity change over 24 hours, POT was the least significant variable between these variables. PEFC was the only significant synoptic variable in the final equation. In the regression for intensity change over 36 hours, POT was still the first variable to be removed. REFC was the only significant synoptic variable in the final equation and was positively correlated with intensity change.

In the regression for intensity change over 48 hours, the first variable that was removed was the POT. POT was removed first during the tfiree successive period (24, 36, and 48- hour). Thus, this indicated that POT was not related to the intensity change very well.

SHEAR and DSHEAR were both significant in the final equation. In the regression for intensity change over 60 hours, PEFC was removed first and the retained variables were

REFC, SHEAR, and DSHEAR. The coefficients for SHEAR and DSHEAR were negative and REFC was positive. In the last period (72 hours), POT was removed first and DSHEAR,

REFC and PEFC were the only synoptic variables in the final regression equation.

113 Table 4.8 shows the normalized regression coefficients for the significant synoptic variables during an ENSO event. The statistical significance of the variables changed markedly between 1996 and 1997. In 1997 REFC was significant at 36, 60, and 72 hours and was positively correlated with intensity changes. This agrees with previously reported research. PEFC was significant at 24 and 72 hours and positively correlated to the intensity changes. SHEAR was only significant at 48 and 60 hours. DSHEAR was significant for the last three periods. The fact that POT and RAM were not significant at any interval was unexpected. No variable dominates the intensity changes through all time intervals in the manner that SHEAR did in 1996. It seems that there must be other factors that influence the intensity changes during an ENSO event. The significance of REFC and PEFC at four of the six time periods seems to indicate that the convergence of angular momentum is more significant during an ENSO event. Since these variables are computed at the 200 mb level, their significance may reflect the changes that occur in the upper troposphere during an

ENSO event. The coefficient of determination, r^, increased with increasing period then indicated that these variables had a better relationship to intensity changes at longer periods.

12h 24h 36h 48h 60h 72h POT — ... --- —------REFC— — 0.382 —- 0.366 0.392 PEFC — 0.326 ----- •— 0.493 RAM —— ------SHEAR --- — -0.694 -0.499 ----- DSHEAR --- -0.489 -0.518 -0.342 R- (%) 11.6 21.4 28.3 30.3 45.9 43.7

Table 4.8: Normalized regression coefficient for residual variables after backward regression for 1997. The statistically significant at the 90% level are presented.

114 4.2.3. The Results of Study for 1998 (after ENSO)

The results for 1998 of the multiple linear regression analysis from SPSS output are

presented in appendix C. In the regression for intensity change over 12 hours, RAM was the

first variable to be removed from the model. REFC was the only significant variable in the

model and was positively correlated with intensity change. In the regression for intensity

change over 24 hours, PEFC was the most insignificant variable. REFC and RAM were both

significant and were positively correlated with intensity change. In the regression for

intensity change over 36 hours, PEFC was still the first variable to be removed. REFC and

RAM were again the only significant synoptic variables.

In the regression for intensity change over 48 hours, the first variable that was removed was the PEFC. PEFC was removed first during the three successive period (24, 36, and 48- hour). This indicated that there was no good relationship between PEFC and intensity change. REFC, RAM, and SHEAR were significant at 48 hours. REFC and RAM were positively related to the intensity and SHEAR was negatively related to the intensity change.

In the regression for intensity change over 60 hours, DSHEAR was removed first and the retained variables were REFC, SHEAR, and RAM. The coefficients for REFC and RAM were positive and SHEAR was negative. In the last period (72 hours), PEFC was removed first. REFC, DSHEAR and SHEAR were significant. REFC was positively correlated with intensity change, while DSHEAR and SHEAR were negatively correlated with intensity change.

115 Table 4.9 presents the normalized coefficients of the synoptic variables after the ENSO

event in 1998. REFC was significant at all time periods and it had a positive impact on

intensity. The maximum normalized regression coefficient was at 12 hours. This indicated

that the ability of explanation for the variance in intensity by REFC decreases with forecast

period. RAM had a positive impact on intensity, while SHEAR was negatively correlated with intensity at longer time intervals. The increasing coefficients indicated that SHEAR had a better explanation of variance in intensity at longer periods. A comparison of Tables 4.7,

4.8, and 4.9 found that RAM was significant in the 1996 and 1998 cases, but not significant in 1997 (ENSO). Since RAM is a measure of the extent of the outer circulation of the typhoon (DeMaria and Kaplan, 1994b), the difference of environmental circulation pattern during ENSO and non-ENSO event is apparent. Factors other than the six variables considered in this study appear to have been more important. The effect of the size and strength of the typhoon is overwhelmed by other factors during the ENSO events. POT was not significant at all periods in these three years. The possible explanation is that the monthly averaged SSTs are not the best choices for using to derive the empirical equation, because the monthly sea surface temperatures can not precisely represent the daily variation of SST.

The lack of daily SSTs can be improved by using better SST data in the future. The increased statistical significance of REFC and PEFC for the year of the ENSO event (1997) and the year after the ENSO event (1998) seem to indicate the importance of changes to the upper troposphere circulation that occur during and after an ENSO event. The positive correlations between PEFC and REFC and intensity changes seem to indicate that the configuration of

116 the 200 mb flow is more favorable for the intensification of tropical cyclones outside regions of enhanced shear.

12h 24h 36h 48h 60h 72h POT — ... —— ...... REFC 0.728 0.542 0.448 0.461 0.450 0.632 PEFC — ... ».••• . . . ™ RAM — 0.371 0.456 0.429 0.460 ... SHEAR — -0.305 -0.314 -0.582 DSHEAR ...... — ... -0.440 R- (%) 74.4 74.8 72.4 74.0 70.9 58.3

Table 4.9: Normalized regression coefficient for residual variables after backward regression for 1998. The statistically significant at the 90% level are presented.

117 4.2.4 Comparison with Previous Studies

Similar studies have been performed by DeMaria and Kaplan (1994b) for Atlantic hurricanes and Petty (1997) for eastern North Pacific tropical cyclones. In this section, the results of this study are compared to these previous studies.

Tables 4.10, 4.11 and 4.12 show the normalized regression coefficients for the predicted variables of Atlantic Ocean (DeMaria and Kaplan, 1994b) and eastem North Pacific Ocean

(Petty, 1997). The six synoptic variables in this study are compared to the previous studies.

The variable POT was not significant for intensity changes at any periods in this study. This result is similar to the study of Petty (1997)(cf. Table 4.11), but opposite to the results of

DeMaria and Kaplan (1994b)(cf. Table 4.10). It reveals that POT is a good predictor for the intensity changes of Atlantic hurricanes, but not good in forecasting the intensity changes of the eastem and western North Pacific tropical cyclones. The possible reason is that each ocean basin has its own characteristics, the importance of POT may be different for each basin. In the Atlantic Ocean features, such as the Gulf Stream, combined with a higher average translational speed of tropical cyclones account for the significance of POT. In the eastem and western North Pacific Ocean, a more uniform SST pattem and slower translational speed, reduce the significance of POT as a predictor of intensity change.

Another explanation is that climatological sea surface temperatures used in this study may not precisely depict the daily variation of SST, so the accuracy of derived POT is also influenced. If the data for daily SSTs were available, it is possible that POT might be significant in the analysis.

118 12h 24h 36h 48h 60h 72h POT +Q32 +0.46 +0.56 +0.63 +0.68 +0.70 SHEAR -0.20 -0.26 -0.31 -0.36 -0.31 -0.25 DVMX +0.40 +0.28 +0.18 +0.16 +0.18 +0.16 REFC +0.03 +0.08 +0.16 +0.22 +0.19 +0.17 PEFC +0.08 +0.12 +0.12 +0.10 +0.10 +0.10 JDATE -0.04 -0.06 -0.07 -0.09 -0.12 -0.13 LONG +0.14 +0.14 +0.08 +0.03 -0.02 -0.09 DTE +0.12 +0.12 +0.09 +0.05 +0.00 -0.09 RAM +0.11 +0.11 +0.09 +0.05 +0.05 +0.03 DSHEAR -0.01 +0.06 +0.13 +0.07 -0.03 -0.11 R (%) 35.7 39.4 44.4 50.4 52.0 53.6

Table 4.10: Normalized regression coefficients for the combined climatological, persistence, and synoptic predictors. The coefficients that are significant at the 95% level are in bold: r is the percent of the total variance explained by the regression (from DeMaria and Kaplan, 1994b).

12h 24h 36h 48h 60h 72h PVMAXI2 +0.62 +0.46 +0.31 +0.19 +0.08 +0.03 VMAX -0.24 -0.31 -0.34 -0.37 -0.39 -0.39 ABSJDAY -0.09 -0.15 -0.21 -0.25 -0.28 -0.30 TS -0.02 -0.04 -0.03 -0.06 -0.31 -0.12 UTS +0.01 +0.02 +0.02 +0.05 -0.21 -0.10 VTS -0.02 -0.06 -0.08 -0.09 -0.03 -0.08 TCLAT -0.21 -0.31 -0.37 -0.41 -0.47 -0.49 TCLONG +0.08 +0.12 +0.18 +0.21 +0.22 +0.25 DTE +0.13 +0.07 +0.19 +0.23 -0.03 +0.06 POT +0.05 +0.06 +0.08 +0.07 +0.03 +0.01 R (%) 35.7 39.4 44.4 50.4 52.0 53.6

Table 4.11. Normalized regression coefficients for the combined climatological and persistence predictors. The coefficients that are significant at the 95% level are in bold (from Petty, 1997).

119 12h 24h 36h 48h 60h 72h PVMAX12 +0.59 +0.42 +0.23 +0.14 VMAX -0.26 -0.34 -0 3 6 -0 3 9 -0.36 -0.38 AJDAY ------0.12 -0.14 -0.19 -0.22 TS ------0.10 -0.13 TCLAT -0.25 -0.36 -0.49 -0.52 -0.57 -0.56 SHEAR — ———— -0.09 -0.09 -0.09 -0.09 -0.07 DSHEAR -0.08 -0.11 -0.12 -0.13 -0.09 -0.09 U ------———— -0.13 -0.11 T +0.08 +0.13 +0.16 +0.16 +0.15 +0.15 AT E -0.09 -0.11 -0.10 -0.06 ————— - - - - - T_E ------+0.10 +0.13 RAM ------+0.08 +0.10 +0.10 +0.11 +0.10 PEFC +0.09 +0.13 +0.11 +0.12 +0.10 +0.09 R (%) 60.2 59.3 60.2 63.0 65.7 67.4

Table 4.12: Normalized regression coefficients for the combined climatological, persistence, and synoptic predictors included in the model. The coefficients that are significant at the 95% level are in bold (from Petty, 1997).

As is shown in Table 4.10 (for Atlantic basin), the variable SHEAR was significant at all periods and had the largest magnitude of coefficient at 48-hour period. The coefficients of

SHEAR at Table 4.12 (for eastern North Pacific Ocean) were identical for the 24 to 60-hour period and slightly dropped at 72 hours. Compared to the previous studies, SHEAR was significant in this study at longer periods and had a better explanation of variance after 48 hours. The negative sign of the coefficients in all studies indicated that SHEAR was negatively related to the intensity change.

The coefficient of DSHEAR in the study of DeMaria and Kaplan (1994b) was positive at 36 hours and negative at 72 hours (cf. Table 4.10). It is reasonable for the negative sign at 72 hours since the intensity decreases with the increasing of vertical shear. The positive

120 coefficient at 36 hours may be a result of an interaction between storm and large scale

features in a positive way (DeMaria and Kaplan, 1994b). The coefficient of DSHEAR for

Petty’s study (1997) was significant at all periods (cf. Table 4.12). The negative relationship

between DSHEAR and intensity changes indicated that increasing vertical shear would

decrease the tropical cyclone intensity. The largest magnitude of the coefficient occurred at

48 hours may be a result of a rather large lag time between the tendency of vertical shear and

intensity changes (Petty, 1997). A similar situation also occurred in this study (cf. Tables 4.7.

4.8, and 4.9). The variable DSHEAR was significant after 48 hours with a negative

regression coefficient. It is apparent that a considerable lag time existed between the

DSHEAR and intensity changes.

The momentum flux variables (REFC and PEFC) were significant at most time periods

in the previous studies of DeMarai and Kaplan (1994b) and Petty (1997). The positive

coefficient is expected while the fluxes are acting to make the upper-level flow more

cyclonic (DeMaria and Kaplan, 1994b). Since the variable REFC was evaluated at the first

time period, the largest coefficient at 48 hours indicated that time lag existed between the

REFC and intensity changes. In this study, the positive coefficient of REFC was significant at all time periods in 1998 (cf. Table 4.9). The magnitude of regression coefficients decreased with time.

In the Atlantic Ocean, the variable RAM was significant at the first three time periods

with positive normalized regression coefficients (cf. Table 4.10). In the eastern North Pacific

Ocean, the positive coefficient was significant from 24 to 72 hours and the largest coefficient was at 60 hours (cf. Table 4.12). In this study, the variable RAM in 1998 also had its largest

121 coefficient at 60 hours with a positive value (cf. Table 4.9). RAM was significant at the longer time periods of 1996 and 1998. This result is similar to that found by Petty (1997).

4.2.5 The influence of ENSO on the Synoptic Variables

Tlie relationship between the synoptic variables and typhoon intensity changes has been discussed in the previous sections. The relative significance of the synoptic variables differed markedly during ENSO and non-ENSO events. To find the possible influence of ENSO on the intensity changes, the environmental conditions of western North Pacific Ocean are discussed in this section.

It is well known that the seasonal frequency of typhoon activity in western North Pacific basin is much less affected by ENSO events than in Atlantic basin (Gray, 1984). A comparison of Tables 4.13 and 4.14 also reveals that ENSO reduced the frequency of hurricanes in Atlantic basin but there is no that significant change in western North Pacific basin. However, a significant decrease in the number of tropical cyclones over the western

North Pacific Ocean was noted in the year after ENSO. Although the frequency o f typhoons was not influenced by ENSO, it dose not mean that ENSO had no effect on the typhoon intensity changes. Figures 4.33 to 4.35 present the track and distribution of typhoons over western North Pacific Ocean during ENSO and non-ENSO events. It is clear that most typhoons originated west of 155°E before ENSO event (1996). However, during the ENSO event (1997), the genesis area of typhoons extended east to 180°. After ENSO (1998), the

122 genesis area of typhoons retreated back to west of 145°E. This difference is partly due to the variation of SSTs between ENSO and non-ENSO events. Figures 4.36 to 4.41 show the summer distribution of SST from 1996 to 1998. The warm pool (SST > 28°C) began to extend eastward from 1996 and reached the eastern boundary of Pacific in 1997, then returned back to its non-ENSO position in 1998.

Another possible reason for the changes in the genesis regions is related to the effect of the monsoonal trough. The formation of western North Pacific typhoons is primarily associated with monsoon trough conditions (Gray, 1984). Changes of motion and structure of typhoons are influenced also by the effects of the large-scale monsoon circulation (Harr and Elsberry, 1991), and the behavior of the subtropical ridge (Lander, 1994).

Tropical Depression Tropical Storm Typhoon Total 1996 (before ENSO) 14 9 21( 7) 44 1997 (ENSO) 4 9 20(11) 33 1998 (After ENSO) 10 8 9( 2) 27

Table 4.13: The frequency of typhoons in the western North Pacific basin during ENSO and non-ENSO events (the numbers in the bracket are the frequency of super typhoons).

Tropical Depression Tropical Storm Hurricane Total 1996 (before ENSO) 0 4 9 13 1997 (ENSO) 1 1 5 7 1998 (After ENSO) 0 4 10 14

Table 4.14: The frequency of hurricanes in the Atlantic basin during ENSO and non-ENSO events.

123 During the summer, the position of the axis of the monsoon trough is usually from 20°N and 110°E to 10°N and 145°E with its normal orientation (NW-SE) (cf. Fig. 4.42a).

Sometimes, the axis of the monsoon trough moves northward and takes on a reverse orientation (SW-NE) (Lander, 1996) (cf. Fig. 4.42b). The number of episodes of reverse orientation, and the total time that the monsoon trough spends in a reverse-orientation state is related to ENSO to some degree (personal communication with Mark Lander). 1996 was a great year for reverse orientation of the monsoon trough. During the ENSO year of 1997, the monsoon trough existed in a reverse oriented state only a small amount of time and extended much further to the east than normal. This may partially explain the typhoons that originated further east in 1997. 1998 had some episodes of the reverse oriented state, but the year as a whole was much less active.

In the previous sections, the varying significance of some of the synoptic variables during

ENSO and non-ENSO events was noted. Relative eddy angular flux convergence (REFC) was not significant in 1996 but was significant in 1997 and 1998. Since REFC is a measure of whether the large-scale flow can strength or weaken the azimuthally tangential wind of the storm (DeMaria and Kaplan, 1994b), the pattern of upper-level, large-scale circulation induced by the reverse orientation of monsoon trough may be not have produced significant

REFC during 1996. After the monsoon trough returned to its normal condition, REFC became sufficiently large to significantly affect the intensity change.

The variable of integrated relative angular momentum (RAM) is significant most of the time during non-ENSO events, but is not significant at all during the ENSO event. Since

124 RAM is a measure of the extent of the outer circulation of the typhoon (DeMaria and Kaplan,

1994b), a change in the pattern of the environmental circulation may explain the different performance of RAM during ENSO and non-ENSO events. Further study is necessary to analyze such a physical mechanism in more detail.

125 Figure 4.35. The tracks of tropical cyclones for western North Pacific Ocean of 1998.

127 12CTE I30*E leor <5arw i2orw Longitude

Ju n1 9 9 B

ore 4'c arc <2 * 0 « arc 2 o rc 2 f c 2B*C 3BTC Sea Surface Tern perjure

«2CrE «50*E taor ifiorw ,20"W Longitude

Jul 1 9 9 6

ore 4*c arc «2*c «arc 2orc 24*c 2 8 'C 32"C Sea Surface Temperjure

Figure 4.36: The distribution of sea surface temperature in the North Pacific Ocean on June and July o f 1996.

128 L,20TE I50*E <6or tacrw <2orw Longitude Auq 199B

Sea Surf aoe Tern perju re

r2(TE rSO'E ifior «sorw I2CTW Longitude Sep 199B

a c 4*C fire (2'C «6*0 2CTC 24*0 2 8 *c arc Sea Surface Temperature

Figure 4.37: The distribution o f sea surface temperature in the North Pacific Ocean on August and September o f 1996.

129 I «20"E <90*E i8cr i5orw i2arwr Longitude J u n 1997

arc 12% «6*0 2orc 24% 2 8 % 32TC Sea Sud aoe Tetn pent ure

(20TE »50*E

12% I arc 2orc 24% 2 8 % 32"C Sea Surface Temperature

Figure 4.38: The distribution o f sea surface temperature in the North Pacific Ocean on June and July of 1997.

130 & ■ I ' ' 1 I I I I 1------1------1------1------1------r

' I ir>

L«20*E «50 E laor 150^ I20TW Longitude Auq 1997

0*C 4*C a*C 12 C «6*0 20rc 2<0 28*0 32*0 Sea Surface Tern perjure

«20*E «50*E «80* iscfw «20VT Longitude Sep 1997

0*0 4*0 8*0 «2*0 «6*0 20*0 24*0 28*0 3STO Sea Surface Temperature

Figure 4.39: The distribution o f sea surface temperature in the North Pacific Ocean on August and September o f 1997.

131 I I I I I 1 I I I I 1------1------r s

î§

I I I I— — j j I I I I ■ ' I ■ «ZOTE 150*E laor 13QTW 12CTW Longitude Jun 1998

Sea Surf aoe Temperature

r20*E «50 E «aor «50*W tzarw Longitude J u l1998

orc 4*0 8*0 «2*0 «6*0 20"O 24*0 28*0 32*0 SeaSurfæe Tem perdure

Figure 4.40: The distribution o f sea surface temperature in the North Pacific Ocean on June and July o f 1998.

132 tZCTE «S)*E «acr isorw i2orw Longitud« Auq 1998

SeaSurfaoe T«mper^ur«

(20TE «SO'E «ar tarw (2orw Longitude Sep 1998

orc 4*0 8*0 12*0 16*0 20*0 24*0 28*0 32*0 Sea Surface Tem perdure

Figure 4.41 : The distribution o f sea surface temperature in the North Pacific Ocean on August and September of 1998.

133 \ z '

I20*E 140-E 160*E

(b)

y 'I

120*E 140*E le O 'E

Figure 4.42: The low-level circulation during the summer in tropics of the western North Pacific: (a) The long-term average, and (b) a schematic example of the low-level circulation associated with a reverse-oriented monsoon trough. Bold zig-zag lines indicate ridge axes, and bold dashed line indicates the axis of the monsoon trough (from Lander, 1996)

134 CHAPTER 5

SUMMARY AND CONCLUSIONS

One major purpose of this study was to derive an empirical equation to relate the sea surface temperature and typhoon intensity over the western North Pacific Ocean. It is well known that sea surface temperature (SST) plays an important role on the intensification of typhoons. Many researchers related the SST and typhoon intensity changes by climatological data (Miller, 1958; Malleus and Riehl, 1960; Merrill, 1987, 1988a,b; Emanuel, 1986; Evans,

1993, Chu, 1994; DeMaria and Kaplan, 1994a; Whitney and Hobgood, 1997). These results reveal that the SST along is not a good predictor for the intensification of a typhoon, but the

SST can be a capping function to provide an upper boimd for the typhoon intensities. It is believed that the climatological SST data of western North Pacific may be used to derive an empirical equation related to the typhoon intensity in this area. This relationship would specify the capping function for the western Pacific.

A linear empirical equation was developed by using 27 years (1965 — 1991) of monthly sea surface temperature data and typhoon intensities. Each value of typhoon intensity was accompanied by a SST. The SSTs were stratified into 11 evenly spaced groups by 1°C intervals from 20.5°C to 3I.5°C. Maximum intensities were found after a search of the

135 largest value of intensity in each SST group. Figure 4.4 showed the relationship of maximum intensity to SST.

Linear regression was used to find a line to represent the line of maximum intensity. In this study, a straight line was selected to fit the maximum intensities. The derived linear function, called maximum potential intensity (MPI), represents most groups of maximum intensities very well except for the 3 1.5°C group (cf. Fig. 4.4). The lack of intense typhoons in the 31.5°C group results in an overestimate of intensity in this group by the MPI fimction.

Although an overestimate of intensity is possible, it is not a serious problem, because the higher SST regions are in the genesis areas of typhoons. Typhoons often intensify and reach their maximum intensity after moving out of this area. Thus, warmer SSTs do not by themselves guarantee higher intensity. The performance of this empirical equation is still very good as a capping function. In a future study, a two-degree curve line can be considered to replace the one-degree straight line in order to obtain better results.

To test the accuracy of the derived empirical equation, a weekly SST data set for 6 years

(1992 - 1997) was used. The SSTs associated with the time and position of typhoons were put into the empirical MPI function. Then the maximum potential intensity was obtained.

This value was compared to the actual intensity at the same time and position to see the difference between them. The results revealed that this derived MPI function provided an effective upper bound on the intensification and development of typhoons. There were no actual intensities that exceeded the maximum potential intensity during the development and

136 intensification stage. Some cases occurred in final stage due to the typhoon moving to

extremely cold water area, but that was not the focus of this research.

In this study, 41.4% of typhoon intensities reached their 50% maximum potential

intensity (MPI), and 10.7% attained 80% of MPI. These numbers are less than those from

the study of DeMaria and Kaplan (1994a), in which 58% and 19% cases reached their 50%

and 80% MPI in the Atlantic Ocean. The numbers are similar to the finding (42% and 11%)

by Whitney and Hobgood (1997) for the eastern North Pacific Ocean. It is found that in the

eastern and western North Pacific Ocean that tropical cyclones are less likely to approach

their MPI than are similar storms over the Atlantic Ocean.

The explanation for this difference between ocean basins is not immediately apparent.

One possible reason is that Atlantic hurricanes usually recurve rapidly northward and move

over cold water. The MPI is decreased due to the colder SST, but if the hurricane can

maintain a strong intensity before spinning down, it has a chance of getting closer to its MPI.

The problem is complicated by the different atmospheric environments over each basin. The thermal structure, upper-level flow pattern, upwelling of colder oceanic and variation of SST are factors that affect the intensity attained by a tropical cyclone.

In order to attempt to identify the significance of some of the environmental factors on intensity, six synoptic variables were related to the intensity changes of typhoons during the

3-year period (1996 — 1998 to represent before ENSO, ENSO, and after ENSO). The intensification potential (POT) was not significant in any periods. This result was disappointing, although it may result from the rather uniform SSTs in the region where typhoons develop. If daily SSTs were available, it may be possible to improve the empirical

137 MPI equation to obtain a better relationship between MPI and SST. Then POT might become

significant in the regression analysis. The relative angular momentum (RAM) is significant

in 1996 (before ENSO) and in 1998 (after ENSO), but not significant in 1997 (ENSO). Since

RAM provides a measure of outer circulation, it is apparent that the ENSO event changed

the large-scale flow at higher levels to reduce the importance of RAM on the intensification

of a typhoon. The possible explanation is the reverse orientation of the monsoon trough thus

changing the environmental circulation. The vertical shear of horizontal wind (SHEAR) is a good predictor in most periods with a negative relationship to the intensity changes. This result is what was anticipated, and it agrees with previous research. The relative angular momentum flux convergence (REFC) is significant in the regressions for 1997 and 1998.

REFC provided a measure of large-scale flow changing the azimuthally averaged tangential wind of the storm (DeMaria and Kaplan, 1994a).

Each variable has different performance at various time periods. For the ENSO (1997) event, only REFC (relatively eddy angular momentum flux convergence), PEFC (planetary eddy angular momentum flux convergence), and DSHEAR (tendency of the shear) are significant in the 3 different time periods. It seems that large-scale flow at higher levels could play an important role on the intensification of typhoon.

In the future, more factors related to large-scale flow can be added to the multiple regression model to investigate the variation of typhoon intensity during ENSO. Although

ENSO is a basin wide event, its influence is global. To see what factors induced by ENSO are significant to typhoon intensity changes, the large-scale environmental flow should to be considered.

138 APPENDEX A

SPSS STATISTICAL OUTPUT FOR 1996

139 Backward regression for 12-hour period

Model Summary*'®'*

Sid. Error Vanables Adjusted of the Model Entered Removed R R Square R Square Estimate 1 OSHEA R. RAM. POT. 481 .231 .082 5.7698 PEFC. REFC. SHEAR"' 1 2 PEFC .480 .231 .111 5.6797 3 .» REFC .477 .228 .134 5.6038 n 4 POT 472 222 154 5.5401 s ' RAM 4SI 204 158 5.5257 6 ' DSHEAR 1 389 151 127 58255 7 ' DSHEAR* 1 399 151 127 5 8255 a Oepenoeni vamaoie iCh a n GE 6. Meihoo Enter c. Method. Backward (criterion Prcoaoii'ly of F-lo-remove >» 100) d. Independent Variables- (Consiant). DSHEAR. RAM. POT. PEFC. REFC. SHEAR e. All requested variables entered. I. Independent Vanables: (Constant). DSHEAR. RAM. POT. REFC. SHEAR g Independent Variables (Constant). DSHEAR. RAM. POT. SHEAR n. Independent Vanabies (Consiant). DSHEAR. RAM. SHEAR I Independent Vanables (Constant). DSHEAR SHEAR I Independent variables (Constant). SHEAR k. Probability of F-io remove » 100 iipms reacneo

ANOVA* Sum of M ean Model Squares df Square F Sig. 1 R egression 309.842 6 51.640 1 551 .195^ Residual 1032 021 31 33.291 Total 1341 862 37 2 Regression 309.584 5 61.917 1.919 .119* Residual 1032 278 32 32.259 Total 1341.862 37 3 R egression 305 580 4 76.395 2.433 .067* Residual 1036 283 33 31.403 Total 1341 862 37 4 R egression 298 328 3 99 4 4 3 3 240 034* Residual 1043 534 34 30 692 Total 134 1 862 37 5 Regression 273 182 2 136 591 4 473 019' Residual 1068 681 35 30 534 Total 1341 862 37 6 Regression 202 592 1 202 592 6 402 016» Residual 1139 270 36 31 646 Total 1341 862 37 7 R egression 202 592 1 202.592 6 402 .016» Residual 1139 270 1 36 31 646 Total 1341 362 ' 37 a Dependent variable iCh a n GE b. Independent Variables: (Constant) DSHEAR RAM. POT. PEFC. REFC. SHEAR c. Independent Vanables: (Constant), DSHEAR. RAM. POT. REFC. SHEAR d Independent variables (Constant), DSHEAR RAM. POT. SHEAR a. independent Variables: (Constant). DSHEAR. RAM. SHEAR f. Independent Variables. (Constant). DSHEAR. SHEAR g. Independent Variables: (Constant). SHEAR 140 Backward regression for 12-hour period

Coefficients*

S ta n d a r d iz e d Unstandardized C o e ffic ie Coefficients n ts S td . M odel 8 E rro r B e ta t S iq. 1 (Constant) 1 1 .0 5 7 3 .4 6 4 3 .1 9 2 .0 0 3 POT -2.8E-02 .065 -.0 6 9 - 4 2 5 6 7 4 REFC 4 .3 E -0 3 .013 071 341 .7 3 5 PEFC 4 1 8 1 8 9 7 4 7 5 5 5 .6 0 1 3 0 8 8 .9 3 0 RAM 3 2E-18 .000 .211 9 6 9 .3 4 0 SM EA R -.8 2 3 ■ 577 - 3 3 0 -1 4 2 7 .1 6 4 DSHEAR .4 0 0 .4 0 0 178 1 000 .325 2 (Constant) 11.043 3 .4 0 6 3 .2 4 2 .0 0 3 POT -2 .8 E -0 2 .064 - 0 7 0 -.4 4 0 .6 6 3 REFC 3 .7 E -0 3 .011 061 3 5 2 .7 2 7 RAM 3 2 E -1 8 0 0 0 .209 .982 .333 SHEAR - 8 3 2 559 - 3 3 3 -1 .4 8 7 .1 4 7 □ S H E A R 3 9 3 386 .1 7 5 1.0 1 9 .3 1 6 3 (Constant) 11.098 3.357 3.306 .002 POT -3 .0 E -0 2 .0 6 3 -.0 7 5 -.481 .6 3 4 RAM 3.1E-18 ' .000 .2 0 2 .9 6 7 .3 4 0 SHEAR -.7 8 5 .5 3 6 -.314 -1 464 .1 5 3 DSHEAR .4 1 2 .3 7 7 .1 8 3 1 .0 9 0 .2 8 3 4 (Constant) 1 0 .0 1 6 2.451 4 0 7 0 .0 0 0 RAM 2 .8 E -1 8 .000 184 905 .3 7 2 SHEAR -.8 1 5 .5 2 6 - 327 -1 550 130 □SHEAR .440 .368 .1 9 6 1 .1 9 6 .2 4 0 5 (C o n s ta n t) 10 4 0 9 2 .4 1 6 4 3 08 .0 0 0 SHEAR -1 .1 3 2 .391 -.4 5 3 -2 8 92 .0 0 7 □ S H E A R 5 3 5 .3 5 2 .2 3 8 1 5 20 .1 3 7 6 (Constant) 9.443 2 .3 7 3 3 9 7 9 .0 0 0 SHEAR - 9 7 0 .384 -.3 8 9 -2 5 30 .0 1 6 7 (Constant) 9 4 4 3 2 .3 7 3 3 9 7 9 0 0 0 SHEAR - 9 7 0 384 - 38 9 -2 5 30 .0 1 6 a Dependent Variable ICHANGE

141 Backward regression for 24-hour period

Modal Summary*-®-'

Std. Error Variables Adjusted Of the Model Entered Removed R R Souare R Square Estimate 1 OSHEA R. POT. RAM. 583 .340 REFC. 212 50521 PEFC. SHEAR®* 2 r POT .583 .340 .237 4.9733 3 g PEFC 583 .339 .259 4 8983 4 h DSHEAR .568 .323 .263 4.8861 s RAM .535 .288 .246 4.9434 6 REFC 4S9 .239 218 5.0329 » 7 REFC* .489 __ .239 ______LU. a Oeoendeni VariaDie ICHANGE e. Method Enter c. Method. Backward {cnlenon Prooaoiiily ot F-to-remove >* 100) d. Independent Variable»- (Constant). OSMEAR. POT. RAM. REFC. PEFC. SHEAR e. All requested vanables entered r. Independent Vanables: (Constant). OSHEAR. RAM. REFC. PEFC, SHEAR g. Independent Variables: (Constant). OSHEAR. RAM. REFC. SHEAR h. Independent Variables: (Constant). RAM. REFC. SHEAR I. Independent Variables: (Constant). REFC. SHEAR i Independent Vanabies (Constant). SHEAR k. Probability o( F-to-remove * 100 limits reached

ANOVA* Sum of M ean Model Squares df Square F SIg. 1 Regression 407.463 6 67.910 2.661 .034^ Residual 791 242 31 25524 Total 1198.705 37 2 R egression 407.230 5 81 446 3.293 .016' Residual 791.475 32 24.734 Total 1198 70S 37 3 Regression 406.918 4 101 730 4.240 .007* Residual 791 787 33 23.994 Total 1198 705 37 4 Regression 386 987 3 128.996 5.403 .004* Residual 811.718 34 23 874 Total 1198 70S 37 5 R egression 343 410 2 171.705 7 026 003' Residual 855 295 35 24 437 Total 1198 705 37 6 R egression 286 840 1 286 840 11.324 002* Residual 911 865 36 25 330 Total 1198 705 37 7 Regression 286.840 1 286 840 11.324 .002» Residual 911 865 36 25.330 Total 1198 705 37 a Dependent Variable iCHANGE b Independent Vanables: (Constant). OSHEAR. POT. RAM. REFC. PEFC. SHEAR c. Independent Variables: (Constant). OSHEAR. RAM. REFC. PEFC. SHEAR d. Independent Variables (Constant). OSHEAR. RAM. REFC. SHEAR e. Independent Variables: (Constant). RAM.REFC.SHEAR (. Independent Variables. (Constant), REFC. SHEAR g. Independent Variables: (Constant). SHEAR 142 Backward regression for 24-hour period

Coefficients*

S ta n d a r d ized Unstandardized C oefficie Coefficients n ts S td . M odel B E rro r B e ta t S iq. 1 (C o n s ta n t) 1 0 .1 0 5 2 .7 6 2 3 .6 5 9 .001 POT 5 .7 E -0 3 .0 6 0 .0 1 4 .0 9 5 .9 2 5 REFC 1 .3 E -0 2 .0 1 0 .2 3 9 1 .3 1 8 .1 9 7 PEFC 5 4 5 9 .7 3 8 4 3 0 1 7 .6 .0 2 8 .1 2 7 .9 0 0 RAM 2 .5 E -1 8 .0 0 0 .1 7 3 .8 9 4 .3 7 8 SHEAR -1.102 .4 7 9 -.601 -2.301 .0 2 8 OSHEAR .6 3 8 .7 3 2 .191 .8 7 2 .3 9 0 2 (C o n s ta n t) 1 0 .2 6 9 2 .1 2 7 4 .8 2 7 .0 0 0 REFC 1 .3 E -0 2 .0 1 0 .2 3 7 1 .3 3 7 .191 PEFC 4 6 6 8 .0 4 0 4 1 5 5 2 .3 .0 2 4 .1 1 2 .911 RAM 2 .5 E -1 8 .0 0 0 .1 7 4 .9 1 3 .3 6 8 SHEAR -1 .0 9 7 .4 6 8 -.5 9 9 -2 .3 4 1 .0 2 6 D S H E A R .6 2 2 .701 .1 8 7 .8 8 8 .381 3 (Constant) 10.278 2 .0 9 4 4 .9 0 9 .0 0 0 REFC 1 .2 E -0 2 .0 0 9 .2 2 9 1 .4 3 6 .161 RAM 2 .5 E -1 8 .0 0 0 .1 7 5 .9 3 5 .3 5 6 SHEAR -1 .1 0 6 45 3 - 604 -2 44 2 .0 2 0 OSHEAR .5 9 7 6 5 5 179 911 36 9 4 (Constant) 9 .3 8 6 1.846 5 0 84 .0 0 0 REFC 1.3E-02 .0 0 9 2 4 0 1.513 .1 4 0 RAM 3 .4 E -1 8 .0 0 0 .2 3 6 1.351 .1 8 6 SHEAR -.8 4 2 347 -.4 6 0 -2 .4 2 5 .021 5 (Constant) 9 348 1.868 5 .0 0 5 .0 0 0 REFC 1 .3 E -0 2 .009 244 1.521 .1 3 7 SHEAR -1 .0 9 9 .294 - 6 0 0 -3 74 3 .001 6 (C o n sta n t) 9 .1 9 9 1 8 9 9 4 8 4 4 0 0 0 SHEAR -.8 9 6 .266 - 4 8 9 -3 .3 6 5 .0 0 2 7 (C o n s ta n t) 9 .1 9 9 1.899 4 .8 4 4 .0 0 0 S H E A R - 8 9 6 2 6 6 - 4 8 9 -3 .3 6 5 0 0 2 a. Dependent Variable: ICHANGE

143 Backward regression for 36-hour period

Model Summery*-®-'

Std. Error Variables Adjusted Of the Model Entarad 1 Removed R R Square 1 OSHEA R. POT. REFC. RAM. .535 .286 .148 5.1239 PEFC. , SHEAR** f 2 DSHEAR 535 288 .174 5.0445 3 • POT 534 .285 .199 4.9688 M 4 REFC 526 .277 .213 4.9231 S I PEFC 492 242 .199 4.9687 « 1 RAM .448 .201 .179 5.0309 7 f RAM* 448 ______221 179 ___ L 2 2 S 1 . Dependent Vaheble: (CHANGE t> Method: Enter c. Metnod Backward (criterion ProoaDiiity o f F-io-remove >» 100). d Indeoendent Venebiee (Conetam), D ShEar, p q t. REFC. RAM. PEFC. SHEAR e. All requested vanaoies entered f. Independent Variables: (Constani). POT. REFC. RAM. PEFC. SHEAR g Independent Variables: (Constant). REFC. RAM. PEFC. SHEAR h. Independent Variables: (Constant). RAM. PEFC. SHEAR I. Indépendant variables: (Constant). RAM. SHEAR I- Independent Variables: (Constant). SHEAR k. Probability of F-io-ramove # .100 limits reached

ANOVA®

Sum of Mean Model Squares df Square F Sig. 1 R egression 326.233 8 54.372 2.071 .086'' Residual 813.869 31 28.254 Total 1140.102 37 2 Regression 325.804 5 65.181 2.581 .047® Residual 814.298 32 25.447 Total 1140 102 37 3 R egression 325.377 4 81.344 3 295 .022® Residual 814 724 33 24.689 Total 1140.102 37 4 R egression 316 031 3 105.344 4.348 .011® Residual 824.071 34 24.237 Total 1140.102 37 5 R egression 278 020 2 138010 5 590 .008' Residual 864 082 35 24 688 Total 1140 102 37 6 Regression 228 933 I 228 933 9 045 .005» Residual 911 169 36 25 310 Toiai 1140.102 37 7 R egression 228 933 1 228 933 9 045 005» Residual 911 169 36 25 310 Total 1140 102 .. Î 1 . a. Dependent Variable ICh a n GE b Independent Vanables (Constant) DSHEAR, POT, REFC. RAM. PEFC. SHEAR c. Independent variables (Consiani). POT REFC. RAM. PEFC. SHEAR d. Independent Variables (Constant). REFC. RAM. PEFC. SHEAR e. Independent Variables: (Constant), RAM. PEFC.SHEAR f Independent Variables: (Constant). RAM.SHEAR 0 Independent Variables: (Constant). SHEAR 144 Backward regression for 36-hour period

Coefficients*

S ta n d a r d iz e d Unstandardized C o efficie Coefficients n ts S td . M o d el B E rro r B e ta t S id . 1 (Constant) 6 .2 8 8 2 .7 3 7 3 .0 2 8 .0 0 5 POT -9 .3 E -0 3 .0 6 3 -.0 2 3 - 1 4 7 .8 8 4 REFC 6 .0 E -0 3 .0 1 1 .110 .575 .570 PEFC 4 4 3 1 6 .8 4 2 9 4 3 .0 .2 4 7 1 .0 3 2 .3 1 0 RAM 4 .1 E -1 8 .0 0 0 .297 1 .4 7 0 .1 5 2 SHEAR -.7 6 5 4 4 9 - 4 9 2 -1 .7 0 4 .0 9 8 DSHEAR -7 .7 E -0 2 .601 -.023 -.128 .899 2 (Constant) 8.337 2 668 3 .1 2 5 0 0 4 POT -8 .0 E -0 3 0 6 2 -.020 -.129 .898 REFC 6 .2 E -0 3 .0 1 0 .113 .602 .551 PEFC 4 4 4 9 2 .5 4 2 2 5 6 .2 .2 4 8 1 .0 5 3 .3 0 0 RAM 4 .0 E -1 8 .0 0 0 .292 1.495 .145 SHEAR -.7 9 2 .3 9 2 -.509 -2.021 .0 5 2 3 (C o n sta n t) 8 .1 0 3 1 .9 3 5 4 .1 8 8 .0 0 0 REFC 6 .2 E -0 3 , .0 1 0 .1 1 4 .6 1 5 .5 4 3 PEFC 4 3 7 2 7 .2 4 1 2 1 2 .5 .2 4 4 1.061 .2 9 6 RAM 4 .0 E -1 8 .0 0 0 2 9 2 1 .5 2 0 .1 3 8 SHEAR -.7 9 0 .3 8 6 -.5 0 8 -2 .0 4 8 .0 4 9 4 (Constant) 8.094 1 .9 1 7 4 .2 2 3 .0 0 0 PEFC 5 0 5 3 7 .5 3 9 3 3 3 .9 .281 1 .2 8 5 .2 0 8 RAM 4 . IE -1 8 .0 0 0 .2 9 8 1 .5 6 8 .1 2 6 SHEAR -.7 2 8 .3 6 9 -.4 6 8 -1 .9 7 4 0 5 7 5 (C o n sta n t) 7 .1 8 8 1 7 9 9 3 .9 9 6 .0 0 0 RAM 3 .6 E -1 8 0 0 0 .2 6 2 1.381 .1 7 6 SHEAR -.4 3 9 .2 9 5 -.282 -1.488 .1 4 6 6 (C o n sta n t) 7 .1 8 4 1 .8 2 2 3 .9 4 4 .0 0 0 SHEAR -.6 9 7 .2 3 2 -.448 -3.008 .0 0 5 7 (Constant) 7 .1 8 4 1 .8 2 2 3 .9 4 4 .0 0 0 SHEAR -.6 9 7 .2 3 2 -.448 -3.008 .005 a. Dependent Variable; {CHANGE

145 Backward regression for 48-hour period

Model Summary*'®'*

Std. Error Variables Of the Model Entered Removed R R Square R Square EsUmaia 1 OSHEA R. POT. RAM. 623 .388 .269 4.7400 REFC. PEFC . , SHEAR" 2 f POT 621 386 .290 4.6719 3 fl REFC 616 .379 .304 4.6283 4 n PEFC 600 360 .304 4.6259 S .* SHEAR .591 349 .312 4 8986 » s SHEARi 591 - - W9 ______lU L 4.598«_ a. Dependant Vanaoie: (CHANGE b. Method: Enter e. Method: Backward (criterion: Probability of F-to-remove >• .100). d. Indépendant Variablea: (Constant). OS h Ea R. POT. RAM. REFC. PEFC. SHEAR a. All requested variables entered. t. independent Variables: (Constant). DSHEAR. RAM. REFC. PEFC. SHEAR g. Independent Venables: (Constant). DSHEAR. RAM. PEFC. SHEAR h. Independent Variables: (Constant). DSHEAR. RAM. SHEAR I. Independent Variables: (Constant). DSHEAR. RAM J. Probability of F-to-remove * lOO limits reached

ANOVA* Sum of Mean Model Squares dt Square F SIQ. 1 R egression 441.085 8 73.514 3.272 .013» Residual 696 482 31 22.467 Total 1137.567 37 2 R egression 439.118 5 87.824 4.024 .006* Residual 696.449 32 21.827 Total 1137.567 37 3 Regression 431.586 4 107.897 5.043 .003^ Residual 705.981 33 21.393 Total 1137.567 37 4 R egression 410 008 3 136.669 6.387 .001» Residual 727.559 34 21.399 Total 1137 567 37 5 R egression 397 424 2 198.712 9.397 .001' R esidual 740 142 35 21.147 Total 1137 567 37 6 Regression 397 424 2 198.712 9.397 001' Residual 740.142 35 21.147 Total 1137 567 . . . - . 1 a. Dependent Vanabie ICHANGE b Independent Variables: (Constant), DSHEAR POT. r a m . REFC. PEFC. SHEAR c Independent Variables (Constant), DSHEAR. RAM. REFC. PEFC .SH EA R d Independent Variables (Constant), OSHEAR. RAM.PEFC. SHEAR e independent Variables: (Constant). OSHEAR RAM. S h e a r I Independent Vanaoies: iConsiani). DSHEAR. RAM

146 Backward regression for 48-hour period

Coefficients*

S ta n d a r d iz e d Unstandardized C o efficie Coefficients n ts S td . M odel B E rro r B e ta t S ig . 1 (Constant) 7.377 2 .6 0 7 2 .8 3 0 .0 0 8 POT -1 .9 E -0 2 .065 -.046 -.296 7 6 9 REFC 5.6E-03 .0 1 0 .0 9 2 .540 .5 9 3 PEFC 45143.6 4 0 0 5 5 .2 .2 8 6 1 .1 2 7 .2 6 8 RAM 4 .5 E -1 8 , .0 0 0 .361 2 .0 4 9 .0 4 9 SHEAR -.3 8 9 .3 6 2 -.3 1 7 -1 .0 7 6 .2 9 0 DSHEAR - .7 3 5 .4 4 6 -.3 2 7 -1 .6 4 9 .1 0 9 2 (C o n sta n t) 6 .8 6 2 1 .9 1 2 3 .5 8 9 .001 REFC 5.9E-03 .0 1 0 .0 9 8 .587 .561 PEFC 4 1 5 8 7 .4 3 7 6 6 1 .3 .2 6 3 1.104 .2 7 8 RAM 4 .5 E - 1 8 .0 0 0 .3 5 8 2 .0 6 5 .0 4 7 SHEAR -.3 8 0 .3 5 5 -.309 -1.070 .2 9 3 DSHEAR - .7 2 6 .4 3 8 -.3 2 3 -1 .6 5 6 .1 0 8 3 (Constant) 6.744 1 .8 8 3 3 .5 8 2 .001 PEFC 3 6 4 0 4 .7 ,• 3 6 2 4 8 .1 .2 3 0 1.004 .3 2 3 RAM 4 .5 E - 1 8 .0 0 0 .3 5 6 2 .0 7 8 ■ .0 4 6 S H E A R -.4 2 4 .3 4 4 -.3 4 5 -1 .2 3 3 .2 2 6 DSHEAR -.6 7 6 .4 2 6 -.301 -1 .5 8 8 .1 2 2 4 (Constant) 5.900 1 .6 8 5 3.502 .001 RAM 4 .1 E -1 8 0 0 0 327 1 936 .061 SHEAR -.2 0 2 .2 6 3 -.1 6 4 • 767 .4 4 8 DSHEAR .7 2 4 .4 2 3 - 32 2 -1.711 .0 9 6 5 (C o n s ta n t) 5 .0 0 9 1 .2 1 3 4 131 .0 0 0 RAM 5 .1 E -1 8 .0 0 0 .4 0 3 2 .9 5 4 .0 0 6 DSHEAR -.9 4 6 .3 0 6 -.421 -3 .0 8 9 .0 0 4 6 (Constant) 5.009 1 .2 1 3 4.131 .0 0 0 RAM 5 .1 E -1 8 .0 0 0 .4 0 3 2 .9 5 4 .0 0 6 D S H E A R - 9 4 6 3 0 6 -.421 -3 .0 8 9 ,004_ a. Dependent Variable: {CHANGE

147 Backward regression for 60-hour period

Model Summary*'®'*

Std. Error Variables Adjusted of tna Model Entered Removed R R Square R Square Estimate 1 OSHEA R. RAM. POT. 640 .409 .295 4.6610 REFC.

2 I POT .639 .409 .316 4.5901 3 .« REFC .639 .408 .336 4.5222 4 K OSHEAR 60S 366 .311 4.6090 S n DSHEAR- _____ S&2- ______3sa_ ■ ■ ,iv — f.flCW a. Dapandani Variabia. ICHANGE b. Mathod; Entar c. Meinod; Backward {cntenon: Probability of F-to-remova >* .100). d. Indapandant Variabiat: (Conatant). OSHEAR. RAM, POT. REFC. SHEAR. PEFC a. All raduaatad vanabiaa antarad. 1. Indapandant Variabiea: (Constant). DSHEAR. RAM. REFC. SHEAR. PEFC 8 Indapandant Vanabiaa: (Constant). OSHEAR. RAM. SHEAR. PEFC n. Indapandant Vanabiaa: (Constant). RAM. SHEAR. PEFC I Probability of F-to*ramova « 100 limits reached

ANOVA* Sum of Mean Model Squares Of Square F Siq. 1 Regression 466.461 6 77.744 3.579 .008® Residual 673.469 31 21.725 Total 1139.930 37 2 Regression 465.713 5 93.143 4.421 .004* Residual 674 217 32 21.069 Total 1139 930 37 3 Regression 465 058 4 116.265 5 635 .001* Residual 674.672 33 20.451 Total 1139 930 37 4 Regression 417.677 3 139.226 6.554 .001* Residual 722.253 34 21.243 Total 1139 930 37 5 R egression 417.677 3 139.226 6.554 .001* R esidual 7 2 2 2 5 3 34 21.243 Total 1139 930 37 a. Dependent Vanabie: ICHANGE b. Indapandant Vanabiaa. (Constant). OSHEAR. RAM. POT. REFC. SHEAR. PEFC c. Independent Vanabies' (Constant). OSHEAR, RAM. REFC. SHEAR. PEFC d. Independent variables (Constant) OSHEAR. RAM. SHEAR. PEFC e Independent Variables (Constant), RAM Sh e a r .PEFC

148 Backward regression for 60-hour period

Coefflcionts*

S ta n d a r d iz e d Unstandardized C o efficie Coefficients n ts S td . M o d el B E rro r B e ta t S iq. 1 (C o n s ta n t) 7 .9 3 3 2 .6 8 9 2 .9 5 0 .0 0 6 POT -1 .4 E -0 2 .0 7 6 -.031 -.1 8 6 .854 REFC 2 .3 E -0 3 .0 1 0 .0 3 6 .2 1 7 .8 3 0 PEFC 64356.9 4 0 4 3 4 .2 .4 2 5 1.592 .1 2 2 RAM 5. I E - 1 8 .0 0 0 .4 1 2 2 .6 4 4 .0 1 3 SHEAR -.6 8 8 . .2 8 0 -.603 -2.452 .0 2 0 DSHEAR -.6 3 6 .4 3 4 -.225 -1.465 .1 5 3 2 (Constant) 7.597 1 .9 5 8 3 .8 7 9 .0 0 0 REFC 1 .7 E -0 3 .0 1 0 .0 2 8 .1 7 6 861 PEFC 61685.6 37211.9 .4 0 7 1.658 .1 0 7 RAM 5 .0 E -1 8 .0 0 0 .4 1 0 2 .6 7 9 .0 1 2 SHEAR -.6 8 1 .2 7 3 - 5 9 7 -2 .4 8 8 .0 1 8 DSHEAR -.6 2 2 .421 -.2 2 0 -1 .4 7 8 .1 4 9 3 (C o n s ta n t) 7 .6 6 2 1 .8 9 5 4 .0 4 3 .0 0 0 PEFC 6 3 0 5 6 8 3 5 8 5 1 .4 .4 1 6 1.759 .088 RAM 5 .0 E - 1 8 ' .0 0 0 .4 0 9 2 .7 1 4 .0 1 0 SHEAR -.6 7 4 .2 6 7 -.5 9 2 -2 .5 2 3 .0 1 7 DSHEAR -.6 2 9 .4 1 3 -.2 2 2 -1 .5 2 2 .1 3 8 4 (C o n s ta n t) 8 .0 2 0 1 .9 1 7 4 .1 8 5 .0 0 0 PEFC 6 7 0 0 6 .4 3 6 4 4 3 .2 .4 4 2 1.839 .0 7 5 RAM 4 .8 E -1 8 .0 0 0 .389 2 .5 4 4 .0 1 6 SHEAR -.8 0 1 .2 5 9 -.703 -3.095 .004 5 (C o n s ta n t) 8 .0 2 0 1 .9 1 7 4 185 .0 0 0 PEFC 6 7 0 0 6 4 3 6 4 4 3 2 4 4 2 1 8 39 .0 7 5 RAM 4 .8 E -1 8 0 0 0 389 2 544 .016 SHEAR - 801 2 5 9 - 703 -3 095 004 a. Dependent Variable ICHANGE

149 Backward regression for 72-hour period

Modal Summary*'*'*

Std. Error Vanabiaa Adjusted of die Modal Entered Removed R R Souare R Square Estimate 1 DSHEA R. RAM. REFC. 614 .377 .256 4.5758 SHEAR. p a n , . PEFC*' 1 2 DSHEAR .610 .373 .274 4.5187 3 .* REFC 592 .350 .272 4.5278 h 4 POT .577 .333 .274 4.5214 5 n PO T 577 ____ 274 4 5214 a. Dapandani vanaoia (CHANGE b Mainod Entar c. Matbod: Backward (crtlanon. Prooab■ .100). d Indapandant Variabiat: (Conatant). DSHEAR. RAM. REFC. SHEAR. POT. PEFC a. All raquttted variabiat antarad f. Indapandant Variabiat: (Conatant). RAM. REFC. SHEAR. POT. PEFC g Indapandant Vanabiaa (Conatant). RAM. SHEAR. POT. PEFC h. Independent Variablea: (Conatani). RAM. SHEAR. PEFC i Probability of F-to-remove = 100 limits reacned

ANOVA* Sum ol Mean Model Squares df Square F Sig. 1 R egression 392.241 6 65.374 3.122 .016* Residual 649 086 31 20936 Total 1041.327 37 2 Régression 387 916 5 77.583 3.800 .008* Residual 653 411 32 20.419 Total 1041 327 37 3 Regression 364.844 4 91.211 4.449 .005* Residual 676 483 33 20.499 Total 1041,327 37 4 R egression 346.267 3 115.422 5.646 .003* Residual 695 059 34 20 443 Total 1041 327 37 5 Regression 346 267 3 115 422 5.646 .003* Residual 695 059 34 20 443 Total 1041 327 . ____ ?I a. Dependant Variable (CHANGE b Independent vanabiaa: (Constant), OSHEAR. RAM. REFC. SHEAR. POT. PEFC c. independent Variables: (Constant), RAM. REFC. SHEAR. POT. PEFC d independent Variables: (Constant), RAM S h e a r , p o t . PEFC e Independent Variables: (Constant). RAM SHEAR.PEFC

150 Backward regression for 72-hour period

Coefficients'

S ta n d a r d iz e d Unstandardized C o e ffic ie Coefficients n ts S td . M odel B E rro r B e ta I Siq. 1 (C o n s ta n t) 8.791 2 .8 6 4 3 .0 7 0 .0 0 4 POT •8 .B E -0 2 .0 8 6 -.2 0 1 -1 .0 1 9 .3 1 6 REFC 1. IE -0 2 .0 1 0 .1 8 8 1 .0 6 5 .2 9 5 PEFC 9 1 3 7 9 .2 41527.1 .596 2 .2 0 0 .0 3 5 RAM 3 .8 E -1 8 .0 0 0 .3 2 7 2 .0 5 4 .0 4 8 SHEAR -.9 7 8 .2 6 8 -.8 8 3 -3 .6 5 1 .001 DSHEAR .1 3 2 .2 8 9 .0 7 6 .4 5 4 .6 5 3 2 (C o n sta n t) 8 .9 3 7 2 .8 1 0 3 .1 8 0 .0 0 3 POT -.1 0 3 .0 7 9 - 2 3 5 - 1 .3 0 2 2 0 2 REFC 1. IE -0 2 .0 1 0 .1 8 5 1 .0 6 3 .2 9 6 PEFC 91410.7 4 1 0 0 9 .0 .5 9 6 2 .2 2 9 .0 3 3 RAM 3 .7 E -1 8 .0 0 0 .3 2 2 2 .0 5 3 .0 4 8 SHEAR -.9 4 5 .2 5 5 -.8 5 4 -3 .7 1 0 .001 3 (C o n s ta n t) 8 .5 4 0 2 .7 9 1 3 .0 6 0 .0 0 4 POT -6 .9 E -0 2 ' .0 7 2 -.1 5 7 -.9 5 2 .3 4 8 PEFC 9 3 9 2 6 .6 4 1 0 2 1 .1 .6 1 2 2 .2 9 0 .0 2 9 RAM 3 .5 E -1 8 .0 0 0 .3 0 3 1.941 .061 SHEAR -.907 .253 - 8 1 9 -3 .5 8 8 .001 4 (C o n s ta n t) 6 .6 7 4 1 .9 8 3 3 .3 6 5 .0 0 2 PEFC 7 4 9 7 9 .6 3 5 8 1 9 .6 .4 8 9 2 .0 9 3 .0 4 4 RAM 3 .4 E -1 8 .0 0 0 .2 8 9 1 .8 6 3 .071 SHEAR -.8 4 4 .2 4 4 -.7 6 2 -3 .4 6 4 .001 5 (C o n sta n t) 6 .6 7 4 1 9 8 3 3 3 6 5 .0 0 2 PEFC 74979 6 3 5 8 1 9 6 4 8 9 2 0 9 3 .044 RAM 3 4 E -1 8 0 0 0 2 8 9 1 .8 6 3 .071 SHEAR . 844 2 44 - 7 6 2 -3 4 6 4 001 a. Dependent Variable: ICHANGE

151 APPENDEX B

SPSS STATISTICAL OUTPUT FOR 1997

152 Backward regression for 12-hour period

Modtl Summary*

Std. Error vanaoiaa AAuatad o f * * Modal Eniarad Ramovad R R Souara R Souara Eatlmai* t OSHEA R. RAM. PEFC. 340 .116 .126 4 .6 1 6 * POT.

Z RAM 340 l i e -0 7 7 4.5174 3 a OSHEAR 331 .110 -.03* 4 .4 3 6 7 4 REFC 310 0*6 -.012 4.37*6 i POT 301 .0*1 .021 4.3061 6 1 SHEAR 207 .043 00* 4 .3 3 7 0 7 • PEFC 0 00 .000 .000 4 .3S 34 • *PEFC .000 ___ AM. ______fiSfi- _ 4 J 5 3 4 t. Otp«nd*ni V iniN c (CHANGE b. IMainob: Entar e. Mathod: Baenwara (crtlanon: ProeabiMy of P-tc^amova >• .100). d. Indapandant Vanabiaa: (Conatant). OS h EAA. HAM. PEFC. POT. SHE a H. HEFC a. AN raduaatad vanabiaa antarad. r. Indapandant Vanabiaa: (Conatant). OSHEAH. PEFC. POT. SHEAR. REFC S indapandant Vanabiaa. (Conatant). PEFC. POT. SHEAR. REFC n. Indapandant Vanabiaa: (Conatant). PEFC. POT. SHEAR I Indapandant Vanabiaa (Conatant). PEFC. SHEAR |. Indapandant vanaoiai (Conaiani). PEFC a Indapandant vanaeia (conjiani) I An raduaatad vanabiaa ramoved

ANOVA*

Sum of Ma an M odal S duaraa 31 S ouara F Sig. 1 RagraaiiOn 61 318 6 10 220 479 817* R aaiduai *69 3 8 22 21 334 Total 333 666 28 2 R agraaaion 61 310 3 12.282 801 .700* R aaiduai 469 336 23 20 407 Total 330 686 28 3 R agraaaion 38 237 4 14.339 740 .574* R aaiduai 472 429 24 19 883 Total 330 566 28 4 R agraaaion 31 133 3 17 043 889 .461* R aaiduai 479 331 23 19 181 Total 530 666 28 i R agraaaion 48 104 2 24 032 1 296 2 9 1 ' R aaiduai 82 362 28 18 360 Total 330 868 28 s R a g ra a a o n 22 837 t 22 807 1 213 281* R aaiduai 307 838 27 18 810 Total 333 666 28 7 R a g ra a a o n 000 0 0 0 0 R aaiduai 330 666 28 18.952 Total 530 666 28 k 8 R agraaaion 0 0 0 0 .0 0 0 R aaiduai 330.666 28 18 * 3 2 Total 530 666 _ 28 a. Casandant Vanao.'a. (CHANGE b. Indapandant vanabiaa (Conttami. OSHEAR. RAM. PEFC. POT. SHEAR. REFC c. Indapandant Vanabiaa (Conatant), OSHEAR. PEFC. POT. SHEAR. REFC d indapandant Vanaoiaa iConatanii PEFC. POT. SHEAR. REFC a Indapandant Vanamaa. (Conatant) PEFC POT SHEAR I Indapandant vanabiaa (Constant), P E F C S h e a r g indapandant vanaoiaa- (Conaiant). PEFC n indapandant Vanaoia iconatant)

153 Backward regression for 12-hour period

Coefficients*

S ta n d a r d iz e d Unstandardized C oefficie Coefficients n ts S td . M odel B E rro r B e ta t Sig. 1 (Constant) 4 .4 5 0 3.437 1.295 .209 POT -2 .5 E -0 2 .0 5 4 • 115 - 4 6 2 .6 4 9 REFC -9.GE-03 015 • 155 - 6 0 6 551 PEFC 4 8 8 1 4 2 4 1 7 5 2 .8 2 4 4 1 169 .2 5 5 RAM 5.4E-20 .000 0 04 0 1 9 .9 8 5 SHEAR .3 2 2 ■ 3 8 8 203 831 .4 1 5 DSHEAR .1 9 2 5 06 100 .3 7 9 .7 0 8 2 (C o n s ta n t) 4 .4 1 9 2 .9 5 8 1 .4 9 4 .1 4 9 POT -2.5E-02 .052 -.1 1 5 - 4 7 3 .641 REFC -9 .0 E -0 3 .0 1 4 -.1 5 4 -.6 3 4 .5 3 2 PEFC 4 8 8 7 4 .6 4 0 7 1 8 .4 ,244 1 .2 0 0 2 4 2 SHEAR .3 2 3 .3 7 9 .2 0 3 .8 5 0 .4 0 4 DSHEAR .1 9 2 .4 9 5 .100 .388 .702 3 (Constant) 4.164 2 .8 3 3 1 .4 7 0 .1 5 5 POT -3 . IE -0 2 .0 4 9 -.1 4 5 -.641 .5 2 7 REFC -8 .3 E -0 3 ' .0 1 4 -.1 4 2 -.601 .5 5 4 PEFC 4 8 5 4 2 .3 3 9 9 6 2 .4 .2 4 3 1 .2 1 4 .2 3 7 SHEAR .3 9 6 .3 2 2 .2 5 0 1 .2 3 0 .231 4 (Constant) 3.420 2.515 1 .3 6 0 .1 8 6 POT -1 .6 E -0 2 .041 -.0 7 7 - 3 9 7 .6 9 4 PEFC 5 1 8 0 9 .7 3 9 1 0 1 .1 .2 5 9 1 .3 2 5 .1 9 7 SHEAR .347 .307 .218 1 .1 2 8 .2 7 0 5 (C o n s ta n t) 2 .8 3 3 2 .0 0 2 1 .4 1 5 .1 6 9 PEFC 4 9 4 4 1 .1 3 8 0 1 3 .4 .2 4 7 1.301 .2 0 5 SHEAR .3 5 3 .3 0 2 .2 2 2 1 .1 6 7 .2 5 4 6 (Constant) 4.941 .8 6 9 5 .6 8 7 .0 0 0 PEFC 41450 5 3 7 6 4 2 .7 2 0 7 1.101 .281 7 (C o n s ta n t) 4 .5 8 2 .8 0 8 5 .6 6 8 .0 0 0 8 (C o n s ta n t) 4 .5 8 2 8 0 8 5 6 6 8 .QQO_ a. Dependent Variable: ICHANGE

154 Backward regression for 24-hour period

Modal Summary*-*'*

Std. Emor V anabies Adjusted of the Model Entered Removed R R Square R Square Estimate 1 DSHEA R. REFC. POT. 462 .214 -.001 5.74Î0 RAM. PEFC. SHEAR** 2 t POT .461 .213 .041 5.6167 3 .» REFC 459 .210 .079 5.5075 4 n RAM .453 205 .110 5.4139 i SHEAR 443 .196 .134 5 3394 0 .1 DSHEAR 326 .107 073 5.5237 7 1 OSHEAR* ____ 225.. ,107 .073 5.5237 a. Dependant Variable: ICHANGE b. Method: Enter c. Method: Backward (criterion: Probability of F- to-remove >« .100). d. Independent Variable#: (Constant), DSHEAR . REFC. POT. RAM. PEFC. SHEAR e. All requested variables entered. f. Independent Venables: (Constant). DSHEAR. REFC. RAM.PEFC. SHEAR g Independent Variables: (Constant). OSHEAR RAM. PEFC. SHEAR h Independent Vanaoies: (Constant). OSHEAR . PEFC. SHEAR I inoepenoent vanaoies (Constant). OS h Ea r PEFC I Inoepenoent Vanaoies (Constant). PEFC k Prooaoilily ol F-lo-remove = 100 limns reac.n< eo

ANOVA* Sum o( Mean Model Squares 01 Square F Sig 1 Regression 196.960 6 32.827 996 452» Residual 725.090 22 32.959 Total 922.050 28 2 Regression 195.942 5 39.166 1.241 .322* Residual 726.109 23 31.570 Total 922.050 28 3 Regression 194.080 4 46.520 1.600 .207* Residual 727 971 24 30.332 Total 922 050 28 4 R egression 189 299 3 63.100 2.153 .119* Residual 732.751 25 29.310 Total 922 050 28 5 Regression 180 80S 2 90.402 3.171 059* Residual 741 246 26 26.509 Total 922.050 26 6 Regression 98.240 1 96.240 3.220 .084» Residual 823.610 27 30.511 Total 922.050 28 7 Regression 96.240 1 96.240 3.220 084S Residual 823.610 27 30.511 Total 922.050 ______2 5 . a. Dependent variable; ICHANGE b. Independent Variables: (Constant), DSHEAR. REFC. POT. RAM. PEFC. SHEAR c. Independent Variables: (Constant), D SHEAR.REFC. RAM. PEFC. SHEAR d. Independent Variables: (Constant), DSHEAR. RAM. PEFC. SHEAR e. Independent Variables: (Constant), OSHEAR.PEFC. SHEAR r. Independent Variables: (Constant), OSHEAR. PEFC y. Independent Variables: (Constant). PEFC 155 Backward regression for 24-hour period

Coefficients*

S ta n d a r d iz e d Unstandardized C o efficie Coefficients n ts S td . M o d el B E rro r B e ta t S ig . 1 (Constant) 5.782 3 .2 5 9 1 .7 7 4 0 9 0 POT - 1 .IE -0 2 0 6 5 -.0 3 9 -.1 7 6 .8 6 2 REFC 4 .5 E -G 3 .0 1 6 .0 8 7 2 8 6 7 78 PEFC 4 9 3 2 0 .6 5 6 6 9 0 .3 .261 .8 7 0 .3 9 4 RAM 1 .IE -1 8 .0 0 0 .0 5 8 2 8 0 .7 8 2 S H E A R -.1 0 9 .3 8 4 -.0 9 4 - 2 8 5 7 7 9 DSHEAR 1 .1 3 7 .731 .3 1 6 1 .5 5 4 .1 3 4 2 (C o n s ta n t) 5 .5 0 6 2 .7 9 6 1 .9 6 9 .061 REFC 3 .5 E -0 3 .0 1 4 .0 6 7 .2 4 3 .8 1 0 PEFC 47463.5 5 4 5 1 1 .5 .2 5 2 871 .3 9 3 RAM 1 .IE -1 8 .0 0 0 .0 5 9 .2 8 9 .7 7 5 SHEAR -.1 3 4 .3 5 0 -.1 1 5 -.3 8 3 .7 0 5 DSHEAR 1 .1 6 7 .6 9 5 3 2 4 1 .6 7 9 .1 0 7 3 (Constant) 5.334 2 .6 5 2 2 .0 1 2 .0 5 6 PEFC 51055.0 51428.3 .271 .9 9 3 .331 RAM 1 .4 E -1 8 '■ .0 0 0 0 7 5 3 9 7 .6 9 5 SHEAR -.1 6 7 3 1 6 - 144 - 52 7 .6 0 3 DSHEAR 1.182 .6 7 9 3 2 8 1.741 .0 9 4 4 (C o n s ta n t) 6 .0 3 0 1.957 3 0 8 0 .0 0 5 PEFC 5 4 2 1 7 .4 4 9 9 4 4 .3 .2 8 7 1 0 8 6 .2 8 8 SHEAR -.1 6 7 .311 - 144 -.5 3 8 .5 9 5 DSHEAR 1.157 .665 .321 1.7 4 2 .094 5 (C o n s ta n t) 5 .1 7 7 1 134 4 5 6 5 .0 0 0 PEFC 73705.6 3 3 9 3 5 .2 .391 2 .1 7 2 .0 3 9 DSHEAR 1.102 6 4 7 .3 0 6 1.7 0 2 .101 6 (C o n s ta n t) 5 .1 1 8 1 .1 7 3 4 .3 6 4 .0 0 0 PEFC 6 1 5 9 3 .0 3 4 3 2 5 .6 .3 2 6 1.7 9 4 .0 8 4 7 (C o n s ta n t) 5 .1 1 8 1.1 7 3 4 36 4 .0 0 0 PEFC 61593.0 34325.6 ____ 1.7 9 4 .0 8 4 a. Dependent Variable: ICHANGE

156 Backward regression for 36-hour period

Modal Summary*'*-*

Sid. Error Variables Adjusted of Die Model Entered Removed R R Square R Square Estim ate 1 OSHEA R. RAM. POT. 532 .283 .088 6.0363 SHEAR. REFC,. PEFC®* t 2 POT .521 .271 .112 S.9SS0 3 .» SHEAR .507 .257 .133 5 8846 « 4 RAM 483 .234 .142 5 8565 S DSHEAR 459 .211 .150 5 8283 s 1 PEFC 382 146 115 5.9480 7 1 PEFC* _ JK 115. 5 9480 a. Oapanoant Variable: ICHANGE b. Melbod: Entar c. Mathod: Backward (cntarion: Probability of F-to-ramova >■ .100). d. Independent Variablea: (Conatant). OSHEAR. RAM. POT. SHEAR. REFC. PEFC a. All requeated variablea eniered. f. Independent Variablea; (Conatant). OSHEAR. RAM. SHEAR. REFC. PEFC g Independent Vanabiaa (Conatant). OSHEAR. RAM. REFC. PEFC h Independent Vanaoies: (Constant). DSHEAR. REFC. PEFC I Independent Vanaoies {Constant). REFC. PEFC I Independent vanabies (Constant) REFC k PfooaO'tily of F-to-remova * 100 limits reacned

ANOVA* Sum of Mean Model Squares df Square F Sig. 1 R egression 317 151 6 52.859 1 451 241» Residual 801 605 22 36.437 Total 1118.756 28 2 R egression 303.125 5 60.625 1.710 .172* Residual 815.631 23 35.462 Total 1118 756 28 3 R egression 287 677 4 71.919 2.077 115* Residual 831 079 24 34.628 Total 1118 756 28 4 R egression 261 296 3 87.099 2.539 .079* Residual 857 460 25 34.298 Total 1 1 18 756 28 5 R egression 235 552 2 117.776 3 467 .046' Residual 883 204 26 33.969 Total 1118 756 28 6 R egression 163.523 1 163.523 4.622 .041» Residual 955 233 27 35.379 Total 1118 756 28 7 Regression 163.523 1 163.523 4.622 .041» Residual 955.233 27 35.379 Total 1118 756 28 a. Oependent Variable: ICHANGE b Independent Vanabiaa: (Constant), OSHEAR. RAM. POT. SHEAR. REFC. PEFC c. Independent Venabiea: (Constant). OSHEAR. RAM.SHEAR. REFC. PEFC d. Independent Variables: (Constant), OSHEAR. RAM. REFC. PEFC e. Independent Variablea: (Constant), OSHEAR.REFC. PEFC r. Independent Vanabiaa: (Constant), REFC. PEFC g. Independent variables: (Constant), REFC 157 Backward regression for 36-hour period

Coefficients*

Standar dized Unstandardized Coefficie Coefficients nts Std. Model 8 Error Beta t Siq. 1 (Constant) -9.875 4 725 -2.090 .048 POT -4.8E-02 .077 -.134 -6 2 0 .541 REFC 3.4E-Q2 017 .419 1.957 .063 PEFC 73187.5 68318.8 .254 1.071 .296 RAM 3.6E-18 .000 167 879 389 SHEAR -.324 .507 -.150 -.640 529 DSHEAR .750 .735 208 1.020 .319 2 (Constant) -8.023 3.613 -2 .2 2 0 .037 REFC 2.9E-02 .015 .361 1 901 .070 PEFC 63378.3 65569.6 .220 .967 .344 RAM 4.0E-18 .000 .186 1.004 .326 SHEAR -.330 .500 -.153 -.660 .516 DSHEAR .746 .726 .206 1.029 314 3 (Constant) -6.476 2.718 - 2.383 .025 REFC 2.8E-02 .015 .345 1.855 .076 PEFC 86691.4 54589.2 .301 1.588 .125 RAM 3.4E-18 .000 .154 .873 .391 DSHEAR .621 .692 .172 .897 .378 4 (Constant) -8.259 1.785 -4 .6 2 8 000 REFC 2.8E-02 .015 .352 1.902 .069 PEFC 88809.8 54274.8 .309 1.636 .114 DSHEAR .596 .688 .165 .866 .395 5 (Constant) -8 .0 7 5 1.763 -4 .5 7 9 .000 REFC 2.6E-02 .015 .317 1.765 .089 PEFC 75373.4 51761.8 .262 1.456 .157 6 (Constant) -7.342 1.725 -4 257 .000 REFC 3 .IE -02 .014 382 2 150 .041 7 (Constant) -7.342 1 725 -4 257 .000 REFC 3.IE-02 014 382 2 150 041 a. Dependent Variable: ICHANGE

158 Backward regression for 48-hour period

Modal Summary*-*'®

Std. Error Vanabies Adjusted of the Model Entered Removed R R Square R S quare Estimate 1 OSHEA R. REFC. RAM. .551 .303 .113 6.4700 PEFC. POT. SHEAR** 2 POT 548 .301 .149 0.3388 3 9 RAM 544 .296 .178 6.2269 n 4 REFC 534 .285 .199 6.1485 s : PEFC .479 .230 .170 6.2571 6 ' -£S£2___ 479 ■ 179 a. Dependant variable. ICHANGE b. Matnod: Enter e. Matliod: Backward (criterion: Probability of F to remov# >■ .100). d. Independent Variables: (Conttani). OSHEAR. REFC, RAM. PEFC. POT. SHEAR a. All reouasiad variables entered f Independent Vanabies: (Constant). OSHEAR REFC. RAM. PEFC. SHEAR g Inoepenoent Variables (Constant) OS m e a r . REFC. PEFC. SHEAR n inoepenoent variables (Constant). OSMEAR. PEFC. SHEAR i inoepenoent Vanabies (Constant). OSMEAR. SHEAR I Probability of F-to-remove » tOO iimijs reacneo

ANOVA* Sum ol Mean Model Squares 01 Square F Sig 1 Regression 400 607 6 66.768 1.595 .196* Residual 920 935 22 41.861 Total 1321 542 28 2 R egression 397 399 5 79.480 1.978 .120® Residual 924 143 23 40.180 Total 1321 542 28 3 R egression 390 650 4 97.737 2.521 .068* Residual 930 592 24 38.775 Total 1321 542 28 4 R egression 376 455 3 125.485 3 319 036* Residual 945 087 25 37.803 Total 1321 542 28 5 R egression 303 603 2 151.802 3.877 .034' Residual 1017,938 26 39.151 Total 1321.542 28 6 R egression 303.603 2 151.802 3.877 .034' Residual 1017.938 26 39.151 Total 1321 542 ___ %L, a. Oependent Variable: ICHANGE b. Independent Variables: (Constant) OSHEAR. REFC. RAM. PEFC. POT. SHEAR c. Independent Venables: (Constant). OSHEAR. REFC. RAM. PEFC. SHEAR d. Independent Vadabios: (Constant), OSHEAR. REFC. PEFC. SHEAR a. Independent Vanabies: (Constant), OSHEAR.PEFC. SHEAR f. Independent Vahables: (Constant). OSHEAR.SHEAR

159 Backward regression for 48-hour period

Coefficients*

Standar dized Unstandardized Coefficie Coefficients nts Std. M odel B Error Beta t Siq. 1 (C onstant) 8 .810 5.145 1.712 .101 POT 2.6E -02 .095 .062 .277 .785 REFC 5.8E -03 .016 .075 .354 .726 PEFC 70438.1 77174.1 .245 .913 .371 RAM 2.2E -18 .000 .095 455 .653 SHEAR -.957 .566 -.565 -1.692 .105 DSHEAR -1 .4 6 4 .749 -.507 -1.954 .064 2 (C onstant) 9.733 3.838 2 536 .018 REFC 7.9E -03 .014 .103 .572 .573 PEFC 76147.4 72858.9 265 1.045 .307 RAM 1.8E-18 .000 .078 .401 .692 SH EA R -.938 .550 -.554 -1.705 .102 DSHEAR -1 .4 5 5 .734 -.504 -1.984 .059 3 (C onstant) 10.367 3.435 3 018 .006 REFC 8.3E -03 .014 108 611 .547 PEFC 82657.9 69770.4 .287 1.185 .248 SHEAR -.865 .510 -.511 -1 696 .103 DSHEAR -1 .4 6 3 .720 -.507 -2.031 .053 4 (C onstant) 9.422 3.030 3 110 .005 PEFC 92859.8 66891.9 .323 1.388 .177 SHEAR -.804 .494 -.475 -1.628 .116 DSHEAR -1.420 .708 -.492 •2 006 .056 5 (C onstant) 10.159 3.036 3 347 .002 SHEAR -1.176 .422 -.694 -2 784 .010 DSHEAR -1.413 .720 -.489 -1.961 .061 6 (C onstant) 10.159 3.036 3.347 .002 SHEAR •1.176 422 -.694 -2 784 .010 OSHEAR -1.413 720 -.489 -1 961 .061 a. Dependent Variable; (CHANGE

160 Backward regression for 60-hour period

Modal Summary*

Std. Error Variablea A^uated of the Model Entered Removed R R Square R Square Eatlmata 1 OSHEA R. PEFC. POT. 677 .459 5.8297 RAM. 311 REFC. SHEAR" 2 f PEFC .676 .457 .339 5.7054 3 ,® RAM 671 .451 .359 5.6201 4 h POT .657 .432 .363 5.6000 n S POT' 657 ____ J l J i ■------J 6 3 Dependant Vanabie: ICHANGE b. Metnod: Enter c. Method: Backward (criienon: Prooabiiity of P-io-remove » .100). d Independent Vanabies: (Conatant). DSHEAR. PEFC. POT. RAM. REFC. SHEAR e. All requeated vanabiaa entered f. Independent Variablea: (Conatant). OSHEAR. POT. RAM. REFC. SHEAR g. Independent Variablea: (Conatant). DSHEAR. POT. REFC. SHEAR n. Independent venabiea" (Conatant). DSHEAR. REFC. SHEAR I. Probability of F-to-remove * lOO limits reacneo

ANOVA* Sum of Mean Model Squares of Square F Sig 1 Regression 632.622 6 105.437 3.106 .023^ Residual 746 907 22 33.950 Total 1379 529 28 2 R egression 630 648 5 126.170 3.878 .011* Residual 748 681 23 32.551 Total 1379 529 28 3 Regression 621 489 4 155.372 4.919 005* Residual 758 039 24 31.585 Total 1379 529 28 4 R egression 595 525 3 198.508 6.330 .002' Residual 784.003 25 31.360 Total 1379 529 28 5 Regression 595.525 3 198.506 6.330 .002* Residual 784.003 25 31.360 Total 1379.529 28 a. Oependent Variable: ICHANGE b Independent Venabiea: (Constant). OSHEAR. PEFC. POT. RAM. REFC. SHEAR c. Independent Venabiea: (Conatant). OSHEAR. POT. RAM. REFC, SHEAR d. Independent Venabiea. (Constant). DSHEAR. POT. REFC. SHEAR e. Independent Variables: (Conatant). DSHEAR.REFC.SHEAR

161 Backward regression for 60-hour period

Coefficients*

S tan d ar dized Unstandardized Coefficie Coefficients nts Std. Model 8 Error Beta t Siq. 1 (Constant) 10.316 3.668 2.813 .010 POT -6.5E-02 .081 -.134 -.803 .431 REFC 2.3E-02 .010 .436 2.373 .027 PEFC 14263.5 62392.9 .055 .229 .821 RAM 2.2E-18 .000 .090 .536 .597 SHEAR -.873 .409 -.577 -2.134 .044 DSHEAR - 2.035 .814 -.536 -2.501 .020 2 (Constant) 10.135 3.507 2.890 .008 POT -6.5E-02 .079 -.135 824 .419 REFC 2.3E-02 .009 .419 2.556 .018 RAM 2.1E-18 .000 .088 .536 .597 SHEAR -.806 .281 -.533 -2.870 .009 OSHEAR -1.954 .717 -.515 -2.725 .012 3 (Constant) 11.034 3.034 3.637 .001 POT -7.0E-02 .077 -.145 -.907 .374 REFC 2.2E-02 .009 .406 2.541 .018 SHEAR -.769 .268 -.508 -2.868 .008 DSHEAR -1.868 .688 -4 9 2 -2.713 .012 4 (Constant) 9.405 2.435 3.862 .001 REFC 2.0E-02 .008 .366 2.392 .025 SHEAR -.755 .267 -.499 -2.831 009 DSHEAR -1 .9 6 5 .677 -.518 -2.901 .008 5 (Constant) 9.405 2.435 3.862 .001 REFC 2.0E-02 .008 366 2.392 .025 SHEAR -.755 267 - 499 -2.831 .009 DSHEAR -1.965 677 -5 1 8 -2 901 008 a. Dependent Variable: ICHANGE

162 Backward regression for 72-hour period

Mod«l Summary*-*-*

Std. Error V anabies Adjusted of the Model Eniered Removed R R Square R Square Estim ate 1 OSHEA R. POT. RAM. 661 .437 .284 REFC. 5.0426 PEFC. s h e a r "* 2 1 POT 652 .426 .301 4.9824 3 s SHEAR 633 .401 .301 4.9822 4 RAM 593 .352 .274 5.0768 s " /VlVL , _____ 552- ____ 352 ______22i_ S J7 6 8 a. Oapandani vanaDia ic h a n g e b. Method. Enter c. Method: Backward (criterion: Probability of F-to-remove >> .100). d. independent Variable*: (Constant). OSHEAR. POT. RAM. REFC. PEFC. SHEAR e. All requested variables entered. r. Independent Vanabies: (Constant). OSHEAR. RAM. REFC. PEFC. SHEAR g. Independent Variables: (Constant). OSHEAR. RAM. REFC. PEFC h Independent Variables; (Constant). OSHEAR. REFC. PEFC I. Probability of F-to-rem ove » 100 limits reacned

ANOVA* Sum of Mean Model Squares of Square F Siq 1 Regression 434 472 6 72.412 2 848 .033“ Residual 559 415 22 25.428 Total 993 887 28 2 R egression 422 936 5 84.587 3 407 .019* Residual 570 950 23 24.824 Total 993 867 28 3 R egression 398 145 4 99.536 4 010 .012* Residual 595 742 24 24.823 Total 993 887 28 4 Regression 349.528 3 116.509 4 520 .012* Residual 644.359 25 25.774 Total 993 887 28 5 R egression 349 528 3 116.509 4 520 .012* R esidual 844.359 25 25.774 Total _S23 ______29- a. Dependent Variable ICHANGE b. Independent Vanabies: (Constant). OSHEAR. POT. RAM. REFC. PEFC. SHEAR c. Independent vanabies: (Constant). OSHEAR. RAM. R E FC .PE FC . SHEAR d. Independent Vanabies: (Constant). OSHEAR. RAM. REFC. PEFC e. Independent Variables: (Constant). OSHEAR.REFC. PEFC

163 Backward regression for 72-hour period

Coefficients*

S tandar dized Unstandardized Coefficie Coefficients nts Std. Model B Error Beta t Sig. _ 1 (Constant) 9.992 3.137 3.185 .004 POT -5.6E -02 .083 -.115 -6 7 4 .508 REFC 1.7E-02 .007 .443 2.514 .020 PEFC 86677.1 41990.7 .450 2.064 051 RAM 3.5E -18 .000 198 1 160 .258 SHEAR -.263 260 - 255 -1 013 .322 DSHEAR - 1 464 630 - 535 -2 322 .030 2 (Constant) 8.711 2 466 3 533 .002 REFC 1.7E-02 .007 431 2 474 .021 PEFC 79 5 6 0 .3 40154.0 413 1 981 .060 RAM 3.4E -18 .000 .189 1.126 .272 SHEAR -.256 .256 -.249 -.999 .328 OSHEAR -1 .4 1 9 .619 -.519 -2.291 .031 3 (Constant) 7.409 2.093 3.539 .002 REFC 1.4E-02 r- .006 .373 2.271 .032 PEFC 97777.5 35776.8 .508 2.733 .012 RAM 4.1 IE-18 .000 .228 1.399 .174 DSHEAR -1 .0 8 9 .524 -.398 -2.078 .049 4 (Constant) 5.354 1.520 3.522 .002 REFC 1.5E-G2 .006 .392 2.348 .027 PEFC 94922.5 36397.0 .493 2.608 .015 DSHEAR -.9 3 5 .522 .342 -1.791 .085 5 (Constant) 5.354 1.520 3.522 .002 REFC 1.5E-02 006 .392 2.348 .027 PEFC 9 4922.5 36397.0 493 2.608 .015 DSHEAR -.9 3 5 .522 -.342 -1 791 .085 a. Dependent Variable: ICHANGE

164 APPENDEX C

SPSS STATISTICAL OUTPUT FOR 1998

165 Backward regression for 12-hour period

H o M Summary***'*

Std. Error Varlj Mes Adlusted R oF the Model Entered Remoeed R R Square Square Estimate 1 DSHEAR. PEFC REFC .#62 .744 .616 3.033# POT. •

K S à " 2 f RAM .#52 .726 .621 3.0143 } 1 POT #22 .676 5#4 3 .I5 # 0 4 .* SHEAR .#0 ) .645 .575 3.191# s PEFC .771 .603 .554 3.2695 6 DSHEAR .721 .529 .502 3.4543 7 DSHEAR* _ . ^ ' 2 1 ' — s iL * . ______- L i m . J. O«0«nd«ni Vjrtjbic ICHANGE b. Method: Enter t . Method: iKkwerd (trtterion: ftooetxlit» o( E lo-remow > • .lOOl d. Independent Verljblei: (Consunt), OSHEAR. PEfC REFC. POT, RAM, SHEAR e. All rcgueited veiUbiei entered. t. Independent Virubiei: (Consunt), OSHEAR, PEFC. REFC, POT, SHEAR

t - Independent Verubles: (Conttent), DSHEAR, PEFC REFC, SHEAR h. Independent VarliMes: I Consunt). DSHEAR, PEFC, REFC I. Independent Vjtleblet: (Consunt), DSHEAR. REFC I. Independent Vjriebles: (Consunt), REFC It. ProbeWRty ol F-to-remove * . 10 0 Dmlts teethed.

ANOVA*

Sum ol Mean Model Squares d( Square F Sif. 1 Regression 320.56# 6 S3 428 s.aos .005* Residual 110.4 51 12 9 .204 Total 431.018 I# 2 Regression 312.899 S 6 2 .5 8 0 6.88 7 .002' Resldsul 118.1 19 13 9 .0 8 6 Toul 4 3 1 .0 1 # 18 3 Regression 2 9 1.394 4 72.848 7.304 .002* Residual 139.625 14 9 .973 Total 4 3 1 .01# 18 4 Recession 2 7 # .2 0 9 3 92.736 9.103 .001* Reddual I5 2 .# 0 9 15 10.187 Total 4 3 1 .0 1 # I# 5 Regression 2 5 9.984 2 129.992 12.161001 . ' Residual 171.035 16 10.690 Total 4 3 1.01# 18 6 Regression 2 2 8.172 1 228.172 19.122 .000* Residual 2 0 2.846 17 11.932 Toul 431.01# 18 7 Regression 2 2 8 .1 7 2 1 228.172 19.122 .000* Residual 2 0 2.846 17 11.932 Total 431.01# 1# *. Dependent VatUMe: ICHANGE b Independent Variables: (Coniuni), OSHEAR. PEFC. REFC. POT, RAM, SHEAR c. Independent Variables: (Coniijni), OSHEAR. PEFC. REFC. POT, SHEAR d. Independent Variables: (Conttani), OSHEAR, PEFC. REFC. SHEAR e. Independent Variables: (Constant), OSHEAR. PEFC. REFC f. Independent Variables: (Consunt), OSHEAR. REFC | . Independent Variables: (Constant), REFC 166 Backward regression for 12-hour period

Coefficients'

Standa rdized Coeffi Unsundardlzec Coefficients dents Model B Std. Error Beta t SIR. 1 (Consunt) -18.396 6.590 -2.791 .016 POT -.102 .065 -.326 -1.578 .140 REFC 1.907E-02 .007 .61 1 2.652 .021 PEFC 9381 1.891 81860.350 .259 1.146 .274 RAM 4.435E -I8 .000 .251 913 .379 SHEAR -.858 .798 -.306 -1.074 .304 DSHEAR .545 .425 .263 1.284 .223 2 (Consunt) • 18.168 6.543 •2.777 .016 POT •9.856E 02 .064 -.315 -1.538 .148 REFC 2.364E02 .005 .758 4.606 .000 PEFC 127736.1 1 1 72467.571 .352 1.763 .101 SHEAR •1.226 .685 -.437 -1.790 .097 DSHEAR .769' .344 .372 2.238 .043 3 (Consunt) -10.220 4.207 -2.430 .029 REFC 2.07SE-02 .005 .665 ■4.146 .001 PEFC 1 34395.942 75787.137 .371 -1.773 .098 SHEAR -.726 .63 1 -.259 -1.1 50 .269 DSHEAR .730 .359 .353 2.032 .062 4 (Constant) - 5.6 1 7 1.306 -4.302 .001 REFC 2.184E-02 .005 .700 4.400 .001 PEFC 7541 1.939 56381.186 .208 1.338 .201 DSHEAR .549 .326 .265 1.682 .1 13 5 (Constant) -5.933 1.316 -4.510 .000 REFC 2 .0 8 6 E 0 2 .005 .668 -4.148 .001 DSHEAR .576 .334 .278 1.725 .104 6 (Consunt) -6.214 1.379 -4.505 .000 REFC 2.270E-02 .005 .728 4.373 .000 7 (Consunt) -6.214 1.379 -4.505 .000 REFC 2.270E-02 .005 .728 4.373 .000 a. Dependent Variable: ICHANGE

167 Backward regression for 24-hour period

Model Summary" * '

Std. Error Varl bles Adlusted R o f the M odel Entered Removed R R Square Square Estimate 1 DSHEAR. POT, REFC, .8 6 5 .7 4 8 .6 2 2 2 .9 7 1 8 PEFC.

1 2 PEFC .8 6 2 .7 4 2 .6 4 3 2 .8 8 8 2 3 • SHEAR .8 5 7 .7 3 5 .6 S 9 2 .8 2 1 7 * 4 POT .8 5 5 .7 3 2 .6 7 8 2 .7 4 2 9 1 5 OSHEAR .8 3 9 .7 0 4 .6 6 7 2 .7 8 9 0 6 DSHEAR' 8 3 9 .7 0 4 .6 6 7 2 .7 8 9 0 i. 0«p«ndent V jd J b lc : (CHANCE b. Method: Enter C. M e th o d : 8.lCkMrjrd (criterion ProbJUilily ol F to-ieniove > - . 100). d. Independent VjniOlej: (Consunt), DSHEAR. POT, REFC, PEFC. R A M , SHEAR e. All requested vjrljbles entered.

f. Independent Variables: (Consunt), DSHEAR, POT, REFC, R A M , SHEAR : Independent Variables: (Consunt), DSHEAR. POT, REFC, RAM h. Independent Variables: (Consunt), OSHEAR, REFC, RAM I. Independent Variables: (Consunt), REFC, RAM |. Probability of F to-remove - .100 llbilts reached.

ANOVA"

Sum of Mean Model Squares <11 Square F Sig. 1 Regression 3 1 4 .7 2 6 6 52.454 5.939 .004 Residual 1 0 5 .9 8 1 12 8 .8 3 2 T o u l 4 2 0 .7 0 7 18 2 Regression 3 1 2 .2 6 7 5 6 2 .4 5 3 7 .4 8 7 .0 0 2 ' Residual 1 0 8 .4 3 9 13 8 .3 4 1 T o u l 4 2 0 .7 0 7 18 3 Repesslon 3 0 9 .2 4 2 4 77.31 1 9.710 . 0 0 1" Residual 1 1 I.4 6 S 1 4 7 .9 6 2 Total 420.707 18 4 Regression 3 0 7 .8 S S 3 102.618 13.640 .000" Residual 1 1 2 .8 5 2 IS 7 .5 2 3 To u l 4 2 0 .7 0 7 18 5 R ercu lo n 296.249 2 148.125 19.043 .0 0 0 ' Residual 1 2 4 .4 5 8 16 7 .7 7 9 Total 4 2 0 .7 0 7 18 6 Regression 2 9 6 .2 4 9 2 1 4 8 .1 2 5 1 9 .0 4 3 .0 0 0 ' Residual 1 2 4 .4 5 8 16 7 .7 7 9 Total 4 2 0 .7 0 7 18 a. Dependent Variable: (C H A N G E b. Independent Variables: (Constant), DSHEAR, POT, REFC, PEFC, RAM, SHEAR c. Independent Variables: (C onsunt), DSHEAR, POT, REFC, RAM, SHEAR d. Independent Variables: (Constant), DSHEAR, POT, REFC, RAM e Independent Variables: (Consunt), DSHEAR, REFC, R A M r. Independent Variables: (C onsunt), REFC, R A M 168 Backward regression for 24-hour period

Cocfficicncs*

Standa rdized Coeffi Unstandardized Coefficients dents Model B Std. Error Beta t SIR. I (Constant) -1 5 .6 6 7 7.568 -2.070 .061 POT -S.740E-02 .078 .159 -.737 .475 REFC l.769E*02 .006 .554 2.780 .017 PEFC 37320.580 70739.001 .098 .528 .607 RAM S.I37E-I8 .000 .294 1.392 .189 SHEAR .592 .774 -.220 -.765 .459 DSHEAR .661 .540 .242 1.224 .244 2 (Constant) -14.584 7.079 -2.060 .060 POT -5.394E-02 .075 -.150 -.715 .487 REFC 1.766E-02 .006 .553 2.856 .014 RAM 5.423E -i8 .000 .31 1 1.529 .150 SHEAR .399* .662 -.148 -.602 .557 DSHEAR .638 .523 .234 1.220 .244 3 (Constant) -10.785 3.138 -3.437 .004 POT -2.i58E-02 .052 -.060 -.417 .683 REFC 1.722E-02 .006 .539 2.870 .012 RAM 5.832E-I8 .000 .334 1.715 .108 DSHEAR .445 .403 .163 1.103 .289 4 (Constant) - 9.816 2.053 -4.781 .000 REFC I.709E-02 .006 .535 2.935 .010 RAM 5.596E-I8 .000 .321 1.716 .107 DSHEAR .478 .385 .175 1.242 .233 5 (Constant) - i0.600 1.987 •5.336 .000 REFC I.730E-02 .006 .542 2.923 .010 RAM 6.471 E-i 8 .000 .371 1.999 .063 6 (Constant) -10.600 1.987 -5.336 .000 REFC I.730E-02 .006 .542 2.923 .010 RAM 6.47IE-I8 .000 .371 1.999 .063 a. Dependent Variable: ICHANGE

169 Backward regression for 36-hour period

Modal Summary*-®-*

Sid. Error Variables A ^uated of the Model Entered R em oved R R Square R Square Estimate 1 OSHEA R. POT. REFC. 851 724 .587 PEFC. 3.3000 RAM. SHEAR** 1 2 PEFC 848 718 .610 3.2068 3 a DSHEAR 842 .708 .626 3.1427 n 4 POT 836 698 638 3.0892 1 5 SHEAR .826 682 .642 3.0726 6 SHEAR' .826 ____ S £ L ■ 3.872? ». Dependant Vanabia; iC h a n GE b. Mainod. Enter c. Metnod Backward (criterion Probability o> F-to-remove >* 100) a. independent vanabies (Ccnsiani). DSmEAR, POT, REFC. PEFC. RAM. SHEAR a All raouastad vanabtat ani#rao I Independent vanabie»: (Constant), DSmEAR POT. REFC. RAM. SHEAR g. Independent vanabies: (Constant). POT. REFC. RAM. SHEAR n. Independent Variables: (C onstant). REFC. RAM, SHEAR I. Independent Variables: (Constant). REFC. RAM J. Probability of F-to-remove « . 100 limits reached

ANOVA*

Sum of Mean Model S q uares df Square F Siq. 1 R egression 343 645 6 57.274 5 269 007® Residual 130 682 12 10 890 Total 474 326 18 2 R egression 340 719 6 68.144 6.630 .003* Residual 133 607 13 10.277 Total 474 326 18 3 Regression 336 067 4 84,014 8.507 .001* Residual 138 270 14 9,876 Total 474 326 18 4 Regression 331 181 3 110.394 11.568 .000* Residual 143 145 15 9.643 Total 474 326 18 6 Regression 323 283 2 161.641 17.123 .000' Residual 151 044 16 0.440 Total 474.326 18 6 Regression 323.283 2 161.641 17.123 .000' Residual 161.044 16 9.440 Total 474 326 18 a. Dependent Variable: ICHANGE b. Independent Vanabies; (Constant), DSMEAR. POT. REFC. PEFC. RAM. SHEAR c Independent Variables: (Constant), DSHEAR. POT. REFC. RAM. SHEAR d independent Variables: (Constant), POT. REFC. RAM. SHEAR a. Independent Variables: (Constant). REFC. RAM.SHEAR (. Independent Variables: (Constant). REFC. RAM

170 Backward regression for 36-hour period

Coefficients' Standar dized Unstandardized Coefficie Coefficients nts Std. Model B Error Beta t Siq. 1 (Constant) -20.927 7.540 -2.776 .017 POT -9.5E-02 .102 -.200 -.932 .370 REFC 1.6E-02 .007 .463 2.275 .042 PEFC 38000.6 73320.3 095 .518 .614 RAM 8.1E-18 .000 394 1.809 .096 SHEAR -.918 .713 -.414 -1.287 .222 DSHEAR .454 .652 .183 .695 .500 2 (Constant) -20.325 7.237 -2.808 .015 POT -9.2E-02 .099 -.195 -.938 .365 REFC 1.6E-02 .007 .467 2.364 .034 RAM 8.3E-18 .000 .406 1.927 076 SHEAR -.783 .645 -.353 -1.214 .246 DSHEAR .425 .632 .171 .674 .512 3 (Constant) -17.500 5.782 -3.027 .009 POT -5.8E-02 .083 -.123 -.703 .494 REFC 1.6E-02 .007 .465 2.398 .031 RAM 9.4E-18 .000 .456 2.357 .034 SHEAR -.440 .388 -.198 -1.134 .276 4 (Constant) -14.271 3.449 -4.138 .001 REFC 1.6E-02 .007 .461 2.421 .029 RAM 9.2E-18 000 450 2 371 032 SHEAR -.287 315 - 129 - 910 377 5 (Constant) -12 028 2 398 -5 016 .000 REFC 1 6E-02 007 448 2 374 .030 RAM 9 4E-18 .000 4 56 2 417 .028 6 (Constant) -12.028 2.398 -5 016 .000 REFC 1.6E-02 007 448 2 374 .030 RAM 9 4E-18 000 456 2 417 026 a. Dependent variable; (CHANGE

171 Backward regression for 48-hour period

Model Suminary*'*'*

Std. Error Van. blei Adiustcd R o f the Model Entered Removed R R Square Square Estimate 1 DSHEAR, POT, RAM, .8 6 0 .7 4 0 .6 1 0 3 .3 7 3 4 PEFC

t 2 PEFC .8S B .7 3 5 .6 3 4 3 .2 7 IS 3 1 P O T .8 4 9 .7 2 0 .6 4 0 3 .2 4 1 2 K 4 OSHEAR .8 3 8 .7 0 1 .6 4 2 3 2 3 9 0 S h DSHEAR' .8 3 8 .7 0 1 4 1 2 3 .2 3 S 0 J. Dependent Varlible: (CHANCE b. M ethod: Enter C. Method: Bjckwjrd (cnterion; Prubjbilitv o( f-to-remove > • .100). d. Independent Virljbles: (Constant). OSHEa R. POT, R A M , PEFC. REFC, SHEAR e. All requested variables entered.

f. Independent Variables: (Constant). OSHEa R. PO T, R A M , REFC, SHEAR

|. Independent Variables: (Constant), OSHEa R, R A M , REFC ,SHEAR h. Independent Variables: (Consunt), RAM, REFC, SHEAR I. Probability of F-to-remove - .100 limits reached.

ANOVA'

Sum of Mean Model Squares d f Square F SIg. 1 Regression 3 8 9 .3 2 2 6 6 4 .8 8 7 5.702 .005'' Residual 1 3 6 .5 6 2 12 1 1 .3 8 0 Total S 2 S .8 8 4 18 2 Regression 386.749 5 77.350 7 .2 2 7 .0 0 2 ‘ Residual 1 3 9 .1 3 4 13 1 0 .7 0 3 Total S 2 S .8 8 4 IS 3 Regression 3 7 8 .8 0 8 4 94.702 9.015 .0 0 1 * Residual 1 4 7 .0 7 6 14 1 0 .5 0 5 Total S 2 S .8 8 4 18 4 Regression 3 6 8 .9 0 2 3 1 2 2 .9 6 7 1 1.750 .000* Residual IS6.98I IS 10.465 Total S 2 S .8 8 4 18 5 Regression 3 6 8 .9 0 2 3 122.967 11.750 .0 0 0 * Residual 156.981 15 10.465 Total 5 2 5 .8 8 4 18 a. Dependent Variable: ICHANGE b. Independent Variables: (Constant), OSHEAR. POT. RAM. PEFC. REFC, SHEAR c. Independent Variables: (Constant), DSHEAR, POT, RAM, REFC, SHEAR d. Independent Variables: (Constant), OSHEAR, RAM, REFC, SHEAR e. Independent Variables: (Constant), RAM, REFC, SHEAR

172 Backward regression for 48-hour period

Cocfflcicnts*

Standa rdized Coeffl Unsundardlzed Coefficients dents M odel B Std. Error Beta t SIg. 1 (Consunt) 2 1 .8 6 2 5 .8 7 7 3 .7 2 0 .0 0 3 P O T -9 .5 9 7 E -0 2 .1 1 6 -.1 4 2 -.829 .4 2 3 REFC 1 .5 9 0 E -0 2 .0 0 8 .4 1 0 1.9 9 4 .0 6 9 PEFC 4 6 0 2 7 .0 5 0 9 6 8 0 6 .8 5 0 .101 .4 7 5 .6 4 3 RAM 7 .9 4 9 E -I 8 .0 0 0 .3 6 1 1.749 .1 0 6 SHEAR •1 .0 7 3 .4 8 9 -.551 -2 .1 9 5 .0 4 9 DSHEAR .6 2 8 .5 3 4 .251 1.176 .2 6 2 2 (Consunt) 2 1 .2 3 8 5 .5 5 6 3 .8 2 3 .0 0 2 PO T -9.670E-02 .1 1 2 -.1 4 3 -.861 .4 0 5 REFC I.6 5 8 E -0 2 .0 0 8 .4 2 7 2 .1 7 8 .0 4 8 RAM 7 .8 8 I E - I 8 .0 0 0 .3 5 8 1 .7 8 9 .0 9 7 SHEAR -.9 4 0 , .3 8 8 -.4 8 3 -2 .4 2 0 .031 DSHEAR .6 3 2 .5 1 8 .2 5 2 1.219 .2 4 5 3 (C onsunt) 1 7 .6 0 3 3 .5 8 1 4 .9 1 6 .0 0 0 REFC I .8 I 4 E - 0 2 .0 0 7 .4 6 7 2 .4 7 8 .0 2 7 RAM 8 .0 8 6 E -I 8 .0 0 0 .3 6 7 1.855 .0 8 5 SHEAR -.7 9 7 .3 4 8 -.4 1 0 -2 .2 9 0 .0 3 8 DSHEAR .4 6 0 .4 7 4 .1 8 4 .971 .3 4 8 4 (Constant) 17.201 3 .5 5 0 4 .8 4 6 .0 0 0 REFC I.7 9 0 E -0 2 .0 0 7 .4 6 ! 2.451 .0 2 7 RAM 9 .4 4 7 E -I8 .0 0 0 .4 2 9 2 .2 9 3 .0 3 7 SHEAR -.5 9 3 .2 7 7 -.3 0 5 •2 .1 4 2 .0 4 9 5 (C o n su n t) 1 7 .2 0 1 3 .5 5 0 4 .8 4 6 .0 0 0 REFC I.7 9 0 E -0 2 .0 0 7 .461 2.451 .0 2 7 RAM 9 .4 4 7 E - I 8 .0 0 0 .4 2 9 2 .2 9 3 .0 3 7 . SHEAR -.5 9 3 .2 7 7 -.3 0 5 -2 .1 4 2 .0 4 9 a. Dependent Variable ICHANGE

173 Backward regression for 60-hour period

Model lummery* * '

Std. Error Variables Adjusted R o f the Model Entered Removed R R SquareSquare Estimate I DSHEAR, POT, PEFC, .8 4 2 .7 0 9 .5 6 3 3 .2 2 8 3 RAM, REFC. „ SHEAR 1 2 DSHEAR 8 3 3 .4 9 3 .5 7 5 3 .1 8 4 7 3 1 PEFC .81 S .6 6 4 .5 6 8 3 .2 1 2 7 4 PI POT .8 0 3 .6 4 5 .5 7 4 3 .1 8 7 1 h POT s .8 0 3 _ ^ 7 4 . 3 .1 8 7 1 *. Dependent Variable: ICHANGE b. M ethod: Enter c. Method: Backward (criterion: Probability oi F-to-remove > ■ .1001. d. Independent Variables: (Constant). DSHEAR. POT. PEFC. RAM. REFC. SHEAR e. A ll requested variables entered. I. Independent Variables: (Constant). POT. PEFC. RAM, REFC. SHEAR |. Independent Variables: (Constant), POT, RAM. REFC, SHEAR h. Independent Variables: (Constant), RAM, REFC, SHEAR I. Probability of F-to-remove ■ . I (X} limits reached.

ANOVA'

Sum of Mean M odel Squares df Square F SIg. t Regression 304.582 6 S0.764 4.871 .010» Residual 1 2 5.061 12 1 0 .4 2 2 Total 4 2 9 .6 4 3 18 2 Regression 2 9 7 .7 9 2 5 5 9 .5 5 8 5 .8 7 2 .0 0 5 ' Residual 131.851 13 1 0 .1 4 2 Total 4 2 9 .6 4 3 18 3 Recession 2 8 5 .1 4 7 4 7 1 .2 8 7 6 .9 0 7 .0 0 3 ' Residual 1 4 4 .4 9 6 14 10.321 Total 4 2 9 .6 4 3 18 4 Recession 277.276 3 9 2 .4 2 5 9 .0 9 9 .0 0 1 ' Residual 1 5 2 .3 6 7 IS 10 .1 5 8 T o u l 4 2 9 .6 4 3 18 s Recession 2 7 7 .2 7 6 3 9 2 .4 2 5 9 .0 9 9 .0 0 1 ' Residual IS 2 .3 6 7 15 10 .1 5 8 Total 4 2 9 .6 4 3 18 a. Dependent Variable: ICHANGE

b. Independent Variables: (Constant), DSHEAR, POT. PEFC, RAM, REFC, SHEAR c. Independent Variables: (Constant), POT, PEFC, RAM, REFC, SHEAR (3. Independent Variables: (Constant), POT, RAM, REFC, SHEAR e. Independent Variables: (Constant), RAM. REFC, SHEAR

174 Backward regression for 60-hour period

Coefficicntr*

5tanda rdized Coeffi Unstandardized Coefficients cients M odel B Std. Error Beta t s'f-.,. 1 (Constant) 2 2 .3 6 6 5 .5 5 2 4 .0 2 9 .0 0 2 PO T -.1 6 0 .1 2 4 -.2 4 3 -1 .2 8 9 .2 2 2 REFC 9 .6 8 4 E -0 3 .0 0 9 .2 6 0 I . I 3 I .2 8 0 PEFC 1 0 9 4 2 6 .7 6 2 8 5 0 8 3 .2 4 8 .3 1 3 1 .2 8 6 .2 2 3 RAM 8.640E -1B .0 0 0 .4 5 3 2 .1 0 5 .0 5 7 SHEAR •1 .0 7 2 .4 5 9 -.6 0 6 -2 .3 3 8 .0 3 8 DSHEAR .3 1 2 .3 8 7 .1 7 6 .8 0 7 .4 3 5 2 (Constant) 2 1 .1 9 7 5 .2 8 7 4 .0 0 9 .0 0 1 PO T -.1 3 8 .1 1 9 -.2 0 9 -1 .1 5 3 .2 6 9 REFC 9.68 1 E-03 .0 0 8 .2 6 0 1 .1 4 6 .2 7 3 PEFC 8 9 8 2 0 .1 6 8 8 0 4 4 1 .5 3 2 .2 5 7 1 .1 1 7 .2 8 4 RAM 1 .0 0 4 E -1 7 .0 0 0 .5 2 7 2 .7 3 5 .0 1 7 SHEAR - .8 5 4 '’ .3 6 5 -.4 8 3 -2 .3 3 6 .0 3 6 3 (Constant) 1 8 .7 5 7 4 .8 5 7 3 .8 6 2 .0 0 2 PO T -.101 .1 1 6 -.1 5 4 -.873 .3 9 7 REFC I.4 5 8 E -0 2 .0 0 7 .3 9 2 2 .001 .0 6 5 RAM 8 .5 4 0 E -I8 .0 0 0 .4 4 8 2 .4 7 8 .0 2 7

s h e a r -.5 9 3 .2 8 4 .3 3 5 -2 .0 9 0 .0 5 5 4 (Constant) 1 5 .9 8 5 3 .6 4 6 4 .3 8 4 .001 REFC 1 .6 76E -02 .0 0 7 .4 5 0 2 .4 6 8 .0 2 6 RAM 8 .7 7 3 E -1 8 .0 0 0 .4 6 0 2 .5 7 4 .021 SHEAR -.5 5 6 .2 7 8 -.3 1 4 -1 .9 9 7 .0 6 4 S (Constant) 1 5 .9 8 5 3 .6 4 6 4 .3 8 4 .001 REFC 1 .6 76E -02 .0 0 7 .4 5 0 2 .4 6 8 .0 2 6 RAM 8 .7 7 3 E -I8 .0 0 0 .4 6 0 2 .5 7 4 .021 SHEAR -.5 5 6 .2 7 8 -.3 1 4 -1 .9 9 7 .0 6 4 a. D ependent Variable: ICH A N G E

175 Backward regression for 72-hour period

Model Summjrjr*-*'*

Std. Error Van, bles Adjusted R of (he Model Entered Removed R R Square Square Estimate 1 OSHEAR. PEFC, POT, .7 6 3 .5 8 3 .3 7 4 2 .7 2 6 4 RAM, REFC, s h e a r f 2 PEFC .7 4 9 .56 1 .3 9 2 2 .6 8 6 8 3 .» POT .7 3 7 .5 4 4 .4 1 3 2 .6 3 9 6 n 4 R A M .7 0 7 .5 0 0 .3 9 9 2 .6 7 0 7 m 5 RAM' .7 0 7 .5 0 0 .3 9 9 2 .6 7 0 7 a. Dependent Variable; ICHANGE b. Method: Enter c. Method: Backward (criterion: Probability of F-to-remove > ■ .100).

d. Independent Variable:: (Constant), OJHEa R, PEFC, P O T, R A M , REFC, SHEAR e. All requested variables entered.

f. Independent Variables: (Conttani), OSHEa R. PO T, R A M , REFC, SHEAR f. Independent Variables: (Constant). DSHEAR, RAM, REFC, SHEAR h. Independent Variables: (Constant), DSHEAR, REFC, SHEAR I. Probability of F-to-remove ■ . 100 limits reached.

ANOVA*

Sum of Mean Model Squares df Square F S'«- . 1 Regression 1 2 4 .5 9 4 6 2 0 .7 6 6 2 .7 9 4 .0 6 l'* Residual 8 9 .1 9 6 12 7 .4 3 3 Total 2 1 3 .7 9 1 18 2 Regression 1 1 9 .9 4 3 5 2 3 .9 8 9 3 .3 2 3 .0 3 8 ' Residual 9 3 .8 4 8 I 3 7 .2 1 9 Total 2 1 3 .7 9 1 18 3 Regression 1 1 6 .2 4 7 4 2 9 .0 6 2 4 .1 71 .020'» Residual 9 7 .5 4 4 14 6 .9 6 7 Total 2 1 3 .7 9 1 18 4 Regression 1 0 6 .8 0 0 3 3 5 .6 0 0 4 .9 91 .0 1 3 * Residual 1 0 6 .9 9 1 15 7 .1 3 3 Total 2 1 3 .7 9 1 18 5 Recession 1 0 6 .8 0 0 3 3 5 .6 0 0 4 .9 9 1 .0 1 3 * Residual 10 6.99 1 IS 7 .1 3 3 Total 2 1 3 .7 9 1 18 a. Dependent Variable: ICHANGE b. Independent Variables: (Constant), DSHEAR, PEFC, POT, RAM, REFC, SHEAR c. Independent Variables: (Constant), OSHEAR, POT, RAM, REFC, SHEAR d. Independent Variables: (Constant), DSHEAR, RAM, REFC, SHEAR e. Independent Variables: (Constant), OSHEAR, REFC, SHEAR

176 Backward regression for 72-hour period

Coefficients*

S u n d a rdized Coeffi Unsundardlzed Coefficients cients M odel B Std. Error Beta t SIg. 1 (Consunt) 1 4 .3 8 3 5 .1 9 2 2 .7 7 0 .0 1 7 P O T .1 2 6 .1 2 3 -.2 6 3 -1.021 .3 2 7 REFC 9 .7 7 2 E 0 3 .0 0 8 .3 4 5 1 .1 9 2 .2 5 6 PEFC 6 6 2 5 7 .7 5 3 8 3 7 5 6 .1 8 4 .2 5 9 .791 .4 4 4 RAM 3 .0 2 7 E -I8 .0 0 0 .2 3 7 1 .1 1 2 .2 8 8 SHEAR -.8 0 4 .4 0 6 -.7 1 4 -1 .9 7 9 .071 DSHEAR • .5 2 9 .3 2 0 -.4 5 5 -1 .6 5 4 .1 2 4 2 (Consunt) 1 2 .3 9 6 4 .4 7 8 2 .7 6 8 .0 1 6 PO T -7.3 lSE-02 .1 0 2 -.1 5 3 -.7 1 6 .4 8 7 REFC I.3 6 7 E -C 2 .0 0 6 .4 8 3 2.1 17 .0 5 4 RAM 3 .0 0 9 E -I8 .0 0 0 .2 3 5 1.1 2 2 .2 8 2 SHEAR -.5 8 1 ,' .2 8 8 -.5 1 6 -2 .0 1 5 .0 6 5 DSHEAR - .4 1 3 .2 8 0 -.3 5 5 -1 .4 7 4 .1 6 4 3 (C onsunt) 1 0 .2 1 2 3 .2 2 0 3.171 .0 0 7 REFC I .5 4 0 E 0 2 .0 0 6 .5 4 4 2 .6 2 0 .0 2 0 RAM 3 .0 6 7 E -I8 .0 0 0 .2 4 0 1 .1 6 4 .2 6 4 SHEAR -.5 4 2 .2 7 8 -.48 1 -1 .9 4 9 .0 7 2 DSHEAR -.4 0 1 .2 7 4 -.34 5 -1 .4 5 9 .1 6 7 4 (Constant) 9 .0 6 9 3 .1 0 3 2 .9 2 3 .0 1 0 REFC I.7 8 9 E -0 2 .0 0 6 .6 3 2 3 .2 2 8 .0 0 6 SHEAR -.6 5 6 .2 6 3 -.5 8 2 -2 .4 9 0 .0 2 5 DSHEAR -.5 1 1 .2 6 1 -.4 4 0 •1.962 .0 6 9 5 (Consunt) 9 .0 6 9 3 .1 0 3 2 .9 2 3 .0 1 0 REFC 1.7 8 9 E -0 2 .0 0 6 .6 3 2 3 .2 2 8 .0 0 6 SHEAR -.656 .2 6 3 -.5 8 2 -2 .4 9 0 .0 2 5 DSHEAR -.5 1 1 .261 -.4 4 0 -1 .9 6 2 .0 6 9 a. Dependent Variable: ICHANGE

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