CLIMATIC VARIABILITY: A STUDY OF TROPICAL CYCLONE TRACK SINUOSITY IN THE

SOUTHWEST PACIFIC

by

Arti Pratap Chand

A supervised research project submitted in partial fulfillment of the requirements for the degree of Masters of Science (M.Sc.) in

Environmental Sciences

Copyright © 2012 by Arti Pratap Chand

School of Geography, Earth Science and Environment Faculty of Science and Technology and Environment

The University of the South Pacific

October, 2012

DECLARATION Statement by Author I, Arti Pratap Chand, declare that this thesis is my own work and that, to the best of my knowledge, it contains no material previously published, or substantially overlapping with material submitted for the award of any other degree at any institution, except where due acknowledgement is made in the text. Signature……………………………………… Date…18th October 2012… Arti Pratap Chand Student ID No.: S99007704 Statement by Supervisors

The research in this thesis was performed under our supervision and to our knowledge is the sole work of Ms Arti Pratap Chand Signature……………………………………… Date…18th October 2012….. Principal Supervisor: Dr M G M Khan Designation: Associate Professor in Statistics, University of the South Pacific

Signature…… ……….Date……18th October 2012…… Co - supervisor: Dr James P. Terry Designation: Associate Professor in Geography, National University of Singapore Signature……………………………………… Date…18th October 2012…… Co - supervisor: Dr Gennady Gienko Designation: Associate Professor in Geomatics, University of Alaska Anchorage

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DEDICATION

To all tropical cyclone victims.

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ACKNOWLEDGEMENTS I am heartily thankful to my co – supervisor, Dr Gennady Gienko, whose trust,

encouragement and initial discussions lead me to this topic. I would like to gratefully

acknowledge my Principal Supervisor, Dr MGM Khan and my co – supervisor Dr James

Terry for their advice, guidance and support from the initial to the final level enabling

me to develop an understanding of the subject and statistical techniques.

I would also like to acknowledge and thank Dr Gennady and Dr Shingo Takeda for

helping me with displaying my results using ArcGIS software. My sincere thanks to

them for their time and patience.

My sincere thanks and appreciation goes to Dr MGM Khan and his student for helping

me with C++ programming technique.

I would also like to thank Dr Tony Weir and Mr Rajendra Prasad (former Director of the

Fiji Meteorological Services) for discussions I had with them regarding my thesis topic.

Special thanks to my family for their encouragement and moral support.

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ABSTRACT Tropical cyclones (TCs) are one of the most destructive natural hazards in the tropical

Pacific, with large impacts on socio-economic and environmental sectors of island

nations. Improved understanding of the characteristics of these intense storms is critical.

A continuing problem lies in forecasting TC movement after formation. One way to add

to existing knowledge in this area is to analyse available data on cyclone track shape, in

order to identify any special patterns. In this context, this study examines statistical

characteristics of several TC track parameters, using archived data from 1970 to 2008

for the South Pacific region. The dataset includes information on 292 TCs, which

includes all storms with wind intensity of 35 knots and above that have their genesis in

tropical waters.

TC paths are analysed within the geographical grid covered by 0 – 25°S and 160° E –

120° W. The particular focus of this study is on track sinuosity values and how these

may be characterised and grouped. River sinuosity has contributed a lot in understanding

fluvial geomorphology (Terry and Feng, 2010) and therefore extending the technique to

study TC track maybe useful. A sinuous track having loops and curves will affect many

more islands than a TC moving along a straight path. Some Islands may be affected

more than once or may be exposed to a TC for a longer time period if the TC makes a

loop during its journey. Sinuosity values for all TC tracks were calculated by measuring

the total distance travelled by each TC and then dividing this by the vector displacement

between cyclogenesis and decay positions.

In this study, the problem of categorising the TCs based on sinuosity index (SI) values

obtained by transformation of sinuosity values allows the grouping of similar TCs. The

SI categories are so constructed that the variance of groups is as small as possible. Thus

in this thesis a technique is developed to construct the SI categories of the TCs that seek

minimization of the sum of weighted deviations of SI from the mean of group. Then the

problem is solved for determining the optimum boundary points of the groups by using a

dynamic programming technique.

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Three TCs from the dataset were found to have very high SI values and therefore were

grouped in a separate SI category as an outlier category. Then the remaining TCs were

grouped into five homogeneous sinuosity index categories using proposed method

within which the TCs were very similar.

The results from above method were compared with the SI categories obtained by

hierarchical cluster analysis with Ward’s method. The comparison results show that the

SI categories constructed by the proposed method are more homogenous with respect to

the sinuosity index values of the TC tracks.

The homogenous SI categories obtained was further explored using GIS tool to study the

geographical distribution of these SI categories in the study area.

Keywords: Track Sinuosity, Cyclogenesis and decay positions, Homogeneous Categories

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ABBREVIATIONS

IPCC Intergovernmental Panel on Climate Change

SI Sinuosity Index

TC Tropical Cyclones

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TABLE OF CONTENTS DEDICATION i

ACKNOWLEDGMENT ii

ABSTRACT iii

ABBREVIATIONS v

TABLE OF CONTENTS vi

LIST OF FIGURES ix

LIST OF TABLES x

LIST OF APPENDICES xi

CHAPTER 1: INTRODUCTION 1

1.1. Tropical cyclones in the Pacific Region 1

1.2. Tropical cyclone variability 3

1.3. Tropical cyclone classification 4

1.4. Tropical cyclone tracks 6

1.5. Sinuosity of cyclone tracks 6

1.6. Research objectives 12

1.7. Chapter organizations 12

CHAPTER 2: LITERATURE REVIEW 14

CHAPTER 3: DATA AND METHODS 20

3.1 Study area and data collection 20

3.2 Sinuosity calculation 22

3.3 Distribution of Sinuosity values 22

3.3.1 Analysis of extreme Tropical Cyclones from sinuosity data 24

3.3.2 Sinuosity index 26

3.3.3 Analysis of extreme Tropical Cyclones from sinuosity index data 26

3.4 Correlation of sinuosity index with other parameters 28

3.5 Methodology for grouping the sinuosity index: a proposed technique 29

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3.5.1 Estimate of the distribution of sinuosity index values 31

3.5.2 Estimate of the parameters of distribution 32

3.5.3 Determination of optimum grouping using dynamic

programming technique 32

3.6 Alternative methodology for grouping the sinuosity index using

Hierarchical Cluster Analysis 34

3.7 A comparison study of grouping methods 35

CHAPTER 4: RESULTS AND INTERPRETATIONS 36

4.1 Tropical Cyclone frequency 36

4.2 Average sinuosity index 36

4.3 Correlation of average sinuosity index with southern oscillation index 37

4.4 Correlation of sinuosity with other tropical cyclone parameters 39

4.4.1. Correlation of sinuosity index with start latitude 39

4.4.2. Correlation of sinuosity index with start longitude 39

4.4.3. Correlation of sinuosity index with end longitude 39

4.4.4. Correlation of sinuosity index with time 40

4.4.5. Correlation of sinuosity index with duration 40

4.5 Grouping the sinuosity index values 40

4.6. Geographical distribution of the tropical cyclone genesis and

decay positions 41

4.7 Tropical Cyclone frequency and percentages in different tropical

cyclone months for the five categories 45

4.8 Mean values for other parameters of the tropical cyclone tracks in

relation to the sinuosity index category mean 46

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CHAPTER 5: DISCUSSION 47

5.1 Tropical cyclone genesis position and sinuosity index 48

5.2 Tropical cyclone decay position and sinuosity index 49

5.3 Tropical cyclone journey and sinuosity index 50

5.4 Sinuosity Index categories 50

CHAPTER 6: CONCLUSIONS 52

REFERENCES 55

APPENDICES 60

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LIST OF FIGURES Figure 1 An aerial photograph of Nadi during March 2012 flooding 2

Figure 2 Flooding in Nadi in April 2012 2

Figure 3 Tropical Cyclone Henrieta track of sinuosity value 1.01 7

Figure 4 Tropical Cyclone Daman track of sinuosity value 1.07 8

Figure 5 Tropical Cyclone Tomas track of sinuosity value 1.16 8

Figure 6 Tropical Cyclone Gavin track of sinuosity value 1.34 9

Figure 7 Tropical Cyclone Xavier track of sinuosity value 1.75 9

Figure 8 Tropical Cyclone Rewa track of sinuosity value 4.36 10

Figure 9 Tropical Cyclone Rewa

(28 December 1993 – 21 January 1994) 16

Figure 10 Tropical Cyclone Zaka (1995) 17

Figure 11 Tropical Cyclone Rae, Olaf, Meena, Percy and Nancy 18

Figure 12 Map of study area 21

Figure 13 Map of study area with 291 TC tracks during

1969/70 – 2007/08 cyclone seasons 21

Figure 14 Sinuosity values for each tropical cyclone track was calculated 22

Figure 15 Histogram for the sinuosity values 23

Figure 16 Boxplot analysis of sinuosity values 24

Figure 17 Boxplot analysis of sinuosity index 27

Figure 18 Dotplot of the sinuosity index 28

Figure 19 P-P plots of sinuosity index 31

Figure 20 Frequency distribution of sinuosity index 32

Figure 21 Tropical Cyclone frequency against tropical cyclone seasons

(1969/70 – 2007/08) 36

Figure 22 Graph of average sinuosity index against tropical cyclone seasons 37

Figure 23 Tropical Cyclone displacement tracks for the 291 tropical cyclones

that occurred between (1969/70 – 2007/08) 42

Figure 24 Tropical Cyclone displacement tracks for the five sinuosity

index categories 43

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Figure 25 Tropical Cyclone frequency and percentages for cyclone months for

different sinuosity index categories 46

LIST OF TABLES

Table 1 Saffir Simpson Scale for categories of hurricane force

tropical cyclones 5

Table 2 Outlier cyclones and their sinuosity values 25

Table 3 Outlier cyclones and their sinuosity index values 28

Table 4 Correlation of sinuosity index with cyclone variables 29

Table 5 Homogeneous categories based on sinuosity index using

dynamic programming approach 34

Table 6 Homogeneous categories based on sinuosity index using

hierarchical cluster analysis 35

Table 7 Number of cyclones, sinuosity and sinuosity index

average and average SOI 38

Table 8 Suggested names for the five sinuosity index categories 41

Table 9 Tropical cyclone frequency and percentages for tropical cyclone

months in each sinuosity index category 45

Table 10 Comparison of mean values of tropical cyclone parameters with

the mean for sinuosity index 46

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LIST OF APPENDICES

Appendix 1 Cyclone dataset for the years 1969/70 – 2007/08 59

Appendix 2 Southern oscillation index (SOI) archives 1969 – 2008 68

Appendix 3 C++ Program for finding the optimum group of cyclones using

Dynamic Programming Technique 69

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CHAPTER I

INTRODUCTION 1.1 Tropical Cyclone in the Pacific region

Tropical cyclones (TCs) are one of the most destructive natural hazards for the

tropical Pacific, and have a large impact on socio-economic and environmental

sectors in island nations therein (Terry, 2007). More than half the population of

tropical Pacific lives in coastal environment making them more vulnerable to the

impacts of the TC events. River flooding, storm surge, landslides, strong winds,

heavy rainfall and coastal erosion are the consequences of TCs that have the

capability of destroying properties and claiming lives of people and livestock.

Water sources in the Pacific are mostly from ground water, rain, river and dams

and therefore are extremely vulnerable to changes and variations in climate,

particularly rainfall because of their limited size, availability, geology and

topography (The Global Mechanism and IFAD). Pipes are run from these sources

to households and factories and all these are affected by flooding. Flooding is

usually huge during TCs and it contaminates water sources and destroys pipes

transporting water. It takes authorities months to restore services back to normal.

The same problem lies in the electricity sector. Electricity is distributed to

households and industries via cables hanging in air supported by posts. The

system is able to withstand winds up to category 3 TCs but lot of damage is done

to the posts and the power lines during category 4 and 5 TCs (Table 1) and the

time it takes to bring services back to normal is several weeks to months.

In the Pacific Island countries, agriculture is the main source of income for rural

dwellers where majority of people still live and depend on subsistence agriculture

(The Global Mechanism and IFAD). While subsistence agriculture provides local

food security, cash crops (such as sugar cane, banana and copra) are exported for

foreign exchange. These farmers are mostly located along the coast or rivers for

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fertile soil but it also makes these areas highly vulnerable to flooding resulting

from heavy rain and high seas associated with TCs. TCs are capable of

destroying vast areas of farms and also buildings with strong winds and flooding.

Figures 1 and 2 below show the extent of water level during two major floods in

Nadi, Fiji in 2012.

Figure 1: An aerial photograph of Nadi Figure 2: Flooding in Nadi in April 2012

during March 2012 flooding Photo courtesy Photo courtesy of Mohammed Ashiq, taken

of Helene Muller, taken 30March, 2012. 12 April, 2012.

There have been some very destructive TCs to strike the study area. TC Tomas in

2010 was the most intense TC to strike Fiji since TC Bebe in 1972 (Gopal, A.

2012). It proved to be very destructive leaving many homeless and entire villages

under water. Many homes were destroyed and washed away by strong winds and

storm surges. Electricity and running water was disrupted in the main land and

numerous outer islands (Gopal, A. 2012). TC Uma in 1987 struck Vanuatu and

resulted in a very destructive cyclone claiming 48 lives and affected 48 000

people and the damage from the cyclone totaled to around USD 25 million (A

Special Submission to the UN Committee for Development Policy on Vanuatu’s

LDC Status, 2009). These are two examples of destructive TCs experienced in

the study area but there are many other TCs that had a great impact on the study

area.

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1.2 Tropical Cyclone Variability

The patterns of TC variability are strongly affected by large-scale modes of

interannual variability. Interannual variability in this context refers to any

mechanism that can modulate the location and intensity of the monsoon troughs

affects the genesis location and frequency of tropical cyclones (Chen et al.,

2006). For example, the eastward shift in tropical cyclone formation positions

over the western North Pacific in response to large-scale circulation changes

during an El Nino – Southern Oscillation event is a particular example of the

interannual variability of TC characteristics (Harr and Elsberry, 1991). The

stronger storms (categories 3-5) tend to show stronger relationships to ENSO

than do weaker storms (tropical storm through category 2 strength) (Frank and

Young, 2007).

The studied dataset (Figure 13) shows that each TC track is unique in its own

way, that is, no two cyclones have followed exactly the same path or same

distance covered or caused the same degree of flooding. All these depend on

various parameters including strength, longevity, position of the TC and the track

they follow. One of the requirements for a TC to form and survive is the moisture

from the sea because as soon as the TC moves on land, the moisture source is cut

off and as a result the cyclone dies out. However, it was seen with two TCs

namely TC Bebe in 1972 and TC Mick in 2009 that passed over Vitilevu Island

in Fiji but they survived and continued their journey. DeMaria et al (2006)

modified the method developed by Kaplan and DeMaria (1995) on TC and wind

decay model that move over narrow landmasses. In the modified model the decay

rate is proportional to the current intensity times the fraction of the storm

circulation area that is over land. In another report by De Velde (2007), it is

reported that smaller land masses lay in the path of TCs. Therefore, it can be said

that Island landmasses are small and narrow for the TCs to pass through and still

maintain its journey. This factor makes the Islands more vulnerable owing to the

nature of the islands being small and narrow in the way that intense TCs will not

easily decay and may affect many Island countries.

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1.3 Tropical Cyclone Classification

TC is a generic name for a tropical depression or low pressure system. At its very

early stage it is called a tropical depression and as the wind force increases it is

categorized accordingly (gale force wind 34-47 knots); a tropical storm (storm

force wind 48-63 knots); and a hurricane or typhoon (hurricane force wind 64

knots and above) (Terry, 2007).

On the Saffir - Simpson Scale, hurricane force category of tropical cyclones is

further divided into five categories according to the maximum sustained winds

(Table 1).

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Table 1: Saffir Simpson Scale for categories of hurricane –force tropical cyclones is a standard

for all tropical cyclones worldwide

Category Winds & Effects Surge

1

74-95mph

(64-82 kt)

No real damage to building structures. Damage primarily to

unanchored mobile homes, shrubbery, and trees. Also, some

coastal flooding and minor pier damage.

4-5 ft

2

96-110mph

(83-95 kt)

Some roofing material, door, and window damage.

Considerable damage to vegetation, mobile homes, etc.

Flooding damages piers and small craft in unprotected

moorings may break their moorings.

6-8 ft

3

111-130mph

(96-113 kt)

Some structural damage to small residences and utility

buildings, with a minor amount of curtainwall failures.

Mobile homes are destroyed. Flooding near the coast

destroys smaller structures with larger structures damaged by

floating debris. Terrain may be flooded well inland.

9-12

ft

4

131-155mph

(114-135 kt)

More extensive curtainwall failures with some complete roof

structure failure on small residences. Major erosion of beach

areas. Terrain may be flooded well inland.

13-18

ft

5

155mph+

(135+ kt)

Complete roof failure on many residences and industrial

buildings. Some complete building failures with small utility

buildings blown over or away. Flooding causes major

damage to lower floors of all structures near the shoreline.

Massive evacuation of residential areas may be required.

18 ft

+

Source: Governor’s Office of Homeland Security & Emergency Preparedness, 2009.

A tropical storm officially becomes a hurricane once it reaches winds of 64 knots

or greater (Terry, 2007). Once this happens the hurricane is then given a category

based on how powerful the winds are. The category also gives an idea of likely

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damages caused by flooding and structural damage once the hurricane hits land

as shown in Table 1.

1.4 Tropical Cyclone Tracks

Atmospheric circulation is the dominant influence on storm properties. As TC

moves poleward, it loses its tropical characteristics when it moves over cooler

water and encounters the increasing vertical wind shears associated with the mid-

latitude westerlies (Sinclair, 2002). The tracks studied in this research are

confined to 0° to 25° south and therefore are restricted to the tropical climate.

The reason to analyse TC tracks without the extratropical atmospheric system

influence is to avoid confusion introduced by tropical and extratropical climates.

Tropical systems, while generally located equatorward of the 20 - 25th parallel,

are steered primarily westward by the east to west winds on the equatorward side

of the subtropical ridge – a persistent high pressure area (Landsea, 2010). The

coriolis force defined as the apparent deflection of objects (such as airplanes,

wind, missiles, and ocean currents) moving in a straight path relative to the

earth’s surface causes cyclonic systems to turn towards the poles in the absence

of strong steering currents ( Briney, 2013). The poleward portion of a tropical

cyclone contains easterly winds (Sinclair, 2002), and the coriolis effect pulls

them slightly more poleward. The general movement of TCs, therefore, is from

the equator towards the poles.

1.5 Sinuosity of Cyclone Tracks

TCs tend to display various track shapes from straight - curvy - single loop -

multiple loops. In this study, I chose to represent the different shapes of cyclone

tracks, the sinuosity value was then correlated with several other tropical cyclone

parameters, including cyclone genesis and decay positions, duration,

displacement, distance travelled and time (in years).

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Sinuosity of the TC track simply means how straight or not straight a cyclone

track is (Terry and Gienko, 2011). A straight moving TC has a sinuosity value of

1, the minimum value for sinuosity. When a sinuosity value exceeds 1, the TC

track becomes more curvy or loopy. Figures 3 - 8 below show cyclone tracks of

six cyclones of differing sinuosity.

Figure 3: Tropical Cyclone Henrietta track of sinuosity value 1.01

S = 1.01

Latit

ude

Longitude

8

Figure 4: Cyclone Daman track of sinuosity value 1.07

Figure 5: Cyclone Tomas track of sinuosity value 1.16

Latit

ude

Longitude

S = 1.16

Latit

ude

Longitude

S = 1.07

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Figure 6: Cyclone Gavin track of sinuosity value 1.34

Figure 7: Cyclone Xavier track of sinuosity value 1.75

Latit

ude

S = 1.34

Longitude

S = 1.75

Latit

ude

Longitude

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Figure 8: Cyclone Rewa track of sinuosity value 4.36

TC Henrietta in figure 3 above having sinuosity value of 1.01 has a fairly straight

track. TC Daman and Tomas have similar track shape but cyclone Daman has

lower sinuosity value than TC Tomas. One reason could be that TC Tomas has

travelled a longer distance and covered greater latitudes than TC Daman and was

therefore more sinuous. TC Gavin has a variety of turns and a sinuosity value of

1.34 and falls in sinuosity category 4. It can be seen that the shape of the track

has various turns which gives it a high sinuosity value. Figure 7 shows track for

TC Xavier from sinuosity category 5 which has sinuosity value of 1.75. TC

Xavier travelled a long distance and had a loop in its journey which contributed

to its high sinuosity value. TC Rewa travelled a great distance and has various

turns and loops making it a highly sinuous track.

The forecasting of TCs is very challenging owing to the complexity of the

contributing factors and the diverse nature of the event. The situation may

worsen with climate change scenarios in terms of future distribution and

characteristics of TCs (IPCC, 2011). For example, large amplitude fluctuations in

the frequency and intensity of TCs can greatly complicate both the long-term

Longitude

S = 4.63

Latit

ude

11

trends and their attribution to rising levels of atmospheric greenhouse gases

(Knutson et al., 2010).

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1.6 Research Objectives

Specific objectives of the research are:

1. Explore available tropical cyclone data set for the Southwest Pacific

region to develop sinuosity and sinuosity index data.

2. Investigate whether there is a correlation between sinuosity values with

other tropical cyclone parameters and Southern Oscillation Index.

3. Implement statistical analyses of the tropical cyclone tracks and develop a

technique to group the tropical cyclone tracks into different categories

according to their sinuosity values.

4. Employ GIS techniques to map and study the distribution of the resulting

sinuosity categories in the study area.

1.7 Chapter Organizations

This study presents the outcome of the cyclone groups, categorised based on

sinuosity index values of cyclones for the period 1969/1970 to 2007/2008 for the

Southwest Pacific.

The thesis is structured in six chapters as follows;

Chapter 1: Introduction

This chapter introduces to the tropical cyclones in the Pacific, classification of

the cyclones, sinuosity of the cyclone tracks and tropical cyclone tracks. The

chapter also describes the objectives of the research carried out and presented in

the thesis.

Chapter 2: Literature Review

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The focus of this chapter was to study similar work done on this topic in in the

region and in other regions (basically western North Pacific) and to study the

nature of some tropical cyclones based on their tracks.

Chapter 3: Data and Methods

The chapter introduces the study area and the nature of the data. It also describes

the various preprocessing steps for the data normalization process and the

categorization methods.

Chapter 4: Results and Interpretation

This chapter analyzes and interprets the results obtained from the categorization

of the cyclone data.

Chapter 5: Discussion

The chapter involves discussing the two methods used for categorization process

and the sinuosity index categories obtained.

Chapter 6: Conclusions

The final chapter summarizes the key findings of this study with

recommendation for further research

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CHAPTER 2

LITERATURE REVIEW

Tropical Cyclone season in the South Pacific is from November to April (Terry,

2007). Based on the studied dataset, the following statistics were calculated (refer

to table 9). The number of TCs varies significantly ranging from 2 – 12 per

season. The average number of TCs per season for 1969/1970 – 2007/2008

periods is 7.5. More than 80% of TCs occur between December – March within

the cyclone season. About 6% of TCs from the total 291 TCs studied, occurred

outside the cyclone season and 81% of these TCs occurred in the El Niño years.

It is evident from the 39 cyclone seasons studied that Southern Oscillation has an

impact on the number of cyclones and off season TCs in the Southwest Pacific.

There are relatively few previous investigations that focus on sinuosity of TC

tracks in the South Pacific. A difficult part of this research was finding

unpublished/ published studies that focus on sinuosity of TC track analysis.

Studies have been conducted to enhance understanding of TC patterns and

behavior and have been used to improve the understanding of the cyclone

characteristics. Most of these studies have been undertaken for the North Atlantic

and Western North Pacific cyclone basins due in part to the reliable record

(Landsea, 1999). However, recently Diamond (2010) has developed an enhanced

Tropical Cyclone Track database for the Southwest Pacific which would attract

researchers to utilize this opportunity to study climatology of TCs in the

Southwest Pacific.

There are some studies done on shapes and trajectories of TC tracks (e.g., Chen

et al. 2006; Camargo, et al, 2007; Harr & Elsberry, 1991; Lander, 1996). Two

principal track types identified in previous studies (e.g., Sandgathe, 1987; Harr

and Elsberry, 1991; Lander, 1996; Camargo et al., 2007) are recurving and

straight - moving track types. Another study by Elsner and Liu (2003) analyzed

typhoon tracks based on the typhoon’s position at maximum intensity and its

final intensity and obtained three clusters; (1) straight – moving; (2) recurving

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and (3) north – oriented tracks. The study employed the K- means cluster

analysis. Camargo et al. (2007) used new probabilistic clustering technique based

on a regression mixture model to categorize the cyclone trajectories in the

western North Pacific. Seven different clusters were obtained and then analyzed

in terms of genesis location, trajectory, landfall, intensity, and seasonality. Only

two studies have focused on the sinuosity of TCs is by Terry and Feng (2010) for

western North Pacific and Terry and Gienko (2011) for the Southwest Pacific.

The calculation of sinuosity values for cyclone tracks for this study is consistent

with the method employed by Terry and Feng (2010) but the categorization

method is different. In Terry and Feng (2010) the categories for track sinuosity

was based on quartile ranges due to the strong skew in the data. Our study is built

on the study of Terry and Feng (2010) but uses a different method of

categorization. In this study, a proposed method using a dynamic programming

technique and Hierarchical Cluster Anaylysis with Ward’s method was used for

categorization.

The greater the sinuosity of a cyclone track is, the greater the potential area

covered during its journey. There are many small islands in the South Pacific.

TCs that tend to curve or loop, are more likely to involve landfall, for example,

TC Rewa (28 December 1993– 21 January 1994) which lasted for 25 days and

underwent several major changes in direction during its lifetime (Bureau of

Meteorology, 2012). TC Rewa track has a sinuosity value of 4.36 (Figure 9).

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Figure 9: Cyclone track for TC Rewa (28 December 1993– 21 January 1994)

Source: Bureau of Meteorology, 2012

“Tropical cyclone Rewa was formed and situated to the north of Vanuatu and

moved in the western direction before moving in the west – southwest direction,

it crossed the southern tip of the island of Malaita before passing south of

Guadalcanal Island in its passage through the Solomons. The system then

recurved to the south and continued in a south – southeasterly direction followed

by southeast and then more easterly direction. Along its path the cyclone passed

over central New Caledonia heading in a northeasterly direction then changed

its course and started moving in a northwest direction for a short while then

continued in a more western direction. It again started moving in a northwest

direction before moving in a northerly direction towards the north – west tip of

Tagula Island in the Louisiade Archipelago. The cyclone then executed a sharp

clockwise turn just off the northern side of Tagula Island and continued in the

southest direction before recurving to the west – southwest approaching the

Queensland coast. Cyclone Rewa then turned south on the track before moving

towards the southeast away from the coast towards north of Lord Howe Island.

The cyclone then moved southeast across the Tasman Sea towards the north of

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the South Island of New Zealand before dying out” (Bureau of Meteorology,

2012).

TC Zaka has a sinuosity value of 1, it formed south of Tonga and moved in the

west direction for a little while before moving in the northwest direction towards

north of New Zealand and died out (Figure 10). It was a very weak category one

cyclone which brought some pesky rain and occasional roaring gusts (Natural

Hazards Spring, 2012).

Figure 10:Ttropical Cyclone track for Cyclone Zaka (1995)

Source: Natural Hazards Spring, 2012

TC tracks for five different TCs are shown in figure 11 below. These five TCs

occurred during 2004/05 within a period of five weeks. Sinuosity values of these

TCs are Rae (1.08), Olaf (1.13), Meena (1.15), Percy (1.18) and Nancy (1.57).

TCs Nancy, Percy, Olaf and Meena having more sinuous tracks than TC Rae also

caused more damage and lasted longer. They brought storm surges, huge waves

which destroyed buildings in coastal areas, seawater inundated buildings along

coastal areas and rubble and trees were strewn on buildings. TC Rae only lasted

for ten hours with no damages to the Island. (Ngari, 2005).

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Figure 11: Cyclone tracks for Cyclone Rae, Olaf, Meena, Percy and Nancy

Source: (Ngari, 2005)

When TCs tend to recurve, it has its peak power and highest sustained wind

speeds (De Velde, 2007). A slow moving TC stays longer in an area and

therefore will have more impact than a cyclone that moves in a straight line.

Tropical cyclones normally (about 70%) recurve to the east, at latitude of

approximately 20° to 30° N/S, following the general air circulation (westerlies)

around the globe (De Velde, 2007). The remaining 30% of the tropical cyclones

continue to travel west, northwest, north, or have an erratic track, or start to loop

back or remain stationary (De Velde, 2007). Therefore, it is important to study

why cyclones tend to differ so much in the way they travel and in order to do

this, the best way will be to study the long term trend of cyclone tracks for

sinuosity and also correlating the sinuosity trend with other parameters such as,

19

cyclogenesis and decay positions, displacement, total distance travelled by TCs,

wind speed and duration.

20

CHAPTER 3

DATA AND METHODS

3.1 Study Area and Data Collection

This study examines TC track parameters using data from 1969/70 to 2007/08.

Appendix 1 gives the date, atmospheric pressure, wind speed and location of the

TCs at starting and ending phase. It also gives the name, duration, azimuth and

sinuosity of the TCs of interest in this study. The primary sources of the data are

the Fiji Meteorological Service and the Tropical Cyclone Warning Centre in New

Zealand. The studied dataset lists the TCs which includes the portion of the TC

tracks with intensity of 35 knots and above and the TCs which have their genesis

in the tropics. The portion of the TC track which was below 35 knots was

eliminated from the analysis. The data set records 6- hourly centre location and

intensities and therefore the track plotted joining the recorded positions. TC paths

analysed are within the geographical grid covered by 0 – 25°S and 160° E – 120°

W. (Figure 12). This area falls under the responsibility of the Fiji Meteorological

Services. In the 39 TC seasons during 1969/70 to 2007/08, the study area

experienced 291 TCs (Figure 13). Data from 1969/70 onwards were analyzed

when satellite observation was introduced so that sinuosity categories are

constructed based on reliable dataset. However, extensive work has been done by

International Best Tracks for Climate Stewardship (IBTrACS) project, under the

auspices of the World Data Centre for Meteorology in compilation of TC best

track data from 12 TC forecast centres around the globe, producing a unified

global best track data set (Diamond, H, 2010). Diamond, H (2010) then

developed an enhanced TC tracks database for the Southwest Pacific for 1840 –

2009. Having such a long term reliable data set would be very useful for this kind

of study, however, it was not possible to incorporate this dataset in this study due

to unavailability of the dataset at the commencement of this study in 2008.

21

Figure 12: Map of Study Area

Source: Modified from Bureau of Meteorology, 2009

Figure 13: Map of study area with 291 TC tracks during 1969/70 – 2007/08 cyclone seasons

180º 160º W 140º W 160º E 140º E

20º S

30º S

10º S

0º

22

3.2 Sinuosity Calculation

In this study TC tracks are studied based on sinuosity values of cyclone tracks.

Sinuosity values for the TC tracks were calculated by dividing displacement of

the track by distance travelled by the cyclone. Only the portion of the cyclone

track which is in the study area and is 35 knots and above was used to calculate

the sinuosity. The following illustration in Figure 14 illustrates how sinuosity of

TC tracks was calculated:

Figure 14: Sinuosity values for each cyclone track was calculated

The red portion of the cyclone track was included in this study as it falls in the

study area and has wind speeds > 35 knots. The distance (in red) and the

displacement (in black) of the TC track were measured using GIS tool. Sinuosity

was calculated as the ratio of the two;

�Distance of tropical cyclone

Sinuosity = Displacement of tropical cyclone

3.3 Distribution of Sinuosity Values

In this section, frequency distribution of sinuosity data is studied as shown in

Figure 15 below.

23

Figure 15: Histogram for the sinuosity data

The histogram shows that the distribution is skewed towards left as the bulk of

the data lies between 1 and 2 and a very extreme value at around 52. Thus,

statistical analysis on this distribution will not be much useful because of the

presence of large extreme value which is making the distribution very skewed.

The option of eliminating three extreme values 52.74, 4.51 and 4.36 was also

tested but distribution was still skewed towards right. Thus, a statistical analysis

using boxplot was conducted to eliminate outliers from the dataset. However, in

the following section, a statistical analysis is carried out to identify extreme

cyclones that can be considered as outliers with respect to the sinuosity values.

24

3.3.1 Analysis of Extreme Tropical Cyclones from sinuosity data

Figure 16: Boxplot analysis of the sinuosity dataset

The boxplot in figure 16 clearly shows that there was one TC with an extreme

sinuosity value. To identify TCs with extreme values in the distribution of

sinuosity, the following quantities are computed:

1. Lower inner fence: 1 1.5Q IQ� �

2. Upper inner fence: 3 1.5Q IQ� �

3. Lower outer fence: 1 3Q IQ� �

4. Upper outer fence: 3 3Q IQ� �

Where, 1Q is the 25th percentile = 1.028

3Q is the 75th percentile = 1.300

IQ is the interquartile range = 3 1Q Q� = 0.27

Substituting the values of 1Q , 3Q and IQ into the equations above we get:

1. Lower inner fence: 1.02790 1.5 0.27150� � = 0.62

25

2. Upper inner fence: 1.29940 1.5 0.27150� � = 1.71

3. Lower outer fence: 1.02790 3 0.27150� � = 0.21

4. Upper outer fence: 1.29940 3 0.27150� � = 2.11

Outlier detection criteria shows sinuosity value beyond an inner fence on either

side is considered as a mild outlier and therefore sinuosities below 0.62 and

above 1.71 are outliers and the value beyond an outer fence is considered as

extreme outlier, which implies all values below 0.21 and above 2.11 are extreme

outliers in this case. Table 2 shows that there are 28 outliers in total and the last

13 out of 28 cyclones are considered as extreme outliers.

Table 2: Shows the outlier cyclones and their sinuosity values.

Tropical cyclones Sinuosity LENA 1.72 ERICA 1.73 NORMAN 1.75 XAVIER 1.75 KERRY 1.77 ZOE 1.77 IMA 1.78 VEENA 1.79 NAMELESSB 1.80 ZUMAN 1.83 BENI 1.84 ABIGAIL 1.85 DANI 1.86 CYC1981 1.86 BETTY 2.11 ESAU 2.21 WATI 2.22 IVY 2.23 FIONA 2.24 CARLOTTA 2.26 HALI 2.33 BOLA 2.44 YANI 2.69 HARRY 2.76 JUNE 2.80 REWA 4.36 TRINA 4.50 KATRINA 52.74

It is true that a dataset needs to be free of outliers before any statistical analysis

could be done on the dataset to concentrate on the bulk of the data. This would

26

allow identifying the most likely response of the sinuosity values but the outliers

in this case are significant as it represents a population and not sample and

therefore it is not appropriate to eliminate 28 cyclones as outliers. An option of

calculating sinuosity index, which is discussed in Terry and Gienko (2010), was

then considered for categorizing the TCs in this research.

3.3.2 Sinuosity Index

From the sinuosity values, sinuosity indexes were calculated using the following

formula (Terry and Gienko, 2010):

3SI = –1 10S � .

Where, SI = Sinuosity Index value, S = calculated sinuosity. Sinuosity Indexes

are cubed – root transformation of sinuosity values in order to normalize the

sinuosity values. The subtraction (S – 1) allows the transformed distribution for

SI to start at zero and product x10 is introduced in order to avoid dealing with

decimal numbers.

The need to calculate sinuosity indexes was to reduce number of outliers from

the dataset so that maximum number of cyclones could be included in the

analysis. It was important to include maximum number of cyclones in the

categorization analysis so that the categories obtained based on sinuosity index

values are true representation of the dataset.

3.3.3 Analysis of Extreme Tropical Cyclones from Sinuosity Index Data

The boxplot in figure 17 still shows some extreme cyclones based on the

sinuosity index values.

27

Figure 17: Boxplot analysis of the sinuosity index values

To identify these outliers, as discussed in Section 3.3.1, the inner and outer

fences for SI values are obtained as follows:

1. Lower inner fence: 3.0330 1.5 3.6569� � = -2.45

2. Upper inner fence: 6.6899 1.5 3.6569� � = 12.18

3. Lower outer fence: 3.0330 3 3.6569� � = -7.94

4. Upper outer fence: 6.6899 3 3.6569� � = 17.66

Thus, TCs whose sinuosity index falls below -2.45 and above 12.18, are

considered to be outliers in this case. There are three outliers found and one of

them is considered to be an extreme outlier, which is tropical cyclone Katrina

with SI value of 37.26 as shown in the Dot-plot (Figure 18).

28

Figure 18: Dotplot of the sinuosity index values

Converting the sinuosity values into sinuosity index values brings distribution

closer to normal and reduces number of outliers from 28 to only 3 TCs (Table 3). Table 3: Outlier cyclones and their sinuosity index values.

Tropical cyclones

Sinuosity Index values

REWA 14.97 TRINA 15.19 KATRINA 37.26

3.4 Correlation of Sinuosity Index values with other Parameters

SI values were correlated with other TC parameters. Sinuosity index value was

negatively correlated with start latitude, start longitude and end longitude and

positively correlated with duration, distance and time (in years). TC displacement

and end latitude did not show any significant correlation with sinuosity index

values. Results from correlation tests are presented in Table 4. Correlations of

sinuosity index with all the parameters are significant at the 0.01 level except

with start longitude which is significant at 0.05 level. Thus, correlation of SI with

six other TC parameters is significant and, therefore, it may be appropriate to use

sinuosity index values to categorize the TCs into different groups or categories.

29

Table 4: Correlation of sinuosity index with tropical cyclone variables.

Other Variable Correlation (r) p-value

Start Latitude -0.20 .001

Start Longitude -0.15 .011

End Longitude -0.21 .000

Distance 0.46 .000

Duration 0.54 .000

Time 0.15 .009

3.5 Methodology for Grouping the Sinuosity Index values: A proposed Technique In this section a method is proposed to categorize the TCs based on the sinuosity index values. Let the sinuosity index ( x ) of size N is to be classified into G mutually exclusive

and homogeneous groups consisting ; ( 1,2,..., )hN h G� units in hth group so as

to

1 2 ... GN N N N� � � �

and the variance of the sinuosity index within the group is as minimum as

possible. That is, in order to make the groups internally homogenous, the groups

should be constructed in such a way that the variance of the groups be as small as

possible. A reasonable criterion to achieve this is,

Let x0 and Gx be the smallest and largest values of sinuosity index x

respectively and � �1 2 1, ,..., Gx x x � denote the set of intermediate optimum boundary

points of the groups. If hix are the values of sinuosity index of i th cyclone that

fall in h th group, then the problem of optimum grouping can be described as to

find the intermediate group boundaries 1 2 1,..., Gx x x � such that the sum of

weighted variance due to the grouping, that is,

2

1

G

h hh

W �� (1)

is minimum.

30

Where hh

NWN

� = the proportion of cyclones that falls in h th group,

� �2

2 1hN

hi hih

h

xN

� �

�� � = the variance of h th group,

and 1hN

hiih

h

xN

� �� � = the mean of h th group.

It should be noted that the values of hN and hix are unknown as the groups are

yet to be constructed. Further, the problem is to determine the best boundaries

that make groups internally homogeneous by minimizing (1), which is not a

function of boundary points. Therefore, a way to achieve the optimum boundary

points effectively is, if (1) can be expressed as the function of boundary points

which is possible when the distribution of sinuosity index known and then create

groups by cutting the range of the distribution at suitable points (See Khan, et al.

2002, 2005, 2008).

Let ( )f x denotes frequency function of the sinuosity index ( x ). Then the values

of weights Wh and the variance 2h of h th group are obtained as the function of

boundary points ( 1hx � , xh ) by

W f x dxhx

x

h

h

��

( )1

(2)

�hh x

x

hWx f x dx

h

h2 2 21

1

� ��

( ) (3)

Where � hh x

x

Wxf x dx

h

h

��

1

1

( ) (4)

Therefore, when the frequency function ( )f x is known and is integrable, using

(2), (3) and (4) 2h hW in (1) could be expressed as a function of xh and xh�1 , and

hence the optimum boundary points are obtained. (Khan et al., 2008).

3.5.1 Estimate of the Distribution of Sinuosity Index values

31

P-P plot (using SPSS): A probability - probability (P-P) plot of sinuosity index ( x ) is obtained to

determine whether the distribution of x matches a particular distribution. Figure

19 shows that x match the gamma distribution as the points cluster around a

straight line.

Figure 19: P-P plot for sinuosity index values (x)

32

Figure 20: Frequency distribution of sinuosity index.

Also figure 20 of relative frequency histogram reveals that x is assumed to

follow Gamma distribution with a probability density function given by

� � 11 ; 0; , 0( )

xr

rf x x e x rr

� ��

��� � ��

. (5)

Where r is the shape parameter and � is the scale parameter. 3.5.2 Estimate of the Parameters of Distribution Using the maximum likelihood estimate (MLE) method for the sinuosity index

data, the parameters of Gamma distribution given in (5) are found to be

Shape, r̂ =3.822976 and scale, �̂ =1.351949 (6) 3.5.3 Determination of Optimum Grouping using Dynamic programming Technique Using (2), (3) and (4), we obtain hW , h� and 2

h as follow:

33

1 1, ,h h hh

x x lW Q r Q r� �� � �� � � �� �� � � �

� � � �

(7)

1 1

1 1

1, 1,

, ,

h h h

hh h h

x x lr Q r Q r

x x lQ r Q r

�� ��

� �

� �

� �

�� �� � � �� � �� � � �� �� � � �� ���� �� � � ��� � � �� �� � � �� �

and

2 2 21 1 1 1

22

1 1 1 1

( 1) 2, 2, 1, 1,

, , , ,

h h h h h

hh h h h h

x x x x lr r Q r Q r r Q r Q r

x x x x lQ r Q r Q r Q r

� �� � � �

� � � �

� � � �

� � � �

�� � � �� � � � � � � �� � � � � � �� � � � � � � �� � � �� � � � � � � �� � � �� �� � � � �� �� � � �� �� � � � � � � �� �� � � � � � � �� �

(8)

Where

1h h hl x x �� � (9) is the width of h th group and

11( , ) ; , 0; ( ) 0( )

r t

x

Q r x t e dt r x rr

�� �� � � �

�

denotes the upper incomplete Gamma function.

Therefore, from (7) and (8), the expression (1) reduces to

2 2 1 1

2 1 1

1 1 1

1, 1,( 1) 2, 2,

, ,

h h hG

h h

h h h h

x x lr Q r Q rx xr r Q r Q r

x x lQ r Q r

�� �

�� �

� �

� �

� �

� � �

� � �� � � �� � �� � � �� �� �� � � � � � � �� �� � � � �� � � �� � � � �� � � �� � � �� � �� � � �� �� � � �� �

� (10)

To obtain the optimum boundary points � �1,h hx x� of the groups, the optimum

widths hl are obtained by formulating a nonlinear optimization problem as given

below (See Khan, et al. 2002, 2005, 2008):

34

Minimize2 2 1 1

2 1 1

1 1 1

1, 1,( 1) 2, 2,

, ,

h h hG

h h

h h h h

x x lr Q r Q rx xr r Q r Q r

x x lQ r Q r

�� ��

� �� �

� �

� �

� � �

�� �� � � �� � �� � � �� �� �� � � � � � � �� �� � � � �� � � �� � �� �� � � �� � � �� � �� � � �� �� � � �� �

�

Subject to 1

G

hh

l d�

�� . (11)

Where d is the range of the sinuosity indexes, that is,

0 12.1561 0 12.1561Ld x x� � � � � . If five groups, that is 5G � , are to be formed, then the proposed method using a

dynamic programming technique by extending Khan, et al. (2002, 2005, 2008)

gives the optimum boundary points for each group by executing a computer

program coded in C++ (See Appendix 3) for Problem (11) as shown in Table 5:

Table 5: Five homogeneous categories using the proposed dynamic programming approach.

Group ( h )

Sinuosity Index ( x )

No. of cyclones ( hN )

Weight ( hW )

Variance ( 2

h )

Weighted Variance ( 2

h hW )

1 0 – 3.03 73 0.25 0.82 0.20 2 3.03 – 4.64 71 0.16 0.12 0.02 3 4.64 – 6.40 65 0.31 0.38 0.12 4 6.40 – 8.84 53 0.18 0.48 0.087 5 8.84 – 12.16 26 0.089 1.05 0.096 288 0.52

3.6 Alternative Methodology for Grouping the Sinuosity Index values using

Hierarchical Cluster Analysis

Hierarchical Cluster Analysis was also used to identify relatively homogeneous

groups of TCs. Using SPSS with Ward’s method, five homogeneous groups of

TCs were determined based on sinuosity index values (Table 6).

35

Table 6: Five homogeneous categories based on sinuosity index using hierarchical cluster analysis.

Group ( h )

Sinuosity Index ( x )

No. of cyclones

( hN )

Weight ( hW )

Variance ( 2

h )

Weighted Variance

( 2h hW )

1 0 – 3.20 103 0.36 1.04 0.37 2 3.20 – 5.01 60 0.21 0.094 0.020 3 5.01 – 7.27 72 0.25 0.43 0.11 4 7.27 – 9.51 42 0.14 0.49 0.071 5 9.51 –12.16 11 0.038 0.37 0.014 288 0.59

3.7 A Comparison Study of Grouping Methods

In Section 3.5 and Section 3.6, the cyclones are categorized into five groups

based on their sinuosity index values using the following two methods,

respectively:

1. A proposed method using a dynamic programming technique by

extending Khan et al. (2002, 2005, 2008).

2. Hierarchical Cluster Analysis method with Ward’s method.

Table 5 and 6 show the results of five SI categories for TC dataset obtained by

the proposed method and Hierarchical Cluster Analysis method, respectively.

The tables also show variance of each group and sum of the weighted variance.

SI categories one, three and four in proposed method have smaller variance as

compared to Hierarchical Cluster Analysis method. Moreover, the sum of

weighted variance (0.52) is also smaller for the proposed method as compared to

Hierarchical Cluster Analysis method (0.58). Thus, on the basis of these

comparisons, it can be concluded that categorization using proposed dynamic

programming technique is a more appropriate approach since it produces more

homogenous SI categories.

36

4.0 RESULTS and INTERPRETATIONS

4.1 Tropical Cyclone frequency

The graph below (Figure 21) shows that number of TCs has slightly decreased

for the study period (1969/70 – 2007/08). The 1997/98 season shows the greatest

frequency of TCs and other seasons recording high frequencies (ten and above

TCs per season) include seasons 1980/81, 1982/83, 1986/87, 1988/89, 1991/92,

1992/93, 1996/97 and 2002/03.

Figure 21: Tropical Cyclone frequency against cyclone seasons (1969/70 – 2007/08)

4.2 Average sinuosity index

Figure 22 obtained from the average sinuosity index calculated in Table 7 shows

that average sinuosity index have slightly increased for the study period. The

three seasons having high sinuosity index average are 1993/94, 1997/98 and

2001/02. All these seasons also include cyclones from outlier category.

37

Figure 22: Graph of sinuosity index averages against cyclone seasons (1969/70 – 2007/08)

One clear observation from the two graphs above is that 1997/98 season has the

highest number of TCs and also highest sinuosity index average.

4.3 Correlation of Average Sinuosity Index with Southern Oscillation

Index (SOI)

Average for sinuosity indexes for each thirty nine TC seasons were calculated

and correlated with Southern Oscillation Index (SOI) averages. SOI was obtained

from the archives of Australian Government Bureau of Meteorology (Appendix

2) and the average of each tropical cyclone season was calculated as shown in

Table 7.

38

Table 7: Number of cyclones, sinuosity, sinuosity index and SOI averages for cyclone seasons

Cyclone Seasons No. of Cyclones

Sinuosity

Index Average Sinuousity Average

Average Southern Oscillation Index

1969 - 70 6 5.31 1.21 -3.3 1970 - 71 6 5.55 1.35 36.4 1971 - 72 9 4.73 1.25 2.9 1972 - 73 8 4.11 1.12 -5.5 1973 - 74 7 2.76 1.03 48.2 1974 - 75 5 5.86 1.34 4 1975 - 76 5 3.53 1.07 12 1976 - 77 9 4.81 1.34 -1.4 1977 - 78 9 4.52 1.18 -11 1978 - 79 6 4.66 1.21 -1.4 1979 - 80 7 2.51 1.03 -4.8 1980 - 81 12 4.79 1.17 -4.4 1981 - 82 6 6.78 1.37 2.6 1982 - 83 14 6.07 1.30 -26.8 1983 - 84 7 3.93 1.16 0.4 1984 - 85 9 3.49 1.07 3 1985 - 86 7 4.4 1.20 0 1986 - 87 12 4.65 1.14 -14.5 1987 - 88 5 6.25 1.41 -1.8 1988 - 89 11 5.86 1.38 13.6 1989 - 90 6 5.57 1.20 -5.7 1990 - 91 2 5.80 1.20 -4.2 1991 - 92 12 5.73 1.19 -16.9 1992 - 93 10 4.79 1.17 -9.7 1993 - 94 5 7.66 1.86 -5.3 1994 - 95 3 4.12 1.13 -6.3 1995 - 96 5 3.83 1.11 3.2 1996 - 97 11 5.52 1.24 0 1997 - 98 16 7.25 4.44 -19.9 1998 - 99 9 5.26 1.33 12.9 1999 - 00 6 3.34 1.07 11.6 2000 - 01 4 4.64 1.15 9.6 2001 - 02 5 6.21 1.75 0 2002 - 03 10 5.51 1.32 -6.3 2003 - 04 3 5.93 1.26 -1.9 2004 - 05 9 5.40 1.23 -9.2 2005 - 06 5 6.11 1.36 6.6 2006 - 07 6 6.00 1.45 -3.1 2007 - 08 4 7.23 1.42 12.7

39

Correlation test of average sinuosity index and average SOI gives (r = -0.273, p–

value = 0.46 at 0.05 level). Therefore it can be said that sinuosity index has a

significant relationship with average SOI but the degree of association is weak.

4.4 Correlation of sinuosity index with other tropical cyclone parameters

Table 4 shows that SI of cyclone tracks have significant correlation with six other

cyclone parameters. However, due to unavailability of any literature, it was not

possible to do any comparison of these correlation results with other studies.

4.4.1 Correlation of sinuosity index with start latitude

From Table 4, it can be seen that the correlation between SI and latitude is -0.20,

which is statistically significant at 0.01 level (p-value = 0.001). Although the

degree of association is weak, the relationship is significant and negative

correlation which means that the TCs forming at higher latitudes are less sinuous

compared to cyclones forming in low latitudes.

4.4.2 Correlation of sinuosity index with start longitude

The correlation between SI and start longitude is weak (-0.15) but significant at

0.05 level (p-value = 0.011). It is a negative correlation meaning that the TCs

forming in the east of the study area are less sinuous.

4.4.3 Correlation of sinuosity index with end longitude

The correlation between SI and end longitude is -0.21, which is significant at

0.01 level (p–value = 0.001). It is a weak and negative correlation meaning that

the TCs that decay more eastward are less sinuous.

4.4.4 Correlation of sinuosity index with time

The correlation between SI and time (in years) is 0.15, which is weak but

significant at 0.01 level (p–value = 0.009). It is a positive correlation which

means that the TCs have become more sinuous with time.

40

4.4.5 Correlation of sinuosity index with duration

The correlation of SI with duration is strong (0.54), which is significant at 0.01

level (p-value < 0.001). The relationship is positive which implies that longer

lived TCs have a tendency to be highly sinuous.

4.4.6 Correlation of sinuosity index with distance travelled by cyclone

The correlation of sinuosity index with total distance of cyclone travel is 0.46 at

0.01 level (p-value < 0.001). The relationship is positive which means that

cyclones that travel greater distance have a chance of being more sinuous than

TCs having short paths.

4.5 Grouping the Sinuosity Index values

Two methods were used in this study for grouping the sinuosity index values.

The first method was a proposed technique using dynamic programming based

on Khan et al (2002, 2005, 2008) where the optimum boundary points for each

group were obtained by executing a computer program coded in C++( see

Appendix 3). An alternative method of hierarchical cluster analysis in SPSS with

Ward’s method was also employed for comparison purpose. The two methods

resulted in comparable categorization but the proposed method provided a better

grouping of the categories as the total weighted variance was small for this

method as compared to the other method. It also met the objective of this study to

categorize the TCs into similar groups so that the variance within the groups is

minimum.

There are six SI categories formed from all the 291 TCs reported during the

study period, which also includes the outlier category. Out of the total 291 TCs,

288 TCs were statistically categorized into five homogeneous SI categories and

the sixth was treated as an outlier category which consisted of three TCs of

extreme sinuosity index values. The reason for grouping the TCs into five SI

categories was to have a middle category with above representing the straight

moving cyclones and the below representing the sinuous tracks. However the

41

straight moving cyclones were divided into two categories to separate the perfect

straight tracks from not so straight tracks and the same was done for the sinuous

tracks. Table 8 below gives the five SI categories and the outlier category with

the suggested category names.

Table 8: Suggested names for the five sinuosity Index categories.

Sinuosity Index

Categories Sinuosity

Index Description

1 0 – 3.03 Straight Tracks 2 3.033 – 4.64 Near Straight Tracks 3 4.6431 – 6.40 Curving Tracks 4 6.4045 – 8.84 Sinuous Tracks 5 8.8374 – 12.16 Wiggly Tracks 6 14.9714, 15.19

and 37.26 Extreme Sinuous Tracks

(Outlier)

4.6 Geographical Distribution of the cyclone genesis and decay positions

The different SI categories coded in different colours were represented graphically

using arcGIS to display the visual differences between the SI categories. Figure 23

below shows the map of the study area with all TC displacement line from the start

point of the cyclone to the end point. When looking at separate maps (Figure 24)

for each category containing cyclone displacement tracks, more clear distribution

of the cyclone genesis (position where tropical cyclone first attained 35 knots

intensity) and decay (position where tropical cyclone had 35 knots before

weakening to depression intensity) can be seen.The displacement line is just used

to show the start (genesis) and end (decay) latitude and longitude point of the

cyclone tracks.

42

Figure 23: Cyclone displacement tracks for the 291 TCs that occurred between 1969/70 – 2007/08. SI category 1 TCs are seemed to have their cyclogenesis and decay positions

quite evenly spread across the study area and SI category 3 TCs seem to be

concentrated somewhere in the middle of the study area around 170° west while

SI categories 2, 4 and 5 TCs are clustered far west of the study area.

Category 2 Category 3 Category 4 Category 1 Category 5 Category 6

43

Sinuosity Index Category 1 (a)

Sinuosity Index Category 2 (b)

Sinuosity Index Category 3(c)

44

Figure 24: (a – f). Tropical Cyclone displacement tracks for the five sinuosity Index categories and the one outlier category.

Sinuosity Index Category 4 (d)

Sinuosity Index Category 5 (e)

Sinuosity Index Category 6 (f)

45

A clear contrast exists between the first two (a and b) and the last two (d and e)

categories (excluding the outlier category). TCs in first two SI categories (straight

and near straight) are distributed quite evenly between 160° east to 130° west. TCs

in SI categories 4 (d) and 5(e) (sinuous and convoluted) are formed and

geographically limited to far west of the study area between 160° east to 180°.

Overall, the sinuosity index categories get more sinuous, TC genesis shifts

westward.

4.7 Tropical Cyclone frequency and percentages in different cyclone months for the five sinuosity index categories.

From Table 9 and Figure 25, it can be seen for all SI categories that the number of

TCs occurring in the months of January, February and March are greater than other

months. No obvious trend is observed as the SI categories get more sinuous,

percentage of TCs occurring in the months of December, January, February and

March is greater for sinuosity index categories (category three, four and five).

Table 9: Tropical Cyclone frequency and percentages for cyclone months in each SI category

Month SI Category 1 SI Category 2 SI Category 3 SI Category 4 SI Category 5 No. of

Cyclones %

No. of Cyclone

s %

No. of Cyclone

s %

No. of Cyclone

s % No. of

Cyclones % October 1 1.4 1 1.4 1 1.5 0 0 1 3.8

November 2 2.8 6 8.5 4 6.2 2 3.8 1 3.8

December 9 12.5 10 14 9 13.8 9 17 1 3.8

January 14 19.4 18 25 21 32.3 10 18.9 6 23 February 19 26.4 18 25 14 21.5 10 18.9 8 30.8

March 17 23.6 9 13 10 15.4 12 22.6 7 26.9 April 10 13.9 5 7 4 6.2 6 11.3 1 3.8 May 1 1.4 3 4.2 2 3.1 2 3.8 1 3.8 June 2 3.8 Total 73 71 65 53 26

46

Figure 25: Tropical Cyclone frequency and percentages for cyclone months in each SI category 4.8 Mean values for other parameters of the tropical cyclone

tracks in relation to the sinuosity index category mean

Table 10: Comparison of the mean values of tropical cyclone parameters with the sinuosity index mean

Cat

egor

ies

Av.

Sin

uosi

ty

inde

x

Av.

star

t la

titud

e

Av.

e

nd la

titud

e

Av.

star

t lo

ngitu

de

Av.

end

lo

ngitu

de

Av.

star

t at

mos

pher

ic

pres

sure

Av.

end

at

mos

pher

ic

pres

sure

Av.

star

t win

d sp

eed

Av.

end

win

d sp

eed

Av.

dur

atio

n

Av.

dis

tanc

e tra

velle

d

Av.

trac

k di

spla

cem

ent

1 2.01 16.9 23.8 178.

9 187.

3 991.7 991.3 38.4 38.3 2.7 1377 1357

2 3.94 15.6 23.5 179.

4 186.

1 993.3 988.6 36.8 41.5 3.2 1577 1482

3 5.41 13.2 24.4 177.

7 184.

3 993.1 984.5 36.9 46.5 4.8 2051 1761

4 7.42 13.3 23.8 176.

6 180.

5 993.3 984.9 36.7 45.9 5.5 2016 1430

5 10.03 15 23.4 170 174.

7 992.5 986.9 38.3 43.7 7.6 2544 1295

When averages of all the TC parameters are calculated and compared with the

mean for the five SI categories (Table 10), there are some obvious patterns seen.

The duration and the total distance of TCs increases as the sinuosity index

categories get more sinuous as expected. The TC displacement track, start and end

longitude decreases as the sinuosity index categories get more sinuous. More

sinuous TCs occur closer towards the equator and further west.

47

5.0 DISCUSSION Sinuosity is a measure of linear shape, specifically how much a TC track deviates

from a straight line (Terry and Feng, 2010). Sinuosity of TCs is a study of the

shape of TC tracks assigning a value to the shape in order to incorporate this

useful parameter in TC studies. Thus, sinuosity of TC track is calculated as a

ratio of the total distance travelled by the TC against the displacement line

between the start and the end points of the TC track (Terry and Gienko, 2011).

Total length of TC track (distance travelled) and displacement can easily be

calculated using GIS tool. Including sinuosity of TC as one of the parameters to

study TCs can be helpful in understanding TC climatology especially since it

correlates well with other TC parameters such as, duration and distance (cyclone

track length). Island Countries in the study area are scattered, small and narrow

and therefore sinuous TC tracks as tested to live longer and travel greater

distance may affect many Islands and may be more than once if TC curves and

makes loops in its journey.

Two categorization methods were used to categorize the TC dataset containing

291 cyclones based on their sinuosity index values with three outliers excluded

from the comprehensive analysis. Both methods involved categorizing as such

that each SI category is homogeneous which means that the variance within a

group is minimum. Three TCs with extreme sinuosity index were not included in

the categorizing process as they were found to be outliers and therefore they

formed a separate SI category. Including these outliers would have greatly

affected the categorization process resulting in skewness in the distribution of data

and obtaining homogenous SI categories.

The two categorization methods used in this study were: a proposed dynamic

programming approach where the optimum boundary points for each group was

obtained by executing a computer program coded in C++ and a hierarchical

cluster analysis in SPSS with Ward’s method. The weighted variance for the

former

48

method was 0.52 and the latter method gave 0.58. Since the aim of this study was

to obtain homogeneous SI categories, the proposed dynamic programming

approach was found to be more useful for the categorization of TCs as it produced

lower value for weighted variance. Thus each category obtained contains the TCs

statistically more similar to each other than the TCs from other SI categories.

Previous work on western North Pacific Typhoon tracks categorized the TCs

based on their sinuosity values into four sinuosity categories and used similar

category names such as straight, quasi-straight, curving and sinuous (Terry and

Feng, 2010). However for this study, five SI categories were formed and named

straight, near straight, curving, sinuous and convoluted. Five SI categories were

chosen to group TCs so that comparisons could be made more convenient. Having

a central category dividing the straight moving and the sinuous cyclones gives an

even distribution of categories. However, the straight moving and sinuous

categories were further divided into two different sinuosity index categories in

order to minimize the difference among the variables.

From a total of thirty nine seasons studied, nine seasons experienced ten and more

TCs (Figure 22). The 1997/98 season experienced the most number of TCs having

sixteen TCs altogether. This season also coincided with the El Niño phase. Other

seasons having high frequencies of cyclones were 1980/81, 1982/83, 1986/87,

1988/89, 1991/92, 1992/93, 1996/97 and 2002/03. One notable observation is that

all seasons having higher frequencies are mostly in a consecutive season and

either one of them coincides with the El Niño event except for 1986/87 and

1988/89 seasons. Therefore, based on this observation, it is very likely that El

Niño years and years before and after El Niño years are expected to bring more

frequent cyclones in the Southwest Pacific which may be due to favorable

conditions provided by the El Niño phase for TCs formation. A study by Diamond

et al., (2012), it was investigated based on the new South Pacific Enhanced

Archive for Tropical Cyclones dataset, that positive relationships exist among

TCs, sea surface temperature, and atmospheric circulation which is consistent

49

with previous studies. The same study also revealed that statistically significant

greater frequency of major TCs was found during the latter half of the study

period (1991 – 2010) compared to the 1970 – 90 period.

The seasons having higher sinuosity index averages are 1993/94, 1997/98 and

2001/02. These are also the three seasons having cyclones with extreme sinuosity

values and are categorized in the outlier category. The 1997/98 season had the

highest number of cyclones and also has the highest sinuosity index average. It

also coincided with the El Niño phase. The correlation test of average sinuosity

index with SOI also shows significant correlation and therefore it can be justified

that El Niño events do have a weak but significant effect on the sinuosity of TC

tracks.

5.1 Tropical Cyclone Genesis Position and Sinuosity Index

The correlation of sinuosity index with initial latitudes and longitudes shows

negative but significant relationship. The mean values for start latitude decreases

as the SI categories get more sinuous. One exception was SI category 5 which did

not follow the trend and increased from SI category 4. The mean value for start

longitude (except for SI Category 2) also decreased as the SI category got more

sinuous. Therefore, TC depressions which are intensified into cyclone intensity at

lower latitude and more eastward tend to display straight tracks when compared

with the TCs forming in high latitudes and more westward of the study area.

5.2 Tropical Cyclone Decay Position and Sinuosity Index

The correlation of sinuosity index with end longitude was tested to be negatively

significant and the mean longitude of the five SI categories also decreased as the

SI categories got more sinuous. Therefore TCs which decay further east in the

southwest Pacific region follow more straight tracks than TCs decaying in the

west. There was no significant correlation of sinuosity index with end latitudes.

One reason for this could be because cyclone tracks were cut off at 25°S for the

purpose of this study and so the decay position studied may not have been the

actual decay position of the TC which may have decayed beyond 25°S.

50

5.3 Tropical Cyclone Journey and Sinuosity Index

The correlation of sinuosity index with both TC duration and total distance

travelled by the TC is positive at 0.01 level. Also, mean for both the parameters

increased as the SI categories became more sinuous (exception was SI category 4

for distance travelled which did not follow the increasing trend). It can be

concluded that longer lived TCs tend to travel longer distance but are sinuous

which means they do not travel far from where they are formed but form loops

and curves and finishes closer to the genesis position. The average displacement

for the straight moving SI categories increases (SI category 1 – SI category 3) but

starts decreasing for the sinuous categories from SI category 3 to SI category 5.

TCs tend to travel further away from the genesis positions as TCs tend to recurve

from straight track but the trend is reversed when ‘curving cyclone tracks’ become

more sinuous and convoluted. One possible reason could be that straight moving

TCs are short lived and therefore do not travel long distances and convoluted

tracks finish close to the formation point in process of forming loops and therefore

not travelling far from the formation point.

5.4 Sinuosity Index Categories

The displacement tracks for the five SI categories in Fig 23 show that straight

moving categories (SI category 1 and 2) which comprises 50 % of the TCs are

distributed quite evenly across the study area. The two sinuous categories (SI

category 4 and 5) comprising of 27.4 % of the total TCs are concentrated in the far

west of the study area. SI category 3 somewhat seems to be in the transition from

straight and sinuous tracks. The TC displacement tracks in SI category 3 are

concentrated between 180° and 170° west. This SI category comprises of 22.6 %

of the total 291 cyclones in the study period.

Thus, from this research it was found that 50 % of the TC tracks can be classified

as straight moving cyclones during the study period between 1969/70 and 2007/08

and the sinuous tracks accounts for 27.4% while the curving tracks which lays

between the straight and sinuous tracks accounts for 22.6%. A cyclone forming in

the Southwest Pacific has therefore 50% chances that it will follow a fairly

51

straight line which could mean that having only 22.6% of sinuous tracks. TCs

following straight tracks may be under normal circumstances and as the

conditions change, tracks become more sinuous.

52

6.0 CONCLUSIONS This study analyzes TC sinuosity variability from 1970 to 2008 for the Southwest

Pacific. Sinuosity index was calculated from sinuosity values in order to reduce

the number of outliers from the dataset. Gamma distribution provided the best fit

to the sinuosity index data. Five categories were formed using a dynamic

programming approach where the optimum boundary points for each group was

obtained by executing a computer program coded in C++. The sinuosity index

categories were named: straight, near straight, curving, sinuous and convoluted

tracks. Three cyclone outliers indentified through boxplot analysis were

categorized into an additional outlier category as category 6.

This study shows that average sinuosity index has slightly increased from 1969/70

to 2007/08 suggesting an increase in more sinuous cyclones could occur in the

Southwest Pacific in the future. The 1997/98 cyclone season had outstanding

values of number of cyclones and sinuosity average. The year also marked a

strong El Niño year. Furthermore, trend analysis of average sinuosity index over

time (years) and comparison with the Southern Oscillation Index show significant

relationship suggesting that climate change may have an effect on the cyclone

track. A report on Tropical Cyclone Trends by Australian Government Bureau of

Meteorology suggests based on substantial evidence from theory and model

experiments that the large-scale environment in which tropical cyclones form and

evolve is changing as a result of Greenhouse Warming (Bureau of Meteorology,

2012). Therefore, these changes in the environment may also have an influence on

TC tracks.

The 288 TCs were categorized based on their sinuosity index due to the fact that it

is well correlated with other parameters and therefore can be used to categorize

TCs. Sinuosity Index of the TC tracks studied correlated weakly with other

parameters such as: start latitude, start longitude, end longitude, time (year), and

Southern Oscillation Index and strongly correlated with duration and distance

travelled by the TCs. Sinuous tracks tend to affect larger number of islands and

believed to stay longer at places where it curves or make loops and therefore more

53

damages. It is evident from this study that sinuous cyclones are formed at lower

latitudes closer to the equator and in the west in the Southwest Pacific. Sinuous

tracks have longer lifetimes and travel greater distance.

Three cyclones which were grouped in the outlier category were not included in

the categorization process as the sinuosity index values for these cyclones were

very large. Several different methods were used to identify the outliers. The

dataset represented a population and any analysis should involve the full dataset

as to give realistic results. However statistical analyses do have its limitations and

therefore three outlier cyclones were grouped in a separate category to avoid

extreme skewness in the distribution of the sinuosity index data to be statistically

categorized into homogenous groups.

The greatest number of cyclones in the Southwest Pacific occurred between

January to March and the higher sinuosity index categories have greater

percentage of cyclones occurring in the months of December, January, February

and March. However there is no significant trend seen in the number of cyclones

per month as the categories become more sinuous.

The only existing studies done on TC tracks based on sinuosity are by Terry and

Feng in 2010 and Terry and Gienko in 2011. Apart from these, studies done on

TC track were based on other parameters. Utilizing sinuosity index to categorize

TC tracks is a convenient method as sinuosity index has significant relationship

with many other TC parameters.

The study concludes that SI of TCs has slightly increased over time during the

study period. Also based on this study, it is observed that the study area

experienced more TCs during El Niño phase. In special report by the IPCC

(2012), it is reported that average TC maximum wind speed is likely to increase,

although increases may not occur in all ocean basins but it is likely that the global

frequency of TCs will either decrease or remain essentially unchanged. The same

study also reports that continued use of climate models to make projections of TC

behavior includes frequency, location, intensity, rainfall and movement remains a

54

high priority for Pacific Climate Change Science Program (PCCSP) region.

Sinuosity of TC can also be included with all these parameters as it is an

important parameter to consider for PCCSP region based on the fact that more

sinuous TC has potential to affect greater number of Islands. Also sinuosity index

categories should be correlated with all the phases of ENSO to study how cyclone

track sinuosity may response to the different phases. The recently developed

South Pacific Enhanced Archive for TCs dataset by Diamond (2010) which

archives information on TC from 1840 – 2009 and the method for categorization

developed in this study provide great opportunity to explore TC dataset based on

sinuosity to study climatology and long term trends in the Southwest Pacific.

55

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60

APP

EN

DIC

ES

APP

EN

DIX

1 –

CYC

LON

E D

ATA

SET

FO

R T

HE

YE

AR

196

9/70

– 2

007/

08

Name

Year Start

Month Start

Latitude Start

Longitude Start

Pressure Start

Speed Start

Year End

Month End

Latitude End

Longitude End

Pressure End

Speed End

Azimuth

Sinuosity

duration (days)

distance travelled

Sinuosity Index

Displacement

PRIS

CILL

A_19

70

1970

12

18

.1 17

6.4

990

40

1970

12

23

.1 18

2.8

997

30

130.7

729

1.022

8 1.5

88

6 2.8

356

866.2

495

GILL

IAN_

1969

19

70

4 16

.5 18

2.3

990

40

1970

4

28

195

980

55

136.4

688

1.027

4 2.5

18

74

3.014

7 18

24.02

2 EM

MA_1

969

1970

2

14.7

200

990

40

1970

3

27.1

212.3

98

0 55

13

9.061

6 1.0

374

4.5

1944

3.3

442

1873

.916

ISA_

1969

19

70

4 10

16

3.3

990

40

1970

4

9 15

4.7

990

40

275.9

569

1.070

3 4

1018

4.1

272

951.1

352

ROSI

E_19

70

1970

12

16

.3 16

4.4

990

40

1971

1

28.8

166.6

99

0 40

17

1.121

2 1.0

92

3 15

32

4.514

4 14

02.93

DO

LLY_

1969

19

70

2 14

.9 16

2.4

990

40

1970

2

27.1

207.8

98

0 55

11

3.709

9 1.2

627

12

6163

6.4

045

4880

.811

HELE

N_19

69

1970

4

16.1

184.9

99

0 40

19

70

4 17

.8 18

6.9

997

30

131.7

372

1.363

2 1.5

38

7 7.1

348

283.8

908

DAW

N_19

69

1970

2

12.2

145.9

99

0 40

19

70

2 25

15

9 99

0 40

13

7.627

1 1.4

799

7 29

25

7.829

2 19

76.48

5 VI

VIEN

NE_1

971

1971

12

18

.1 20

6.1

990

40

1971

12

20

20

8.5

997

30

130.1

645

1 0.5

32

9 0

329

DORA

_197

0 19

71

2 21

.5 15

6.1

990

40

1971

2

25.1

160.8

99

0 40

13

0.577

5 1.0

017

1 62

6 1.1

935

624.9

376

CYC1

9711

104_

1971

19

71

11

21.9

166.7

99

0 40

19

71

11

25.1

170.6

99

0 40

13

2.422

3 1.0

067

1 53

7 1.8

852

533.4

26

IDA_

1970

19

71

2 16

.6 15

6.9

990

40

1971

2

23.3

164.2

99

7 30

13

5.340

1 1.0

126

3.5

1078

2.3

27

1064

.586

URSU

LA_1

971

1971

12

8.4

16

5 99

0 40

19

71

12

25.2

176.6

98

0 55

14

7.889

2 1.3

266

7 29

58

6.886

6 22

29.76

LE

NA_1

970

1971

3

15.1

157.5

99

0 40

19

71

3 25

.2 16

8.7

997

30

135.4

929

1.721

7 6.5

27

85

8.969

9 16

17.58

7 FI

ONA_

1970

19

71

2 22

.3 15

8.8

990

40

1971

2

21

161.8

99

7 30

65

.6902

2.2

41

3 76

7 10

.7463

34

2.257

9 CO

LLET

TE_1

972

1972

11

11

.1 18

3.8

990

40

1972

11

15

18

2.6

990

40

196.6

546

1.001

3 1

451

1.091

4 45

0.414

5 ID

A_19

71

1972

5

6.7

156.9

98

0 55

19

72

6 27

.8 17

3.4

980

55

145.2

39

1.026

3 4.5

29

90

2.973

8 29

13.37

8 YO

LAND

E_19

71

1972

3

16.5

174.2

99

0 40

19

72

3 25

.4 16

4.6

980

55

223.7

48

1.047

2 4

1468

3.6

139

1401

.833

AGAT

HA_1

971

1972

3

16.8

199.7

99

0 40

19

72

3 25

.1 20

0 99

0 40

17

8.107

5 1.0

825

4 99

5 4.3

533

919.1

686

WEN

DY_1

971

1972

2

10

176

990

40

1972

3

25.5

159.8

98

0 55

22

2.813

1.0

955

7.5

2654

4.5

709

2422

.638

BEBE

_197

2 19

72

10

7.5

180.6

99

0 40

19

72

10

27.5

194

997

30

149.0

681

1.257

5 7.5

33

03

6.362

26

26.64

DI

ANA_

1972

19

72

12

9.7

167.6

99

0 40

19

72

12

26.8

164.7

99

7 30

18

8.779

5 1.2

694

8.5

2434

6.4

585

1917

.441

GAIL_

1971

19

72

4 13

.7 15

5 99

0 40

19

72

4 15

.7 16

9.2

997

30

100.0

019

1.423

2 8

2199

7.5

078

1545

.11

CARL

OTTA

_197

1 19

72

1 14

.6 15

8 98

0 55

19

72

1 25

.9 17

2.4

970

65

132.0

652

2.256

8 13

44

09

10.79

17

1953

.651

HENR

IETT

A_19

72

1973

3

12.3

172.7

99

0 40

19

73

3 18

.4 18

3.2

997

30

122.2

212

1.007

1 1.5

13

23

1.922

13

13.67

3 GL

ENDA

_197

2 19

73

1 18

.9 19

5.1

990

40

1973

2

22.8

198

990

40

145.5

527

1.023

2 1

539

2.852

1 52

6.778

7 JU

LIETT

E_19

72

1973

4

15.1

174.1

99

0 40

19

73

4 26

.3 19

2.6

997

30

125.7

987

1.024

2 2.5

23

43

2.892

5 22

87.63

9

61

CYC1

9731

106_

1973

19

73

11

16.7

189.9

99

0 40

19

73

11

26.6

191.8

99

7 30

17

0.167

2 1.0

427

2.5

1161

3.4

952

1113

.455

LOTT

IE_1

973

1973

12

15

.5 17

2.3

990

40

1973

12

28

19

2 99

0 40

12

7.571

9 1.0

574

4.5

2598

3.8

575

2456

.97

FELIC

ITY_

1972

19

73

1 16

.4 19

5.8

990

40

1973

1

25.2

202.2

99

7 30

14

6.72

1.087

2 3

1283

4.4

344

1180

.096

ELEN

ORE_

1972

19

73

1 12

18

4 99

0 40

19

73

2 26

.6 18

5.2

990

40

175.7

258

1.318

8 5.5

21

38

6.831

3 16

21.17

1 NE

SSIE

_197

3 19

74

1 24

.9 17

0 99

0 40

19

74

1 27

.2 17

2.2

990

40

139.6

501

1 0.5

33

7 0

337

VERA

_197

3 19

74

1 17

.7 15

1 99

0 40

19

74

1 26

16

7 99

7 30

12

1.882

1 1.0

113

2.5

1911

2.2

44

1889

.647

TINA

_197

3 19

74

4 17

17

9.2

990

40

1974

4

21.7

193.1

99

7 30

11

1.828

3 1.0

148

1.5

1572

2.4

552

1549

.074

MONI

CA_1

973

1974

1

20

167

990

40

1974

1

25.5

172.4

99

0 40

13

8.692

4 1.0

329

1.5

851

3.204

3 82

3.893

9 PA

M_19

73

1974

1

12.2

178.8

99

0 40

19

74

2 26

.3 15

9.3

955

80

229.7

867

1.068

1 5

2745

4.0

837

2569

.984

FLOR

A_19

74

1975

1

15.8

158.7

99

0 40

19

75

1 25

.4 18

3 99

0 40

11

6.776

3 1.0

188

5 27

93

2.659

27

41.46

1 GL

ORIA

_197

4 19

75

1 17

.5 14

8.7

990

40

1975

1

25

168

990

40

115.8

422

1.050

5 4

2275

3.6

963

2165

.635

VAL_

1974

19

75

1 13

.8 18

3.5

980

55

1975

2

25.7

173.8

96

0 75

21

6.123

2 1.1

655

6 19

38

5.490

3 16

62.80

6 AL

ISON

_197

4 19

75

3 16

.2 17

2.5

990

40

1975

3

25.5

165.8

97

0 65

21

2.967

9 1.3

581

4.5

1688

7.1

012

1242

.913

BETT

Y_19

74

1975

5

14

168.6

99

0 40

19

75

5 27

17

5 99

7 30

15

6.175

8 2.1

121

8 33

49

10.36

05

1585

.626

LAUR

IE_1

976

1976

12

14

18

8.5

990

40

1976

12

19

20

1 99

7 30

11

4.215

6 1.0

06

1 14

53

1.817

1 14

44.33

4 JA

N_19

75

1976

4

19.3

168.5

99

0 40

19

76

4 24

.3 17

4.7

997

30

131.9

29

1.007

3 1

853

1.939

9 84

6.818

2 KI

M_19

76

1976

12

14

.5 18

9 99

0 40

19

76

12

24

211

997

30

117.8

374

1.010

2 2.5

25

62

2.168

7 25

36.13

1 DA

VID_

1975

19

76

1 15

.4 16

8 99

0 40

19

76

2 25

.5 14

2.3

997

30

243.1

61

1.022

7 39

29

64

2.831

4 28

98.21

1 HO

PE_1

975

1976

3

20

164.5

99

0 40

19

76

3 25

.7 15

7.1

990

40

228.8

801

1.027

5 2

1014

3.0

184

986.8

613

FRAN

CES_

1975

19

76

2 22

22

0 99

0 40

19

76

2 25

.5 20

8.2

965

70

249.8

168

1.063

1 3

1343

3.9

812

1263

.287

ELSA

_197

5 19

76

1 14

.2 16

7.5

990

40

1976

1

26.5

160

990

40

208.6

711

1.205

4.5

18

92

5.896

4 15

70.12

4 TE

SSA_

1977

19

77

12

12.5

212

990

40

1977

12

14

.5 21

7 99

7 30

11

2.803

1 1.0

012

1.5

585

1.062

7 58

4.298

8 CY

C197

7021

9_19

76

1977

2

21

198

990

40

1977

2

27

201

997

30

155.9

251

1.002

7 1

733

1.392

5 73

1.026

2 CY

C197

7020

2_19

76

1977

2

18.3

176.2

99

0 40

19

77

2 21

.2 18

0.3

997

30

127.4

407

1.003

8 1.5

53

8 1.5

605

535.9

633

STEV

E_19

77

1977

11

6.7

17

6 99

0 40

19

77

11

19

175

997

30

184.4

577

1.029

5 4.5

14

05

3.089

9 13

64.74

PA

T_19

76

1977

3

19.5

185

990

40

1977

3

28

197

997

30

129.8

833

1.031

2

1590

3.1

414

1542

.192

ANNE

_197

7 19

77

12

13.8

181.5

99

0 40

19

77

12

24

194.5

99

7 30

13

1.465

1.1

531

5 20

44

5.349

6 17

72.61

3 MA

RION

_197

6 19

77

1 15

.3 16

7 99

0 40

19

77

1 23

18

1 99

7 30

12

2.228

8 1.1

666

6.5

1983

5.5

025

1699

.811

ROBE

RT_1

976

1977

4

13

205

990

40

1977

4

24

218

980

55

133.4

841

1.274

4 5.5

23

36

6.498

2 18

33.01

9 NO

RMAN

_197

6 19

77

3 12

.3 16

5.8

980

55

1977

3

25.5

171.5

99

0 40

15

8.527

2 1.7

522

9 27

67

9.094

5 15

79.15

8 JU

NE_1

976

1977

1

17.5

161

990

40

1977

1

21.5

168

997

30

122.2

064

2.796

3 4.5

23

98

12.15

61

857.5

618

GWEN

_197

7 19

78

3 21

15

5.5

990

40

1978

3

25

161

997

30

129.2

019

1.000

8 1

717

0.928

3 71

6.426

9 BO

B_19

77

1978

2

11

178.3

99

0 40

19

78

2 26

.5 16

5.5

990

40

216.3

078

1.015

6 5.5

22

13

2.498

7 21

79.00

7 FA

Y_19

78

1978

12

10

17

5 99

0 40

19

78

12

26

184

980

55

152.9

912

1.017

2 3

2044

2.5

813

2009

.438

HAL_

1977

19

78

4 13

14

5 99

0 40

19

78

4 27

.5 16

2 99

0 40

13

4.806

5 1.1

699

6 27

94

5.538

6 23

88.23

8

62

DIAN

A_19

77

1978

2

14

200

990

40

1978

2

23

207.5

99

7 30

14

2.640

3 1.2

421

5 15

80

6.232

5 12

72.03

9 CH

ARLE

S_19

77

1978

2

14.5

194

990

40

1978

2

27

204.3

98

0 55

14

3.932

1 1.5

068

10.5

2635

7.9

728

1748

.739

ERNI

E_19

77

1978

2

14

175

990

40

1978

2

24

182

997

30

147.4

217

1.514

8 4.5

20

13

8.014

6 13

28.88

8 LE

SLIE

_197

8 19

79

2 20

18

7.3

990

40

1979

2

29

194

980

55

147.0

751

1.000

5 1.5

12

06

0.793

7 12

05.39

7 OF

A_19

79

1979

12

14

.3 18

1 99

5 35

19

79

12

22.4

202

997

30

115.1

022

1.009

5 2.5

24

13

2.117

9 23

90.29

2 HE

NRY_

1978

19

79

1 15

.5 16

9 99

0 40

19

79

2 28

17

1.5

990

40

169.8

612

1.040

1 3

1464

3.4

228

1407

.557

GORD

ON_1

978

1979

1

8.5

172

990

40

1979

1

19.7

152

997

30

237.9

748

1.117

7

2777

4.8

91

2486

.124

MELI_

1978

19

79

3 15

.5 18

4.5

990

40

1979

3

26

176.5

97

0 65

21

4.284

6 1.3

559

4.5

1938

7.0

867

1429

.309

KERR

Y_19

78

1979

2

7.8

166

990

40

1979

3

16.5

147.6

99

7 30

24

2.589

4 1.7

708

17.5

3930

9.1

688

2219

.336

RAE_

1979

19

80

2 14

.9 17

0.2

990

40

1980

2

16.9

172.4

99

7 30

13

3.506

7 1

0.5

323

0 32

3 SI

NA_1

979

1980

3

17.5

159.7

99

5 35

19

80

3 25

.5 16

7.5

970

65

138.9

891

1.010

6 2

1211

2.1

967

1198

.298

TIA_

1979

19

80

3 15

17

6.8

990

40

1980

3

28.8

200

997

30

126.5

04

1.025

4 3.5

29

06

2.939

5 28

34.01

6 PE

NI_1

979

1980

1

12

173.5

99

0 40

19

80

1 19

.2 17

8 99

7 30

14

9.372

2 1.0

271

2 95

7 3.0

037

931.7

496

VAL_

1979

19

80

3 13

18

0.5

990

40

1980

3

17.1

188.5

99

7 30

11

8.804

1.0

277

1.5

999

3.025

7 97

2.073

6 DI

OLA_

1980

19

80

11

18.1

220.7

99

5 35

19

80

11

24

216

997

30

215.9

713

1.076

6 2

878

4.246

9 81

5.530

4 W

ALLY

_197

9 19

80

4 15

.3 17

8.5

995

35

1980

4

17

177.8

99

7 30

20

1.604

9 1.0

779

1.5

218

4.270

8 20

2.245

1 CY

C198

1_23

RD_1

980

1981

3

22

187.4

99

5 35

19

81

3 26

19

2.5

995

35

131.5

026

1.010

7 1

689

2.203

6 68

1.705

7 FR

AN_1

980

1981

3

14.9

201.6

99

5 35

19

81

3 27

.1 21

4 99

0 40

13

8.411

9 1.0

142

4 18

91

2.421

6 18

64.52

4 CY

C198

1_16

TH_1

980

1981

2

19.5

197

990

40

1981

2

28

202

987

45

152.5

398

1.022

7 1

1095

2.8

314

1070

.695

ESAU

_198

0 19

81

3 11

.2 17

9.6

995

35

1981

3

23

198

997

30

126.1

642

1.057

5 3

2485

3.8

597

2349

.882

CLIF

F_19

80

1981

2

14.5

168

990

40

1981

2

25.6

156.4

98

7 45

22

2.779

2 1.1

026

3.5

1902

4.6

815

1725

.014

TAHM

AR_1

980

1981

3

20

205

990

40

1981

3

25.9

217

980

55

120.2

162

1.109

5 2.5

15

45

4.784

1 13

92.51

9 DA

MAN_

1980

19

81

2 17

.1 19

3 99

0 40

19

81

2 25

.5 20

1.4

987

45

138.3

143

1.139

5 1.5

14

52

5.186

3 12

74.24

3 BE

TSY_

1980

19

81

1 17

18

9.8

995

35

1981

2

20.5

186.8

99

7 30

21

8.761

9 1.1

706

2.5

585

5.546

2 49

9.743

7 AR

THUR

_198

0 19

81

1 13

.5 17

9 99

0 40

19

81

1 26

17

8 99

0 40

18

4.17

1.171

2 4

1625

5.5

527

1387

.466

FRED

A_19

80

1981

2

15.5

144.6

99

5 35

19

81

3 27

.5 16

7 97

5 60

12

3.600

7 1.2

962

9.5

3457

6.6

659

2667

.027

GYAN

_198

1 19

81

12

11.6

168.4

99

0 40

19

81

12

22.6

165.3

99

7 30

19

4.731

1 1.4

907

6.5

1880

7.8

875

1261

.152

CYC1

981_

18TH

_198

0 19

81

2 12

18

8 99

5 35

19

81

3 22

.5 19

3.5

997

30

154.0

532

1.860

6 5.5

24

20

9.511

9 13

00.65

6 JO

TI_1

982

1982

11

10

17

0.9

995

35

1982

11

16

.7 16

4 99

0 40

22

4.491

9 1.1

111

5 11

69

4.807

3 10

52.11

1 IS

AAC_

1981

19

82

2 13

.5 19

0.2

995

35

1982

3

25.5

184.8

96

0 75

20

2.254

7 1.1

137

3.5

1608

4.8

446

1443

.836

BERN

IE_1

981

1982

4

7.8

158

990

40

1982

4

25.5

164.6

97

5 60

16

1.095

6 1.1

243

5.5

2339

4.9

906

2080

.406

KINA

_198

2 19

82

11

12.1

172.1

99

5 35

19

82

11

17

171.5

99

7 30

18

6.728

2 1.1

407

1.5

623

5.201

1 54

6.155

9 HE

TTIE

_198

1 19

82

1 18

.1 17

2 99

5 35

19

82

2 27

.4 17

8 98

0 55

15

0.219

4 1.2

461

6.5

1495

6.2

667

1199

.743

LISA_

1982

19

82

12

14.7

206

990

40

1982

12

23

.9 20

5.9

997

30

180.5

753

1.321

4 4

1346

6.8

499

1018

.617

CLAU

DIA_

1981

19

82

5 13

15

6.5

995

35

1982

5

11.7

161.3

99

7 30

75

.1209

1.3

736

3 74

4 7.2

023

541.6

424

63

ABIG

AIL_

1981

19

82

1 17

.8 15

4.4

995

35

1982

2

22.6

174.5

99

7 30

10

7.556

1.8

495

12

4004

9.4

708

2164

.909

PREM

A_19

82

1983

2

12.4

197.6

99

0 40

19

83

2 14

20

7 99

7 30

10

0.908

7 1.0

076

2 10

42

1.966

1 10

34.14

1 SA

BA_1

982

1983

3

15.8

223.8

99

0 40

19

83

3 26

.1 23

1 99

5 35

14

7.933

6 1.0

11

3 13

78

2.224

13

63.00

7 SA

RAH_

1982

19

83

3 13

.2 17

7.5

995

35

1983

3

26.2

181.1

98

5 50

16

5.880

8 1.1

358

5 16

89

5.14

1487

.058

ATU_

1983

19

83

12

15.8

170.3

99

5 35

19

83

12

21.3

173.6

99

7 30

15

0.728

2 1.1

475

2.5

805

5.283

6 70

1.525

1 NA

NO_1

982

1983

1

13.4

220.4

99

0 40

19

83

1 27

23

5 99

0 40

13

6.945

5 1.1

71

4.5

2506

5.5

505

2140

.051

TOMA

SI_1

982

1983

3

11.5

199.7

99

0 40

19

83

4 26

.3 19

3.9

990

40

199.5

744

1.181

5.5

20

64

5.656

7 17

47.67

1 OS

CAR_

1982

19

83

2 13

.5 17

3.5

990

40

1983

3

27

183

990

40

147.9

494

1.186

2 7

2126

5.7

103

1792

.278

NISH

A_19

82

1983

2

13.8

216.8

99

5 35

19

83

2 24

21

9 99

0 40

16

8.740

9 1.4

288

5.5

1647

7.5

408

1152

.716

REW

A_19

82

1983

3

11.7

212.7

99

5 35

19

83

3 26

22

3 99

5 35

14

7.100

1 1.4

519

8 27

84

7.673

9 19

17.48

7 W

ILLIA

M_19

82

1983

4

10.9

227.3

99

5 35

19

83

4 25

23

7 99

7 30

14

8.018

5 1.6

425

7 30

66

8.628

9 18

66.66

7 MA

RK_1

982

1983

1

12

174

990

40

1983

1

19

175.1

99

7 30

17

1.478

1.6

624

5.5

1303

8.7

171

783.8

065

VEEN

A_19

82

1983

4

12.2

221.5

99

0 40

19

83

4 25

21

8.8

987

45

190.9

633

1.793

9 6

2592

9.2

595

1444

.897

NAME

LESS

A_19

83

1984

2

25

175

990

40

1984

2

26.6

175

987

45

180

1 0.5

17

7 0

177

BETI

_198

3 19

84

2 16

.3 16

1.2

995

35

1984

2

22.2

172.4

99

7 30

12

0.780

7 1.0

105

3.5

1360

2.1

898

1345

.868

CYRI

L_19

83

1984

3

17.9

175.7

99

0 40

19

84

3 25

18

6.4

997

30

127.1

981

1.016

4 2.5

13

81

2.540

7 13

58.71

7 HA

RVEY

_198

3 19

84

2 16

.3 15

4.7

990

40

1984

2

21

163.4

99

7 30

12

0.882

5 1.0

398

4.5

1097

3.4

142

1055

.011

MONI

CA_1

984

1984

12

12

14

6 99

0 40

19

84

12

28

163

990

40

137.5

274

1.075

9 4

2694

4.2

34

2503

.95

CYC_

1984

_58T

H_19

84

1984

12

8.4

17

8.4

995

35

1984

12

10

.1 18

0 99

7 30

13

7.048

6 1.0

781

1.5

278

4.274

5 25

7.861

1 GR

ACE_

1983

19

84

1 15

15

0.5

995

35

1984

1

24.4

160.3

99

7 30

13

6.922

8 1.1

072

5.5

1618

4.7

504

1461

.344

NAME

LESS

B_19

83

1984

3

14.9

175.1

99

0 40

19

84

3 17

.4 18

7 99

7 30

10

3.880

3 1.7

96

7 23

39

9.267

7 13

02.33

9 GA

VIN_

1984

19

85

3 15

.9 17

0.5

995

35

1985

3

27.4

184.2

99

0 40

13

4.288

1.0

053

4.5

1913

1.7

435

1902

.915

ERIC

_198

4 19

85

1 15

.6 16

5.5

990

40

1985

1

25.5

198

987

45

113.3

105

1.013

6 4

3599

2.3

87

3550

.71

ODET

TE_1

984

1985

1

14.8

150.5

98

7 45

19

85

1 21

17

3.5

997

30

109.0

992

1.013

6 4

2563

2.3

87

2528

.611

FRED

A_19

84

1985

1

19.1

199

985

50

1985

1

26

188.7

96

0 75

23

2.306

8 1.0

177

2 13

28

2.606

1 13

04.90

3 NI

GEL_

1984

19

85

1 16

.2 15

6 99

0 40

19

85

1 21

.4 19

4.9

997

30

104.1

809

1.022

4 6.5

42

23

2.818

9 41

30.47

7 DR

ENA_

1984

19

85

1 12

.1 18

5 99

5 35

19

85

1 18

.7 18

8 99

7 30

15

6.586

8 1.0

678

3 85

2 4.0

776

797.9

022

HINA

_198

4 19

85

3 13

.9 16

5.9

990

40

1985

3

29.8

182

955

80

139.3

741

1.322

2 5

3196

6.8

555

2417

.183

MART

IN_1

985

1986

4

12.9

171.4

99

5 35

19

86

4 19

.9 18

5.9

997

30

118.4

95

1.006

8 3

1742

1.8

945

1730

.234

ALFR

ED_1

985

1986

3

16.5

154.6

99

5 35

19

86

3 21

.5 17

1.3

997

30

110.0

882

1.007

4 2.2

5 18

56

1.948

7 18

42.36

6 LU

SI_1

985

1986

3

18.4

161

995

35

1986

3

24.4

178.6

99

7 30

11

3.086

4 1.0

231

3.75

1985

2.8

48

1940

.182

KELI_

1985

19

86

2 19

16

8.1

995

35

1986

2

24.7

189.8

99

7 30

10

9.614

5 1.0

353

3.25

2409

3.2

804

2326

.862

OSEA

_198

6 19

86

11

13.1

168.2

99

5 35

19

86

11

17.3

174.5

99

7 30

12

5.264

9 1.0

42

2 85

5 3.4

76

820.5

374

JUNE

_198

5 19

86

2 21

.5 21

9.9

995

35

1986

2

25.4

225.5

98

0 55

14

8.913

9 1.0

602

1.25

538

3.919

2 50

7.451

4 SA

LLY_

1986

19

86

12

13.3

195.8

99

5 35

19

87

1 25

.1 20

6.5

980

55

140.8

973

1.273

1 8.2

5 21

93

6.487

9 17

22.56

7

64

PATS

Y_19

86

1986

12

11

.5 17

0 99

5 35

19

86

12

25.8

165.6

99

0 40

19

5.683

8 1.2

994

6 21

43

6.689

9 16

49.22

3 RA

JA_1

986

1986

12

11

.4 17

7.5

995

35

1987

1

25.2

181.7

98

0 55

16

4.411

7 1.4

252

9.25

2267

7.5

197

1590

.654

NAMU

_198

5 19

86

5 8.3

16

3.1

990

40

1986

5

18.6

163.1

99

7 30

18

0 1.4

563

4.5

1660

7.6

987

1139

.875

IMA_

1985

19

86

2 17

.5 19

2.2

990

40

1986

2

26.2

206.1

97

5 60

12

6.289

5 1.7

814

8.25

3078

9.2

107

1727

.854

NONA

ME_1

986

1987

2

16.6

198.6

99

5 35

19

87

3 25

.5 20

4.4

990

40

149.5

418

1.002

1 1.5

11

57

1.280

6 11

54.57

5 UM

A_19

86

1987

2

13.2

162.6

99

5 35

19

87

2 21

.5 17

4 99

5 35

12

8.760

9 1.0

217

3.75

1552

2.7

892

1519

.037

BLAN

CH(E

)_19

86

1987

5

11.7

160.7

99

5 35

19

87

5 16

.3 15

7 99

7 30

21

7.715

3 1.0

734

2.75

695

4.187

64

7.475

3 ZU

MAN_

1986

19

87

4 11

.5 18

6.4

995

35

1987

4

23.8

199.2

99

7 30

13

6.850

6 1.0

856

3.5

2085

4.4

072

1920

.597

VELI_

1986

19

87

2 14

15

5.3

995

35

1987

2

24.5

180

997

30

117.8

96

1.086

6 4.2

5 30

84

4.424

2 28

38.21

1 YA

LI_19

86

1987

3

16.6

163.7

99

5 35

19

87

3 18

.7 16

4.2

997

30

167.2

162

1.095

9 2.2

5 26

1 4.5

773

238.1

604

TUSI

_198

6 19

87

1 9.1

18

7.9

995

35

1987

1

25.5

199.4

99

0 40

14

7.590

1 1.1

054

6.5

2416

4.7

237

2185

.634

WIN

I_198

6 19

87

2 12

.5 18

0.2

995

35

1987

3

25.1

198.3

96

5 70

12

8.838

8 1.1

465

4.75

2704

5.2

716

2358

.482

CILL

A_19

87

1988

2

18.2

200.6

99

5 35

19

88

3 26

.5 21

1.5

980

55

131.2

779

1.011

4 2

1466

2.2

506

1449

.476

DELIL

AH_1

988

1988

12

17

.6 15

4.4

995

35

1989

1

25.1

170

985

50

119.8

669

1.065

2 2.7

5 19

35

4.024

8 18

16.56

ES

ETA_

1988

19

88

12

19.1

171.5

99

5 35

19

88

12

25.3

174.7

98

5 50

15

4.918

8 1.1

104

2.5

846

4.797

2 76

1.887

6 AG

I_198

7 19

88

1 11

.3 15

3.9

995

35

1988

1

19.2

162.3

99

7 30

13

5.125

4 1.1

63

3.25

1460

5.4

626

1255

.374

ANNE

_198

7 19

88

1 6.1

17

8.8

995

35

1988

1

24.7

165.5

99

0 40

21

3.188

5 1.1

974

6.75

2994

5.8

226

2500

.418

DOVI

_198

7 19

88

4 17

.5 16

9.8

995

35

1988

4

25.9

174.3

98

0 55

15

4.208

1 1.2

677

5.75

1318

6.4

449

1039

.678

BOLA

_198

7 19

88

2 15

.1 17

7.5

995

35

1988

3

27

178.5

97

0 65

17

5.662

1 2.4

403

8.5

3225

11

.2932

13

21.55

9 FI

LI_19

88

1989

1

18.8

189

995

35

1989

1

25.6

195.4

98

5 50

13

9.933

7 1.0

01

2.25

1002

1

1000

.999

MEEN

A_19

88

1989

5

13.4

160.6

99

5 35

19

89

5 12

.2 14

3.7

997

30

272.2

228

1.078

6 4.2

5 19

84

4.283

6 18

39.42

1 LIL

I_198

8 19

89

4 12

.5 16

2.5

995

35

1989

4

24.8

169.1

99

7 30

15

3.904

1 1.0

9 4.7

5 16

66

4.481

4 15

28.44

UN

NAME

D_19

88

1989

2

21.4

180.7

99

5 35

19

89

2 26

.8 19

1.1

990

40

121.5

48

1.095

7 2

1330

4.5

741

1213

.836

FELIC

ITY_

1989

19

89

12

15.8

139.2

99

0 40

19

89

12

22.2

161

997

30

110.5

407

1.15

5 27

59

5.313

3 23

99.13

GI

NA_1

988

1989

1

14.6

187.3

99

5 35

19

89

1 19

.8 18

7.1

997

30

182.0

882

1.172

3 2.2

5 67

5 5.5

645

575.7

912

JUDY

_198

8 19

89

2 19

20

8 99

5 35

19

89

2 26

.7 19

9.1

990

40

225.3

136

1.222

6 4.7

5 15

27

6.060

5 12

48.97

8 KE

RRY_

1988

19

89

3 20

.1 17

8.8

995

35

1989

4

25.7

187.7

99

7 30

12

5.855

4 1.3

287

3.25

1466

6.9

013

1103

.334

IVY_

1988

19

89

2 17

.2 16

7.7

995

35

1989

3

23.6

169.7

99

5 35

16

3.922

9 2.2

27

7.75

1645

10

.7057

73

8.661

9 HA

RRY_

1988

19

89

2 17

.7 16

1.4

995

35

1989

2

25.8

165.2

98

7 45

15

7.014

8 2.7

648

10.75

27

07

12.08

46

979.0

943

RAE_

1989

19

90

3 20

17

3 99

0 40

19

90

3 25

.1 18

8.2

990

40

112.6

793

1.043

4 2.2

5 17

33

3.514

2 16

60.91

6 PE

NI_1

989

1990

2

10.2

199

990

40

1990

2

25.5

207.1

97

0 65

15

4.263

7 1.1

347

4.25

2153

5.1

261

1897

.418

OFA_

1989

19

90

1 8

180.2

99

5 35

19

90

2 25

.8 19

0.3

970

65

152.6

86

1.138

6 7.5

25

53

5.175

1 22

42.22

7 SI

NA_1

990

1990

11

10

.3 17

3.8

995

35

1990

12

25

.4 20

0.5

988

40

124.2

306

1.183

6 6.2

5 38

77

5.683

6 32

75.6

NANC

Y_19

89

1990

1

15.3

158.5

99

5 35

19

90

2 25

.2 15

4 98

0 55

20

2.472

2 1.3

45

2 16

04

7.013

6 11

92.56

5 HI

LDA_

1989

19

90

3 19

.4 15

3.2

995

35

1990

3

26

165

985

50

123.2

666

1.385

3.5

19

59

7.274

8 14

14.44

65

ARTH

UR_1

991

1991

12

22

.7 21

7.5

995

35

1991

12

18

22

8.1

997

30

66.73

91

1.031

4.2

5 12

60

3.141

4 12

22.11

4 VA

L_19

91

1991

12

9.5

18

1.9

995

35

1991

12

25

.5 19

7.5

975

60

139.0

197

1.191

5 8

2883

5.7

64

2419

.639

LISA_

1990

19

91

5 9

155.3

99

5 35

19

91

5 20

16

9.8

996

30

129.5

484

1.207

4.7

5 23

88

5.915

5 19

78.45

9 W

ASA_

1991

19

91

12

11

201

995

35

1991

12

23

.4 21

5.7

995

35

133.2

574

1.230

2 7.7

5 25

55

6.128

7 20

76.89

8 TI

A_19

91

1991

11

8.6

17

0.1

995

35

1991

11

16

.4 17

1.4

997

30

170.8

335

1.651

7 4.5

14

44

8.669

9 87

4.250

8 HE

TTIE

_199

1 19

92

3 14

21

0 99

5 35

19

92

3 26

21

8.5

990

40

147.5

626

1.037

4 2.7

5 16

57

3.344

2 15

97.26

2 CL

IFF_

1991

19

92

2 11

.3 21

6 99

5 35

19

92

2 25

.6 22

6 99

5 40

14

7.745

6 1.0

658

3 20

26

4.037

2 19

00.91

9 DA

MAN_

1991

19

92

2 12

.6 17

0 99

5 35

19

92

2 26

15

8.5

975

60

217.4

124

1.068

4 3

2042

4.0

896

1911

.269

KINA

_199

2 19

92

12

11.6

170.6

99

5 35

19

93

1 25

20

0 99

7 30

11

9.706

7 1.0

712

9.5

3677

4.1

447

3432

.599

NINA

_199

2 19

92

12

14.6

150

985

50

1993

1

17.2

191

997

30

99.43

84

1.074

4 6.2

5 47

19

4.205

9 43

92.21

9 GE

NE_1

991

1992

3

14.5

194

995

35

1992

3

26

197.8

98

5 50

16

3.308

5 1.1

054

2.75

1474

4.7

237

1333

.454

FRAN

_199

1 19

92

3 13

.5 18

4 99

0 35

19

92

3 25

.3 15

3.1

990

40

243.3

248

1.162

3 11

40

53

5.454

7 34

87.05

2 JO

NI_1

992

1992

12

10

.2 18

0 99

5 35

19

92

12

27

185.5

98

5 50

16

3.481

5 1.2

07

6.5

2350

5.9

155

1946

.976

INNI

S_19

91

1992

4

11.7

171.5

99

5 35

19

92

5 26

18

1 99

0 40

14

9.111

4 1.2

322

3.5

2306

6.1

464

1871

.449

BETS

Y_19

91

1992

1

9.5

169.6

99

5 35

19

92

1 25

.3 15

7.9

975

60

213.8

177

1.292

4 7

2769

6.6

373

2142

.526

ESAU

_199

1 19

92

2 15

.5 16

7.3

995

35

1992

3

26.5

165.8

97

5 60

18

7.038

4 2.2

121

8.5

2716

10

.6622

12

27.79

3 NI

SHA_

1992

19

93

2 17

.5 19

6.6

995

35

1993

2

26

210

980

55

126.5

3 1.0

071

2.5

1686

1.9

22

1674

.114

OLI_1

992

1993

2

16.8

176.7

99

5 35

19

93

2 25

.5 18

2.4

990

40

149.4

112

1.011

8 1.7

5 11

44

2.276

6 11

30.65

8 PO

LLY_

1992

19

93

2 16

.4 15

8.2

990

40

1993

3

25.9

167.9

94

5 85

13

7.892

1 1.0

754

5 15

65

4.224

6 14

55.27

2 MI

CK_1

992

1993

2

18.2

186.7

99

0 40

19

93

2 25

.3 17

8.7

990

40

225.0

461

1.080

2 2.7

5 12

32

4.312

5 11

40.53

LIN

_199

2 19

93

1 13

.2 18

6.6

995

35

1993

2

26

193.2

99

5 35

15

5.001

5 1.0

978

4.5

1730

4.6

073

1575

.879

PREM

A_19

92

1993

3

13.7

171.8

99

5 35

19

93

4 25

.4 17

7.4

975

60

156.4

832

1.434

5

2039

7.5

712

1421

.897

ROGE

R_19

92

1993

3

12

155.8

99

0 40

19

93

3 25

.5 17

2.5

995

35

132.7

712

1.668

9.7

5 38

45

8.741

6 23

05.15

6 RE

WA_

1993

19

93

12

10.3

164.5

99

5 35

19

94

1 25

.3 15

5.1

987

45

209.6

523

4.356

4 23

84

27

14.97

24

1934

.395

THEO

DORE

_199

3 19

94

2 10

.5 15

4.5

995

35

1994

2

25.8

171.4

96

8 65

13

5.821

1 1.0

533

4 25

88

3.763

4 24

57.04

TO

MAS_

1993

19

94

3 12

.5 17

1.4

995

35

1994

3

25.4

189.5

98

7 45

12

9.527

2 1.1

555

4 27

46

5.377

5 23

76.46

US

HA_1

993

1994

3

12.4

160.5

99

5 35

19

94

3 25

.5 16

7.4

997

30

154.4

336

1.316

6 4.2

5 21

34

6.815

6 16

20.84

2 VA

NIA_

1994

19

94

11

12.5

169.2

99

5 35

19

94

11

19

166.2

99

7 30

20

3.692

1.3

576

3.75

1069

7.0

979

787.4

19

SARA

H_19

93

1994

1

15

164

995

35

1994

1

25.4

177.1

97

5 60

13

2.179

9 1.4

04

8 25

08

7.392

5 17

86.32

5 W

ILLIA

M_19

94

1995

1

16

198

990

35

1995

1

27.5

214

987

45

130.3

433

1.017

2.7

5 21

20

2.571

3 20

84.56

2 VI

OLET

_199

4 19

95

3 15

.8 15

2 99

5 35

19

95

3 25

.5 16

0.5

965

70

141.9

053

1.019

3 2.7

5 14

18

2.682

4 13

91.15

1 ZA

KA_1

995

1996

3

22.2

169.5

99

2 35

19

96

3 24

17

4 99

6 30

11

4.255

4 1

0.5

502

0 50

2 CE

LEST

E_19

95

1996

1

19.5

148

990

40

1996

1

16.9

162.5

99

7 30

81

.7068

1.0

188

3.5

1589

2.6

59

1559

.678

YASI

_199

5 19

96

1 22

.3 18

7.6

996

35

1996

1

26.5

198.5

99

6 30

11

5.011

5 1.0

666

2.25

1279

4.0

534

1199

.137

CYRI

L_19

96

1996

11

14

.8 16

0.5

995

35

1996

11

19

.8 16

2.1

997

30

163.1

447

1.111

9 2.5

64

4 4.8

188

579.1

888

66

ATU_

1995

19

96

3 21

.5 16

8.5

996

35

1996

3

25.2

172.5

99

7 30

13

5.829

1.2

021

2.5

696

5.868

4 57

8.986

8 BE

TI_1

995

1996

3

13

169

996

35

1996

3

25.5

168.1

98

0 55

18

3.770

3 1.2

805

5.75

1776

6.5

46

1386

.958

FERG

US_1

996

1996

12

12

.8 16

0 99

5 35

19

96

12

26

173.8

96

5 70

13

7.345

8 1.4

113

5.5

2900

7.4

368

2054

.843

HINA

_199

6 19

97

3 12

.8 18

0.7

990

40

1997

3

25.2

188.5

97

0 65

15

0.297

8 1.0

134

2 16

20

2.375

2 15

98.57

9 IA

N_19

96

1997

4

20.1

176.1

99

5 35

19

97

4 23

18

7 99

7 30

10

7.835

8 1.0

159

1.75

1192

2.5

146

1173

.344

LUSI

_199

7 19

97

10

8.6

169.6

99

5 35

19

97

10

23.8

178.2

99

7 30

15

2.432

4 1.0

21

2.75

1956

2.7

589

1915

.769

MART

IN_1

997

1997

10

10

.1 19

4.2

992

35

1997

11

26

21

8.7

995

35

127.5

473

1.030

1 4.8

8 32

18

3.110

7 31

23.96

9 FR

EDA_

1996

19

97

1 22

17

5.9

995

35

1997

1

25.5

177.7

98

0 55

15

5.025

1 1.0

314

1.5

442

3.154

8 42

8.543

7 NU

TE_1

997

1997

11

12

16

3.4

995

35

1997

11

20

.6 15

8.5

1000

25

20

8.169

2 1.0

651

2.5

1157

4.0

23

1086

.283

OSEA

_199

7 19

97

11

12.3

202.1

99

5 35

19

97

11

21.4

212

998

30

135.0

092

1.066

9 4.2

5 15

55

4.059

5 14

57.49

4 PA

M_19

97

1997

12

11

.5 19

7.3

995

35

1997

12

24

.9 20

4.6

997

30

153.5

606

1.106

7 4.2

5 18

49

4.743

16

70.73

3 EV

AN_1

996

1997

1

13.6

190.5

99

5 35

19

97

1 27

.2 19

2.2

975

60

173.5

612

1.125

7 3

1707

5.0

093

1516

.39

HARO

LD_1

996

1997

2

14.8

156.8

99

5 35

19

97

2 26

.5 16

4.5

994

35

149.5

074

1.190

5 4.2

5 18

13

5.753

9 15

22.89

JU

NE_1

996

1997

5

14

174.5

99

0 40

19

97

5 17

.6 17

6.9

996

30

147.4

774

1.196

1 2.2

5 56

7 5.8

098

474.0

406

GAVI

N_19

96

1997

3

9.6

173.7

99

5 35

19

97

3 26

.2 17

6.8

940

85

170.3

084

1.338

8 5.7

1 24

98

6.971

3 18

65.85

KE

LI_19

96

1997

6

8.6

183.5

99

5 35

19

97

6 20

20

2 99

7 30

12

4.336

4 1.4

977

5.5

3531

7.9

248

2357

.615

DREN

A_19

96

1997

1

14.7

164.1

99

5 35

19

97

1 25

.5 16

7.5

970

65

163.9

975

1.706

6 5.2

5 21

28

8.906

9 12

46.92

4 BA

RT_1

997

1998

4

17.2

220.2

99

5 35

19

98

5 19

.9 22

4.6

997

30

123.4

411

1.018

8 1.5

56

3 2.6

59

552.6

109

URSU

LA_1

997

1998

1

14.1

208

999

35

1998

2

25.2

224.1

97

5 60

12

8.557

8 1.0

415

2.5

2171

3.4

622

2084

.494

VELI_

1997

19

98

2 13

.7 20

7.2

995

35

1998

2

23.2

216.7

99

7 30

13

7.751

7 1.0

632

2.75

1544

3.9

833

1452

.22

WES

_199

7 19

98

2 11

.7 16

8.4

995

35

1998

2

17.3

158.5

99

7 30

23

8.688

7 1.0

671

3.5

1316

4.0

636

1233

.249

CORA

_199

8 19

98

12

15.2

181.8

99

4 35

19

98

12

25.2

196.9

97

0 65

12

7.489

4 1.0

707

3.75

2061

4.1

35

1924

.909

SUSA

N_19

97

1998

1

12.4

172.9

98

7 45

19

98

1 26

.4 18

3.6

940

90

145.6

993

1.251

5.5

23

92

6.308

19

12.07

TU

I_199

7 19

98

1 13

.3 18

7.5

995

35

1998

1

14.6

187.7

99

5 35

17

1.478

8 1.2

537

1.25

182

6.330

5 14

5.170

3 RO

N_19

97

1998

1

9.6

192.3

99

0 40

19

98

1 28

.2 19

1.5

975

60

182.2

23

1.402

7 6.7

5 28

91

7.384

6 20

61.02

5 AL

AN_1

997

1998

4

11.8

201.4

99

5 35

19

98

4 16

.4 20

8 99

7 30

12

6.298

6 1.5

436

4.75

1352

8.1

613

875.8

746

YALI_

1997

19

98

3 13

.3 16

3.7

995

35

1998

3

25.1

162.1

99

0 40

18

7.088

9 1.5

707

5.25

2069

8.2

947

1317

.247

ZUMA

N_19

97

1998

3

13.9

170.2

99

6 35

19

98

4 27

17

1 10

00

25

176.8

394

1.826

5 7

2653

9.3

846

1452

.505

KATR

INA_

1997

19

98

1 16

.9 15

2.3

995

35

1998

1

17.9

152.5

99

7 30

16

9.160

2 52

.7437

21

.5 59

44

37.26

37

112.6

959

GITA

_199

8 19

99

2 24

.5 20

4 99

5 35

19

99

2 25

.5 20

4.5

990

40

155.6

083

1 0.2

5 12

2 0

122

ELLA

_199

8 19

99

2 11

16

3 99

5 35

19

99

2 25

17

0 99

9 30

15

5.441

3 1.0

202

2.25

1751

2.7

234

1716

.33

OLIN

DA_1

998

1999

1

17.2

158.3

99

5 35

19

99

1 25

.4 16

8.5

990

50

132.3

873

1.052

4 2.8

8 14

66

3.742

1 13

93.00

6 26

F_19

98

1999

5

20

162.5

99

2 40

19

99

5 25

.5 16

2 99

2 40

18

4.724

6 1.0

548

1.75

645

3.798

3 61

1.490

3 PE

TE_1

998

1999

1

15

151.8

99

4 35

19

99

1 23

.8 16

9.6

997

30

120.2

94

1.105

5 5.2

5 23

27

4.725

2 21

04.93

FR

ANK_

1998

19

99

2 20

.2 16

0 99

5 35

19

99

2 25

.2 16

4.8

987

45

139.2

1 1.4

516

2.75

1076

7.6

722

741.2

51

67

DANI

_199

8 19

99

1 15

.9 16

4.9

995

35

1999

1

26.2

172.5

97

5 60

14

6.588

5 1.8

57

7 25

74

9.498

6 13

86.10

7 HA

LI_19

98

1999

3

20.2

199.8

99

5 35

19

99

3 24

.6 19

8.9

997

30

190.6

002

2.332

5.5

11

57

11.00

28

496.1

407

LEO_

1999

20

00

3 24

.7 19

6.6

995

35

2000

3

25.6

195.4

99

0 40

23

0.257

9 1

0.25

157

0 15

7 IR

IS_1

999

2000

1

15.5

164.3

99

6 35

20

00

1 19

.4 17

7.7

998

30

108.8

114

1.027

9 3.2

5 15

28

3.033

14

86.52

6 JO

_199

9 20

00

1 17

.9 17

3.1

995

35

2000

1

25.1

179

975

60

143.5

582

1.032

2.5

10

36

3.174

8 10

03.87

6 KI

M_19

99

2000

2

23.2

224.4

99

4 35

20

00

2 25

.7 22

0.1

935

90

236.7

032

1.044

3 1.7

5 53

9 3.5

384

516.1

352

NEIL_

1999

20

00

4 20

17

8.4

995

35

2000

4

22.7

179.4

99

7 30

16

1.044

8 1.0

722

1 33

9 4.1

64

316.1

724

MONA

_199

9 20

00

3 18

.8 18

5.5

995

35

2000

3

25.5

187.8

96

0 75

16

2.689

3 1.2

305

2.5

958

6.131

4 77

8.545

3 OM

A_20

00

2001

2

21.6

196.5

99

0 40

20

01

2 26

20

2.8

987

45

128.4

387

1.005

7 1

810

1.786

3 80

5.409

2 VI

CKY_

2001

20

01

12

12.6

202.5

99

6 35

20

01

12

13.6

202.7

99

7 30

16

8.930

9 1.0

55

0.5

119

3.803

11

2.796

2 PA

ULA_

2000

20

01

2 12

.2 16

4.9

997

35

2001

3

25.6

185.3

97

0 65

12

7.624

4 1.0

832

5 28

22

4.365

6 26

05.24

4 W

AKA_

2001

20

01

12

11.3

185.5

99

5 35

20

02

1 25

.7 19

1.4

960

75

159.5

265

1.113

8 3.2

5 19

05

4.846

17

10.36

1 SO

SE_2

000

2001

4

14

165.5

99

5 35

20

01

4 25

.5 16

9.7

990

40

161.6

02

1.169

3 5

1575

5.5

32

1346

.96

RITA

_200

0 20

01

2 19

.3 22

3.7

998

35

2001

3

25.1

223.6

99

0 40

18

0.901

3 1.3

266

3.17

852

6.886

6 64

2.243

3 TR

INA_

2001

20

01

11

21.5

201

995

35

2001

12

21

.4 20

1.3

996

30

70.45

61

4.503

9 1.2

5 14

9 15

.1886

33

.0824

4 YO

LAND

E_20

02

2002

12

20

.4 18

5.8

995

35

2002

12

21

.7 18

7.9

996

30

123.7

762

1.000

2 0.5

26

1 0.5

848

260.9

478

DES_

2001

20

02

3 19

.4 15

9.5

993

40

2002

3

24.4

168.1

99

7 30

12

3.474

4 1.0

439

1.88

1093

3.5

277

1047

.035

CLAU

DIA_

2001

20

02

2 20

.5 15

6.5

995

35

2002

2

25.1

162

970

65

133.0

91

1.050

8 1.2

5 79

9 3.7

036

760.3

73

ZOE_

2002

20

02

12

10.8

175.5

99

5 35

20

03

1 20

.3 17

5.1

997

30

182.2

862

1.772

4 6.1

3 18

65

9.175

2 10

52.24

6 FI

LI_20

02

2003

4

20.4

188.4

99

5 35

20

03

4 27

19

0 98

5 50

16

7.730

8 1.0

001

0.38

749

0.464

2 74

8.925

1 CI

LLA_

2002

20

03

1 18

18

2 99

5 35

20

03

1 25

19

4.7

1002

35

12

2.718

2 1.0

977

3.5

1675

4.6

057

1525

.918

AMI_2

002

2003

1

10.8

180.6

99

5 35

20

03

1 26

.8 19

0.2

970

70

151.6

846

1.113

4 3

2269

4.8

403

2037

.902

ESET

A_20

02

2003

3

15.5

172.4

99

7 35

20

03

3 25

.3 19

4.7

965

70

118.6

301

1.119

2 4

2868

4.9

214

2562

.545

DOVI

_200

2 20

03

2 14

19

7.3

995

35

2003

2

26

191

986

50

205.3

735

1.134

6 5.0

4 16

82

5.124

9 14

82.46

1 GI

NA_2

002

2003

6

11.3

169.1

99

5 35

20

03

6 16

.5 16

2 99

7 30

23

2.33

1.340

4 4

1285

6.9

823

958.6

691

ERIC

A_20

02

2003

3

19.7

149.7

10

01

40

2003

3

26.5

174

960

75

111.4

187

1.733

3 12

44

99

9.017

7 25

95.62

7 BE

NI_2

002

2003

1

13.2

161.2

99

2 35

20

03

1 24

.3 16

3.5

997

30

169.1

87

1.838

9 6.7

5 23

03

9.431

3 12

52.37

9 JU

DY_2

004

2004

12

19

.5 21

4.7

995

35

2004

12

27

21

2.7

993

40

193.4

572

1.020

5 2

873

2.736

9 85

5.463

GR

ACE_

2003

20

04

3 16

.5 14

8.4

993

35

2004

3

22

166

997

30

110.9

97

1.095

6 4.2

5 21

32

4.572

5 19

45.96

6 HE

TA_2

003

2004

1

8 18

5.8

995

35

2004

1

25.6

195.6

95

5 80

15

3.079

6 1.1

14

5.25

2459

4.8

488

2207

.361

IVY_

2003

20

04

2 15

17

2.5

995

35

2004

2

26.6

171.8

95

0 80

18

3.128

2 1.5

83

4.88

2036

8.3

539

1286

.166

SHEI

LA_2

004

2005

4

17.4

189.4

99

5 35

20

05

4 20

.9 19

5.2

997

30

123.3

41

1.007

8 0.7

5 72

8 1.9

832

722.3

655

RAE_

2004

20

05

3 20

.5 19

5.3

995

35

2005

3

22.9

198.7

99

7 30

12

7.683

5 1.0

797

0.75

476

4.303

5 44

0.863

2 OL

AF_2

004

2005

2

9 18

2.4

995

35

2005

2

26.6

199.2

96

5 70

13

9.859

8 1.1

305

5.75

2977

5.0

723

2633

.348

MEEN

A_20

04

2005

2

14.4

191.8

99

5 35

20

05

2 25

.4 20

5.5

950

80

132.5

007

1.149

6 4.2

5 21

60

5.308

6 18

78.91

4

68

PERC

Y_20

04

2005

2

8.2

180.7

99

5 35

20

05

3 25

.2 20

4.5

980

50

129.5

516

1.175

9 8

3703

5.6

03

3149

.077

KERR

Y_20

04

2005

1

13.3

171.6

99

5 35

20

05

1 25

15

8.2

997

30

225.3

855

1.271

3 8.5

24

30

6.473

7 19

11.42

9 NA

NCY_

2004

20

05

2 12

.8 19

4.2

995

35

2005

2

25.1

195.2

99

4 35

17

5.731

5 1.5

725

4.75

2147

8.3

034

1365

.342

LOLA

_200

4 20

05

1 22

.6 18

3.8

995

35

2005

2

24.8

184

998

35

175.2

547

1.690

2 1.5

41

3 8.8

374

244.3

498

URMI

L_20

05

2006

1

14.6

185.6

99

5 35

20

06

1 25

.3 18

9.8

989

40

160.3

219

1.038

7 1.5

13

12

3.382

5 12

63.11

7 TA

M_20

05

2006

1

14.5

181.5

99

5 35

20

06

1 27

19

2 98

8 45

14

3.429

7 1.0

858

2 19

13

4.410

6 17

61.83

5 JIM

_200

5 20

06

1 18

.1 14

8.4

995

35

2006

2

26.4

173.3

98

7 45

11

4.188

9 1.1

566

4.75

3146

5.3

901

2720

.042

VAIA

NU_2

005

2006

2

17.4

185.1

99

5 35

20

06

2 25

.1 18

6.8

980

55

168.6

061

1.298

2 3.5

11

30

6.680

9 87

0.436

XA

VIER

_200

6 20

06

10

10.5

167.8

99

5 35

20

06

10

15.2

170.6

98

7 45

14

9.991

6 1.7

537

4 10

56

9.100

5 60

2.155

4 W

ATI_2

005

2006

3

15.7

164.5

99

5 35

20

06

3 25

.1 16

1.6

965

75

195.7

311

2.221

1 5.5

24

07

10.68

85

1083

.697

YANI

_200

6 20

06

11

12.3

162.4

99

5 35

20

06

11

13.5

162

987

45

198.0

635

2.688

8 2.5

37

6 11

.9086

13

9.839

3 CL

IFF_

2006

20

07

4 17

.2 18

0.6

995

35

2007

4

25.2

186.2

98

5 50

14

7.691

1.0

19

1.75

1079

2.6

684

1058

.881

ZITA

_200

6 20

07

1 14

.2 20

2.7

995

35

2007

1

25.4

209.9

99

0 45

14

9.834

8 1.0

366

1.75

1504

3.3

202

1450

.897

ARTH

UR_2

006

2007

1

14.5

192.5

99

5 35

20

07

1 26

.3 21

1.5

980

55

126.4

41

1.071

2 2.7

5 25

39

4.144

7 23

70.23

9 BE

CKY_

2006

20

07

3 13

.1 16

3 99

5 35

20

07

3 20

.8 16

7.6

995

35

150.7

431

1.112

6 2.5

10

93

4.828

9 98

2.383

6 DA

MAN_

2007

20

07

12

12.1

177.7

99

5 35

20

07

12

18.5

181.9

99

7 30

14

8.034

9 1.5

86

4.17

1331

8.3

682

839.2

182

ELIS

A_20

07

2008

1

21.4

184.4

99

4 35

20

08

1 24

.8 19

1.4

997

30

119.0

445

1.100

1 1.7

5 89

1 4.6

431

809.9

264

FUNA

_200

7 20

08

1 14

.8 16

4.8

990

35

2008

1

25.2

172.4

94

5 85

14

6.595

3 1.4

713

3.5

2057

7.7

821

1398

.083

GENE

_200

7 20

08

1 17

.4 17

8.4

995

35

2008

2

25.2

173

970

65

212.0

305

1.537

4 6.5

15

82

8.130

2 10

29.01

69

APPENDIX 2 – SOURTHERN OSCILLATION INDEX (S. O. I) ARCHIVES 1969 - 2008.

Year Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 1969 -13.5 -6.9 1.8 -8.8 -6.6 -0.6 -6.9 -4.4 -10.6 -11.7 -0.1 3.7 1970 -10.1 -10.7 1.8 -4.6 2.1 9.9 -5.6 4 12.9 10.3 19.7 17.4 1971 2.7 15.7 19.2 22.6 9.2 2.6 1.6 14.9 15.9 17.7 7.2 2.1 1972 3.7 8.2 2.4 -5.5 -16.1 -12 -18.6 -8.9 -14.8 -11.1 -3.4 -12.1 1973 -3 -13.5 0.8 -2.1 2.8 12.3 6.1 12.3 13.5 9.7 31.6 16.9 1974 20.8 16.2 20.3 11.1 10.7 2.6 12 6.6 12.3 8.5 -1.4 -0.9 1975 -4.9 5.3 11.6 14.4 6 15.5 21.1 20.7 22.5 17.7 13.8 19.5 1976 11.8 12.9 13.2 1.2 2.1 0.2 -12.8 -12.1 -13 3 9.8 -3 1977 -4 7.7 -9.5 -9.6 -11.4 -17.7 -14.7 -12.1 -9.4 -12.9 -14.6 -10.6 1978 -3 -24.4 -5.8 -7.9 16.3 5.8 6.1 1.4 0.8 -6.2 -2 -0.9 1979 -4 6.7 -3 -5.5 3.6 5.8 -8.2 -5 1.4 -2.5 -4.7 -7.5 1980 3.2 1.1 -8.5 -12.9 -3.5 -4.7 -1.7 1.4 -5.2 -1.9 -3.4 -0.9 1981 2.7 -3.2 -16.6 -5.5 7.6 11.5 9.4 5.9 7.5 -5 2.6 4.7 1982 9.4 0.6 2.4 -3.8 -8.2 -20.1 -19.3 -23.6 -21.4 -20.2 -31.1 -21.3 1983 -30.6 -33.3 -28 -17 6 -3.1 -7.6 0.1 9.9 4.2 -0.7 0.1 1984 1.3 5.8 -5.8 2 -0.3 -8.7 2.2 2.7 2 -5 3.9 -1.4 1985 -3.5 6.7 -2 14.4 2.8 -9.6 -2.3 8.5 0.2 -5.6 -1.4 2.1 1986 8 -10.7 0.8 1.2 -6.6 10.7 2.2 -7.6 -5.2 6.1 -13.9 -13.6 1987 -6.3 -12.6 -16.6 -24.4 -21.6 -20.1 -18.6 -14 -11.2 -5.6 -1.4 -4.5 1988 -1.1 -5 2.4 -1.3 10 -3.9 11.3 14.9 20.1 14.6 21 10.8 1989 13.2 9.1 6.7 21 14.7 7.4 9.4 -6.3 5.7 7.3 -2 -5 1990 -1.1 -17.3 -8.5 -0.5 13.1 1 5.5 -5 -7.6 1.8 -5.3 -2.4 1991 5.1 0.6 -10.6 -12.9 -19.3 -5.5 -1.7 -7.6 -16.6 -12.9 -7.3 -16.7 1992 -25.4 -9.3 -24.2 -18.7 0.5 -12.8 -6.9 1.4 0.8 -17.2 -7.3 -5.5 1993 -8.2 -7.9 -8.5 -21.1 -8.2 -16 -10.8 -14 -7.6 -13.5 0.6 1.6 1994 -1.6 0.6 -10.6 -22.8 -13 -10.4 -18 -17.2 -17.2 -14.1 -7.3 -11.6 1995 -4 -2.7 3.5 -16.2 -9 -1.5 4.2 0.8 3.2 -1.3 1.3 -5.5 1996 8.4 1.1 6.2 7.8 1.3 13.9 6.8 4.6 6.9 4.2 -0.1 7.2 1997 4.1 13.3 -8.5 -16.2 -22.4 -24.1 -9.5 -19.8 -14.8 -17.8 -15.2 -9.1 1998 -23.5 -19.2 -28.5 -24.4 0.5 9.9 14.6 9.8 11.1 10.9 12.5 13.3 1999 15.6 8.6 8.9 18.5 1.3 1 4.8 2.1 -0.4 9.1 13.1 12.8 2000 5.1 12.9 9.4 16.8 3.6 -5.5 -3.7 5.3 9.9 9.7 22.4 7.7 2001 8.9 11.9 6.7 0.3 -9 1.8 -3 -8.9 1.4 -1.9 7.2 -9.1 2002 2.7 7.7 -5.2 -3.8 -14.5 -6.3 -7.6 -14.6 -7.6 -7.4 -6 -10.6 2003 -2 -7.4 -6.8 -5.5 -7.4 -12 2.9 -1.8 -2.2 -1.9 -3.4 9.8 2004 -11.6 8.6 0.2 -15.4 13.1 -14.4 -6.9 -7.6 -2.8 -3.7 -9.3 -8 2005 1.8 -29.1 0.2 -11.2 -14.5 2.6 0.9 -6.9 3.9 10.9 -2.7 0.6 2006 12.7 0.1 13.8 15.2 -9.8 -5.5 -8.9 -15.9 -5.1 -15.3 -1.4 -3 2007 -7.3 -2.7 -1.4 -3 -2.7 5 -4.3 2.7 1.5 5.4 9.8 14.4 2008 14.1 21.3 12.2 4.5 -4.3 5 2.2 9.1 14.1 13.4 17.1 13.3

Source: Australian Bureau of Meteorology, 2011

70

APPENDIX 3 - C++ PROGRAM FOR FINDING THE OPTIMUM GROUP OF CYCLONES USING DYNAMIC PROGRAMMING TECHNIQUE. /*This program finds the optimum group of cyclones based on sinuosity index values with Gamma distribution*/ #include <iostream> #include <math.h> #include <assert.h> #include <conio.h> #include <stdio.h> using namespace std; typedef double Number; /********************************************************************* Returns the imcomplete gamma function P(a,x) = (int_0^x e^{-t} t^{a-1} dt)/Gamma(a) , (a > 0). C.A. Bertulani May/15/2000 *********************************************************************/ Number gammp(Number a, Number x) { voidgcf(Number *gammcf, Number a, Number x, Number *gln); voidgser(Number *gamser, Number a, Number x, Number *gln); Number gamser,gammcf,gln; if (x < 0.0 || a <= 0.0) cerr<< "Invalid arguments in routine gammp"; if (x < (a+1.0)) { gser(&gamser,a,x,&gln); returngamser; } else { /* Use the continued fraction representation */ gcf(&gammcf,a,x,&gln); /* and take its complement. */ return 1.0-gammcf; } } /********************************************************************* Returns the imcomplete gamma function Q(a,x) = 1-P(a,x) = (int_x^infinity e^{-t} t^{a-1} dt)/Gamma(a) , (a > 0).

71

C.A. Bertulani May/15/2000 *********************************************************************/ Number gammq(Number a, Number x) { voidgcf(Number *gammcf, Number a, Number x, Number *gln); voidgser(Number *gamser, Number a, Number x, Number *gln); Number gamser,gammcf,gln; if (x <= 0.0 || a <= 0.0) cerr<< "Invalid arguments in routine gammq"; if (x < (a+1.0)) { /* Use the series representation */ gser(&gamser,a,x,&gln); return 1.0-gamser; /* and take its complement. */ } else { /* Use the continued fraction representation. */ gcf(&gammcf,a,x,&gln); returngammcf; } } /********************************************************************* Returns the imcomplete gamma function P(a,x) evaluated by its series representation as gamser. Also returns ln(Gamma(a)) as gln. C.A. Bertulani May/15/2000 *********************************************************************/ #define ITMAX 1000 #define EPS 3.0e-7 voidgser(Number *gamser, Number a, Number x, Number *gln) { Number gamma_ln(Number xx); int n; Number sum,del,ap; *gln=gamma_ln(a); if (x <= 0.0) { if (x < 0.0) cerr<< "x less than 0 in routine gser"; *gamser=0.0; return; } else { ap=a; del=sum=1.0/a;

72

for (n=1;n<=ITMAX;n++) { ++ap; del *= x/ap; sum += del; if (fabs(del) <fabs(sum)*EPS) { *gamser=sum*exp(-x+a*log(x)-(*gln)); return; } } cerr<< "a too large, ITMAX too small in routine gser"; return; } } #undef ITMAX #undef EPS /********************************************************************* Returns the imcomplete gamma function Q(a,x) evaluated by its continued fraction representation as gammcf. Also returns ln(Gamma(a)) as gln. C.A. Bertulani May/15/2000 *********************************************************************/ #define ITMAX 1000 /* Maximum allowed number of iterations. */ #define EPS 3.0e-7 /* Relative accuracy */ #define FPMIN 1.0e-30 /* Number near the smallest representable */ /* floating point number. */ voidgcf(Number *gammcf, Number a, Number x, Number *gln) { Number gamma_ln(Number xx); int i; Number an,b,c,d,del,h; *gln=gamma_ln(a); b=x+1.0-a; /*Setup fr evaluating continued fracion by modified Lent'z*/ c=1.0/FPMIN; /* method with b_0 = 0. */ d=1.0/b; h=d; for (i=1;i<=ITMAX;i++) { /* Iterate to convergence. */ an = -i*(i-a); b += 2.0;

73

d=an*d+b; if (fabs(d) < FPMIN) d=FPMIN; c=b+an/c; if (fabs(c) < FPMIN) c=FPMIN; d=1.0/d; del=d*c; h *= del; if (fabs(del-1.0) < EPS) break; } if (i > ITMAX) cerr<< "a too large, ITMAX too small in gcf"; *gammcf=exp(-x+a*log(x)-(*gln))*h; /* Put factors in front. */ } #undef ITMAX #undef EPS #undef FPMIN /******************************************************************** Returns the value of ln[Gamma(xx)] for xx > 0 ********************************************************************/ Number gamma_ln(Number xx) { Number x,y,tmp,ser; static Number cof[6]={76.18009172947146,-86.50532032941677, 24.01409824083091,-1.231739572450155, 0.1208650973866179e-2,-0.5395239384953e-5}; int j; y=x=xx; tmp=x+5.5; tmp -= (x+0.5)*log(tmp); ser=1.000000000190015; for (j=0;j<=5;j++) ser += cof[j]/++y; return -tmp+log(2.5066282746310005*ser/x); } /*********************************************************************/ /*Program written by Karuna G. Reddy as per the MPP for Gamma Study Variable*/ # define z 100 //(refine to 5 dp )

74

# define b 1 //beta value-will be found from data # define r 3.822976 //shape parameter-will be found from data # define t 1.351949 //theta-scale parameter-will be found from data //# define ts 8.630574831 // theta square //# define m 4.9028809776729 /*complete gamma function with only one argument: //Gamma(3.836157) value*/ //# define m1 18.808221182667 // gamma(r+1) //# define m1s 353.749184 // [gamma(r+1)]^{2} //# define m2 90.959510530101 //gamma(r+2) //# define ms 24.03824187 //[gamma(r)]^{2} /*Recursive function receives the parameter k and dk,yk to calculate f.*/ doubleRootVal(int k, double d, double y); /*calculates the value of the minimal elements*/ double fun(int,int,double ,int,int ,bool ); double Minimum(double val1,double val2) // returns minimum of 2 numbers { if(val1<=val2) { return val1; } else { return val2; } } //Change here for the number of stages and the distance g and initial value x0 int h ; // number of stages const double g = 12.1561; // g is the distance double s; // s=x0, the initial value const doubleinc = 0.001; //PRECISION AMMOUNT const double inc2 = 0.00001; //PRECISION AMMOUNT const doubleprec = 1/inc; constint stages = 8; constint points = 1000 ; //Keep this to be 1/inc constint factor =4; /* eg. function(3,1) will be passed as function(3,1000), your value divided by inc to make it precise*/ intylimits[10]; //stores the 3dp values for refining constint e = (int)(g*points*z+1);

75

constint p=(int)(g*points); double minkf2[stages][e]; //stores minimum f to 6dp double dk2[stages][e]; //stores minimum d for the 6dp calculations main() { //initialize minkf cout<<"Initializing points ...."<<endl; for (int i=0; i <stages;i++) for(int j=0;j<(p+1);j++) minkf2[i][j]= -9999; for (int k=0; k <stages;k++) for(int l=0;l<e;l++) minkf2[k][l]= -9999; cout<<"Initialiation complete"<<endl<<endl<<"Calculating...."<<endl<<endl; cout<<"enter h = Number of Stage " <<endl; cin>> h; cout<<"enter s = Initial value " <<endl; cin>> s; double f=fun(h,p,inc ,0,p ,true); float d6,d5,d4,d3,d2,d1, y6,y5,y4,y3,y2,y1; int temp; //backward calculation for the 3dp results d6 = g; y6 = dk2[6][p]; d5=d6-y6; temp = (int)(d5*points); y5=dk2[5][temp]; d4=d5-y5; temp = (int)(d4*points); y4=dk2[4][temp]; d3=d4-y4; temp = (int)(d3*points); y3=dk2[3][temp]; d2=d3-y3; temp = (int)(d2*points); y2=dk2[2][temp]; d1=d2-y2; y1=d1; //setup the limits for the 6dp calculations

76

temp = (int)(y6*points*z); ylimits[6] = temp; temp = (int)(y5*points*z); ylimits[5] = temp; temp = (int)(y4*points*z); ylimits[4] = temp; temp = (int)(y3*points*z); ylimits[3] = temp; temp = (int)(y2*points*z); ylimits[2] = temp; temp = (int)(y1*points*z); ylimits[1] = temp; f=fun(h,e-1,inc2 ,ylimits[h]-factor*z,ylimits[h]+ factor*z ,false);//for k>=2 cout<<"stage: h = " << h << " distance: g = " << g<<endl; printf("\nf(h,g): %.10f \n" ,f); //Backward calucation for the 6 dp d6=g; y6 = dk2[6][(e-1)]; d5=d6-y6; temp = (int)(d5*points*z); y5=dk2[5][temp]; d4=d5-y5; temp = (int)(d4*points*z); y4=dk2[4][temp]; d3=d4-y4; temp = (int)(d3*points*z); y3=dk2[3][temp]; d2=d3-y3; temp = (int)(d2*points*z); y2=dk2[2][temp]; d1=d2-y2; y1=d1; printf("\nd6: %f y6: %f",d6,y6); printf("\nd5: %f y5: %f",d5,y5); printf("\nd4: %f y4: %f",d4,y4); printf("\nd3: %f y3: %f",d3,y3); printf("\nd2: %f y2: %f",d2,y2); printf("\nd1: %f y1: %f",d1,y1); getch(); } //end main doubleRootVal(int k, double d, double y)/*calculate the root value of the

77

current distribution*/ { doublertval; doublecalc; /*double c1 = (gammq(r,(s/t))-gammq(r,(d+s)/t))/(gammq(r,(d-y+s)/t) -gammq(r,(d+s)/t));//error case 1 (being used now) double c2 = (t*r*(gammq(r+1,(d-y+s)/t)-gammq(r+1,(d+s)/t)))/(gammq(r,(d-y+s)/t) -gammq(r,(d+s)/t));//error case 2 double c3 = (pow(t,2)*r*(r+1)*(gammq(r+2,(d-y+s)/t) -gammq(r+2,(d+s)/t)))/(gammq(r,(d-y+s)/t)-gammq(r,(d+s)/t))*/ //double c1 = 1;//error case 1 (being used now) //double c2 = 11.26991907;//error case 2 //double c3 = 164.4962888;//error case 3 - out of range double c = 0;//error calculated from sugar mill data calc=(pow(b,2)*pow(t,2))*(r*(r+1)*(gammq(r+2,(d-y+s)/t)- gammq(r+2,(d+s)/t))*(gammq(r,(d-y+s)/t)-gammq(r,(d+s)/t)) -pow(r,2)*pow((gammq(r+1,(d-y+s)/t)-gammq(r+1,(d+s)/t)),2)) +(c)*pow((gammq(r,(d-y+s)/t)-gammq(r,(d+s)/t)),2); if(calc<0) { //cout<<"\nError: Negative Root\n"; //rtval = -1; } else { calc = sqrt(calc); } rtval = calc; returnrtval; } double fun(intk,intn,doubleincf,intminYk,intmaxYk,boolisFirstRun) /*this functions performs the same actions as "function". It only defers in terms of the iterations of the for loop.*/ { assert (k>=1); //Abort if k is negative doubledblRetVal; double d =n*incf; //d value for the function double y; double min; doubleval; doubleminy;

78

int col; if(k==1) //base case { y = d; dblRetVal = RootVal(k,d,y); } else { for(int i=minYk;i<=maxYk;i++)/*iterate over the interval allowed to calculate the 6dp results*/ { y = i*incf;//this sets to precission of y to 6dp double root; root = RootVal(k,d,y); //calculate the root. if(root != -1) //if root is valid { col =n-i;//get the current d value if(minkf2[k-1][col]==-9999) {/*check if the result has been previously calculated*/ if(isFirstRun){ val = root+ fun((k-1),col,incf,0,col,true);//if not, // calculate the result } else{ val = root+ fun((k-1),col,incf,ylimits[k-1]- factor*z,ylimits[k-1]+ factor*z,false);//if not, //calculate the result } } else val = root+ minkf2[k-1][col];//if result exists, use it for calculations } if (i==minYk) { min =val;//base case } else { min = Minimum(min,val);//get the minimum if the result and the current mininmum } if(min == val){miny=y;}//get the position of the current minimum }//end for

79

dblRetVal = min; }//end else //store the f and the d value of the minimum calculated. col = n; minkf2[k][col] = dblRetVal; dk2[k][col]=miny; returndblRetVal; }//end function