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