1 23

Natural HazardsJournal of the International Societyfor the Prevention and Mitigation ofNatural Hazards ISSN 0921-030XVolume 59Number 2 Nat Hazards (2011) 59:1161-1174DOI 10.1007/s11069-011-9827-3

Developing a new sinuosity index forcyclone tracks in the tropical South Pacific

James P. Terry & Gennady Gienko

1 23

Your article is protected by copyright and

all rights are held exclusively by Springer

Science+Business Media B.V.. This e-offprint

is for personal use only and shall not be self-

archived in electronic repositories. If you

wish to self-archive your work, please use the

accepted author’s version for posting to your

own website or your institution’s repository.

You may further deposit the accepted author’s

version on a funder’s repository at a funder’s

request, provided it is not made publicly

available until 12 months after publication.

ORI GIN AL PA PER

Developing a new sinuosity index for cyclone tracksin the tropical South Pacific

James P. Terry • Gennady Gienko

Received: 22 December 2009 / Accepted: 20 April 2011 / Published online: 6 May 2011� Springer Science+Business Media B.V. 2011

Abstract This paper introduces a new metric for tropical cyclone track shape within the

tropical South Pacific (TSP) basin, based on measurements of track sinuosity. A sinuosity

index (SI) is developed by applying a simple cube-root transformation to original track

sinuosity values. Based on the resulting near-normal SI distribution, an ordinal four-

category (quartile) naming system is then proposed for track-type classification. Track

sinuosity patterns are also investigated over the last four decades (1970–2008). Analytical

findings suggest that cyclone track sinuosity is an important parameter influencing the

potential vulnerability of island archipelagoes to cyclone hazard. Principally, sinuously

moving cyclones show some tendency for greater longevity and intensity than straighter-

tracking storms and make up a larger proportion of systems forming in the western tropical

South Pacific than those generated farther east. Although no long-term statistical trend can

be established, track sinuosity is highly variable through time, implying that the TSP basin

and the islands therein will continue to experience large but irregular inter-annual fluc-

tuations in cyclone track morphology.

Keywords Tropical cyclones � South Pacific � Track sinuosity

1 Introduction and aims

The majority of developing island nations across the South Pacific Ocean are vulnerable to

both the environmental and economic impacts of tropical cyclones. In terms of numbers of

communities afflicted and overall hardship produced, these severe storms pose the most

J. P. Terry (&)Department of Geography, National University of Singapore, AS2, 1 Arts Link,Kent Ridge 117570, Singaporee-mail: geojpt@nus.edu.sg

G. GienkoDepartment of Geomatics, School of Engineering, University of Alaska Anchorage,3211 Providence Drive, Anchorage, AK 99508-4514, USAe-mail: afgg@uaa.alaska.edu

123

Nat Hazards (2011) 59:1161–1174DOI 10.1007/s11069-011-9827-3

Author's personal copy

significant annual threat to the livelihoods of scattered populations inhabiting the region

and adversely affect the sustainability of small-island economies when they strike. For

example, widespread flooding generated by Cyclone Kina in 1993 across Fiji wiped out

food crops and livestock herds, with the total costs of flood damage reaching FJD188

million (FMS 1997; Raucher 2000). Similarly, Cyclone Heta in 2004 wrought devastation

on the tiny nation of Niue (Barnett and Ellemor 2007), amounting to approximately double

the national GDP. Fortunately, not all tropical cyclones result in such extreme conse-

quences. Nevertheless, such examples highlight the importance of maintaining a concerted

scientific focus on understanding cyclone behaviour in the tropical South Pacific (TSP)

region, especially because evolving scenarios of climate change suggest that some cyclone

characteristics (e.g. intensity and rainfall) may respond to rising sea-surface temperatures

associated with enhanced greenhouse conditions (e.g. Emanuel 2004; Elsner et al. 2008;

Knutson and Tuleya 2008).

While research has traditionally focused on the origins, frequency and intensity of

tropical cyclones in affected ocean basins (e.g. Emanuel 2004; Webster et al. 2005), in part

because these characteristics bear directly on the insurable risk of the hazard, there has also

been a growing interest in examining the nature of and patterns in cyclone tracks (e.g.

Dengler 1997; Fraedrich and Leslie 1989; Chand and Walsh 2009). The track is the

‘meandering’ path a cyclone follows as it matures and migrates away from its point of

cyclogenesis. As track shape is the surficial linear expression of cyclone movement,

impetus for investigating this feature arises both from the influence it has on which parts of

the South Pacific (and therefore which islands) face a risk of strike by active cyclones and

from overarching questions about how cyclone track characteristics globally might be

affected by long-term climate change (Walsh 2004; Kossin et al. 2010). Furthermore,

assessment of track density and clustering has recently been demonstrated to assist in

determining whether cyclone activity is enhanced or suppressed by certain (phases of)

broad-scale environmental modulators such as ENSO or MJO (Kim et al. 2010a; Kossin

et al. 2010).

Within this context, one parameter that has received less attention in studies of cyclone

movement is the sinuosity of the storm tracks. Sinuosity is one measure of linear shape,

specifically how much a meandering track deviates from a straight line (Terry and Feng

2010). For a flat surface, sinuosity is simply calculated as the ratio of the actual distance

(numerator) against the straight-line distance between two points (denominator) (DeMers

2008). The lowest possible sinuosity measurement is therefore 1. In the case of cyclones

moving over the curved surface of the Earth, determining sinuosity is slightly more

involved: the ‘actual’ and ‘straight’ distances are measured using the law of haversines

from spherical trigonometry. Nonetheless, sinuosity can be easily quantified if tracks are

analysed within a GIS environment. It is perhaps surprising that track sinuosity has been

neglected in cyclone research since it is both a simple metric to comprehend and is

mathematically easier to manage than, for instance, trying to fit complex non-linear

equations to convoluted track shapes. Also, if track sinuosity correlates well with other

important cyclone parameters such as duration, it may prove to be a useful indicator of the

hazard facing particular islands within the TSP region.

Tropical cyclones in the TSP region generally move south and east away from their

point of formation (Terry 2007), although individual systems may follow any compass

bearing at some stage in their lifespan. Consequently, many storm tracks have relatively

simple shapes without sharp bends, but others describe complex morphology with sharp

inflections or recurving backtracks. Infrequently, storm tracks loop with either open or

tight curvature, in clockwise or counter-clockwise directions. The movement of cyclones

1162 Nat Hazards (2011) 59:1161–1174

123

Author's personal copy

describing these atypical track shapes is notoriously hard to predict. In spite of these

considerations, no analysis has yet determined whether cyclone track sinuosity is geo-

spatially organised across the region or shows any temporal change over the modern period

of satellite observations. Hence, the objectives of the current investigation are to: 1.

measure sinuosity (S) values for all individual cyclone tracks in the study area since 1970,

2. devise an appropriate ‘sinuosity index’ (SI) metric based on transformed (normalised)

sinuosity values, 3. categorise cyclone track sinuosity into appropriately named groups and

4. identify any spatio-temporal patterns in sinuosity. Key findings are then summarised

with reference to the vulnerability of small island nations in the TSP region.

2 Study area, data and methods

The study area falls under the responsibility of the Regional Specialized Meteorological

Centre (RSMC) for the tropical South Pacific (TSP), based at Nadi in the Fiji Islands. The

RSMC-Nadi area of responsibility extends from the Equator to 25�S and from 160�E to

120�W. Within this vast oceanic expanse are thousands of remote islands vulnerable to the

impacts of cyclone strike (Fig. 1). It is the task of the RSMC-Nadi to detect, name and

monitor all tropical cyclones originating in this operational region. Cyclones originating in

the Coral Sea to the west of 160�E are named by the Tropical Cyclone Warning Centre in

Brisbane (TCWC-Brisbane) in Australia, but are included in the TSP dataset if they move

east of 160�E. Similarly, the TSP dataset includes information on storms moving south of

25�S, which is monitored by the TCWC-Wellington in New Zealand. The complete TSP

dataset is archived by the Climate Services Division of the Fiji Meteorological Services

(FMS).

The conventional TSP cyclone season spans the austral summer, extending for 6 months

from November to April, although cyclones can also occur outside these months. The

median cyclone frequency in the TSP is 7 events per season. The analysis for this work

uses cyclone position data from 1970 to 2008. This period is coincident with the modern

Fig. 1 Area of responsibility of the RSMC-Nadi in Fiji (grey box) and the spread of island nations andterritories across the tropical South Pacific (TSP)

Nat Hazards (2011) 59:1161–1174 1163

123

Author's personal copy

era of satellite observation (Steiner 1980). At the start Fiji relied on imagery from US and

Russian (Meteor series) polar-orbiting satellites, until 1979 when geostationary satellite

imagery became available (S. Ready personal communication, New Zealand Meteoro-

logical Service). Thus, there are issues surrounding data homogeneity as satellite coverage

was thinner and image quality poorer in the 1970s compared to recent times (see ‘Results

and Discussion’).

The current RSMC-Nadi best-track data comprise a set of records containing the

cyclone name, time stamp, position (latitude, longitude), sea-level pressure and wind speed

recorded at fixed time intervals. Although essential information from 1970 until 2008 is

generally congruent, various different arrangements to store data have been used over time.

The source data were therefore reformatted into a uniform style to create a single database

containing information on 291 tropical cyclones in the TSP study area. Several iterations

were developed for data checking and consistency of date/time stamps, while geographical

coordinates were checked automatically by programming appropriate scripts. The uniform

database was then filtered to exclude the early or late depressional phases of storms (winds

B34 knots). Since wind speed has been recorded in 5-knot increments, the first position

along a track with wind strength at 35 knots was therefore selected to identify the genesis

location for each cyclone. To establish decay points, in practice, it was decided against

using the mathematically closest recorded value (35 knots) as the threshold, as the storm is

still in a cyclonic phase at this wind speed. Instead, the first reading of 30 knots was chosen

to identify the end of the cyclone track.

Filtering also excluded position data beyond the southern boundary of the TSP region

(25�S). In practice, this means that of the total 291 cyclones on record, entire tracks are

used for 122 storms that decayed within the TSP area, whereas partial tracks are used for

the 169 storms that travelled poleward of 25�S. Intuitively, quantifying sinuosity for a mix

of whole and partial tracks may appear questionable, but there are compelling arguments

for taking this approach. The principal reason is that most of the territory and virtually all

the islands of developing South Pacific nations are located above 25�S, and it is within the

framework of island vulnerability to tropical cyclones that this study is carried out. A

previous study of cyclone climatology successfully used similar methodology (Terry and

Gienko 2010). Another consideration is that cyclones migrating beyond 25�S become

extra-tropical systems, the remains of which may eventually transform into mid-latitude

depressions. Recognising the time of this transition is not always easy, thus affecting the

location of ‘official’ track end points. Lastly, comparison of ‘like with like’ is important.

The majority of cyclones surviving into sub-tropical waters follow relatively straight tracks

poleward of 25�S, even if they meandered significantly within the tropics (Terry 2007).

Consequently, measuring sinuosity of a whole cyclone track that might stretch as far as the

mid-latitudes gives a misleading impression of track shape within the tropical zone,

thereby making comparison difficult with the 42% of cyclones that remained entirely

within the TSP region. For illustration, Fig. 2 plots cyclones Harry in February 1989 and

Zuman in March 1998. Both show far more sinuous track morphology equatorward of 25�S

than poleward of this boundary. Such examples indicate how analysis of track sinuosity

patterns across the tropical South Pacific requires sinuosity values measured within the

equivalent area, but not beyond.

Within the confines outlined above, track sinuosity for each cyclone was measured

using GIS tools as the actual distance of storm travel, divided by the vector distance

between start and finish points. Each pair of distances was measured on the Earth-surface

sphere using the law of haversines from spherical trigonometry.

1164 Nat Hazards (2011) 59:1161–1174

123

Author's personal copy

3 Results and discussion

3.1 Sinuosity values: statistical distribution and data transformation

Table 1 summarises the sinuosity observations for 291 cyclone tracks in the TSP region

between 1970 and 2008. Figure 3a shows the shape of the data distribution. It is seen that

although the sinuosity median is small (1.105), the range is large (1–52.7), thus giving a

Fig. 2 Tracks of cyclones Harry (February 1989) and Zuman (April 1998) illustrate how sinuous cyclonetracks within the tropical South Pacific (north of 25�S) normally become straighter if storms migrate deepinto extra-tropical latitudes. Consequently, track sinuosity here is measured only until the 25�S boundary ofthe study area, to validate comparison with the proportion of cyclones (42%) that remain entirely withintropical waters

Table 1 Sinuosity distribution and descriptive statistics for cyclone tracks in the tropical South Pacific

Statisticalparameter

Measuredsinuosity (S)(to 25�S)

Measured sinuosity(S) (to end ofcyclone track)

Sinuosity indexvalues (SI)(to 25�S)

Sinuosity indexvalues (SI) (to endof cyclone track)

No. of cyclones 291 291 291 291

Mean 1.426 1.446 5.155 5.501

Median 1.105 1.123 4.724 4.975

SD 3.047 3.045 3.266 3.123

Kurtosis 280.386 280.335 31.498 36.264

Skewness 16.602 16.599 3.614 3.966

Range 51.744 51.744 37.264 37.264

Minimum 1 1 0 0

Maximum 52.744 52.744 37.264 37.264

Dataset statistical attributes are similar for track sinuosity measured to the 25�S boundary and for completetracks to cyclone decay (see text)

Nat Hazards (2011) 59:1161–1174 1165

123

Author's personal copy

highly skewed distribution (skewness = 16.6). Observed skewing is directly related to the

mathematical limits of sinuosity values, since the minimum possible S-value is unity

whereas high S-values have no upper bound. To exemplify the point, the largest measured

value for track sinuosity is 52.7 for Cyclone Katrina in January 1998, meaning this storm

travelled nearly 53 times as far as the straight distance between its genesis and decay

points. This and other cases of highly convoluted tracks effectively stretch the right side of

the sinuosity distribution to produce the strong positive skewing. Consequently, it is less

meaningful to perform statistical analysis on the raw sinuosity observations because a few

extreme values in the dataset are likely to produce spurious results.

In response, measured sinuosity values were checked against various distributions using

both graphical and quantitative (parametric) approaches. First, the histogram in Fig. 3a was

examined to identify the general form of data distribution, and then several theoretical

distributions were tested to fit the real data. Fitting theoretical distributions suggested that

the Frechet distribution (Fisher-Tippett type 2) has the best fit to the source data with

DXCDF = 2.95%. DXCDF is the absolute difference between calculated and observed fre-

quencies in the cumulative density function, expressed as a percentage. Next, in order to

Fig. 3 Distributions of a measured sinuosity values (S) and b normalised values of a proposed sinuosityindex (SI), for 291 cyclone tracks in the tropical South Pacific over the period 1970–2008

1166 Nat Hazards (2011) 59:1161–1174

123

Author's personal copy

bring the observed distribution close to normal, the original data need to be transformed.

There are many valid reasons for utilising data transformations, including improvement of

normality, variance stabilization and conversion of scales to interval measurement. Here,

transforming the data to approach a normal shape is beneficial so that outliers can be

identified and eliminated from further analysis and to validate the use of parametric sta-

tistics in the investigation of relationships (e.g. correlation) between sinuosity and other

cyclone variables of interest.

Data transformations are the application of a mathematical modification to the values of

a variable. There are a great variety of possible data transformations, from adding constants

to multiplying, squaring or raising to a power, converting to logarithmic scales, inverting

and reflecting, taking the square root of the values and even applying trigonometric

transformations such as sine wave transformations (Osborne 2002a). Some other trans-

formations include Logit, Normal z-transform, Box–Cox (power transforms) and angular

transforms (Kottegoda and Rosso 1997; De Smith et al. 2007, Rosenshein et al. 2011). The

most common transformation techniques used for data normalisation are: radical trans-

formation (N-th root, but mostly square root and cube root), log transformations

(with different bases) and inverse transformation (computing 1/X for the source variable

X) (Osborne 2002b). Several transformations were tested to bring observed sinuosity

values close to the normal distribution (Table 2).

As the square-root transformation shows better results in comparative tests, several

further options were explored based on radical function (roots) to normalise the sinuosity

values. The source variables were transformed by a combination of data shift, multipli-

cation and squaring. The general formula for calculating the SI (a dimensionless norma-

lised sinuosity index) is as follows:

SI ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðS� 1Þnp

� 10

where, SI = Sinuosity Index value, S = measured sinuosity for an individual cyclone

track

The subtraction (S-1) allows the transformed distribution for SI to start at zero. The

product 910 is introduced for convenience, so that SI values are mainly [1, to avoid

dealing in small decimal fractions. Results of applying several transformations, based on

radical functions with different N numbers, were tested against various theoretical distri-

butions. Transformation with N = 3 (cube root) yields a ‘quasi-normal’ approximation of

the original sinuosity data, with reasonable deviation from theoretical normal distribution

(DXCDF = 3.53%). While higher N numbers result in slightly closer approximations to the

normal distribution, such transformations more rigorously alter the original data.

Table 2 Results of applying various data transformations on measured values of cyclone track sinuosity

Applied transformation Resulting distribution DXCDF (%)

Square root Log-normal 0.95

Inverse Exponential 1.57

Freeman-Tukey (for inverse sinuosity) Exponential 1.65

Natural log Frechet (Fisher-Tippett, type 2) 2.67

Box–Cox (K = 2) Frechet (Fisher-Tippett, type 2) 3.63

Exponential Frechet (Fisher-Tippett, type 2) 9.17

Nat Hazards (2011) 59:1161–1174 1167

123

Author's personal copy

Consequently, the following function was chosen to transform the original sinuosity data

and yield dimensionless and quasi-normalised ‘Sinuosity Index’ values:

SI ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðS� 1Þ3p

� 10

Using the chosen transformation, the original highly skewed cyclone track sinuosity

measurements now approach a near-normal distribution, as shown in Fig. 3b. Statistical

properties of the SI dataset are summarised in Table 1.

3.2 Sinuosity categorisation

From the derived set of transformed and quasi-normalised SI values described above, we

propose a four-category division, based on quartile ranges (Table 3). Only four categories

are designated for two main reasons: so that the median SI value forms the central

boundary between upper and lower sinuosity categories (instead of falling within a cate-

gory) and to facilitate the application of simple yet qualitative names to the categories. The

proposed category names are ‘straight’, ‘quasi-straight’, ‘curving’ and ‘sinuous’. Several

features of this approach can be highlighted, differentiating it from alternatives proposed

elsewhere.

First, although different names have been suggested in the past for common kinds of

track shapes, such as ‘straight-moving’, ‘recurving’, ‘elliptical’ and ‘s-shaped’ (Harr and

Elsberry 1995; Lander 1996; Ho et al. 2004), these terms are often defined with reference

to trajectory direction and/or location within particular sub-basins (e.g. Elsner and Liu

2003, Kim et al. 2010a, b), but without necessarily incorporating measurement of any

track-shape parameter. Second, some recent studies have successfully employed other

metrics, such as polynomial regression curves and mass moments, to identify hurricane

track clusters in the North Atlantic and North Pacific basins (Camargo et al. 2007a, b,

2008; Nakamura et al. 2009; Kossin et al. 2010). Such approaches are proving valuable for

investigating major climatic influences on track-cluster properties or for seasonal fore-

casting of cyclone activity (e.g. Chu et al. 2010). However, they involve relatively complex

mathematical procedures for the initial definition of the track clusters. Our proposed

method does not attempt clustering, instead stratifying tracks into four sinuosity-based

categories. Among the advantages are that sinuosity is a dimensionless parameter, easily

understood and simply captured within GIS. Even tortuous track shapes such as multiple

loops are measured without difficulty, compared to more problematic mathematical curve-

fitting techniques. Third, our chosen category names provide an ordinal (i.e. ranked)

nomenclature that allows a general impression of track shape to be visualised. Fourth,

preliminary tests have indicated a close statistical similarity between track sinuosity data

Table 3 Proposed categorisation for cyclone track sinuosity; n = 291

Quartile Category ranges Category names No. of cyclones

Measured sinuosity (S) Sinuosity index (SI)

1st 1.000–1.028 0–3.06 Straight 73

2nd 1.029–1.105 3.07–4.72 Quasi-straight 72

3rd 1.106–1.299 4.73–6.69 Curving 74

4th C1.300 C6.70 Sinuous 72

1168 Nat Hazards (2011) 59:1161–1174

123

Author's personal copy

for TSP cyclones and North Pacific typhoons, so demonstrating the inter-basin transfer-

ability of a sinuosity-based track classification system (Terry and Feng 2010).

Therefore, the intention here is not to promote our track-sinuosity metric or categori-

sation as superior to alternatives developed elsewhere, but to demonstrate that the meth-

odology provides a convenient system for comparing temporal and spatial changes in one

neglected feature in cyclone track morphometric analysis, as described below.

3.3 Variability and trends

Figure 4 illustrates several types of temporal pattern in cyclone track SI values over the

study period in the TSP region. To avoid the inclusion of possibly spurious extreme values,

only SI values within ±two standard deviations of the mean are used for temporal analysis.

Theoretically (for a normal distribution), this means only the central 95% of the dataset is

used, with 5% of observations in the upper and lower tails being excluded. In practice,

adopting ±2r limits here eliminates six observations at the upper end of the SI range

([11.69). Despite removing these outliers, Fig. 4 nonetheless illustrates the large amount

of variability in track sinuosity, between successive cyclone events, within individual

years, and also year-on-year. Extended periods lasting several years when sinuosity was

notably higher (e.g. 1981–83) or lower (e.g. 1999–2002) than normal can be clearly

identified, although the physical basis for these fluctuations is unknown and warrants

further investigation. Although this is beyond the scope of the current paper, reanalysis of

the regional synoptic patterns during anomalous periods may help to illuminate which

climatic features most strongly influence cyclone track sinuosity.

Against the large background variability, SI values suggest a weak upward tendency

over the complete four decades of record. However, for trend analysis to be meaningful, it

is necessary to plot two separate trend lines for the periods pre- and post-1986, owing to

two main issues relating to data homogeneity. First, while early tracking techniques used

Fig. 4 Sinuosity Index (SI) values for individual cyclones (grey markers), long-term trends (dashed lines)and variability in running means of seven storms (solid black line) from 1970 to 2008 in the tropical SouthPacific. Extreme (possibly spurious) values in the dataset beyond the population mean ± 2r are excludedfrom analysis. Notes: 1. Separate trend lines for SI values are necessary for pre- and post-1986 periods (seetext for explanation); 2. Grey markers are spaced equidistantly along the horizontal, so the time axis is non-linear

Nat Hazards (2011) 59:1161–1174 1169

123

Author's personal copy

12-h intervals to mark cyclone positions, monitoring since 1986 used 6-h fixes to obtain

more precise positioning. The lower temporal resolution for cyclone tracks before 1986

causes sinuosity measurements to be underestimated relative to the later period, especially

for more elaborate track shapes. Second, high-resolution satellite imagery for the RSMC-

Nadi region only became available in 1986 (R. Prasad, personal communication, former

director of the Fiji Meteorological Services and RSMC-Nadi). These secular changes

affecting data homogeneity therefore restrict the use of the dataset in toto for investigating

long-term trends in track sinuosity over the entire period since 1970. Similar problems

have been highlighted elsewhere as limiting both our abilities to recognise changes in

cyclone activity and the possibilities for extrapolation and prediction (Kuleshov et al.

2010; Buckley et al. 2003).

Notwithstanding these challenges, commenting on the measured trends over the two

sub-periods remains worthwhile. For the pre-1986 sub-set of cyclone tracks, the apparent

positive trend in sinuosity is likely to be spurious. With reference to Australian region

datasets, observed trends in several cyclone parameters are in reality artefacts of advances

in technology leading to improvements in observing capabilities and cyclone detection

(Solow and Nicholls 1990), and increased understanding of tropical storms allowing better

discrimination between cyclones and other systems, with consequent adjustments to

cyclone definition (Nicholls et al. 1998). Such influences can be assumed to have affected

RSMC-Nadi cyclone observations also (Terry and Gienko 2010). In contrast, for the more

homogenous post-1986 data sub-set, the lack of a statistically significant trend in track

sinuosity is probably more realistic, and suggests that this feature of cyclone behaviour

remains unaffected by recent climate change. An absence of any long-term trend in track

sinuosity has also been established for typhoons in the north west Pacific (Terry and Feng

2010).

Further analysis of the post-1986 dataset (n = 155 with 5 outliers removed) reveals that

track SI values show their strongest and most significant positive correlations with cyclone

duration (Pearson’s r = 0.64, P B 0.001, Fig. 5), i.e. longer-lasting storms tend to be those

that follow more complex tracks, although no causality is implied. For example, the record

for most sinuous track is set by Cyclone Katrina, which survived for over 21 days in

Fig. 5 Relationship between track Sinuosity Index (SI) values and durations of tropical cyclones from 1986to 2008 in the tropical South Pacific; n = 155 with 5 statistical outliers removed

1170 Nat Hazards (2011) 59:1161–1174

123

Author's personal copy

January 1998 and attained a minimum pressure of 940 hPa. Katrina and other storms with

high SI values are those that described elaborate looping tracks and/or backtracked to

decay relatively near their origins. SI values also return significant although weaker linear

correlations with several other cyclone parameters such as cyclone minimum pressure

(r = 0.48, P B 0.001) and track length (r = 0.37, P B 0.001).

3.4 Spatial patterns

Apparent geospatial patterns in cyclone track sinuosity are also suggested by the maps

presented in Fig. 6. These show all cyclone tracks in each sinuosity category from 1970 to

2008. Straighter tracks seem to be spread more evenly across the TSP study region study,

whereas sinuous category storms (SI C6.7, upper quartile) show some tendency for

bunching in the west. As a preliminary test of this apparent pattern, analysis using chi-

square (v2) was performed on numbers of cyclones falling into different track sinuosity

categories, sorted into 10� longitudinal zones according to cyclogenesis origin (Table 4).

The v2 test did not reveal a significant difference between the 10� zones in terms of general

sinuosity characteristics. However, a v2 test performed only on the percentages of cyclones

in each 10� zone falling in the sinuous category did indicate a significant difference

(P B 0.001) between the zones, i.e. revealing that the proportion of sinuous tracks in each

10� zone is not consistent from west to east across the South Pacific. Exploring this finding

further, scrutiny of top-end sinuosity values shows that over three quarters ([78%) of the

most convoluted tracks (measured sinuosity C2, SI C10) were produced by cyclones

originating within an 11� longitudinal band in the western portion of the study area

(158�–169�E).

4 Conclusions

The sinuosity of 291 tropical cyclone tracks from 1970 to 2008 in the tropical South Pacific

was measured using GIS tools. Observed sinuosity values are highly positively skewed, but

may be transformed using a simple cube-root function to Sinuosity Index (SI) values

characterised by a near-normal distribution. Using SI as a measurement of cyclone track

shape is simpler than mathematical curve fitting and, within certain limitations associated

with data homogeneity, permits investigation of spatial and temporal patterns. To aid track-

shape conceptualisation, four sinuosity categories are proposed based on quartile ranges of

SI values, with an ordinal system of names: straight, quasi-straight, curving and sinuous.

This improves on existing binary nomenclature that tends often to distinguish only

‘straight’ or ‘recurving’ track types.

Analytical findings are as follows, several of which have implications regarding the

vulnerability of South Pacific islands to cyclone hazards. First, track sinuosity displays a

high degree of variability over the last four decades, suggesting that the region is likely to

continue to experience episodes of anomalous cyclone behaviour at irregular intervals in

future. Second, no overall trend can be established in track sinuosity since the mid-1980s;

an apparent increasing sinuosity trend from 1970 to 1985 is probably unreliable owing to

improving cyclone monitoring over this period. Third, island groups in the west of the TSP

region face a greater chance than elsewhere of experiencing cyclones that follow more

convoluted tracks, the movement of which is difficult to predict and model compared to

‘normal’ storm migration. Fourth, other cyclone variables being equal (e.g. size, speed and

precipitation), cyclones following sinuous tracks pose a greater risk for several reasons.

Nat Hazards (2011) 59:1161–1174 1171

123

Author's personal copy

1172 Nat Hazards (2011) 59:1161–1174

123

Author's personal copy

They show some tendency for longer lifespans and higher intensity than storms that

migrate along straighter tracks. Also, cyclones with looping tracks may strike an island

nation more than once, as has been observed occasionally in the historical record. These

findings indicate that further scope exists for examining the physical influences on atypical

cyclone track shape, especially in the vicinity of island archipelagoes or immediately prior

to landfall. More generally, the evidence above also reinforces the need for improved

cyclone hazard education, better community preparedness and effective national disaster

response planning throughout the developing Pacific Islands.

Acknowledgments This work would not have been possible without the kind assistance of the FijiMeteorological Services. Rajendra Prasad and Simon McGree (former Director of FMS and Head of ClimateServices Division) in particular are thanked for their advice on many issues concerning historical obser-vations of cyclones in the South Pacific. The insightful comments of two anonymous referees are appre-ciated, as these enabled the original manuscript to be improved. Research funding from the Taiwan TradeMission to Fiji, the University of the South Pacific and the National University of Singapore is gratefullyacknowledged.

References

Barnett J, Ellemor H (2007) Niue after Cyclone Heta. Aust J Emerg Manag 22:3–4Buckley BW, Leslie LM, Speer MS (2003) The impact of observational technology on climate database

quality Tropical cyclones in the Tasman Sea. J Clim 16:2640–2645Camargo SJ, Robertson AW, Gaffney SJ, Smyth P, Ghil M (2007a) Cluster analysis of typhoon tracks: part

I: general properties. J Clim 20:3635–3653Camargo SJ, Robertson AW, Gaffney SJ, Smyth P, Ghil M (2007b) Cluster analysis of typhoon tracks: part

II: large-scale circulation and ENSO. J Clim 20:3654–3676Camargo SJ, Robertson AW, Barnston AG, Ghil M (2008) Clustering of eastern North Pacific tropical

cyclone tracks: ENSO and MJO effects. Geochem Geophys Geosyst 9:Q06V05. doi:10.1029/2007GC001861

Chand SS, Walsh KJE (2009) Tropical cyclone activity in the Fiji region: spatial patterns and relationship tolarge-scale circulation. J Clim 22:3877–3893

Chu P-S, Zhao X, Ho C-H, Kim H-S, Lu M-M, Kim J-H (2010) Bayesian forecasting of seasonal typhoonactivity: a track-pattern-oriented categorization approach. J Clim 23:6654–6668. doi:10.1175/2010JCLI37101

Table 4 Numbers (and percentages) of cyclone tracks in four sinuosity categories, arranged by 10� lon-gitudinal zones of cyclogenesis origin

Sinuosity category Cyclone origin

150�–160�E 160�–170�E 170�E–180� 180�–170�W 170�–160�W 160�–150�W

Straight 11 (31) 12 (19) 17 (27) 14 (27) 10 (33) 4 (22)

Quasi-straight 9 (25) 15 (23) 14 (22) 13 (25) 5 (17) 6 (33)

Curving 6 (17) 11 (17) 18 (28) 19 (37) 10 (33) 5 (28)

Sinuous 10 (28) 26 (41) 15 (23) 6 (12) 5 (17) 3 (17)

Total no. of cyclones 36 (100) 64 (100) 64 (100) 52 (100) 30 (100) 18 (100)

1. Data for 1970–2008; 2. n = 264; 3. Zones 140�–150�E, 150�–140�W and 140�–130�W are omitted due tolow cyclone counts (i.e. \10)

Fig. 6 Tropical cyclone track maps for 1970–2008, plotted according to four quartile sinuosity categories:a straight, b quasi-straight, c curving, d sinuous. Note: track sinuosity within the tropical South Pacific (TSP)is determined from either whole or partial tracks lying north of 25�S (see text)

b

Nat Hazards (2011) 59:1161–1174 1173

123

Author's personal copy

De Smith M, Goodchild M, Longley P (2007) Geospatial analysis, 2nd edn. Troubador, Leicester, UKDeMers MN (2008) Fundamentals of geographical information systems, 4th edn. Wiley, New YorkDengler K (1997) A numerical study of the effects of land proximity and changes in sea surface temperature

on hurricane tracks. Q J Royal Meteorol Soc 123:1307–1321Elsner JB, Liu KB (2003) Examining the ENSO-typhoon hypothesis. Clim Res 25:43–54Elsner JB, Kossin JP, Jagger TH (2008) The increasing intensity of the strongest tropical cyclones. Nature

455:92–95Emanuel K (2004) Response of tropical cyclone activity to climate change: theoretical basis. In: Murnane

RJ, Liu K-B (eds) Hurricanes and typhoons: past present and future. Columbia University Press, NewYork, pp 395–407

FMS (1997) Fiji Meteorological Services. In: Tropical cyclone damages in Fiji (from 1939/40–96/97).Information sheet no. 123, Climate Services Division, Nadi Airport, Fiji

Fraedrich K, Leslie LM (1989) Estimates of cyclone track predictability I: tropical cyclones in the Aus-tralian region. Q J Royal Meteorol Soc 115:79–92

Harr PA, Elsberry RL (1995) Large-scale circulation variability over the tropical western north Pacific partI: spatial patterns and tropical cyclone characteristics. Mon Weather Rev 123:1225–1246

Ho CH, Baik JJ, Kim JH, Gong DY, Sui CH (2004) Interdecadal changes in summertime typhoon tracks.J Clim 17:1767–1776

Kim H-M, Webster PJ, Curry JA (2010a) Modulation of north Pacific tropical cyclone activity by threephases of ENSO. J Clim 24:1839–1849. doi:10.1175/2010JCLI3939.1

Kim H-S, Kim J-H, Ho C-H, Chu P-S (2010b) Pattern classification of typhoon tracks using fuzzy c-meansclustering method. J Clim 24:488–508. doi:10.1175/2010JCLI3751.1

Knutson TR, Tuleya RE (2008) Tropical cyclones and climate change: revisiting recent studies at GFDL. In:Diaz HF, Murnane RJ (eds) Climate extremes and society. Cambridge University Press, UK,pp 120–143

Kossin JP, Camargo SJ, Sitkowski M (2010) Climate modulation of north Atlantic hurricane tracks. J Clim23:3057–3076

Kottegoda NT, Rosso R (1997) Statistics probability and reliability methods for civil and environmentalengineers. McGraw-Hill, New York

Kuleshov Y, Fawcett R, Qi L, Trewin B, Jones D, McBride J, Ramsay H (2010) Trends in tropical cyclonesin the south Indian Ocean and south Pacific Ocean. J Geophys Res 115:D01101. doi:10.1029/2009JD012372

Lander MA (1996) Specific tropical cyclone track types and unusual tropical cyclone motions associatedwith a reverse-oriented monsoon trough in the western north Pacific. Weather Forecast 11:170–186

Nakamura J, Lall U, Kushnir Y, Camargo SJ (2009) Classifying north Atlantic tropical cyclone tracks bytheir mass moments. J Clim 22:5481–5494

Nicholls N, Landsea C, Gill J (1998) Recent trends in Australian region tropical cyclone activity. MeteorolAtmospheric Phys 65:197–205

Osborne JW (2002a) Normalizing data transformations. ERIC digest (ERIC No. ED470204). ERIC clear-inghouse on assessment and evaluation, College Park, MD

Osborne JW (2002b) Notes on the use of data transformations. Pract Assess Res Eval 8(6)Raucher RS (2000) Economic implications of climate change in two Pacific Island country locations. Case

illustration of Tarawa, Kiribati and Viti Levu. Report prepared under sub-contract to the Centre forInternational Climate and Environmental Research, Oslo, Norway for the World Bank, Stratus Con-sulting, Boulder, Colorado, December, 16 chapters individually paginated

Rosenshein L, Scott L, Pratt M (2011) Finding a meaningful model. ArcUser, Winter 2011: 40–45. Accessedfrom http://www.esri.com/news/arcuser/0111/files/findmodel.pdf

Solow A, Nicholls N (1990) The relationship between the southern oscillation and tropical cyclone fre-quency in the Australian region. Journal Clim 3:1097–1101

Steiner JT (1980) The climate of the south-west Pacific region. A review for pilots. New Zealand Meteo-rological Service, Miscellaneous Publication no. 166, Wellington

Terry JP (2007) Tropical Cyclones: Climatology and Impacts in the South Pacific. Springer, New York,p 210

Terry JP, Feng CC (2010) On quantifying the sinuosity of typhoon tracks in the western north Pacific basin.Appl Geogr 30:678–686

Terry JP, Gienko G (2010) Climatological aspects of south Pacific tropical cyclones, based on analysis of theRSMC-Nadi (Fiji) regional archive. Clim Res 42:223–233

Walsh KJE (2004) Tropical cyclones and climate change: unresolved issues. Clim Res 27:77–83Webster PJ, Holland GL, Curry JA, Chang H-R (2005) Changes in tropical cyclone number, duration, and

intensity in a warming environment. Science 309:1844–1846

1174 Nat Hazards (2011) 59:1161–1174

123

Author's personal copy