International Journal of Geosciences, 2010, 1, 121-129
doi:10.4236/ijg.2010.13016 Published Online November 2010 (
Copyright © 2010 SciRes. IJG
Kernel Density Estimation of Tropical Cyclone Frequencies
in the North Atlantic Basin
Timothy A. Joyner, Robert V. Rohli
Department of Geography and Anthropology, Louisiana State University, Baton Rouge, USA
Received August 31, 2010; revised September 13, 2010; accepted Se pt em ber 30, 2010
Previous research has identified specific areas of frequent tropical cyclone activity in the North Atlantic ba-
sin. This study examines long-term and decadal spatio-temporal patterns of Atlantic tropical cyclone fre-
quencies from 1944 to 2009, and analyzes categorical and decadal centroid patterns using kernel density es-
timation (KDE) and centrographic statistics. Results corroborate previous research which has suggested that
the Bermuda-Azores anticyclone plays an integral role in the direction of tropical cyclone tracks. Other tele-
connections such as the North Atlantic Oscillation (NAO) may also have an impact on tropical cyclone
tracks, but at a different temporal resolution. Results expand on existing knowledge of the spatial trends of
tropical cyclones based on storm category and time through the use of spatial statistics. Overall, location of
peak frequency varies by tropical cyclone category, with stronger storms being more concentrated in narrow
regions of the southern Caribbean Sea and Gulf of Mexico, while weaker storms occur in a much larger area
that encompasses much of the Caribbean Sea, Gulf of Mexico, and Atlantic Ocean off of the east coast of the
United States. Additionally, the decadal centroids of tropical cyclone tracks have oscillated over a large area
of the Atlantic Ocean for much of recorded history. Data collected since 1944 can be analyzed confidently to
reveal these patterns.
Keywords: Atlantic Tropical Cyclone Frequencies, Decadal Centroid Patterns, Kernel Density Estimation
(KDE), Centrographic Statistics, Bermuda-Azores Anticyclone, Teleconnections
1. Introduction
Tropical cyclones are a major environmental hazard for
the southeastern United States. Approximately 12 per-
cent of the world’s tropical cyclones form in the north
Atlantic/Caribbean/Gulf of Mexico basin, with about 23
percent of those striking the U.S.A. [1,2]. As coastal de-
velopment continues to increase in the southeastern
U.S.A. and elsewhere, it is increasingly important to im-
prove our understanding of the spatial patterns and tem-
poral trends of tropical cyclone tracks and landfalls to aid
environmental planners and risk assessors in minimizing
the loss of lives and property.
This study has two main objectives: 1) to identify the
spatial distribution of North Atlantic basin tropical cy-
clones by category based on a kernel density estimation
(KDE) approach that utilizes the Fotheringham et al. [3]
smoothing algorithm; and 2) to identify th e inter-decadal
movement of tropical cyclones through the period of
record based on decadal centroids found through the use
of centrographic statistics.
2. Background
Keim et al. [4] found that the shortest return periods for
tropical cyclones occurred in three specific areas of the
U.S.A.: the north central Gulf of Mexico coast, the Flor-
ida Atlantic coast, and the North Carolina coast around
the Outer Banks. This and other research [5,6] suggests
that multiple broad-scale controlling mechanisms dictate
the spatio-temporal patterns of tropical cyclone tracks
and landfalls at intra-seasonal to millennial time scales.
While some studies [4,7-9] attribute variability in the
spatial pattern of twentieth century return periods along
the Gulf-Atlantic coast to the North Atlantic Oscillation
(NAO), other research [8-10] suggests that the Ber-
muda-Azores high alone plays a stronger role in regulat-
ing Atlantic basin tropical cyclone tracks and landfalls at
broader time scales.
The NAO indirectly affects the spatial patterns of
tropical cyclones based on the positioning of the Ber-
muda-Azores high [4,11]. A positive NAO index occurs
when the Bermuda-Azores high is stronger than normal
and displaced to the north and east of the mean position
and mid-tropospheric winds over the Atlantic are from
generally west to east. A negative NAO index occurs
when the Bermuda-Azores high is weaker than normal
and displaced to the south and west, with anomalous
mid-tropospheric ridging and troughing and weak circu-
lation over the Atlantic. During a negative NAO index
period, tropical cyclones track in a more westward direc-
tion and usually resist the normal curve to the northwest
The “Bermuda-Azores high hypothesis” [5,12] alludes
to an increase in tropical cyclone landfall frequency on
the Gulf coast when the Bermuda-Azores anticyclone is
in a more southwesterly location than usual and the NAO
index is negative. Similarly, an increase in tropical cy-
clone landfall frequency on the Atlantic coast occurs when
the Bermuda-Azores anticyclone is displaced northeast-
ward and the NAO index is positive. During times of a
strong Bermuda-Azores anticyclone, tropical cyclones
have been shown to be more affected by its steering
mechanisms, while the opposite is true of periods with a
weak Bermuda-Azores anticyclone [9], with its migra-
tion being a strong indicator of track and landfall loca-
tion at the annual, decadal, and multi-decadal time scales
Two other modulators of Atlantic tropical cyclone
frequency have been widely recognized in the literature:
the El Niño/Southern Oscillation (ENSO) [11,1 3] and the
Atlantic Multi-decadal Oscillation (AMO) [9,14]. Bove
et al. [13] concluded that El Niño (La Niña) events are
associated with a reduction (increase) in the probability
of U.S.A. landfalling tropical cyclones. The decrease in
tropical cyclone frequencies during El Niño events has
been attributed to the anomalously strong tropical up-
per-tropospheric westerlies that tend to shear the top s off
of developing tropical cyclones [15]. However, evidence
of ENSO’s influence on tropical cyclone tracks is weak
[11]. The AMO involves long-term variability in the spa-
tial extent of above- and below-normal sea surface tem-
peratures (SSTs) in the north Atlantic Ocean but its role
in affecting the tracking of tropical cyclones is unknown
[16]. SSTs alone also play a more critical role in the de-
velopment rather than the track of tropical cyclones [17,
The co mparison of cu rrent tracks with historic tenden-
cies is often made to address questions on the forcing
mechanisms that allow for tropical cyclone formation
and development. For example, Knowles and Leitner [12]
used visualization techniques to identify the spatial rela-
tionship between historic tropical cyclone tracks and
intensity of th e Bermuda -Azores anticyclone. Bossak and
Elsner [19] used historical tropical cyclone documenta-
tion from the early nineteenth century in conjunction
with the NOAA best- track dataset, which begins in 1851,
to estimate the track and intensity of storms from the
pre-1851 period [20]. Other research [21] using known
historical tracks is being conducted to reanalyze that
dataset to reduce the perceived errors noted by numerous
manuscripts [22,23].
Because systematic aircraft reconnaissance began to
monitor tropical cyclones and disturbances that had the
potential to develop into tropical cyclones only since
1944, a potential discontinuity exists in the ability to
detect and record tropical cyclone frequency, features,
and tracks. Therefore, Neumann et al. [24] and Landsea
[25] suggested that only data recorded since 1944 should
be used for climatological analysis. Conversely, some
researchers [23,26] have chosen to use the frequency
data but disregard the documented intensities in the
pre-1944 period because of perceived inaccuracies.
After completion of a reanalysis of the historical hurri-
cane dataset [21], it may be beneficial to reevaluate the
pre-1944 record of the best-track dataset, but for the
purposes of our study we have chosen to include only
post-1944 data.
Geographic Information Systems (GIS) have become
the common platform for displaying and analyzing
tropical cyclone data [11,12]. Th e use of spatial statistics
is also gaining in popularity [12,27]. Centrographic sta-
tistics (e.g., mean center, median center, standard dis-
tance) estimate basic parameters of the spatial distribu-
tion of a set of points in space [28,29]. These indices can
be used to describe spatial and temporal patterns in
tropical cyclones, but their use in the literature is limited
to date. More often, centrographic statistics are used to
describe other patterns of spatial distribution, such as the
movement of crime [30,31]. McGregor [27] used 20-year
standard deviational ellipses to analyze the spatial and
temporal characteristics of tropical cyclo nes in the South
China Sea while Knowles and Leitner [12] used KDE to
examine tropical cyclone patterns in the Atlantic basin
related to the Bermuda-Azores high. For kernel density
estimation a symmetrical kernel function is placed on an
underlying, smooth continuous surface. Each point on
the surface is given an equal weight with the weight de-
creasing with increasing distance away from the point.
The density distribution is then estimated by summating
the kernels at each location, thus producing a smooth
density surface [32].
Previous research has noted the inherent problem
concerning bandwidth (bin sizes) for KDE [3]. Fother-
ingham et al. [3] suggested a conservative approach that
oversmooths to some extent, but according to the ap-
Copyright © 2010 SciRes. IJG
proach any maxima observed in the estimated density
curves are more likely to be real rather than a product of
undersmoothing. Knowles and Leitner [12] showed that
KDE, when performed correctly, can be a useful tool for
identifying areas of high tropical cyclone intensity and
that KDE output is easily interpreted.
3. Data and Methods
3.1. Tropical Cyclone Data
A spatial database was created based on tropical cyclone
position records from 1851-2009 obtained from the Na-
tional Oceanic and Atmospheric Administration (NOAA)
Coastal Services Center [33]. The database contains the
storm category, latitude, longitude, and wind speed for
each six-hour interval that each tropical cyclone existed.
From the original database containing records from
1851-2009, a second database was established for this
study that excluded all pre-1944 data. Any storm below
hurricane strength (following the Saffir-Simpson classi-
fication – Table 1) was excluded; thereby minimizing
the problems associated with uneven detection capabili-
ties over the study period.
The dataset presented two different types of shapefiles
that could be used for spatial analysis: tropical cyclone
tracks (line data) and tropical cyclone 6-hour interval
locations (point data). Th e 6-hour interval locations (also
recognized as observation points) were selected, so that a
slower-moving tropical cyclone would receive a higher
density because of the higher number of observation
points recorded, and vice versa for a faster-moving sys-
tem. This approach is reasonable because the duration of
time that the forcing mechanisms favor the tropical cy-
clone’s existence is proportional to the representation in
the KDE analysis.
3.2. Methods of Spatial Analysis
ArcMap 9.2 [34] was used to display tropical cyclone
locations, centrographic statistics, and KDEs. Tropical
cyclones were separated into five categories (as desig-
nated by the Saffir-Simpson scale) using the symbology
tool. Centrographic statistics and KDEs were calculated
using CrimeStat III [32], but the output was also added to
ArcMap for visual display purposes.
Table 1. The Saffir Simpson Scale showing the wind speed
related to each category of tropical cyclone.
Classification Category 1 Category 2Category 3 Category 4Category 5
Wind Speeds
(mph) 74-95 96-110 111-130 131-155155+
Wind Speeds
(km/h) 119-153 154-177178-209 210-249250+
CrimeStat III was used to calculate the KDE of each
category of tropical cyclone from 1944-2009. A square
grid surface was created as a reference file for the area to
be modeled, with the lower left bounding coordinates at
(99.5°W, 7.5°N) and upper right bounding coordinates at
(4.25°W, 62.5°N). A normal method of interpolation
with a fixed interval bandwidth was selected. The band-
width (interval) was created using the following equation
described by Fotheringham et al. [3]:
hopt = [2/3n]1/4
where hopt is the optimal bandwidth, n is the number of
observations (or tropical cyclones), and is the standard
distance deviation for each category (found from centro-
graphic statistics computed earlier). The interval and area
units were set to kilometers and the output units are re-
ported in absolute densities.
CrimeStat III was also used to compute the centro-
graphic statistics, including mean center [30,35], median
center [36,37], minimum distance [38,39], and standard
deviational ellipse [31,40], for each decade from 1944-
2009. The mean center is the simplest descriptor of dis-
tribution and describes the mean of the X and Y coordi-
nates [41]. The median center is the intersection between
the median of the X and Y coordinates. This creates mul-
tiple points where lines intersect and thus produces an
area of non-uniqueness in which any part of the area be-
tween the lines could be considered the median center
[32]. The minimum distance defines the point at which
the sum of the distance to all other points in a distribu-
tion is minimized [41]. The standard deviational ellipse
describes dispersion in two dimensions by finding the
standard deviations in the X and Y directions that define
an ellipse [28]. The standard deviational ellipse shows
where the majority of points exist as well as the direc-
tional trend of those points. Standard distance deviation
was also computed for each category of hurricane for
calculating bandwidth for KDEs. Standard distance de-
viation is the standard deviation of the actual distance of
each point from the mean center and it provides a single
summary statistic in kilometers [32].
4. Results and Discussion
A plot of the longitude and latitude coordinates of all
tropical cyclone observation points in the dataset by Saf-
fir-Simpson category reveals the more southerly loca-
tions of major (Category 3 or greater) tropical cyclones
(Figure 1). Major tropical cyclones tend to be located in
a narrow part of the Atlantic Ocean east of the Bahamas
and slightly north of Puerto Rico, in the Caribbean Sea,
and in the central Gulf of Mexico.
The KDEs of all tropical cyclones are illustrated in
Figure 2(a). While tropical cyclones have struck the
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Copyright © 2010 SciRes. IJG
entire Gulf-Atlantic coast of the U.S.A., the most fre-
quent areas of occurrence were in two zones: the north-
ern Caribbean Sea/southern Gulf of Mexico, and the At-
lantic coast from the sou thern tip of Florida to Cape Hat-
teras extending out to the Lesser Antilles and Bermuda.
Figure 2(b) displays the KDE of Category 1 storms,
which tend to occur in two locations of high density in
similar areas of the Atlantic Ocean as most other storms
combined from Figure 2(a). However, another area of
high density occurs in the western region of the Gulf of
Mexico south of Texas. Category 2 storms (Figure 2(c))
show relatively high density stretching from the western
tip of Cuba, across south Florida, and in a large section
of the Atlantic Ocean along the Atlantic seaboard and out
to Bermuda. Category 3 storms show a comparatively
large area of high density (Figure 2(d)) in an oval pat-
tern from the southeastern Gulf of Mexico to an area
north of the Lesser Antilles. The KDE of Category 4
storms assumes more of a flattened oval pattern and is
located slightly farther south of Category 2 and 3 storms,
but also farther west into the central and northern Gulf of
Mexico (Figure 2(e)). Overall, category 4 storms occur
predominantly east of the Yucatan peninsula in the Car-
ibbean Sea and in an area of the Atlantic Ocean south
and east of the Bahamas. Category 5 storms (Figure 2(f))
are concentrated in two main areas: the southern Carib-
bean Sea and adjacent central Gulf of Mexico, and the
Atlantic Ocean east of the Bahamas.
The KDEs showed similarities for each category of
tropical cyclone, with the highest densities concentrated
in the Atlantic Ocean between the eastern U.S.A., Ber-
muda, Haiti, and parts of the Gulf of Mexico (Figure 2).
Higher SSTs are most likely the main factor for the
southward shift in tropical cyclone densities for stronger
category tropical cyclones [17]. The highest densities of
category 4 and 5 storms were concentrated in the Carib-
bean Sea and Gulf of Mexico. These areas retain high
SSTs longer in the tropical cyclone season.
Some unexpected contrasts in tropical cyclone location
by category were observed. A small area in the western
Gulf of Mexico along the U.S.A./Mexican border
showed a high density of category 1, 4 and 5 storms, but
category 2 storms were almost non-existent in this same
area. Some category 4 storms showed a propensity to
venture northward toward the Outer Banks of North
Carolina, but the densities of category 5 storms tapered
off dramatically north of approximately 30°N latitude.
Most of the observed tropical cyclone densities corrobo-
rate previous research [12,16], but the KDE approach
helps to highlight often overlooked disparities such as
the peculiar absence of category 2 storms in the western
Gulf of Mex i co.
Figure 1. Location of all tropical cyclone observation points since 1944.
Figure 2. KDE’s of all tropical cyclones (a), category 1 (b), category 2 (c), category 3 (d), category 4 (e), and category 5 (f).
The ability to define a bandwidth for the KDE ap-
proach aided greatly in accurately identifying density
centers for each category of tropical cyclone and the
method provided a reasonable measure of comparison
across categories. Fotheringham et al. [3] described sev-
eral methods of determining bandwidth for kernel den-
sity procedures. The chosen formula created an optimum
bandwidth that used the standard distance deviation for
Copyright © 2010 SciRes. IJG
each category to find an outcome that sought to balance
the two primary concerns of oversmoothing and overfit-
ting. Elsner and Jagger [42] examined tropical cyclone
frequencies using Bayesian modeling in an effort to pre-
dict future tropical cyclone frequencies by using a band-
width calculation formula from Venables and Ripley [43].
The formula took a similar approach to the bandwidth
problem by disregarding insignificant peaks, while still
highlighting actual peaks that may help to relate tropical
cyclone frequencies with certain teleconnection indices.
Multiple centrography statistics (e.g., mean center,
median center, mean distance, and standard deviational
ellipse) that describe the decadal spatial patterns of all
tropical cyclones since 1944 were calculated and exam-
ined (Figures 3(a-g)). The centrographic patterns for 1944-
1953 (Figure 3(a)) and for 1954-1963 (Figure 3(b)) reveal
a spatial distribution cen tered to the east of the Bahamas
with a slight movement eastward in the 1954-1963 dec-
ade. Centrographic patterns for 1964-1973 (Figure 3(c))
and for 1974-1983 (Figure 3(d)) show a better-defined
SW to NE pattern as depicted by the standard deviational
ellipse with the spatial distribution centered to the south
(1964-1973) and southeast (1974-1983) of Bermuda.
Figures 3(e) and 3(f) illustrate the centrograp hic patterns
for 1984-1993 and 1994-2003, respectively. The direc-
tional pattern became less defined in these two decades
and a slight shift southward occurred in the 1994-2003
decade. Centrographic patterns for the last few years
(2004-2009, Figure 3(g)) suggest a shift toward the
south and west closer to the Bahamas. A slight direc-
tional trend (WSW to ENE) also emerged.
Figure 3. Multiple centrographic statistics describing decadal spatial patterns: 1944-1953 (a), 1954-1963 (b), 1964-1973 (c),
1974-1983 (d), 1984-1993 (e), 1994-2003 (f), 2004-2009 (g).
Copyright © 2010 SciRes. IJG
Copyright © 2010 SciRes. IJG
All of the centrographic statistics (mean center, me-
dian center, and minimum distance) were concentrated in
the same general area for each decade (Figure 3), thus
increasing our confidence in analyzing the decadal cen-
troid patterns of tropical cyclone tracks. Of the three
measures of centrography, the mean center statistic was
selected because it calculates the mean distribution, or
central tendency, of all X and Y tropical cyclone coordi-
nates occurring in each decade and is the most widely
used centrographic statistic [30,35,44]. A temporal
analysis of decadal mean centers (centroids) of tropical
cyclones since the 1940s reveals a trend toward the east
until the 1980s, when the pattern shifted back toward a
more westward and southward displacement (Figure 4).
Previous research has indicated that shifting tropical
cyclone patterns are often the result of influential tele-
connections – most specifically the NAO and Ber
muda-Azores high [9,16]. The temporal trends of decadal
centroids are likely representative of the location and
strength of the Bermuda-Azores high. It could be in-
ferred from Figure 4 that the Bermuda-Azores high, on
average, shifted to the east in the 1940s, 1950s, 1960s,
and 1970s, but then began to shift back to the west in the
1980s, 1990s, and 2000s. This oscillation trend can also
often be seen by examining landfall frequencies over
time [4]. More research is needed to examine the precise
degree of influence of the Bermuda-Azores high on a
seasonal/annual basis. This relationship may be unclear,
however, because the frequency of tropical cyclones can
be influenced by multiple factors. Further research
should explore centroids created from different time pe-
riods such as five-year periods or different end points
such as ten-year periods that begin in 1949 instead of
1944. Such work may highlight inter-decadal trends and
confirm that multi-annual spatial patterns may occur
most likely in relationship to NAO and the Bermuda-
Azores high [11].
Decadal centroids found in this study seem to contra-
dict tropical cyclone landfall patterns identified by Elsner
et al. [9], who found that more tropical cyclones made
landfall on the Atlantic coast of the U.S.A. in the 1950s,
1980s, and 1990s, while an increased percentage of
tropical cyclones made landfall on the Gulf coast of the
U.S.A. in the 1960s and 1970s. This seems to suggest
that the centroid for 1955-1964 (i.e., 1964 in Figure 4)
and for 1965-19 74 (i.e., 1974 in Figure 4) should be the
Figure 4. Decadal centroids of all tropical cyclones since 1944 with each labeled year representing the first year of the 10 year
period (e.g., 1944 means 1944-1953, etc.). Note: centroid for 2004 only covers 6-year period (2004-2009).
Copyright © 2010 SciRes. IJG
westernmost centroids instead of two of the easternmost
centroids. The contradiction is likely the result of multi-
ple factors. The main factor is probably related to the
longitude where the tropical cyclones formed each dec-
ade [9]. Tropical cyclones that formed in the Caribbean
Sea and Gulf of Mexico were probably less affected by
the position of the Bermuda-Azores high whereas tropi-
cal cyclones that formed in the central and eastern Atlan-
tic were probably influenced more by the Bermuda-
Azores high. A m ore sout h westerly Berm uda-Azo res hi g h
may have also caused Gulf tropical cyclones to curve
northward near the beginning of th eir life cycle resulting
in a more easterly located decadal centroid. The uncer-
tainty implies that more statistical methods must be em-
ployed to confirm current spatial trends and hypotheses
as well as to identify previously undetected spatial pat-
terns. This study may lead to more novel applications of
spatial statistics to reveal undiscovered tropical cyclone
5. Summary and Conclusions
Through the use of a smoothing bandwidth proposed by
Fotheringham et al. [3], kernel d ensity estimation (KDE)
identified areas of highest density of occurrence for each
category of tropical cyclone in the north Atlantic basin
from 1944 through 2009. Results confirmed previous
hurricane density assessments, but also found nuances in
location of densities for each storm category. Centro-
graphic statistics provided a new perspective on multi-
year spatial shifts of tropical cyclones, but the results
should be examined more thoroughly in future research
efforts to fully understand the reason(s) for these shifts.
The principal findings of th is study are as follows:
1) The highest tropical cyclone densities occurred in
the Atlantic Ocean between the eastern U.S.A., Bermuda,
and Haiti and parts of the Gulf of Mexico with stronger
storms (3+) concentrated in the Caribbean Sea, Gulf of
Mexico, and southern Atlantic Ocean.
2) An area in the Gulf of Mexico near the U.S.A./
Mexico border exhibited high densities of most storm
categories except category 2 storms.
3) The bandwidth calculations proposed by Fother-
ingham et al. [3] were useful in highlighting hurricane
4) Centrographic statistics identified decadal move-
ments of the center of gravity of hurricane tracks as well
as decadal changes in directional dispersion.
6. Acknowledgment
The authors would like to thank the reviewers for their
excellent editorial suggestions during the review of this
manuscript. Dr. Andrew Curtis and Gerardo Boquin were
helpful in the design and implementation of this study
and Dr. Jason Blackburn assisted in reviewing and mak-
ing suggestions for the geo-statistical components.
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