Atlas

1
Atlas of Probable Storm Effects in the
Caribbean Sea
Sponsored by the
Caribbean Disaster Mitigation Project
Models and data output by Watson Technical
Consulting, Inc. Editing and presentation by Ross
Wagenseil, Ph.D. March 2000
The Caribbean Disaster Mitigation Project (CDMP)
was a joint effort of the Organization of
American States (OAS) and the US Agency for
International Development (USAID) to promote the
adoption of natural disaster preparedness and
loss reduction practices by both the public and
private sectors The CDMP was started in 1993,
and was completed in 1999. During the course of
the project, country agencies responsible for
coastal planning and regional agencies such as
the Caribbean Institute for Meteorology and
Hydrology (CIMH) expressed concern with the lack
of data on the impact of tropical storms on
coastal areas. In response to these concerns, the
CDMP developed a regional storm hazard assessment
capacity, now installed at CIMH, and undertook a
comprehensive study to estimate the probable
storm effects throughout the Caribbean basin.
Link to the World Wide Web
or
Continue on this Disk
Caribbean Disaster Mitigation Project (CDMP)
Organization of American States (OAS)
US Agency for International Development (USAID)
2
To Navigate Through this Atlas,
there are hyperlinks on each
page.
On most pages you will see a button labeled
Return to Directory to take you directly to the
Directory and Table of Contents. That is a page
that links to all sections. You may also see
green buttons which allow you to go back or
forward in the slide sequence or to back-track to
the last slide viewed. These buttons are
restricted to a particular section. You may
click to the next slide right now to see the
Directory (with links to support materials), or
you may click on a key map, below, to pick a
region.
Return to Directory
Previous slide
Back-track to last slide viewed (within the
region)
Next slide
When you jump to a new region, you will see an
orientation map with a few place names. You will
also see a key pad like the one at left. Use
the key pad to jump to another map for your
current region. You can select by the probable
return time and by the phenomenon. For instance,
if you want to view the maps of wave heights with
probable return times of 10, 25, 50, and 100
years, just click along the second row, from left
to right. Once you have a map displayed, the
corresponding button on the keypad is orange.
(The keypad at left is not connected you will
have to pick a region first.)
To leave the Atlas, press the ESC key on your
computer. You may have to press it several times
to close all the sections.
Esc
3
Supporting Materials in this Atlas
Directory and Table of Contents
Includes a short note on the sponsoring project,
CDMP.
Title Page
Hyperlinks and graphical keys.
To Navigate Through This Atlas
Brief, for the generalist.
Introduction
For technical background.
Methodology of the Statistics
Examples of statistical and field validation.
Validation of the Model
Weaknesses in the input data show in several
specific ways.
Known Issues in the Input Data
The interaction of wind, waves, and surges.
A Short Review of Storm Effects
There are cartographic distortions in the maps,
but not the model.
Distortions of the Projection
Wind, wave, and surge have specific
meanings in this Atlas.
Definitions
Discussion of alternative wind durations and
altitudes.
Measures of Wind Speed
Supporting Materials on the World Wide Web
Links to the Maps
Caribbean Disaster Mitigation Project (CDMP)
Organization of American States (OAS)
TAOS Storm Hazard Modeling
Watson Technical Consulting, Inc.
TAOS Data Sources
Caribbean Institute of Meteorology and Hydrology
(CIMH)
US Agency for International Development (USAID)
US National Hurricane Center
4
Introduction page 1/3
This Atlas presents the Caribbean as it has never
been seen before. The maps in this Atlas show
potential storm phenomena which are most likely
to occur (Maximum Likelihood Estimates, or MLEs)
during specific durations of time. There are
three phenomena maximum winds, maximum wave
heights, and maximum storm surges. Each of the
three phenomena is shown for four return periods
10, 25, 50 and 100 years. There are twelve
regional sections of maps starting with views of
the Caribbean as a whole, windowing-in on three
main basins of the sea, and windowing even
further onto eight sub-regions with significant
land masses. Each of the regions includes a
simple orientation map, but the essence of the
Atlas is in the twelve maps which follow. This
could be a bewildering array of information, so
every effort has been made to help the user
explore without getting lost. The maps are
color-coded, and it takes no more than two
hyperlinks to go from one map to any other in the
Atlas.
The maps do not show what exists, but what might
exist. Indeed, the concept is even more
restricted than that, since the phenomena shown
on a single map could not possibly exist at a
single point in time. The figure at right is an
example. It shows the magnitude of storm surge
most likely to occur once in 50 years, on a
long-term average, over the East Basin of the
Caribbean. In any one location, there is only a
2 chance of such a large surge occurring in any
single year, and there is a 64 chance that the
value could be exceeded in any particular period
of 50 years. Most important, it is impossible for
all these values to happen at the same time
because the sea water must be borrowed from one
area to surge up in another.
Hurricane Historical Records In that sense, the
map is not a continuous field but an array of
points. Each of these points got its value from
mathematical manipulation of the historical
record kept by the US National Hurricane Center.
The historical record includes 973 tropical
cyclones (tropical storms and hurricanes), over
the 114 years from 1885 to 1998, inclusive.
What makes the maps coherent is that the
historical record was processed by an advanced
numerical model, TAOS (The Arbiter of Storms),
which applied basic equations of physics to a
digital, three-dimensional topographic map. For
the map above, TAOS calculated the surge that
each one of those 973 storms would have caused at
each location. This required mapping the storms
as they passed, calculating the resultant winds
and pressure, and calculating the fluid dynamics
of the sea water as it flowed around the coasts
and over the depths of a three-dimensional model
of the Caribbean until it reached the location in
question.
Probability that the 50 year return value will
be exceeded at least once in a 50-year period P
1-(1-1/T)N. With T50 and N50, P 0.63583
Return to Directory
5
Introduction page 2/3
Once all the storms had been modeled for a point,
the maximum for each year was selected. That
gave 114 maxima, to which a smooth curve was
fitted. That curve was taken as the probability
density function of surge for the single point.
The 2 cumulative probability was taken as the
Maximum Likelihood Estimate (MLE) for the surge
with a 50-year return time at that location, and
the corresponding surge value was mapped for the
location. Each point on the map was calculated
individually in this way.
Marilyn, 1995
And yet the points do fit together. Anyone who
has followed storm reports during the hurricane
season in the Caribbean has developed an
intuition for what is likely to develop. There
is a pattern. Recognizing Patterns Hurricane
Marilyn and Hurricane Gilbert are examples.
Although they were not predictable, they were
both, in some way, typical. The maps of this
Atlas show that they both moved through areas of
high probability a southern pathway over Jamaica
and a pathway curving north of Puerto Rico. The
model calculated the pattern by applying the laws
of physics to the reefs and islands of the
topographic map.
Gilbert, 1988
Click for enlargement
Both Marilyn and Gilbert started in the Western
Atlantic and passed just north of Barbados. This
pathway is sometimes referred to as hurricane
alley. The hurricane alley is far enough south
for the sea water to have warmed to 27C, a
critical temperature that sustains convective
clouds which move along with the trade winds. The
alley is also far enough north for a strong
Coriolis effect, and it is far enough west for
the Coriolis effect to have had time enough to
twist convective clouds, moving with the trade
winds, into circular storm systems. These storm
systems are tropical cyclones, and the strongest
of them, in the Caribbean, are the hurricanes.
This part of the pattern is already
well-known. The Atlas shows other parts of the
pattern, some of which are less-known or only
guessed at up until now. For instance, there is
a distinct shadow to the west and north of the
Greater Antilles. This is not a result of
decreased activity or changes to the steering
patterns directing the tropical cyclones. A
review of the track maps indicates that there are
as many tropical cyclones moving over the Greater
Antilles as there are to the immediate north and
south. What decreases is not the frequency of
the storms but their intensity. This is due to
several related factors 1. Air circulation at
the low and middle levels is disrupted by the
extensive mountains of Hispaniola and Cuba. 2.
Surface humidities decrease slightly under the
larger air mass. 3. Direct evaporation from the
sea is cut off while the convective core of the
storm is over land.
Return to Directory
6
Introduction page 3/3
Most of the islands do not disrupt storms very
much, because the islands are smaller than the
core circulation of a tropical cyclone. Jamaica
and Puerto Rico are almost big enough to disrupt
a storm. In fact, Jamaica does affect storms
moving from south to north, but such storms are
much rarer than storms arriving from the east and
this barely shows on the probability maps. As
storms move over Hispañola, however, they begin
to break up and they cannot recover until they
pass Cuba. By far the prevailing direction of
motion of storms in the Caribbean is from
east-southeast to west-northwest, but some
storms such as Marilyn move on a track closer to
southeast-northwest, depending on upper-level
winds and frontal systems in the Temperate Zone.
Thus, the shadow of the Greater Antilles is a
complex interaction of the increase in intensity
from south to north, the disruptive effect of the
largest islands, and the interaction of tropical
cyclones with the Easterlies above 20 degrees
north latitude. The effect is subtle and complex,
but it is real. The Atlas shows the probable
results of all these factors together. Interpreta
tion of Maps These maps are not designed to be
queried out of context, on a cell-by-cell basis.
Doing so would create a false impression of
accuracy which cannot be delivered from the input
data available at this time. The input
topographic data has a nominal resolution of 30
arc-seconds (slightly less that 1 kilometer), but
in some areas the data are from coarser datasets.
Site-specific accuracy can only be obtained from
an analysis at a much higher resolution (in the
range of 3 arc-seconds), which requires a
significant investment in high-resolution
bathymetry and elevation data. CDMP has done
several high-resolution studies with good
success. Evaluation of these studies shows that
the results are consistent with the results
obtained in this Atlas. On the other hand, some
of the patterns in the Atlas are poorly
understood, and site-specific studies may help to
investigate these effects. Hurricane Marilyn and
Hurricane Gilbert caused substantial damage and
they are fresh in memory, but it has been
difficult to know how soon such storms would come
again. It has been difficult to gauge the risk,
to plan for the next emergency. The information
contained in this Atlas enables emergency
managers and physical planners to better
understand the probability of occurrence of
winds, waves, and surges associated with tropical
cyclones. Areas of higher risk from one or more
of these hazards may require specific development
policies or building standards. Emergency
management plans will need to pay special
attention to settled areas or critical
infrastructure located in areas of high risk.
The definition of MLE used in this study is
consistent with the definition commonly used in
building codes such as the ASCE-7. MLE values
can thus be used in the formulas suggested in the
codes. Since the MLE values corresponding to a
given return period can easily be exceeded during
that period (the 50-year return wind speed has a
64 probability of being exceeded), higher
estimates, corresponding to more stringent
prediction limits (75, 90 or 95), may be
called for when planning or designing facilities
that need to withstand even the most unlikely
events. These estimates can be produced for given
locations by the CIMH.
Return to Directory
Wind Loading Standards produced by the American
Society of Civil Engineers
7
Statistical Methodology Page 1/3
Slight variations in storm track can make large
differences in the effects a storm has on one
area. For any given location, a hurricane
passing fifty miles away may cause the same winds
as a moderate tropical storm passing right
overhead. For each grid cell in the study area,
the TAOS model was used to calculate wind effects
for each storm in the tropical cyclone database
(973 events in the Atlantic as of December 1998)
on that location. We then used the output to
perform a maximum-likelihood-analysis to generate
the optimal estimates of parameters for a
two-parameter Weibull model. The two-parameter
Weibull distribution has the cumulative
distribution function (cdf)
And the probability density function (pdf)
where xgt0 is the magnitude of the event, ?
is the shape parameter, ? is the scale
parameter.
Return to Directory
This distribution is positive, right skewed,
unimodal and flexible enough to accommodate
distribution shapes encountered in this project.
If the shape parameter ? is unity (1), then the
curve is a simple exponential, with the highest
probability density at zero. That would imply
that most years have no wind or storm surge at
all. If ? is higher than one, then there is a
mode at some value above zero. Either way, there
are more low values than high ones, but high
values are possible. The shape parameter and the
scale parameter can both be estimated from data
using the method of maximum likelihood. The
maximum likelihood estimators of the two
parameters are approximately bivariate normally
distributed with mean vector (?, ?) and
covariance provided by the observed Fisher
information matrix.
8
Statistical Methodology Page 2/3
The maximum likelihood estimator of the return
period wind is obtained by inverting the
distribution function at the appropriate
percentile
Where 90th percentile implies 10 year return
period wind speed, 96th percentile implies 25
year return period wind speed, 98th percentile
implies 50 year return period wind speed, 99th
percentile implies 100 year return period wind
speed.
To obtain simulated confidence limits, we
generate realizations of (?, ?) according to its
asymptotic distribution, compute the
corresponding return period wind speed, and then
sort the values to extract suitable limits
reflecting the uncertainty in estimation.
General principles of maximum likelihood
estimation can be found in standard graduate
mathematical statistics books. The simulation
process is straightforward (Johnson, Multivariate
Statistical Simulation, Wiley, 1987). In brief
1. The annual maxima are treated in the fitting
process as independent and identically
distributed variates. Extensive consideration of
lag correlations reveals little regularity in
cycles relative to noise. 2. The
two-parameter Weibull distribution is used for
annual maxima. Consideration of potential
competing lognormal and inverse Gaussian
distributions revealed the relative superiority
of the Weibull distribution. Goodness-of-fit
tests applied throughout the Atlantic Basin (over
600,000 locations) demonstrated the adequacy of
the Weibull distribution. 3. In terms of data
quality, many sensitivity analyses have been
conducted to support the use of the full
1886-present data set. Supposed difficulties
with the older events are not reflected in
analyses with various subsets of the data.
Hence, there appears to be no gain for dropping
pre-1950 data. 4. Our analyses are not
dominated by the single most extreme event at a
particular site. This is quite comforting in
that we wish to smooth the storm history to
regions that have not experienced many extreme
events. The Weibull fitting methodology provides
an indirect smoothing that appears reasonable and
is consistent with the historical record.
Return to Directory
9
Statistical Methodology Page 3/3
Below is an example of the Weibull curve fitted
to the HURDAT historic record for a project
completed in 1998. For each storm, the model TAOS
calculated the winds produced over downtown
Kingston, Jamaica. The winds were grouped by
years, and the peak wind for each year of the 112
years in the database selected. Then the 112
peak yearly winds were grouped for this
histogram.
Kingston, Jamaica Histogram of Historic
Occurrences and Two-Parameter Weibull fit ?
1.194302 ? 28.483850 ?2 20.568573
K-S 0.098214 K-S prob. 0.630202
Return to Directory
10
The TAOS Model and Model Validation Page 1/2
The Arbiter of Storms (TAOS) is a computer-based
numerical model that produces estimates of
maximum sustained wind vectors at the surface and
still water surge height and wave height at the
coastline for any coastal area in the Caribbean
basin. Model runs can be made for any historical
storm, for probable maximum events, or using
real-time tropical storm forecasts from the US
National Hurricane Center (NHC). TAOS is
integrated into a geographic information system
(GIS), which eases entry of model data, enables
the presentation of model results in a format
familiar to meteorological officials in the
Caribbean region and allows the results to be
combined with locally available GIS and map
information.
, meters
Return to Directory
The TAOS model has been tested extensively
against hurricanes and typhoons around the world.
There are 460 observations on the US Gulf and
Atlantic coasts, 36 observations in Hawaii, 42
observations in the Caribbean, and 28
observations in the remainder of the world (such
as Japan, Taiwan, India and Bangladesh), for a
total of 566 peak surge observations from 27
storms worldwide. Including comparisons with
hourly tide-gauge readings, there are over 1200
observations in the TAOS verification database.
From this, TAOS/C appears to generate results
within 0.3 meters (less than 1 foot) 80 of the
time, and less than 0.6 meters (about 2 feet) 90
of the time. The scatter plot above shows the
results of US mainland storm surge comparisons.
11
The TAOS Model and Model Validation Page 2/2
Because the TAOS model uses basic physical
relationships, it works across a wide range of
scales. For instance, a study was done of the
west coast of Dominica, using a resolution of 30
meters. In 1995, as the study was finishing,
Hurricane Marilyn visited the island. A field
visit several weeks later found that the model
had accurately predicted damage areas as small as
two to three cells wide.
CDMP Storm Hazard Modeling Page
Return to Directory
12
Known Issues in the Input Data
The input data used to develop this atlas is
based on USGS digital data for deep ocean
bathymetry, Digital Chart of the World data for
land boundaries and rough topography, satellite
imagery for foreshore bathymetry and land cover.
This base information was then updated with point
sounding and trackline information. The input
data has a nominal resolution of 30 arc-seconds
(926 meters or less, depending on latitude and
orientation), but it is not reliable in such
detail. Storm track information used for modeling
was derived from a database developed by the U.S.
National Hurricane Center. See the web link in
the directory for more information on data
sources. The database is not designed to be
queried out of context, on a cell-by-call basis.
Doing so would create a false impression of
accuracy which can not be delivered from the
input data available at this time. It is a
measure of the power of the model that it reveals
weaknesses in the input data at the geographic
locations where they occur, without spreading
inconsistencies across wide areas. Data issues
show up in several specific ways
Return to Directory
13
A Short Review of Storm Effects Page 1/5
Rain and wind
In an ordinary thunderstorm, the rain falls out
of the cloud leaving the air warmer and drier.
The warm air rises, drawing winds from outside
the cloud to fill the space. In a hurricane, the
thunderstorm is so large that it is twisted by
the spin of the Earth and the winds form a
spiral, directed inwards from all points of the
compass.
Return to Directory
Photo by permission of Michael Bath.
http//australiansevereweather.simplenet.com/photo
graphy/cbincu11.htm
14
A Short Review of Storm Effects Page 2/5
Cyclonic structure
Return to Directory
All of the Caribbean is north of the Equator, so
hurricanes in the Caribbean spin
counter-clockwise.
Photo by permission of Scott Dommin.
http//members.aol.com/hotelq/index.html
15
A Short Review of Storm Effects Page 3/5
Topographic effects
Acceleration
Turbulence
Back Pressure
LAND
OPEN SEA
Definitions
When winds reach an obstacle, they may accelerate
in order to squeeze past or they may be slowed by
back pressure. In the lee of an obstacle, the
winds are confused and turbulent.
Return to Directory
16
A Short Review of Storm Effects Page 4/5
Wind over water
As storm winds blow over the sea, they drag on
the water, forming waves and storm currents
In this Atlas, wind speeds represent sustained
1-minute winds at 10 meters above the surface.
Wave build-up
Wind-induced Current
Deep counter-currents and upwelling develop in
order to compensate for the drift near the
surface. These effects may penetrate down to 200
meters depth.
Definitions
Return to Directory
17
A Short Review of Storm Effects Page 5/5
In this Atlas, 1. Wave heights are the heights
of wave crests above the storm surge. 2. Storm
surges include astronomical tide and setups from
pressure, wind and wave, but not wave runup.
Definitions
Return to Directory
18
Hurricane Marilyn passed just north of Puerto
Rico and then turned northeast as it caught the
effect of weather systems in the north temperate
region.
Marilyn, 1995
Hurricane Gilbert passed directly over Jamaica
without being disrupted. If it had passed
over the Dominican Republic, Haiti, or Cuba, the
large land masses would have changed and weakened
it.
Storms originating east of Barbados may head
directly west-northwest or veer to the north.
Gilbert, 1988
Return to Directory
19
Distortions of the Projection
The WGS84 datum models the Earth as an ellipsoid.
Calculations of distortions of units of
Longitude for using a square grid
representation of Latitudes longitudes on
a WGS84 datum Major semiaxis
6378137.00000 meters Minor semiaxis
6356752.31400 Latitude tangent(lat) rat
io stretching comments 0 0 1.00000 1 equator 8 0
.140540835 0.99020 1.009893 Full frame,
S 9 0.15838444 0.98761 1.012549 Carib Frame,
S 10.25 0.180829457 0.98394 1.016327 East Basin,
S 10.75 0.189855932 0.98234 1.017982 Mid Basin,
S 11.5 0.203452299 0.97979 1.020623 Windwards,
South, S 14 0.249328003 0.97010 1.030817 West
Basin, S 14.25 0.253967646 0.96903 1.031957 Windw
ards North, S 14.25 0.253967646 0.96903 1.031957
Windards, South, N 15.8 0.282971477 0.96198 1.039
525 Belize, S 16.5 0.296213495 0.95856 1.043232 L
eewards, S 16.6667 0.299380981 0.95772 1.044142 W
indwards North, N 17 0.305730681 0.95603 1.045993
Jamaica, S 17 0.305730681 0.95603 1.045993 PRVI,
S 17.5 0.315298789 0.95343 1.048849 Haiti,
S 17.5 0.315298789 0.95343 1.048849 Dom Rep,
S 18.6 0.336537181 0.94744 1.055472 Belize
N 18.75 0.339454259 0.94660 1.056412 Leewards,
N 19 0.344327613 0.94518 1.057998 Jamaica,
N 19.5 0.354118573 0.94229 1.061247 PRVI,
N 20.166667 0.367267976 0.93832 1.065737 DomRep,
N 20.25 0.368919477 0.93781 1.066311 East Basin,
N 20.3333 0.370572096 0.93731 1.066888 Haiti,
N 20.75 0.378866109 0.93474 1.069816 Mid basin,
N 23 0.424474816 0.92003 1.086919 Carib frame,
N 35 0.700207538 0.81825 1.222127 North
Carolina 45 1 0.70592 1.416594 Maine 75 3.732050
808 0.25801 3.875832 Hudson Bay
The formula of an ellipse is
Where a and b are the major and minor semiaxes.
a b

In re-projecting to the Plate Carrée, north-south
distances are undistorted, but east-west
distances are distorted in proportion to their
latitude. The distortion can be calculated by
finding the ratio of the local rotational radius
(x) to the length of the major semiaxis (a)
Return to Directory
Latitude
20

• Definitions
• WINDS The winds displayed in this product are
  compatible with one-minute sustained winds, 10
  meters above the surface, as reported by the U.S.
  National Hurricane center (NHC).
• For a brief discussion of converting from one
  standard of wind measurement to
• another, click HERE
• SURGES include astronomical tide and setups from
  pressure, wind and wave, but not wave run-up.
  Surges over land are shown as elevation above sea
  level, not water depth.
• WAVES are the heights of wave crests above the
  storm surge level in open water. Shoreline
  effects do not appear at this resolution.

Measures of Wind Speed
Return to Directory
21
Measures of Wind Speed
The winds displayed in this Atlas are one-minute
sustained winds, 10 meters above the surface,
which are compatible with the wind speed
representation used by the U.S. National
Hurricane center (NHC) in its forecasts and
reports of tropical cyclones. The NHC is
designated by the World Meteorological
Organization (WMO) as the Regional Specialized
Forecast Center for tropical cyclones in the
Atlantic Basin. Internally, TAOS computes
instantaneous values for mean wind at the top of
the boundary layer, which is effectively the same
as the 10-minute averaged wind used by the WMO.
To conform to the slightly different one-minute,
sustained winds 10 meters above the surface
reported by the NHC, the wind values produced by
the TAOS model are then brought down to the
surface with boundary-layer calculations and
converted to one-minute sustained averages at an
elevation of 10 meters. Users requiring
alternate wind representations may use the
following conversion factors to obtain
approximate values
Return to Directory
For example, to get 10-minute winds, multiply
values from this Atlas by 0.8125. Research is
continuing into the relationships between these
various measures. Turbulent flow over land is
particularly complex, and gust factors may need
to be site-specific. Further discussion is in
Simiu and Scanlan, Wind Effects on Structures,
3rd edition, Wiley, 1996, and in Sparks, P.R.,
and Huang, Z., "Wind speed characteristics in
tropical cyclones", Proceedings of the Tenth
International Conference on Wind Engineering,
Copenhagen Denmark, 21-24 June 1999. In this
Atlas, wind speed over land includes both surface
friction (keyed to land cover) and topography
along the flow path at a resolution of 30
arc-seconds. If using wind damage models or
building codes which internally include surface
friction or topographic corrections, the nearest
open-water wind speed should be used as input.