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Operations Research Models and Methods
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Historic Hurricanes

Historic Hurricanes
 William G. Lesso
July 2004

This program was started in the mid 1970's as a follow on to a hurricane damage model developed by the author, for the Texas Coastal and Marine Council. This agency was supporting a bill in the Texas Legislature that required homes being built in the 19 coastal counties of Texas meet a new standard of withstanding 140 mph winds. The current standard was 104 mph. It was felt that homes built to the new standard would suffer 50% less damage. To build to the new standard would increase the coast of the building by 0.5 to 1.5 %. Of course, many of the homes on the coast were built to no standard. In the course of that work, the author visited the National Hurricane Center to obtain data for the damage simulation model. There he met with Dr Herb Saffir, one of the leading experts on hurricanes and wind damage. Dr. Saffir was coauthor of the Saffir-Simpson scale for hurricanes. Later, the National Hurricane Center (NHC) provided the author with a tape that contained historical data on over 700 tropical storms dating back to 1886. This data was used to develop the first forecasting models. (Note: The building standard bill did not pass. The Real Estate lobby was more powerful than the Insurance lobby!)
Hurricanes are said to be the most powerful and deadly of nature’s phenomena. Besides winds that can exceed 200 mph, they generate storm surges that can exceed 35 feet. One example of this was Hurricane Camille in 1968. It hit the town of Port Christian, Mississippi with a 30-foot surge of water. A group of 30 or more people were having a ‘hurricane’ party on the third floor of the Richelieu Apartments.
Appartments before

When the storm surge hit, all the people were swept out of the building. All but one perished. She was found in a tree several miles down the coast.

Appartments after


The movement of hurricanes is often unpredictable. The author, while being interviewed for a newspaper article in the 1980s commented on this and said, “That’s why they are named after women.” The lady reporter retorted, “Young man. Women are NOT unpredictable! They just reserve the right to change their mind!”

A good example of this is Hurricane BARRY (1983). It was proceeding north off the east coast of Florida. Just opposite Cape Canaveral with a space shuttle on the pad, it made a 90-degree left turn. (Perhaps it wanted to check out the shuttle!) It then proceeded to cross Florida and enter the Gulf of Mexico. It gathered more strength and eventually hit Brownville, Texas. (I got a call from a radio station in Brownsville at 4 AM asking where the storm was. I suggested politely that they look out their window. Barry is one of the storms in the HISTORIC HURRICANE set in the Excel data file historic_hurricane.xls.
If one looks at the comments about these storms, two factors become apparent. Except of the Hurricane of 1900 that killed 600 people, there are few deaths in the US and many on the Caribbean Islands. There is little dame on the Islands and a lot in the US. A possible explanation for the first is that we have improved our warning capability and the population has time to evacuate AND they have someplace to go. The poor people on the Islands are trapped! Likewise there is less infrastructure on the Islands and much along the US coast. We love to live on the seashore!


The First Models


The hurricane wind damage model was presented as a technical paper by the author at a national conference on hurricanes. One of the speakers from the NHC announced that one of the primary forecasting models in use at that time gave results two and three quarter hours after they obtained a position report on the eye of the hurricane, instead of three hours and fifteen minutes. (Its hard to remember that computers in the late 1970 were so slow compared to what we have today!) A portion of the audience cheered. Later we found out that forecasters were to give their forecasts three hours after the position report and then wait another fifteen minutes to see how wrong they were.

The first models described the movement of hurricanes as a Markov process – a “random walk” in two dimensions. During the course of a graduate seminar on ‘Problems in Operations Research,’ the author described the hurricane damage model that had been presented and the incident of the ‘quicker’ forecasts from the NHC. The author made the boast, “If I couldn’t do better than that, I’d eat their computer tape of data!” One of the graduate students suggested that we use a Markov process. As he said, “ After all, a hurricane is much like a two-dimensional random walk!” Originally four separate models were tried. Two were soon abandoned as too cumbersome. Later the features of the other two were combined into the basis of the current model.

The first version of the model had the characteristic of being either very “good” or very “bad” with no prior indication of what mode it would be in. The criterion used to evaluate the model were a standard proposed by the NHC in the 1970’s. Their goal was to have the mean position error for the 72 hour (3 day forecast) to be less than 125 nautical miles. At that time, their actual mean position error for 72 hours was about 375 nm.

For the original model, when it was “good”, the mean position error was less than 100 nm and when it was “bad” the error was over 500 nm. After several attempts to improve the model, Dr Tom Curry, as his PhD dissertation, developed a modified Markov process model and gave consistent results. Currently the mean position error for the model is about 175nm for the 72 hr forecast.


The Next Model


The model uses position reports of latitude and longitude as provided by the National Weather Service. At the time the model was constructed, these position reports were given every 6 hours. For a Markov process the probability of the system being in any state depends only on the previous state. The process is said to have a memory of one. Translating this to the movement of hurricanes, the process can be defined as: “The probability that a hurricane is at any given position (Latitude and Longitude) at a given time, only depends on where it was at some previous period of time. Since we are interested in movement, this implies distance and direction. To achieve this, we need to use the previous TWO six hour positions of the hurricane. These give is a measure of the average velocity it traveled and the direction. The model did not just simply project this movement in a straight line but used a probability table for possible locations based on the latest latitude and longitude.

As mentioned previously, the initial models were either very good or very poor. During the research work of Dr. Tom Curry, we discovered we needed to include a “steering” effect based on the diurnal movement of storms, i.e. they slowed down at night and sped up during the day. So the Markov process was modified to include the position report of the storm 24 hours previous to the latest position. Also, at this time we found a way to collapse the massive probability transition matrix of possible latitudes and longitudes based on the latest position to a set of regression equations simply based on latitude. These greatly simplified the running of the model.

The model requires a minimum of five six-hour position reports of latitude and longitude. The model will then project the movement of the center of the storm for the next 90 hours, in six-hour increments. As additional position reports are obtained they are entered to update the projections.

This version of the model was programmed in the late 1970’s and updated with features from time to time. As such it is characteristic of the types of programs written at the time with a Main menu page with a series of options. There is a catalog of storm data for past storms. The error analysis option was not operable on this version since it was used in the early running of the model to determine the mean position error at 6-hour intervals. Two of the major features added to the model were the set of forecasting equations cited above and a plot option that shows the forecasted movement of the storm.


The Current Model


The model was not been updated in the last fifteen years to incorporate the current mode of “pull-down” menus or different forecasting intervals. Over the past several years the NWS has at times issued position reports at 3-hour intervals and even 2-hour intervals. The current model can only use 6-hour increments. Where there are 3-hour reports, the ploy we have used is to run two series of forecast, e.g. Hugo-A and Hugo-B and run them alternately as the reports come in. As a point of interest, the error in forecasting the landfall of Hugo 72 hours in advance was less than 30 nm.

In 2004, Dr. Paul Jensen implemented the model using the Visual Basic for Applications (VBA) macro language for Microsoft EXCEL. This version incorporates a plotting function using maps. Also, the error analysis function is made fully operational. A full description on the use of the model and a file of ‘Historic Hurricanes’ can be found on this website.


Future Models


Early in the research into hurricane movement, two characteristics became apparent. First, storms have a diurnal cycle. They slow down at night and speed up during daylight hours due to the energy absorption from the sun. This characteristic is modeled in part by having the forecast depend on the five-step-back position that tells the location one day back.

The second characteristic became apparent through the examination of a sequence of satellite photos. These gave the same effect as watching a movie film. They showed that the eye of the hurricane pulses and wobbles. The pulsing was perhaps due to the diurnal effect. The wobble had the appearance of following a cycloid path. That is, the path a point on a wheel would follow as the wheel rolls along. This wobble has the effect of introducing an error in the forecasts. Since the position reports are taken every six hours (every three hours as the storm approaches land), the direction of movement could be off depending on where the storm was in the cycloid cycle. If the characteristic of this wobble could be determined by estimating the parameters of the equation of the cycloid, then a correction could be made and the accuracy of the forecast might be improved. This is the direction of current studies.



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Operations Research Models and Methods
by Paul A. Jensen
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