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Operations Research Models and Methods
Computation Section
Hurricane Tracking and Forecasting
hurricane menu The Hurricane program tracks and forecasts hurricanes in and around the Gulf of Mexico. It accepts data published by the National Hurricane Center (NHC). The tracking program is implemented using VBA modules in an Excel workbook, hurricane.xls. The workbook also contains the data for Hurricane Allen that is used in this section to illustrate the use of the program. To download the workbook, click on the Workbook link at the left. Clicking the link labeled Historic Hurricanes will download a workbook with the data and descriptions of 36 important hurricanes that have been observed since 1900. The Error Analysis link downloads a Microsoft Word document by W. Lesso that discusses the problem of predicting landfall location. The method is illustrated in the Arlene_05 Excel workbook that contains data for hurricane Arlene.

Note that the modules are in a workbook (.xls) rather than an add-in (.xla). Open hurricane.xls by double clicking or through the Open command of the file menu. Data should be kept in the same workbook as the macros. A single file can store several storms. The file can also be duplicated to store multiple storms.

The Hurricane workbook contains buttons created on the author's computer. Before you can use these buttons, you must link them to the macros in your computer. You can do that by selecting the Reset Buttons menu item. The program replaces buttons with new buttons linked to the programs in your computer.


The original forecast models were developed in the late 1970s by Bill Lesso, Professor Emeritus of the University of Texas. They were based on using a Markov process to model the movement of a storm, i.e. the next position only depends on the current position. To develop the probability transition matrices, several hundred historic storms tracks dating back to 1886 were used. The result was a simple, fast computer model that could be run on the newly introduced PC’s. On contract the NHC was using several different models that could be described as ‘aerosol physics’ models consisting of several hundred partial differential equations that, at that time took several hours to run.

The first Lesso models were fast but inconsistent. The models gave either very good forecasts or forecasts so bad that one colleague stated that one were better off spitting upwind! To improve the consistency, a two-step Markov process was introduced and later, the probability transition matrices were changed to be latitude and longitude dependent. Finally, Tom Curry did an extensive analysis of the storms as part of his PhD dissertation research, "Time Series Prediction of Hurricane Landfall", May, 1986, and added a new variation. The current model uses the current position of the storm; the position six hours back and the position of the storm one-day (24 hours) back. Also, he replaced the probability transition matrices with a set of regression equations that are specific for each five-degree band of latitude. The result is a model that is consistent and gives good accurate forecasts.

As with all forecasts, the results rarely indicate the exact path of a hurricane. Any use of this program is not the responsibility of the authors. Don’t bet your life or your property on them!


Adding a Hurricane


The examples of this section as well as all the macros and other resources necessary are contained in the Hurricane Workbook. To use the workbook, simply open it as any Excel workbook by double clicking its icon or using the Open command on the Files menu. Depending on the security measures set on your copy of Excel, the program may ask if you want to enable the macros in the program. If you want to use the features of the workbook, you must answer yes.

If you are opening a workbook containing hurricane worksheets created on another computer, you may have trouble using the buttons on a worksheet. If so, select the Reset Buttons menu item. The program replaces buttons with new buttons linked to the programs in your computer.

To illustrate the use of the workbook, we use the hurricane Allen, a large hurricane that occurred in 1980. To create a new hurricane, select New from the Hurricane menu.

hurricane menu

A dialog is presented as below. The name entered on the dialog is used as the name of a worksheet and to provide Excel names for a number of ranges on the worksheet. Once selected the name cannot be changed. The dialog provides boxes for the initial date, time, latitude and longitude. Although longitudes in the Gulf area are negative, for simplicity they will be entered as positive numbers. The latitudes accepted by the program are between 10 and 45 degrees. The longitudes accepted are between 50 and 100 degrees.


The worksheet named Allen is created in the workbook, and a form is placed on this worksheet with space for 50 observations of the hurricane location. The initial data specified in the dialog is placed in the first row. The Observation entry in cell B2 is the current entry. As subsequent observations are entered, the macro changes this number. The Map designated in cell D2 is used to plot forecasts.

Initially, the NHC issued storm position reports at six-hour intervals. This model is based on the six-hour interval and the forecasts are made on this basis. Later, the NHC began issuing position reports at 3 and even 2-hour intervals as the storm approached landfall. To accommodate a change in interval, we suggest that a second forecasting series be started, with a new name, say ‘Allen-B’, and the two models be used alternately to model the storm. (To get the second series started, you may want to develop ‘fictitious’ first 4 points by interpolating between points of the first series.)


Adding Observations


To the right of the form are three buttons. The first is used to enter a new observation, the second is to create a forecast and the third to perform an error analysis. We discuss adding observations first.

Clicking the New Observation button presents the dialog below. The observation number is one greater than the current observations. The time is automatically entered. Note that times are specified by the day and hour. The day is given as in 08/03. After a space, the time is given as in 06. The purpose of this dialog is to enter the new latitude and longitude. You can also change the observation and time if your purpose is to correct an earlier error.

The new information is placed on the worksheet. The number in the Move column is the number of nautical miles between the first and second observations. This value is computed by a function that takes into account the latitudes and longitudes of the two observations. The Speed column shows the speed required to move this distance in the six hour interval. The cells in these columns are colored yellow to indicate that the cells contain formulas that should not be changed by the user.

The data in this table can be changed directly on the worksheet. If additional observations are manually entered, the observation number in B2 must be manually adjusted.


After 13 observations the data form appears as below. The observations on the table are the positions actually observed in 1980.


Making a Forecast


With at least 5 observations, a forecast can be made. To make a forecast click on the Forecast button. There is also a Forecast item on the menu that performs the same operation. The dialog below is presented. Normally the forecast is made from the last observation, 13 in this case. The Last Observation button makes this selection. There may be occasions when it is instructive to forecast at some earlier observation to see how well a forecast tracks actual observations. Then the Specified button is checked and the desired observation number is placed in the field to the right of the button. We illustrate this case later.

The default value of the Number in Forecast is 15, representing 90 hours into the future. To see a map of the past observations and the forecast, click the Show Map checkbox.

On clicking OK, a forecast table is constructed on the worksheet to the right of the data. The example is shown below. The first entry is the known position at observation 13. The other positions are based on forecasting formulas. The green colored cells indicate that the program computes these values. The yellow colored cells hold Excel formulas.

Columns are provided for the Move distance and speed for the forecasted values. The Error column has meaning only when the forecast observation is less than the current observation.


A map of the observations is automatically created on a worksheet called Allen_Map. The example map is shown below.

A less reduced portion of the map is shown below to illustrate some detail.

The white circles on the map show actual data and the red circles show forecasted positions. Every fourth circle has a heavier outline to indicate the passage of one day. Dates and times are shown adjacent to these circles.


After the entire data set has been entered, the final path of hurricane Allen is shown below.

  The workbook contains a single map (1000 points in width) is on worksheet Map. Additional maps may be created by the user. Data describing a map is stored in worksheet cells behind the map graphic. It is important that the workbook include the worksheet with the map used in the forecast.

Hurricane Allen required 32 observations when the storm was classified as a hurricane. After all 32 entries we choose to forecast from observation 18 by using the forecast button and filling in the dialog as below.

Since the forecast observation starts from 18, the results can be compared with the actual positions for observations 19 through 32. The resulting errors are shown in column P below. This Error column is used in the error analysis to be described later.

For this option both the forecasted and actual positions are shown on the map. The darkened circles, every fourth observation, help compare the actual to the forecasted path.


Additional Storms


A workbook can hold several storms. A reasonable choice is to include all storms that occur in a year in a single workbook.

The Hurricane workbook can be duplicated to hold additional storms or storms from different years. Simply select the Hurrican.xls file, duplicate it and rename the copy. The worksheets holding old storms can be manually deleted with Delete Sheets command on the Edit menu or by using the Old command from the Hurricane menu.

Entering the name of the storm and clicking the Delete Storm checkbox will cause the data sheet and the map worksheet for the storm to be deleted. If the checkbox is not checked, the program will make the hurricane data page active.

It is important that the map worksheets not be deleted from duplicated workbooks. The macros holding the programs are passed to a duplicated workbook.


Error Analysis

  Clicking the Error Analysis button after all the observations have been entered creates an analysis of the errors made for all forecasts. The result is shown below. The program goes through all possible forecast observations (6 through 31) and computes the position errors of the forecasts compared to the actual observations. The errors are transferred to a new worksheet called Allen_Error. The forecast errors for observation 6 are place in column F. There is an error for each of the time intervals 6 through 90 hours. The errors for each of the other observations are placed to the right. Some columns are hidden in the figure. The forecasts near the last observation (32) have errors for only a few intervals.


Summary error statistics are computed in columns B through E. The mean error together with one standard deviation above and below the mean is plotted in the graph placed below the table.

As expected, the mean error increases as the forecast interval increases. The standard deviation also increases with interval. The error for 72 hours (or three days) is particularly interesting since that is a measure used by NHC for comparing forecasting methods.


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Operations Research Models and Methods
by Paul A. Jensen
Copyright 2004 - All rights reserved

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