Linear and nonlinear statistical modelling

of hurricane force winds

R.D.Wooten, C.P.Tsokos

Department of Mathematics and Statistics, University of South Florida

Tampa, Florida 33620, USA

The subject of work is the problems of modelling important nature phenomena. In the present study, the primary aim concentrates on the modelling of hurricane force winds; that is, maximum sustained winds related to pressure, location and linear velocity. We were successful in modelling the wind speed within storm as a function of the contributing entities. In this study, we were able to re-evaluate the association between wind speed and pressure within storms; this knowing will lead to historical breakthroughs in how we see hurricanes and predict hurricanes. This paper is the first paper of a series, and its analysis of wind speed versus pressure indicates that further analysis of the Saffir-Simpson Scale is necessary, as well as determining if pressure is an indicator or a consequence of a hurricane force wind speed.

For introduction we note There are statistical models in forecasting the track of hurricanes, but how well do we understand the mechanics underlying the birth and pathway (track) of a tropical storm? What are the contributing variables and how do they rank in comparison; that is, what are the explanatory variables according to their contribution to the model?š What are the significantly contributing interactions?

To answer these questions, data gleaned from UNISYS Tropical Prediction Center were used which included five recent storms classified into categories. Provision included: charts on the track of the storm, tracking information, position in latitude and longitude, maximum sustained winds in knots, and central pressure (hPa) and date including month, day and time as well as several other derived variables.

In the paper, we will be interested in which parameter to include in the model. In terms of location, this is a question of latitude and longitude or the transformed x and y. Since x and y illustrate the real linear movement of the storm, this transformed information with be included in the following model.

With our results we obtain.

Statistically, with just a few prior pieces of information, we can estimate with high degree of accuracy the associated wind speed; that is, our model explains 97.1% of the variation in the wind speed. Some of the secondary result, estimating the coefficients for the various categories may need to be re-evaluated since it has be shown that the Saffir-Simpson scale does not categorize hurricane force winds appropriately according to significant changes in the pressure. Reclassification of the categories might yield a better fitting model when regressed categorically. Furthermore, coupling physics with statistics should produce a much more reliable model; however, categories aside, the non-linear statistical model developed can still be used to accurately estimate the intensity of a storm.

In conclusion we note.

With the present day technology and the historical data now readily available, hurricane prediction will become more accurate in the near future. While this model predicts the intensity of the storm, now we need to address the issues of direction and duration and how this relates to the intensity. The "spaghetti string" models, averaged and used to make the cone shaped predictions and forecast as new information is gathered, can be adjusted to be more accurate or simply replaced by stochastic systems developed by statisticians working with meteorologists.