Probabilistic Models for Texas Gulf Coast Hurricane Occurrences

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Abstract
The occurrence of Texas Gulf Coast hurricanes is analyzed using various statistical methods. Simple Poisson, periodic Poisson, and Markov chain models are fitted to the occurrence data for a site offshore of Mustang Island, near Corpus Christi. Use of the periodic Poisson model permits a relatively simple description of cyclical occurrence phenomena. The goodness of fit of the three different models is compared, using interarrival time, hazard function, and comparative maximum likelihood tests. The auto-covariance function for the data is investigated, and the effects of varying-record-Iengths are considered. Results found for other Texas sites are also compared with those found for the Padre Island site. While the simple Poisson and Markov chain models seem to provide a reasonable fit to the occurrence history, the periodic Poisson model is seen to provide a much better fit to the data. Reasons for the acceptance of a periodic model for hurricane occurrences are discussed. The cyclical hurricane occurrence pattern implied by the acceptance of the periodic Poisson model is shown to have a very significant effect on the design of both offshore and onshore structures. An important indication of this study is that the Texas coast is currently nearing the peak of cycle of high hurricane occurrence likelihood. INTRODUCTION The Gulf Coast of the United States is frequently visited by hurricanes, resulting in very large property damages. Since hurricanes are the most severe type of storm generally affecting the region, the high winds and waves associated with such storms produce the critical conditions for which many offshore structures must be designed. Offshore structure designers require some method of predicting hurricane occurrences over time spans of several years. Such prediction models may then be used to develop the suitable design criteria for a particular structure. Study of the Gulf Coast storm records reveals the rather irregular nature of hurricane arrivals at coastal sites. This irregularity suggests the treatment of hurricane occurrences as a stochastic process; that is, a random process in time. Hurricane occurrence probabilities may be obtained from the models of such a random process. This investigation is concerned with the development of probabilistic models for the prediction of hurricanes offshore of Mustang Island,, near Corpus Christi, Texas. (Figure 1) ';. The forecasting methods used in this study are based solely upon the available historical storm occurrence data. The methods utilized are valid only for long term forecasts made in ignorance of future weather conditions. Thus, the probabilistic treatment of long-term hurricane prediction serves as a complement to synoptic weather forecasting procedures, which are suitable only for short-term predictions. Various stochastic models for hurricane predictions with parameters derived from the storm data at the site are investigated and compared. DATA The assembly, categorizing, and interpretation of the available hurricane occurrence data is a very important step in making predictions of future storm likelihoods. The past record of storm occurrences is the information upon which the stochastic models of this study are based.

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