A Statistical Method for Regional Design Wave Heights in the Gulf of Mexico
Authors: Chouinard L.E. 
Published: October 2008

A new parametric model is proposed for the evaluation of hurricane hazards at a given site which can account for regional variations in hurricane severity. The recurrence rate and relative position of hurricane tracks are modeled as a line process. The characteristics of the line process and of the probability distribution function for the severity of the hurricanes are estimated locally in space from a catalog of historical hurricanes using maximum likelihood and smoothing functions. A procedure is proposed for selecting the optimal local model for the occurrence and severity of hurricanes using cross-validation. Significant regional variations in the recurrence rate and the severity of hurricanes are identified for the Gulf of Mexico. The latter seem to be strongly correlated to the average water temperature of the first two hundred feet of water. Although many issues remain unanswered, our results seem to validate the existence of hurricane alleys, which warrants further analysis into the physical process of such phenomenon.

INTRODUCTION

A review of the results of the recently completed GUMSHOE study (GUlf of Mexico Storm Hindcast of Oceanographic Extremes) suggests the possible existence of two alleys where hurricanes seem on average more intense than elsewhere. A paper by Cooper1 in the present proceedings investigates the physical basis of alleys. The present paper proposes a statistical method for estimating models of hurricane severity that can account for regional variations of the occurrence and severity of hurricanes irrespective of the underlying physical mechanisms at the source of these variations. The model is general in its formulation and can, at the limit, reproduce results from more traditional approaches.

REVIEW OF PRESENT PROCEDURES

Depending on their treatment of historical hurricanes, hurricane hazard analysis methods can be classified into two categories: source-model methods (Haring et al. 2) and historic methods (Ward et al. 3). The former procedures are based on three steps:Describe the hurricane recurrence rate for the region that makes significant contributions to hurricane hazard at a given site. This description includes the time, location, and size of future hurricanes, all regarded as random variables.For any given hurricane location and size, describe the effect of the hurricane at the site (e.g., the significant wave height, hs' e.g., Cooper4). This description is known as the attenuation model.Calculate the rate ? (hs) at which Hs exceeds h hs using information from the previous two steps.

Historic methods avoid the fitting of hurricane models and estimate ? (hs) in only one step. The function ? (hs) is estimated by treating the historical or hindcasted observations at a site as a statistical sample. The function ? (hs) may be estimated through various parametric or nonparametric procedures. A common procedure for determining design values for significant wave heights at a given location is to fit an extreme-type distribution to a sample of observations or hindcasted values. A variation of this procedure is to average estimates from neighboring locations in order to decrease the variability.