Stochastic Modeling of Hurricane Damage

Richard W. Katz Environmental and Societal Impacts Group, National Center for Atmospheric Research,* Boulder, Colorado

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Abstract

A compound Poisson process is proposed as a stochastic model for the total economic damage associated with hurricanes. This model consists of two components, one governing the occurrence of events and another specifying the damages associated with individual events. In this way, damage totals are represented as a “random sum,” with variations in total damage being decomposed into two sources, one attributable to variations in the frequency of events and another to variations in the damage from individual events. The model is applied to the economic damage, adjusted for societal vulnerability, caused by North Atlantic hurricanes making landfall in the continental United States. The total number of damaging storms per year is fitted reasonably well by a Poisson distribution, and the monetary damage for individual storms is fitted by the lognormal. The fraction of the variation in annual damage totals associated with fluctuations in the number of storms, although smaller than the corresponding fraction for individual storm damage, is nonnegligible. No evidence is present for a trend in the rate parameter of the Poisson process for the occurrence of storms, and only weak evidence for a trend in the mean of the log-transformed damage from individual storms is present. Stronger evidence exists for dependence of these parameters, both occurrence and storm damage, on the state of El Niño.

Corresponding author address: Dr. Richard W. Katz, Environmental and Societal Impacts Group, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307-3000. rwk@ucar.edu

Abstract

A compound Poisson process is proposed as a stochastic model for the total economic damage associated with hurricanes. This model consists of two components, one governing the occurrence of events and another specifying the damages associated with individual events. In this way, damage totals are represented as a “random sum,” with variations in total damage being decomposed into two sources, one attributable to variations in the frequency of events and another to variations in the damage from individual events. The model is applied to the economic damage, adjusted for societal vulnerability, caused by North Atlantic hurricanes making landfall in the continental United States. The total number of damaging storms per year is fitted reasonably well by a Poisson distribution, and the monetary damage for individual storms is fitted by the lognormal. The fraction of the variation in annual damage totals associated with fluctuations in the number of storms, although smaller than the corresponding fraction for individual storm damage, is nonnegligible. No evidence is present for a trend in the rate parameter of the Poisson process for the occurrence of storms, and only weak evidence for a trend in the mean of the log-transformed damage from individual storms is present. Stronger evidence exists for dependence of these parameters, both occurrence and storm damage, on the state of El Niño.

Corresponding author address: Dr. Richard W. Katz, Environmental and Societal Impacts Group, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307-3000. rwk@ucar.edu

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