Stochastic modeling of damage associated with extreme weather events

Much concern has been expressed (especially within the insurance industry) about increases in economic damage associated with extreme weather events. Questions remain about the extent to which these trends are attributable to changes in climate, as opposed to increased societal vulnerability. A case in point is the damage caused by North Atlantic tropical cyclones (primarily hurricanes) making landfall in the U.S. In an attempt to control for changes in vulnerability, this damage data set has been adjusted for inflation, wealth, and population at risk (Pielke and Landsea, 1998).

The basic stochastic model is a compound Poisson process, so that total annual damage is represented as a random sum. The total number of damaging cyclones per year is fit reasonably well by a Poisson distribution, and the monetary damage for individual storms by the lognormal. However, the extreme right-hand tail of the storm damage distribution appears to be heavy, with the estimated shape parameter of a generalized Pareto indicating that its variance is not necessarily finite.

Exploiting the random sum representation with a lognormal distribution of storm damage, only a relatively small fraction of the variation in annual damage totals is associated with fluctuations in the number of cyclones. Weak evidence is present of an increasing trend in the intensity parameter of the Poisson process governing the occurrence of cyclones, as well as somewhat stronger evidence of a decreasing trend in the mean of the log-transformed storm damage (adjusted for societal vulnerability). Quite a bit stronger evidence exists of a dependence of these parameters on covariates such as the El Nino phenomenon. Implications of the apparently heavy-tailed distribution of storm damage are also explored, making use of its relationship to the distribution of maximum annual damage.