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Figure 10.5. (a) Cumulative percent of total losses as a function of percent ranking. The reference lines indicate the oft-cited 80%/20% relationship, whereby the top 20% of the strongest hurricanes account for 80% of the losses. A split of the event counts into (b) large loss events and (c) small loss events based on losses exceeding US\$100 mn is shown as annual time series. For reference, 2004 experienced four large and two small loss events.

Figure 10.5. (a) Cumulative percent of total losses as a function of percent ranking. The reference lines indicate the oft-cited 80%/20% relationship, whereby the top 20% of the strongest hurricanes account for 80% of the losses. A split of the event counts into (b) large loss events and (c) small loss events based on losses exceeding US\$100 mn is shown as annual time series. For reference, 2004 experienced four large and two small loss events.

remaining 65 events (36.5%) account for only 0.6% of the total losses. Thus it might be reasonable to assume that the small loss events are at the "noise" level. Time series of the annual number of large and small loss events are shown in Figure 10.5. The rank correlation between the two series is a negligible 0.06.

Next we examine the influence of the covariates, discussed in the previous section, on both the magnitude of annual loss and the number of annual loss events. For the number of loss events, we consider small and large loss events separately. Using the preseason Atlantic SST, we are able to explain 13% of the variation in the logarithm of loss values exceeding US\$100 mn using an ordinary least squares regression model. The relationship is positive, indicating that warmer Atlantic SSTs are associated with larger losses as expected. The rank correlation between the amount of loss (exceeding US\$100 mn) and the May-June Atlantic SST is + 0.31 (p-value = 0.0086) over all years in the dataset and is + 0.37 (p-value = 0.0267) over the shorter 1950-2005 period.

We also examine models for the number of loss events using the covariates. We find that the NAO is useful in predicting both the number of large loss events and the number of small loss events. The relationship is negative, indicating that when the preseason value of the NAO decreases, the probability of a loss event increases. The rank correlation between the total number of loss events and the preseason NAO is -0.29 (p-value = 0.0032) over all years and is —0.12 (p-value = 0.3812) over the shorter 1950-2005 period. Interestingly, we find no significant preseason relationship between event counts and SST or the SOI.

The analysis confirms that it is reasonable to model small and large loss events separately. However, it should be noted that it might be more appropriate to add measurement error to the data so as to reduce the weight of the smaller measurements rather than separate the data as is done here. Our final strategy combines a model for the loss amount with two models for the number of loss events: one for large losses and the other for small losses. We use the NAO for predicting the number of loss events (both large and small) and the SST for predicting the amount of damage given a loss event. We find that including the preseason SOI covariate does not help in forecasting the upcoming season's losses either for the amount of loss or for the number of loss events. This result is consistent with those for the models developed in Elsner and Jagger (2006) and Elsner et al. (2006b) for predicting coastal hurricane activity based on preseason data. Since it is well known that ENSO has an influence on shear during the hurricane season, it might be advantageous to include a predicted value of the SOI for the hurricane season rather than a preseason value as is done here.