An adaptive exponential model for extreme wind speed estimation

Abstract

The peaks-over-threshold (POT) method is a useful alternative to classical annual-maxima method for the estimation of extreme wind speeds from limited historical data. The basic idea is to model peak wind speeds exceeding a high threshold by the Pareto distribution, which is their domain of attraction. However, practical applications of POT method are confounded by the indeterminate nature of correct threshold beyond which the Pareto model becomes effective. This difficulty is further compounded by acute threshold sensitivity of wind speed estimates, which can be attributed to erratic variation of model and sampling errors with selected threshold values. To improve the statistical accuracy and reduce the threshold sensitivity of POT estimates, the paper presents an adaptive exponential model that relies on a quantitative notion of uncertainty used in information theory. In the proposed approach, an exponential prior is assigned to suitably preconditioned data, and it is augmented with additional sample information in an optimal sense through the principle of Minimum Cross-Entropy (Cross-Ent). Novel features of this model are systematic minimization of model error and significant reduction in sampling error by the use of probability-weighted moments. The performance of the proposed approach is compared with widely used Pareto and exponential models. Simulation-based examples illustrate that Cross-Ent estimates of 50 and 1000-year quantiles are almost unbiased and insensitive to the threshold value. POT analyses of US wind speed data also reveal a remarkably stable trend of Cross-Ent estimates. Bootstrap simulations also confirm higher accuracy of the proposed method in comparison to other traditional methods.