Bias reduction of high return levels for extreme hazard modelling

Abstract

Abstract Many existing extremal data span only a few decades, often resulting in large bias and uncertainty in the estimated shape parameter of the extreme hazard model. This in turn leads to unreliable predicted extreme values at high average recurrence intervals (ARI’s). This paper illustrates a statistical method that provides a mechanism to obtain a hazard model that produces return levels at high ARI’s with reduced bias. The method makes use of the maximum recorded values of extremal data independently recorded from a number of observational sites. The logarithmically transformed probability of the maximum recorded value at a site is shown to follow the Gumbel (Type I extreme-value) distribution, therefore multiple, say m, sites provide a sample of size m transformed probabilities of extreme values, each from a distinct site. The sample can be treated as being drawn from a Gumbel distribution, irrespective of the underlying hazard-generating mechanisms or the statistical hazard models. The method is demonstrated by an analysis of the extreme wind gust data collected from automatic weather stations in South Australia. The results are compared to the specifications in the Australian standard AS/NZS 1170.2:2021 and indicates that the standard may have overestimated the wind gust hazard, hence the specified design wind speeds may fall on the conservative side for South Australia.