On reducing bias at high return levels for extreme value analysis

Abstract

: Estimates of extremal return levels at high average recurrence intervals (ARIs) are strongly dependent on the shape parameter of the statistical model. Because of scarcity in occurrences, however, 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 ARIs. A common approach to ameliorate this shortcoming is the ‘super-station’ (or station-year) approach which extends the length of record and should reduce the uncertainty in high ARIs. However, the problem of predicted bias remains for return levels beyond the record length of the super-station. This paper illustrates a statistical method that provides a mechanism to obtain a hazard model that produces return levels at high ARIs with reduced bias. For an ensemble of independently collected records from a number of observational sites, the method makes use of the maximum recorded value of each of the extremal data of the ensemble, as shown in Figure 1 as the starred points (green points represent synoptic and red points non-synoptic wind gusts). 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 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.