Frequency analysis of a sequence of dependent and/or non-stationary hydro-meteorological observations: A review

Abstract

Frequency analysis is a technique of fitting a probability distribution to a series of observations for defining the probabilities of future occurrences of some events of interest, e.g., an estimate of a flood magnitude corresponding to a chosen risk of failure. The use of this technique has played an important role in engineering practice. The assumptions of independence and stationarity are necessary conditions to proceed with such analyses. However, in the context of climate change, it is possible that these assumptions would no longer hold and the results of conventional frequency analysis would become doubtful. Under such circumstances, it is important that recourse be made to other suitable approaches which incorporate non-independence and non-stationarity of hydro-meteorological extremes. In paper, a brief review of the current approaches to these issues is presented. Approaches that remove the effect of serial dependence to obtain independent observations are presented and the ones that involve kernel or wavelet-based probability density estimation are only discussed for frequency analysis of dependent observations. For frequency analysis of non-stationary observations, the reviewed approaches include the extremal, r-largest, peaks-over-threshold, time-varying moments, pooled flood frequency analysis, local likelihood and quantile regression. Synthesis of the reviewed approaches is presented, issues related to establishing non-stationary behavior are discussed and future challenges in frequency analysis of hydro-meteorological extremes are discussed as well. Extensions to some of the reviewed approaches and new avenues of research have been identified for further development and improvement. It is also concluded that, to be most useful, non-stationarity considerations be incorporated into new risk assessment frameworks.