Articles | Volume 20, issue 9
Research article
05 Sep 2016
Research article |  | 05 Sep 2016

The transformed-stationary approach: a generic and simplified methodology for non-stationary extreme value analysis

Lorenzo Mentaschi, Michalis Vousdoukas, Evangelos Voukouvalas, Ludovica Sartini, Luc Feyen, Giovanni Besio, and Lorenzo Alfieri

Abstract. Statistical approaches to study extreme events require, by definition, long time series of data. In many scientific disciplines, these series are often subject to variations at different temporal scales that affect the frequency and intensity of their extremes. Therefore, the assumption of stationarity is violated and alternative methods to conventional stationary extreme value analysis (EVA) must be adopted. Using the example of environmental variables subject to climate change, in this study we introduce the transformed-stationary (TS) methodology for non-stationary EVA. This approach consists of (i) transforming a non-stationary time series into a stationary one, to which the stationary EVA theory can be applied, and (ii) reverse transforming the result into a non-stationary extreme value distribution. As a transformation, we propose and discuss a simple time-varying normalization of the signal and show that it enables a comprehensive formulation of non-stationary generalized extreme value (GEV) and generalized Pareto distribution (GPD) models with a constant shape parameter. A validation of the methodology is carried out on time series of significant wave height, residual water level, and river discharge, which show varying degrees of long-term and seasonal variability. The results from the proposed approach are comparable with the results from (a) a stationary EVA on quasi-stationary slices of non-stationary series and (b) the established method for non-stationary EVA. However, the proposed technique comes with advantages in both cases. For example, in contrast to (a), the proposed technique uses the whole time horizon of the series for the estimation of the extremes, allowing for a more accurate estimation of large return levels. Furthermore, with respect to (b), it decouples the detection of non-stationary patterns from the fitting of the extreme value distribution. As a result, the steps of the analysis are simplified and intermediate diagnostics are possible. In particular, the transformation can be carried out by means of simple statistical techniques such as low-pass filters based on the running mean and the standard deviation, and the fitting procedure is a stationary one with a few degrees of freedom and is easy to implement and control. An open-source MATLAB toolbox has been developed to cover this methodology, which is available at (Mentaschi et al., 2016).

Short summary
The climate is subject to variations which must be considered studying the intensity and frequency of extreme events. We introduce in this paper a new methodology for the study of variable extremes, which consists in detecting the pattern of variability of a time series, and applying these patterns to the analysis of the extreme events. This technique comes with advantages with respect to the previous ones in terms of accuracy, simplicity, and robustness.