| 12 May 2025
Transformed-Stationary EVA 2.0: A Generalized Framework for Non-Stationary Joint Extremes Analysis
Abstract. The increasing availability of extensive time series on natural hazards underscores the need for robust non-stationary methods to analyze evolving extremes. Moreover, growing evidence suggests that jointly analyzing phenomena traditionally treated as independent, such as storm surge and river discharge, is crucial for accurate hazard assessment. While univariate non-stationary extreme value analysis (EVA) has seen substantial development in recent decades, a comprehensive methodology for addressing non-stationarity in joint extremes – compound events involving simultaneous extremes in multiple variables – is still lacking. To fill this gap, here we propose a general framework for the non-stationary analysis of joint extremes that combines the Transformed-Stationary Extreme Value Analysis (tsEVA) approach with Copula theory. This methodology implements sampling techniques to extract joint extremes, applies tsEVA to estimate non-stationary marginal distributions using GEV or GPD distributions, and utilizes time-dependent copulas to model evolving inter-variable dependencies. The approach's versatility is demonstrated through case studies analyzing historical time series of significant wave height, river discharge, temperature, and drought, uncovering dynamic dependency patterns over time. To support broader adoption, we provide an open-source MATLAB toolbox that implements the methodology, complete with examples, available on GitHub.
The authors present the generalization of a method for statistically analyzing the joint extremes of different environmental variables under non-stationary conditions.
The work is scientifically relevant and addresses a current problem, especially under the conditions of ongoing climate change.
The provision of the code for applying the analysis to other case studies is highly appreciated. I believe the paper could be published after some minor revisions.
In Table 1, I would suggest adding an explanation of the meaning of the third column.
In the description of the first case study, it would be appropriate to add a justification for the choice of a 45-day time window between two extremes. At first glance, this may seem strange, given that it involves the analysis of joint flood probabilities in small basins and wave heights. The choice could make sense if one wishes to consider the joint probability of events with a view to recovery between one event and the next, but I believe this needs to be explained further.
From the text, it appears that in some cases the analyses are based on model results rather than recorded data. This, due to a possible bias between the simulations and the actual data, could impact the quantification of return periods, and I believe it should be explicitly stated. Or, if it has been done, specify whether any form of bias correction was applied to the model data.