A generalized method for the analysis of non-stationary joint extremes based on the transformed-stationary extreme value analysis

Extreme value analysis (EVA) includes a range of methods used to study the frequency and magnitude of rare but catastrophic events, with applications in science and engineering. These methods rely on mathematical theories that assume stable input data over time. However, many long-term datasets, especially those related to natural hazards, show clear changes over time (non-stationarity). With the availability of long-term climate records, there is a need for a reliable approach to analyze non-stationary extreme events that occur together (compound events), which is crucial for hazard assessment. This study introduces a method to analyze non-stationary joint extremes by combining Transformed-Stationary Extreme Value Analysis (tsEVA) with copula theory. This approach accounts for changes in the relationship between variables over time. The method includes sampling strategies to select relevant events, applying tsEVA for non-stationary univariate distributions, and using time-varying copulas to model the evolving relationships between variables. It thus considers all possible sources of non-stationarity that may affect joint extremes. The framework also incorporates statistical tools like the Mann-Kendall test to assess the significance of trends and Monte Carlo resampling for model validation and uncertainty analysis. Using this approach, the joint distribution of extremes in various natural hazards, such as river discharge, wave height, temperature, and drought, was successfully analyzed. The results highlighted the method's effectiveness in addressing diverse sources of non-stationarity and revealed dynamic patterns in variable interrelationships. Furthermore, the methodology developed in this study offers a viable tool for future research focused on generating statistically consistent hazard scenarios to support comprehensive risk assessments.