Nonstationary hydrological frequency analysis using the Metastatistical extreme value distribution

Abstract

The nonstationary hydrological frequency analysis (NS-HFA) aids in assessing the recurrence of hydrological extremes under nonstationarity, but its reliability is often questioned due to relatively limited record lengths. The Metastatistical extreme value (MEV) distribution, which harnesses the ordinary event records along with the extremes, has proven advantageous under stationarity and in instances with limited records. Yet, nonstationary applications of the MEV distribution are lacking, and only modified versions, such as the simplified MEV (SMEV) and block-based MEV (MEVBB) distributions, have been proposed. This paper develops the nonstationary version of the MEV distribution for NS-HFA (called the MEV-based model), which incorporates an explicit nonstationary structure and preserves the stochastic interannual variability of ordinary events. The developed model is assessed using several benchmark models in both simulation studies and real applications for both in-sample fitting and out-of-sample prediction from the perspectives of uncertainty, accuracy, and fitting efficiency. The benchmark models for comparison included the MEVBB as well as the SMEV- and Generalized Extreme Value distribution (GEV)-based models. The results demonstrated that the proposed MEV-based model outperformed the MEVBB regarding overfitting and captured the underlying process more efficiently, accurately, and with less uncertainty. In addition, the MEV-based model was superior to the GEV-based model due to its higher accuracy, equivalent or better fitting efficiency, and lower uncertainty. Furthermore, although the MEV-based model performed overall equivalently to the SMEV-based, the MEV-based model was shown advantageous for adopting nonstationary stochastic physical covariates and facilitating out-of-sample predictions. Overall, these results demonstrated that the proposed MEV-based model has distinct advantages for the NS-HFA, and consequently promotes its implementation.