Estimation of Daily Rainfall Extremes Through the Metastatistical Extreme Value Distribution: Uncertainty Minimization and Implications for Trend Detection

Abstract

AbstractThe accurate estimation of hydrologic extremes is central to planning and engineering mitigation and adaptation measures. The traditional extreme value theory is based on often overlooked assumptions that preclude the use of all available observations and negatively affect estimation uncertainty. The Metastatistical Extreme Value Distribution (MEVD) was introduced to make full use of available data and was shown to significantly improve estimation uncertainty for large extremes. However, no systematic understanding existed as to how to optimally apply the MEVD depending on the statistical properties of the observed variables. With reference to daily rainfall, we identify here the local climatic factors that define the optimal MEVD formulation. We analyze a large set of long daily rainfall records, as well as synthetic time series with prescribed statistical characteristics, and find that (1) in most climates the MEVD should be based on yearly estimates of the ordinary rainfall distributions, and only in climates with less than 20–25 year the estimation of distributional/year the estimation of distributional parameters requires samples longer than 1 year; (2) the interannual variability in the distributions of rainfall should be explicitly resolved when 20–25 rainy days/year. Finally, we use the optimized MEVD to study the variability of daily rainfall extremes over 294 years in Padova (Italy) and compare it to traditional extreme value estimates. We find that, through its improved accuracy for short observations, MEVD better resolves high‐quantile fluctuations and allows the emergence of long‐term trends over estimation noise.