Estimating extreme monthly rainfall for Spain using non-stationary techniques

Abstract

In hydrology, extreme value analysis is normally applied at stationary yearly maxima. However, climate variability can bias the estimation of extremes by partially invalidating the stationary assumption. Extreme value analysis for sub-yearly data may depart from stationarity (since maxima from one month may not be exchangeable with maxima from another) in terms of requiring to include it in the analysis. Here, we analyse the non-stationary structure of extreme monthly rainfall in Spain using two approaches: a parametric approach and an approach based on autoregressive time series models. Our analysis considers seasonality, climate variability and long-term trends for both approaches, and it compares both including their goodness of fit and complexity. The approach uses maximum likelihood estimation and Bayesian techniques. Our results show that autoregressive models outperform parametric models, providing a more accurate representation of extreme events when extrapolating outside of the period of fit.