Nonstationary frequency analysis of extreme precipitation: Embracing trends in observations

Knowledge of the recurrence intervals of precipitation extremes is vital for infrastructure design, risk assessment, and insurance planning. However, trends and shifts in rainfall patterns globally pose challenges to the application of extreme value analysis (EVA) which relies critically on the assumption of stationarity. In this paper, we explore: (1) the suitability of nonstationary (NS) models in the presence of statistically significant trends, and (2) their potential in modeling out-of-sample data to improve frequency analysis of extreme precipitation. We analyze the benefits of using a nonstationary Generalized Extreme Value (GEV) model for annual extreme precipitation records from Southern Brazil. The location of the GEV distribution is allowed to change with time. The unknown GEV model parameters are estimated using Bayesian techniques coupled with Markov chain Monte Carlo simulation. Next, we use GAME sampling to compute the evidence (and their ratios, the so-called Bayes factors) for stationary and nonstationary models of annual maximum precipitation. Our results show that the presence of a statistically significant trend in annual maximum precipitation alone does not justify the use of a NS model. The location parameter of the GEV distribution must also be well defined, otherwise, stationary models of annual maximum precipitation receive more support by the data. These findings reiterate the importance of accounting for GEV model parameters and predictive uncertainty in frequency analysis and hypothesis testing of annual maximum precipitation data records. Furthermore, a meaningful EVA demands detailed knowledge about the origin and persistence of observed changes.