A Bayesian formulation of the Metastatistical Extreme Value Distribution accounting for rainfall interannual variability

Abstract:

Here we introduce a Bayesian framework for modelling extreme values of rainfall time series which explicitly accounts for the low-frequency interannual variability of precipitation time series. This is achieved by adopting a hierarchical model structure in which the distributions of both rainfall events frequency and intensity vary at the annual time scale. Inference is conducted following a numerical Bayesian approach which allows for the inclusion of relevant prior information on the properties local rainfall regimes. This methodology leads to a fully probabilistic description of quantities of practical interest for hydrological applications, such as the frequency of annual maxima rainfall quantiles. Here we apply the proposed model to a large dataset of daily rainfall obtained from long instrumental records covering the Continental United States. We show that this approach i) leads to improved inference in the case of relatively short datasets, and ii) can benefit from prior information on the physical processes involved in order to reduce estimation uncertainty. Further, we show how synoptic-scale climatic information can be explicitly included in the statistical description of rainfall. By focusing on the position of the North Atlantic Subtropical High, a circulation index relevant for our study region, we show how low-frequency climate information can be use to infer local variations in both rainfall frequency and intensity. This information can in turn be instrumental in studying statistical properties of rainfall conditional to future values of the climate index. Overall, we find that that accounting for low frequency variability often leads to statistical models for daily rainfall which are characterized by heavier tails, thus underlining the importance of climatic variability in determining the extreme-value statistical properties of rainfall sequences.