Multivariate and data-driven regional frequency analysis for rainfall extremes

Due to the limited length of locally available sequences of precipitation extremes, point rainfall depth associated with given duration and return period is usually estimated through regional frequency analysis. Several statistical regionalization methods proposed in the literature enable one to exploit sequences of precipitation extremes observed at homogeneous pooling groups of sites, that supposedly share the same frequency regime of rainfall extremes with the site of interest. Homogeneous sites can be identified by looking at specific climatic descriptors; for instance, some reliable authors successfully utilize Mean Annual Precipitation (MAP) as the sole proxy for locally characterizing the frequency regime of sub-daily rainfall extremes, and for grouping sequences of rainfall extremes records. We aim at advancing this traditional approach (1) by relaxing the hypothesis of the existence of a homogeneous pooling group of sites characterized by a unique regional parent distribution and (2) by incorporating additional morphological and climatic information in the regional model. We rely on more than 2350 Annual Maximum Series of rainfall depth for different time-aggregation intervals between 1 and 24 hours, observed since 1928 to 2011 in a vast study area in Northern Italy.  We refer to MAP as well as to additional morphologic descriptors (e.g.  minimum distance to Tyrrhenian (Adriatic) Sea, mean elevation and slope around the station, etc.).

We train a probabilistic neural network that models the frequency regime of observed annual maxima of rainfall depth resorting to a Generalized Extreme Value (GEV) distribution, whose parameters are data-driven functions of the local values of the selected descriptors and duration. Then, several cross-validation experiments are performed to assess the accuracy of the developed regional model relative to a simpler regional GEV model, whose parameters are functions of MAP and time-aggregation intervals.

Our analyses address several research problems: (a) identifying the most descriptive morphological proxies to combine with MAP for representing the frequency regime of sub-daily rainfall extremes in the study area, (b) highlighting limitations and potential of data-driven multivariate regional models of the frequency regime of rainfall extremes, (c) the advantages of a multivariate approach relative to a regionalization scheme based on MAP alone.