A critical analysis of the shortcomings in spatial frequency analysis of rainfall extremes based on homogeneous regions and a comparison with a hierarchical boundaryless approach

We investigate and discuss limitations of the approach based on homogeneous regions (hereafter referred to as regional approach) in describing the frequency distribution of annual rainfall maxima in space, and compare its performance with that of a boundaryless approach. The latter is based on geostatistical interpolation of the at-site estimates of all distribution parameters, using kriging for uncertain data. Both approaches are implemented using a generalized extreme value theoretical distribution model to describe the frequency of annual rainfall maxima at a daily resolution, obtained from a network of 256 raingauges in Sardinia (Italy) with more than 30 years of complete recordings, and approximate density of 1 gauge per 100 km2. We show that the regional approach exhibits limitations in describing local precipitation features, especially in areas characterized by complex terrain, where sharp changes to the shape and scale parameters of the fitted distribution models may occur. We also emphasize limitations and possible ambiguities arising when inferring the distribution of annual rainfall maxima at locations close to the interface of contiguous homogeneous regions. Through implementation of a leave-one-out cross-validation procedure, we evaluate and compare the performances of the regional and boundaryless approaches miming ungauged conditions, clearly showing the superiority of the boundaryless approach in describing local precipitation features, while avoiding abrupt changes of distribution parameters and associated precipitation estimates, induced by splitting the study area into contiguous homogeneous regions.