A New Parsimonious Methodology of Mapping the Spatial Variability of Annual Maximum Rainfall in Mountainous Environments

The estimation of rare frequency rainfall is an essential prerequisite for the design of engineering structures\udand to determine risk areas. Index-based methods are among the most applied for regional frequency analysis of hydrological variables such as discharge and rainfall and comprise two stages: the mapping of a scale or “index” factor and the derivation of rainfall growth curves. The underlying hypothesis of these\udmethods is that cumulative distribution functions of a certain random variable can be assumed homogeneous on a given region, except for the index factor, which varies spatially in that region and is often represented by the expected value of the random variable itself at a given location. Methods either to single\udout homogeneous regions or to evaluate the index factor can be purely statistical and physically based.\udIn this paper a robust and transferable physically based methodology is proposed to estimate the index factor for rainfall in mountainous regions referred to in the following text as “index rainfall.” Index rainfall is defined as the expected value of annual rainfall maxima recorded in a fixed time window: a time window\udof 1 h is used. Reliable estimates of the index rainfall are obtained at ungauged sites by applying a relationship, based on a multivariate linear regression obtained at gauged sites, of rainfall and selected synthetic descriptors for atmospheric climate and orography. An extended and general set of descriptors is\udchosen from parameters that are considered in the literature to affect rainfall intensity. The relevant relief descriptors, defining slope, elevation, orientation, etc., at a given location, are extracted from digital elevation models (DEMs). A 2D Fourier series analysis of the DEM is performed and a spectral analysis is\udcarried out to single out the components with the highest morphological information content. The synthetic\udrelief descriptors are evaluated along different cross sections of the 2D truncated Fourier series to single out\udthe role of the prevailing convection direction of extreme rainfall-producing meteorological patterns. The\udoptimal descriptor subset for the study area is then extracted to maximize transferability of the method.\udApplication to the Italian and French Alps and the Apennines shows encouraging results. Descriptor subset\udextraction has been tested and validated on independent subsets of index rainfall estimates in the regions.\udResults demonstrate that the proposed method is robust, transferable, and reliable for the evaluation of the\udindex rainfall in ungauged sites