Spatial Modeling of Rainfall Accumulated over Short Periods of Time

A variety of spatial (or spatio-temporal) models have been explored for the rainfall data, since it is an hydrological variable of paramount importance and the key for the natural evolution of ecosystems and for the operation of man–made structures such as water distribution and irrigation systems. This work deals with the rainfall data accumulated over short periods of time in a given region.

A new random field spatial model is proposed to describe the spatial variation of this type of rainfall data. The model is intended to satisfy a set of desiderata motivated by the understanding of rainfall generating mechanisms and exploratory data analysis of datasets. First and second order properties of the proposed model are derived, including the mean and covariance functions, as well as the families of marginal and bivariate distributions. Properties of the proposed model are shown by a mix of analytical derivations and numerical exploration that use Gauss–Hermite quadrature to approximate the required integrals. The proposed model is found empirically to satisfy a stochastic dominance property, which is argued to be sensible and consistent with most rainfall data of this type.

Two different approaches are proposed to estimate the parameters, and the properties of these esti- mators are explored based on simulated data. Another modified approach is developed according to the results of estimation, which is based on fixing one of the parameters. This is motivated by the finding that several model features are not sensitive to changes of the aforementioned parameter, rendering it poorly identifiable from the data. The analysis on real data of rainfall amount collected around Guadalupe River Basin is carried out for 20 days in 2004.