Spatial modeling of rainfall accumulated over short periods of time

This article proposes a new random field model to describe the spatial variation of rainfall amounts accumulated over short periods of time. The model is intended to satisfy a set of desiderata motivated by the understanding of rainfall generating mechanisms and exploratory data analysis of datasets of this type. 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 also satisfies a stochastic dominance property, which is argued to be sensible and consistent with most rainfall data of this type. A study of identifiability is carried out, which strongly suggests all model parameters are identifiable. The generalized method of moments is proposed to estimate the parameters, and the properties of these estimators are explored based on simulated data.