Spatial Poisson Models of Stationary Storm Rainfall: Parameterization, Evaluation and Numerical Simulation

Abstract

Eight years of summer raingage observations are analyzed for a dense, 93 raingage, network operated by the U.S. Department of Agriculture, Agricultural Research Service, in the 150 km2 Walnut Gulch catchment near Tucson, Arizona. Storms are defined by the total depths collected at each raingage during the noon-to-noon period for which there was depth recorded at any of the gages. For each of the resulting 428 storm days, the 93 gage depths are interpolated onto a dense grid and the resulting random field is analyzed to obtain storm depth isohyets, the first three moments of point storm depth, the spatial correlation function, the spatial variance function, and the spatial distribution of total rainstorm depth. The sample is split and half is used to estimate for each storm day the three parameters of each of three conceptual spatial Poisson process models proposed elsewhere [Rodriguez-Iturbe, Cox and Eagleson, 1986]. The distributions of these parameters are estimated and used to evaluate the absolute and relative worth of the three Poisson models in comparison with the second half of the sample.