Eight years of summer storm rainfall observations from 93 stations in and around the 154 km² Walnut Gulch catchment of the Agricultural Research Service, U.S. Department of Agriculture, in Arizona are processed to yield the total station depths of 428 storms. Statistical analysis of these random fields yields the first two moments, the spatial correlation and variance functions, and the spatial distribution of total rainfall for each storm. The sample is then split, and half is used to estimate, for each storm day, the distributions of the three parameters of each of the three conceptual spatial Poisson process models proposed previously by Rodriguez-Iturbe et al. (1986). The absolute and relative worth of the three Poisson models are evaluated by comparing their prediction of the spatial distribution of storm rainfall with observations from the second half of the sample. The effect of interstorm parameter variation is examined.