A Neyman-Scott model with continuous distributions of storm types

Abstract

A point process rainfall model is further developed that has storm origins occurring in space-time according to a Poisson process, where each storm origin has a random radius so that storms occur as circular regions in two-dimensional space, where the storm radii are taken to be independent exponential random variables. Each storm origin is of random type z, where z follows a continuous probability distribution. Cell origins occur in a further spatial Poisson process and have arrival times that follow a Neyman-Scott point process. Each cell origin has a radius so that cells form discs in two-dimensional space, where the cell radii are independent exponential random variables. Each cell has a random lifetime and an intensity that remains constant over both the cell lifetime and cell disk area. Statistical properties up to third order are given for the model. Using these properties, the model is fitted to 10 min series taken from 23 sites across the Rome region, Italy. Distributional properties of the observed annual maxima are compared to equivalent values sampled from series that are simulated using the fitted model. The results indicate that the model will be of use in urban drainage projects for the Rome region. Copyright 2010 by the American Geophysical Union.