A stochastic spatial-temporal disaggregation model for rainfall

A stochastic model for disaggregating spatial-temporal rainfall data is presented. In the model, the starting times of rain cells occur in a Poisson process, where each cell has a random duration and a random intensity. In space, rain cells have centres that are distributed according to a two-dimensional Poisson process and have radii that follow an exponential distribution. The model is fitted to seven years of five-minute data taken from six sites across Auckland City. The historical five-minute series are then aggregated to hourly depths and stochastically disaggregated to five-minute depths using the fitted model. The disaggregated series and the original five-minute historical series are then used as input to a network flow simulation model of Auckland City's combined and wastewater system. Simulated overflow volumes predicted by the network model from the historical and disaggregated series are found to have equivalent statistical distributions, within sampling error. The results thus support the use of the stochastic disaggregation model in the intended application.