A space and time model for design storm rainfall

Realistic rainfields that represent storms with a known return period are required as input to design calculations for hydrological projects that cover a wide range of hydrological scales. The current standard practice is to assume either that the storm is uniform in time and space or that it varies in some very simple manner. Multiaffine models of rainfall, based on the concept of a multiplicative cascade, provide the possibility of generating a stochastic series of space and time rainfall that reproduces the observed behavior. The spatial distribution of a field of instantaneous rain rates is modeled using the multiplicative cascade approach. The temporal development of the cascade weights at each level in the cascade is modeled with a simple autoregressive ARMA(1,1) model where the parameters vary in a systematic manner with scale. The model is verified using rain fields produced by a monsoonal depression that passed over a weather radar at Darwin, Australia. Radar data for the event were used to estimate the model parameters. The model was able to reproduce the observed temporal and spatial correlation functions over a range of scales, and the probability distributions over a range of scares, for both the instantaneous and the hourly accumulations.