A simulation method for calibrating cluster-process rainfall models

Abstract

Cluster-process rainfall models such as the Bartlett-Lewis and Neyman-Scott Rectangular Pulses models typically use the method of moments to calibrate model properties to sample moments from observed data. This procedure requires derivation of the analytic properties of the model, but the requirement of analytic tractability can inhibit the flexibility of model specification. This paper compares the effectiveness of calibration for a Neyman-Scott model using analytically derived properties to a Monte Carlo Simulation (MCS) method based on matching observed and simulated statistics. The MCS method proceeds by simulating the rainfall sequence of finite length from a given parameter set, calculating statistical estimates from this sequence and comparing them to the same statistics from observed data. The main advantage of the simulated approach is demonstrated for its ability to use a variety of statistics for calibration without the need to derive the properties of the model. The computational feasibility of the MCS method is discussed with particular concern for efficiently simulating over a spatial domain. A case-study for selected rainfall sites in Tasmania is used to demonstrate the feasibility of the MCS method.