Coupling the strengths of optimization and simulation for calibrating Poisson cluster models

Many hydrological applications require use of rainfall data across a wide range of time scales. To simulate rainfall at fine time scales, stochastic approaches are usually enrolled. A leading representative is the Bartlett-Lewis model, which belongs to the family of Poisson-cluster processes that represent rainfall events. The usual approach of model calibration comprises the incorporation of the theoretical model equations in an objective function and the optimization of that function. However, it is obvious that this procedure is limited to the case that analytical equations exist for the modelled stochastic properties of the process. Yet such analytical equations cannot be derived for key characteristics such as skewness and parameters determining the distribution of extreme values. Here we present an innovative approach that remedies those weaknesses through the combined use of simulation and optimization. During model calibration, the model statistics are derived by Monte Carlo simulation, instead of theoretical equations. Various calibration criteria as well as statistical parameters are introduced aiming at more faithful representation of the rainfall process at different time scales. The efficiency of the proposed method is demonstrated using a long data series from a rain gauge in Athens.