A comparison of three stochastic multi-site precipitation occurrence generators

Abstract

Summary This paper presents a comparison of three multi-site stochastic weather generators for simulation of point rainfall occurrences at a network of 30 raingauge stations around Sydney, Australia. The approaches considered include a parametric hidden Markov model (HMM), a multi-site stochastic precipitation generation model (proposed by [Wilks, D.S., 1998. Multi-site generalization of a daily stochastic precipitation model, J. Hydrol. 210, 178–191.]) and a non-parametric K-nearest neighbour (KNN) model. The HMM generates the precipitation distribution conditional on a discrete weather state representing certain identified spatial rainfall distribution patterns. The spatial dependence is maintained by assumption of a common weather state across all stations while the temporal dependence is simulated by assuming the weather state to be Markovian in nature. The Wilks model preserves serial dependence through the assumption of an order one Markov dependence at each location. The spatial dependence is simulated by prescribing a dependence pattern on the uniform random variates used to generate the rainfall occurrence at each location from the associated conditional probability distribution. The K-nearest neighbour approach simulates spatial dependence by simultaneously generating precipitation occurrence at all locations. Temporal persistence is simulated through Markovian assumptions on the rainfall occurrence process. The three methods are evaluated for their ability to model spatial and temporal dependence in the rainfall occurrence field and also the relative ease with which the assumptions of spatial and temporal dependence can be accommodated. Our results indicate that all the approaches are successful in reproducing spatial dependence in the multi-site rainfall occurrence field. However, the different orders of assumed Markovian dependence in the observed data limit their ability in representing temporal dependence at time scales longer than a few days. While each approach comes with its own advantages and disadvantages, the alternative proposed by Wilks has an overall advantage in offering a mechanism for modelling varying orders of serial dependence at each point location, while still maintaining the observed spatial dependence with sufficient accuracy.