Abstract:
Many hydrological and agricultural studies require simulation of weather variables that reflect the spatial and temporal dependence observed in point rainfall at multiple locations. This paper assesses three approaches for stochastic generation of multi-point daily rainfall that use different rationales for representing the spatio-temporal dependence that is observed. This assessment is based on an application of the three approaches to point rainfall occurrences at a network of 30 raingauge stations around Sydney, Australia, the rainfall amounts subsequently being generated on the wet days using a nonparametric amount model independent of the occurrence process. The approaches considered consist of a multisite modified Markov model (proposed by Mehrotra and Sharma, 2007b), a method for reconstructing space-time variability (proposed by Clark et al., 2004), and the nonparametric k-nearest neighbour (KNN) model (as outlined in Lall and Sharma, 1996). The Modified Markov model simulates precipitation occurrences at individual locations considering low as well as high order Markovian dependence, the spatial dependence being simulated through the use of random innovations that exhibit a spatial dependence structure. In the reconstructing approach, the realisations for a given simulated day are ranked and matched with the rank of the days randomly selected from the similar dates in the historical record. The realisations are then re-ordered to correspond to the original order of the selected historical record thereby reflecting the observed spatio-temporal dependence in the generated series. The k-nearest neighbour approach reproduces spatial precipitation distribution structure by simulating precipitation occurrences jointly at multiple locations. Temporal persistence is preserved through Markovian assumptions on the rainfall occurrence process.
The three methods are evaluated for their ability to model various spatial and temporal rainfall attributes over the study area. Our results indicate that all the approaches are successful in reproducing the spatial pattern of the multi-site rainfall 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 Mehrotra and Sharma (2007b) 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. The reordering method of Clark et al. (2004) is simple and intuitive, however, is primarily driven by the variability of the observed record, and may not be suited in applications where exogenous covariates can be of help in the simulation process. Implications of using these methods in a water resources management study are discussed.
