A nested multisite daily rainfall stochastic generation model

Abstract

Summary This paper describes a nested multisite daily rainfall generation model which preserves the statistics at daily, monthly and annual levels of aggregation. A multisite two-part daily model is nested in multisite monthly, then annual models. A multivariate set of fourth order Markov chains is used to model the daily occurrence of rainfall; the daily spatial correlation in the occurrence process is handled by using suitably correlated uniformly distributed variates via a Normal Scores Transform (NST) obtained from a set of matched multinormal pseudo-random variates, following Wilks [Wilks, D.S., 1998. Multisite generalisation of a daily stochastic precipitation generation model. Journal of Hydrology 210, 178–191]; we call it a hidden covariance model. A spatially correlated two parameter gamma distribution is used to obtain the rainfall depths; these values are also correlated via a specially matched hidden multinormal process. For nesting, the generated daily rainfall sequences at all the sites are aggregated to monthly rainfall values and these values are modified by a set of lag-1 autoregressive multisite monthly rainfall models. The modified monthly rainfall values are aggregated to annual rainfall and these are then modified by a lag-1 autoregressive multisite annual model. This nesting process ensures that the daily, monthly and annual means and covariances are preserved. The model was applied to a region with 30 rainfall sites, one of the five sets reported by Srikanthan [Srikanthan, R., 2005. Stochastic Generation of Daily Rainfall Data at a Number of Sites. Technical Report 05/7, CRC for Catchment Hydrology. Monash University, 66p]. A comparison of the historical and generated statistics shows that the model preserves all the important characteristics of rainfall at the daily, monthly and annual time scales, including the spatial structure. There are some outstanding features that need to be improved: depths of rainfall on isolated wet days and sequences of wet days do not depend on the duration of the wet spell as well as they should; the remedy is not trivial, but will be addressed in a follow-up study. The skewness of monthly rainfall was not preserved well which appears to be a deficiency, but this is not considered important, because nearly all other validation statistics are well captured by the model and comparative cumulative frequency distribution plots of the daily depths show satisfactory matches.