A nested multisite daily rainfall stochastic generation model

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.