Fitting a multisite daily rainfall model to New Zealand data

This study considers a generalisation of a multisite daily rainfall generation model originally proposed by Wilks (1998) [Wilks, D.S., 1998. Multisite generalization of a daily stochastic precipitation generation model. J. Hydrol. 210, 178–191.] in the context of weather simulation. This particular model is reformulated as a hidden Markov model and its properties are determined. Maximum likelihood estimation procedures are developed, including the EM (Expectation-Maximisation) algorithm, as well as simple method of moments estimation procedures that build on those proposed in Wilks (1998). A restricted maximum likelihood procedure is also proposed as a computationally efficient and practical strategy for fitting the general model, providing consistent and reliable estimates of the model parameters that typically show small differences when compared to full maximum likelihood. The fully-parameterised model and the Wilks reduced form of the model are fitted to selected New Zealand rainfall data and their performance assessed. The Wilks model was not generally favoured over the fully-parameterised model except for a few months mainly associated with the drier months during the austral summer. In the light of this experience, further research developments and initiatives are highlighted.