Mixture Model For Overdispersion of Precipitation

Abstract

Stochastic models fit to time series of daily precipitation amount generally ignore any year-to-year (i.e., low frequency) source of random variation, and such models are known to underestimate the interannual variance of monthly or seasonal total precipitation. To explicitly account for this ?overdispersion? phenomenon, a mixture model is proposed. A hidden index, taking on one of two possible states, is assumed to exist (perhaps representing different modes of atmospheric circulation). To represent the intermittency of precipitation and the tendency of wet or dry spells to persist, a stochastic model known as a chain-dependent process is applied. The parameters of this stochastic model are permitted to vary conditionally on the hidden index. Data for one location in California (whose previous study motivated the present approach), as well as for another location in New Zealand, are analyzed. To estimate the parameters of a mixture of two conditional chain-dependent processes by maximum likelihood, the ?expectation-maximization algorithm? is employed. It is demonstrated that this approach can either eliminate or greatly reduce the extent of the overdispersion phenomenon. Moreover, an attempt is made to relate the hidden indexes to observed features of atmospheric circulation. This approach to dealing with overdispersion is contrasted with the more prevalent alternative of fitting more complex stochastic models for high-frequency variations to time series of daily precipitation.