Mixture model for overdispersion of precipitation

Stochastic models fit to time series of daily precipitation amount generall y ignore any year-to-year (i.e., low frequency) source of random variation, and such models are known to underestimate the interannual variance of mon thly or seasonal total precipitation. To explicitly account for this "overd ispersion" phenomenon, a mixture model is proposed. A hidden index, taking on one of two possible states, is assumed to exist (perhaps representing di fferent modes of atmospheric circulation). To represent the intermittency o f precipitation and the tendency of wet or dry spells to persist, a stochas tic model known as a chain-dependent process is applied. The parameters of this stochastic model are permitted to vary conditionally on the hidden ind ex. Data for one location in California (whose previous study motivated the pre sent approach), as well as for another location in New Zealand, are analyze d. To estimate the parameters of a mixture of two conditional chain-depende nt processes by maximum likelihood, the "expectation-maximization algorithm " is employed. It is demonstrated that this approach can either eliminate d r greatly reduce the extent of the overdispersion phenomenon. Moreover, an attempt is made to relate the hidden indexes to observed features of atmosp heric circulation. This approach to dealing with overdispersion is contrast ed with the more prevalent alternative of fitting more complex stochastic m odels for high-frequency variations to rime series of daily precipitation.