Mixtures of stochastic processes: Application to statistical downscaling

Analyses of mixtures of stochastic processes have begun to appear in climate research in recent years. Some general properties of mixtures that are well known within statistics, but not ordinarily utilized in complete generality in climate applications, are reviewed. How these issues apply in certain types of statistical downscaling is described. An important distinction is drawn between 'conditional' models, sometimes utilized in downscaling, and 'unconditional' models, utilized in more traditional approaches. Through a combination of the individual conditional models, a single overall (or 'induced') model is obtained. Among other things, the mixture concept suggests physically plausible mechanisms by which more complex stochastic models could arise in climate applications. As an application, the stochastic modeling of time series of daily precipitation amount conditional on a monthly index of large- (or regional) scale atmospheric circulation patterns is considered. Chain-dependent processes are used both as conditional and unconditional models of precipitation. For illustrative purposes, precipitation measurements for a site in California, USA, were fitted. How the mixture approach can aid in determining the properties of climate change scenarios produced by downscaling is demonstrated in this example. In particular, changes in the relative frequency of occurrence of the states of the circulation index would be associated not just with changes in mean precipitation, but with changes in its variance as well.