MIXTURES OF STOCHASTIC-PROCESSES - APPLICATION TO STATISTICAL DOWNSCALING

Analyses of mixtures of stochastic processes have begun to appear in c limate research in recent years. Some general properties of mixtures t hat are well known within statistics, but not ordinarily utilized in c omplete generality in climate applications, are reviewed. How these is sues apply in certain types of statistical downscaling is described. A n important distinction is drawn between 'conditional' models, sometim es utilized in downscaling, and 'unconditional' models, utilized in mo re traditional approaches. Through a combination of the individual con ditional models, a single overall (or 'induced') model is obtained. Am ong other things, the mixture concept suggests physically plausible me chanisms by which more complex stochastic models could arise in climat e applications. As an application, the stochastic modeling of time ser ies of daily precipitation amount conditional on a monthly index of la rge- (or regional) scale atmospheric circulation patterns is considere d. Chain-dependent processes are used both as conditional and uncondit ional models of precipitation. For illustrative purposes, precipitatio n measurements for a site in California, USA, were fitted. How the mix ture 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 sta tes of the circulation index would be associated not just with changes in mean precipitation, but with changes in its variance as well.