Stochastic Modeling of Daily Summertime Rainfall over the Southwestern United States. Part I: Interannual Variability

Abstract

The interannual variability of summertime daily precipitation at 78 stations in the southwestern United States is studied using chain-dependent models and nonparametric empirical distributions of daily rainfall amounts. Modeling results suggest that a second-order chain-dependent model can optimally portray the temporal structure of the summertime daily precipitation process over the southwestern United States. The unconditioned second-order chain-dependent model, in turn, can explain approximately 75% of the interannual variance in the seasonal total wet days over the region and 83% of the interannual variance in the seasonal total precipitation. In addition, only a small fraction (generally smaller than 20%) of the observed years at any given station show statistically significant changes in the occurrence and intensity characteristics, related to either the number of seasonal total wet days or the distributions of daily rainfall amounts. Investigations of the year-to-year variations in the occurrence and intensity characteristics indicate that both variations are random (on interannual time scales), and they display similar significance in explaining the remaining 17% of interannual variance of seasonal total precipitation over the region. However, numerical tests suggest that the interannual variations of the two are not independent for the summertime monsoon precipitation, and that complex covariability that cannot be described with simple stochastic statistical models may exist between them.