A spatiotemporal model for downscaling precipitation occurrence and amounts

A stochastic model that relates synoptic atmospheric data to daily precipitation at a network of gages is presented. The model extends the nonhomogeneous hidden Markov model (NHMM) of Hughes et al, by incorporating precipitation amounts. The NHMM assumes that multisite, daily precipitation occurrence patterns are driven by a finite number of unobserved weather states that evolve temporally according to a first-order Markov chain. The state transition probabilities are a function of observed or modeled synoptic scale atmospheric variables such as mean sea level pressure. For each weather state we evaluate the joint distribution of daily precipitation amounts at n sites through the specification of n conditional distributions. The conditional distributions consist of regressions of transformed amounts at a given site on precipitation occurrence at neighboring sites within a set radius. Results for a network of 30 daily precipitation gages and historical atmospheric circulation data in southwestern Australia indicate that the extended NHMM accurately simulates the wet-day probabilities, survival curves for dry- and wet-spell lengths, daily precipitation amount distributions at each site, and intersite correlations for daily precipitation amounts over the 15 year period from 1978 to 1992.