A hidden Markov model for downscaling synoptic atmospheric patterns to precipitation amounts

Nonhomogeneous hidden Markov models (NHMMs) provide a relatively simple fra mework for simulating precipitation at multiple rain gauge stations conditi onal on synoptic atmospheric patterns. Building on existing NHMMs for preci pitation occurrences, we propose an extension to include precipitation amou nts. The model we describe assumes the existence of unobserved (or hidden) weather patterns, the weather states, which follow a Markov chain. The weat her states depend on observable synoptic information and therefore serve as a link between the synoptic-scale atmospheric patterns and the local-scale precipitation. The presence of the hidden states simplifies the spatio-tem poral structure of the precipitation process. We assume the temporal depend ence of precipitation is completely accounted for by the Markov evolution o f the weather state. The spatial dependence of precipitation can also be pa rtially or completely accounted for by the existence of a common weather st ate. In the proposed model, occurrences are assumed to be conditionally spa tially independent given the current weather state and, conditional on occu rrences, precipitation amounts are modeled independently at each rain gauge as gamma deviates with gauge-specific parameters. We apply these methods t o model precipitation at a network of 24 rain gauge stations in Washington state over the course of 17 winters. The first 12 yr are used for model fit ting purposes, while the last 5 serve to evaluate the model performance. Th e analysis of the model results for the reserved years suggests that the ch aracteristics of the data are captured fairly well and points to possible d irections for future improvements.