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

Nonhomogeneous hidden Markov models (NHMMs) provide a relatively simple framework for simulating precipitation at multiple rain gauge stations conditional on synoptic atmospheric patterns. Building on existing NHMMs for precipitation occurrences, we propose an extension to include precipitation amounts. The model we describe assumes the existence of unobserved (or hidden) weather patterns, the weather states, which follow a Markov chain. The weather 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-temporal structure of the precipitation process. We assume the temporal dependence of precipitation is completely accounted for by the Markov evolution of the weather state. The spatial dependence of precipitation can also be partially or completely accounted for by the existence of a common weather state. In the proposed model, occurrences are assumed to be conditionally spatially independent given the current weather state and, conditional on occurrences, precipitation amounts are modeled independently at each rain gauge as gamma deviates with gauge-specific parameters. We apply these methods to 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 fitting purposes, while the last 5 serve to evaluate the model performance. The analysis of the model results for the reserved years suggests that the characteristics of the data are captured fairly well and points to possible directions for future improvements.