A class of stochastic models for relating synoptic atmospheric patterns to regional hydrologic phenomena

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Abstract
A model for multistation precipitation, conditional on synoptic atmospheric patterns, is presented. The model, which we call the nonhomogeneous hidden Markov model (NHMM), postulates the existence of an unobserved weather state, which serves as a link between the large‐scale atmospheric measures and the small‐scale spatially discontinuous precipitation field. The weather state effectively acts as an automatic classifier of atmospheric patterns. The weather state process is assumed to be conditionally Markov, given the atmospheric data. The rainfall process is then assumed to be conditionally independent given the weather state. Various parameterizations for the weather state process and the rainfall process are discussed, and a likelihood‐based estimation procedure is described. Model‐based estimates of the storm duration distribution and first and second moments of the rainfall process are derived. As an example the model is fit to a four‐station network of rain gauge stations in Washington state. The observed first and second moments are reproduced very closely. The fitted duration distributions are somewhat lighter tailed than the observed distribution at two of the four stations but provide a good fit at the other two. We conclude that the NHMM has promise as a method of relating synoptic atmospheric data to rainfall and other regional or local hydrologic processes.