A CLASS OF STOCHASTIC-MODELS FOR RELATING SYNOPTIC ATMOSPHERIC PATTERNS TO REGIONAL HYDROLOGIC PHENOMENA

A model for multistation precipitation, conditional on synoptic atmosp heric patterns, is presented. The model, which we call the nonhomogene ous hidden Markov model (NHMM), postulates the existence of an unobser ved weather state, which serves as a link between the large-scale atmo spheric measures and the small-scale spatially discontinuous precipita tion field. The weather state effectively acts as an automatic classif ier of atmospheric patterns. The weather state process is assumed to b e conditionally Markov, given the atmospheric data. The rainfall proce ss is then assumed to be conditionally independent given the weather s tate. Various parameterizations for the weather state process and the rainfall process are discussed, and a likelihood-based estimation proc edure is described. Model-based estimates of the storm duration distri bution and first and second moments of the rainfall process are derive d. As an example the model is fit to a four-station network of rain ga uge stations in Washington state. The observed first and second moment s are reproduced very closely. The fitted duration distributions are s omewhat lighter tailed than the observed distribution at two of the fo ur 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.