Incorporating Spatial Dependence and Atmospheric Data in a Model of Precipitation

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Abstract
Nonhomogeneous hidden Markov models (NHMM) provide a method of relating synoptic atmospheric measurements to precipitation occurrence at a network of rain gauge stations. In previous work it was assumed that, conditional on the current atmospheric pattern (termed a “weather state”), rain gauge stations in a network could be considered spatially independent. For a spatially dense network, this assumption is not tenable. In the present work, the NHMM is extended to include the case of spatial dependence by postulating an autologistic model for the conditional probability of rainfall given the weather state. Methods for fitting the parameters, assessing the goodness of fit of the model, and generating rainfall simulations are presented. The model is applied to a network of 24 stations in the Puget Sound region of western Washington State. Abstract Nonhomogeneous hidden Markov models (NHMM) provide a method of relating synoptic atmospheric measurements to precipitation occurrence at a network of rain gauge stations. In previous work it was assumed that, conditional on the current atmospheric pattern (termed a “weather state”), rain gauge stations in a network could be considered spatially independent. For a spatially dense network, this assumption is not tenable. In the present work, the NHMM is extended to include the case of spatial dependence by postulating an autologistic model for the conditional probability of rainfall given the weather state. Methods for fitting the parameters, assessing the goodness of fit of the model, and generating rainfall simulations are presented. The model is applied to a network of 24 stations in the Puget Sound region of western Washington State.

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