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Stochastic precipitation generators (SPGs) are a class of statistical modelswhich generate synthetic data that can simulate dry and wet rainfall stretchesfor long durations. Generated precipitation time series data are used inclimate projections, impact assessment of extreme weather events, and waterresource and agricultural management. We construct an SPG for dailyprecipitation data that is specified as a semi-continuous distribution at everylocation, with a point mass at zero for no precipitation and a mixture of twoexponential distributions for positive precipitation. Our generators areobtained as hidden Markov models (HMMs) where the underlying climate conditionsform the states. We fit a 3-state HMM to daily precipitation data for theChesapeake Bay watershed in the Eastern coast of the USA for the wet seasonmonths of July to September from 2000--2019. Data is obtained from theGPM-IMERG remote sensing dataset, and existing work on variational HMMs isextended to incorporate semi-continuous emission distributions. In light of thehigh spatial dimension of the data, a stochastic optimization implementationallows for computational speedup. The most likely sequence of underlying statesis estimated using the Viterbi algorithm, and we identify the differences inthe weather regimes associated with the states of the proposed model. Syntheticdata generated from the HMM can reproduce monthly precipitation statistics aswell as spatial dependency present in the historical GPM-IMERG data.

Stochastic Precipitation Generation for the Chesapeake Bay Watershed using Hidden Markov Models with Variational Bayes Parameter Estimation