Variational Bayes Estimation of Hidden Markov Models for Daily Precipitation with Semi-Continuous Emissions
Reetam Majumder, Matthias K. Gobbert, Amita V. Mehta, Nagaraj K. Neerchal · Maryland Shared Open Access Repository (USMAI Consortium) · 2021
Stochastic precipitation generators can simulate dry and wet rainfall stretches for long durations. Generated precipitation time series data are used in climate projections, impact assessment of extreme weather events, and water resource and agricultural management. Daily precipitation is specified as a semi-continuous distribution with a point mass at zero and a mixture of Exponential or Gamma distributions for positive precipitation. Our generators are obtained as hidden Markov models (HMM) where the underlying climate conditions form the states. Maximum likelihood estimation for HMMs has historically relied on the Baum-Welch algorithm. We implement variational Bayes as an alternative for parameter estimation in HMMs. In our simulation study for a 3-state HMM with positive rainfall specified as a mixture of 2 Exponential distributions, we get good posterior estimates when the model is initialized with the correct number of states and mixture components. We also fit a similar model to a single grid point within the Chesapeake Bay watershed based on GPM-IMERG remote sensing data for the wet season between July to September from 2000–2019. Synthetic data generated from the fitted model is able to replicate the monthly proportion of dry days at the location, as well as the total monthly precipitation.