Copula-based Correlation Structure for Multivariate Emission Distributions in Hidden Markov Models

Abstract

Hidden Markov models (HMM) for multi-site daily precipitation usually assume that precipitation at each location is independently distributed conditional on the daily state; correlation in precipitation at different locations is induced by the state process. In practice, however, spatial correlations are underestimated especially when working with remote sensing data. This results in simulated data which cannot recreate the spatiotemporal patterns of the historical data. We construct a daily precipitation generator based on a hidden Markov model with Gaussian copulas (HMM-GC) using GPM-IMERG (Integrated Multi-satellitE Retrievals for Global Precipitation Measurement) remote sensing data for the Chesapeake Bay watershed on the East Coast of the USA. Daily precipitation from 2000–2019 for the wet season months of July to September is modeled using a 6-state HMM. Positive precipitation at each location is given by a two-part distribution with a delta function at zero and a mixture of two Gamma distributions; Gaussian copulas are used to accommodate the correlation in precipitation at different locations. Based on 20 years of synthetic data simulated from an HMM and an HMM-GC, we conclude that the HMM-GC captures key statistical properties of IMERG precipitation better than the HMM.