Improved Hidden Markov Model Incorporated with Copula for Probabilistic Seasonal Drought Forecasting

Drought is a natural hazard driven by extreme macroclimatic variability, and generally resulting in serious damage to the environment over a sizable area. Accurate, reliable, and timely forecasting of drought behavior plays a key role in early warning of drought management. In this study, a hybrid hidden Markov model coupled with multivariate copula (HMC) is proposed for probabilistic drought forecast. It is an extension of the regular hidden Markov model (HMM) in which the mixture distribution for each forecast is a weighted combination of posterior copula conditional distributions, which are allowed to vary with different predictors. Bayesian inference is used to optimize model structure and parameters. The cascaded sampling procedure is used to obtain conditional probability of a pair copula. The HMC model is performed for multistep meteorological drought forecast at the stations of Hanchuan and Tianmen, China, with the widely used Standardized Precipitation Index (SPI) time series. HMM, artificial neural network (ANN), and autoregressive moving average (ARMA) drought forecasting are also implemented for comparison. Results demonstrate that HMC drought forecast is much more accurate than HMM, ARMA, and ANN for point forecasts as well as interval forecasts. This study is of great significance for understanding drought uncertainty and extending drought early warning.