A Bayesian Framework for Probabilistic Seasonal Drought Forecasting

Abstract

easonal drought forecasting is presented within a multivariate probabilistic framework. The standardized streamflow index (SSI) is used to characterize hydrologic droughts with different severities across the Gunnison River basin in the upper Colorado River basin. Since streamflow, and subsequently hydrologic droughts, are autocorrelated variables in time, this study presents a multivariate probabilistic approach using copula functions to perform drought forecasting within a Bayesian framework. The spring flow (April?June) is considered as the forecast variable and found to have the highest correlations with the previous winter (January?March) and fall (October?December). Incorporating copula functions into the Bayesian framework, two different forecast models are established to estimate the hydrologic drought of spring given either the previous winter (first-order conditional model) or previous winter and fall (second-order conditional model). Conditional probability density functions (PDFs) and cumulative distribution functions (CDFs) are generated to characterize the significant probabilistic features of spring droughts. According to forecasts, the spring drought is more sensitive to the winter status than the fall status, which approves the results of prior correlation analysis. The 90% predictive bound of the spring-flow forecast indicates the efficiency of the proposed model in estimating the spring droughts. The proposed model is compared with the conventional forecast model, the ensemble streamflow prediction (ESP), and it is found that their forecasts are generally in agreement with each other. However, the forecast uncertainty of the new method is more reliable than the ESP method. The new probabilistic forecast model can provide insights to water resources managers and stakeholders to facilitate the decision making and developing drought mitigation plans.