Bayesian analyses of seasonal runoff forecasts

Abstract

Forecasts of seasonal snowmelt runoff volume provide indispensable information for rational decision making by water project operators, irrigation district managers, and farmers in the western United States. Bayesian statistical models and communication frames have been researched in order to enhance the forecast information disseminated to the users, and to characterize forecast skill from the decision maker's point of view. Four products are presented: (i) a Bayesian Processor of Forecasts, which provides a statistical filter for calibrating the forecasts, and a procedure for estimating the posterior probability distribution of the seasonal runoff; (ii) the Bayesian Correlation Score, a new measure of forecast skill, which is related monotonically to theex ante economic value of forecasts for decision making; (iii) a statistical predictor of monthly cumulative runoffs within the snowmelt season, conditional on the total seasonal runoff forecast; and (iv) a framing of the forecast message that conveys the uncertainty associated with the forecast estimates to the users. All analyses are illustrated with numerical examples of forecasts for six gauging stations from the period 1971–1988.