Short‐Term, Single, Multiple‐Purpose Reservoir Operation: Importance of Loss Functions and Forecast Errors

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Abstract
Short‐term operation policy for multipurpose reservoirs can be derived from an optimization model with the objective of minimizing short‐term losses (opportunity costs). Construction of such loss functions requires the definition of target values for the decision variables, assessment of reliabilities with which inflows can be predicted, and an explicit statement of operational objectives. Formulation and evaluation of a model is complicated by the uncertainties inherent in the prediction of future streamflows and by controversies about the criteria of evaluation. We discuss these issues and illustrate some of our arguments with simple numerical experiments. A series of synthetic short‐term forecasted values (which satisfy a specified distribution of forecast errors) is used to examine operation of a single reservoir. The quality of forecasted values is represented by the mean and variance of these errors or the coefficient of prediction (Cp). The objective function of the operation model is assumed to be the best possible tradeoff between probable deviations from two operation targets: release and storage volume. Reservoir release was effected according to the solution of the optimization model conditioned upon the forecasted streamflow volumes for a given time increment. The storage volume was then corrected to reflect actual streamflow for the forecasted period. This became the initial storage for the next forecast period. Actual losses, deviations between actual and forecasted losses, the variance of storage and release volumes, and operational performance measures, including reliability, resiliency, and vulnerability, were found to be sensitive to the relative importance given to deviations from release or storage targets and the quality of forecasts. The performance of an operation policy based on a model that uses predicted streamflows as deterministic inputs cannot be correlated directly with the shape of the assumed loss function.

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