Linear decision rule in reservoir management and design: 3. Direct capacity determination and intraseasonal constraints

A chance-constrained model for multipurpose reservoir operation is reviewed and extended. The model minimizes required capacity subject to chance constraints for water supply, recreation, and flood control. A linear decision rule is used to make commitments based on existing storage. A study of the structure of this linear programing formulation reveals a direct solution in the special case when as much water as possible is reliably committed, a reasonable case for water supply. The structure of the model requires an adequate degree of continuity. This requirement generally restricts the usefulness of the model to multipurpose reservoirs. Using an execution rule to specify when within a decision period water will be released, we can extend the model to include constraints on storage within a decision period. Increasing the length of a decision period is seen to produce a large increase in reservoir capacity due to the making of commitments for a longer future of uncertain inflows. Numerical examples are provided that demonstrate the increased capacity required in a seasonal model over that required in a monthly model and the effect of using intraseasonal constraints.