Optimizing Spillway Capacity with Uncertainty in Flood Estimator

The spillway design flood is a function of social, moral, economic, and technological restrictions. Given the significant initial cost of a spillway and the very high cost of dam failure and downstream damages, the economic sizing of the spillway becomes a very important decision. This paper presents a model that minimizes the social cost of a spillway. The model incorporates the uncertainty of the flood magnitude estimator in the optimization of spillway capacity, using an estimated flood probability density function and a relationship between spillway capacity and cost. The spillway design flood is explicitly treated as a decision variable, which is useful in the planning phase of a reservoir. To determine the effect of uncertainty in the flood magnitude estimator, the optimum spillway design flood is examined for different flood probability density functions with varying sample sizes. It is shown that with a limited sample size, the optimum spillway design flood may be as high as the probable maximum flood.