Optimizing Spillway Capacity With an Estimated Distribution of Floods

A model of social cost minimizing spillway capacity for dams is constructed using (1) the estimated distribution of peak flows from historical data, (2) the estimated relationship between spillway capacity and cost, and (3) a characterization of downstream flood damage from dam failure. Net social cost is the sum of construction costs and expected flood damage. This model is applied to data for the Rio Grande River at Embudo, New Mexico. Minimum social cost is attained at a spillway capacity much smaller than that needed to handle a probably maximum flood.