Risk Assessment of Extreme Events: Application

Abstract

The safety of many existing dams could be improved by modifying hem structurally in accordance with recent advances in statistical hydrology and mproved availability of meteorological and hydrological data. Any increase insafety that might be gained by structural changes must be balanced against their costs. The risk analysis methodology known as the partitioned multiobjective risk method (PMRM) is explored in this paper through a dam‐safety problem. The PMRM is well suited to the task of solving the probabilistic optimization problem posed by such risk‐versus‐cost considerations. With the PMRM, a number of conditional expected‐damage functions are generated. Of these, one that represents events of a more extreme and catastrophic character is of particular interest here. The close relationship that exists between the expectation of damage and the statistics of extremes is shown to simplify the implementation of the PMRM, and the relationship also permits the derivation of closed‐form equations that determine (for any partitioning of the probability axis) the expected damage, given that a flood with a return period that equals or exceeds n years occurs. Finally, an analysis is made as to how the choice of the distribution function representing the annual flood peaks might affect the conditional expectations.