RISK OF EXTREME EVENTS IN A MULTIOBJECTIVE FRAMEWORK

ABSTRACT: This paper summarizes advances made in risk‐based decisionmaking in water resources through use of the partitioned multiobjective risk method (PMRM). (Risk is a measure of the probability and severity of adverse effects.) in the PMRM, the risk of extreme events is differentiated from risk involving less extreme damage severity and is evaluated within a multiobjective framework. Study of the extreme‐event risk function f₄(*) has addressed the following issues: methods for calculating f₄(*); the sensitivity of f₄(*) to various parameters, particularly to the partitioning point of the extreme‐event range and the selection of probability density functions; insight provided by the statistics of extremes; and the impact of f₄(*) on risk management, for example, in the application of the PMRM to water resources problems. In particular, this paper shares with the reader recent research results on the PMRM, the relationship between the statistics of extremes and the conditional expected value, derived formulas for f₄(*), distribution‐free estimates of f₄(*), documented case studies in dam safety, and future research directions.