Expected Probability and Annual Damage Estimators

Abstract

Controversy continues over the relative merits of traditional frequency estimators and the “expected probability” estimator of flood risk that incorporates an adjustment for parameter uncertainty. Both have solid theoretical motivation, but address different concerns. The description of hydrologic risk and uncertainty provided by new risk and uncertainty procedures adopted by the U.S. Army Corps of Engineers, and risk-based design procedures developed by others, are shown to be equivalent to the expected probability model in simple cases. A 1995 National Research Council (NRC) report recommended against use of the expected probability model for evaluating expected annual damages and the probability of flooding; in particular, the NRC analysis and the 1989 Arnell analysis demonstrated that expected probability estimators yield risk and damage estimators that generally have large positive biases. Historical arguments and related issues are reviewed. Resolution of this controversy and success of the new U.S. Army Corps of Engineers (USACE) risk and uncertainty procedures require a clear framework for understanding what is meant by risk, variability, and uncertainty. Such risk analyses can better represent a community's vulnerability to flooding and the large uncertainty in estimates of expected damages and residual flood risk.