An assessment of exceedance probabilities of envelope curves

Envelope curves are often used to provide summary accounts of our flood experience, but their operational use has been limited by our previous inability to assign to them an exceedance probability ‘‘EP.’’ General expressions are derived for the EP of an envelope curve at a particular site in a heterogeneous region, as well as measures of central tendency of EP across sites. Analytic results are reported for the case when floods follow a Gumbel or generalized extreme value distribution, and these results are contrasted with those of previous studies that sought to estimate the exceedance probability of extraordinary floods such as the flood of record (FOR) and the probable maximum flood (PMF). A case study involving FOR and PMF discharges for 226 rivers across the U.S.A. indicates that relatively consistent estimates of the average exceedance probability associated with both FOR and PMF envelope curves can be obtained using the theoretical approach introduced here.