An assessment of exceedance probabilities of envelope curves

[1] 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.

[1]  R. Vogel,et al.  Multivariate probabilistic regional envelopes of extreme floods , 2007 .

[2]  Irving I. Gringorten,et al.  A plotting rule for extreme probability paper , 1963 .

[3]  A. Brath,et al.  Assessing the effectiveness of hydrological similarity measures for flood frequency analysis , 2001 .

[4]  E. J. Gumbel,et al.  Statistics of Extremes. , 1960 .

[5]  Masaaki Sibuya,et al.  Bivariate extreme statistics, I , 1960 .

[6]  J. O’Connor,et al.  Spatial distribution of the largest rainfall‐runoff floods from basins between 2.6 and 26,000 km2 in the United States and Puerto Rico , 2004 .

[7]  Lester B. Lave,et al.  Evaluating dam safety retrofits with uncertain benefits: The Case of Mohawk Dam (Walhonding River, Ohio) , 1990 .

[8]  R. Vogel,et al.  Probabilistic behavior of a regional envelope curve , 2005 .

[9]  C. S. Jarvis.  Flood Flow Characteristics , 1924 .

[10]  R. Vogel,et al.  Probabilistic Behavior of Floods of Record in the United States , 2006 .

[11]  J. Stedinger.  Frequency analysis of extreme events , 1993 .

[12]  Francis C. McMichael,et al.  Safety goals for high‐hazard dams: Are dams too safe? , 1990 .

[13]  William L. Baldewicz,et al.  Dam Failures: Insights to Nuclear Power Risks , 1984 .

[14]  A. Jenkinson.  The frequency distribution of the annual maximum (or minimum) values of meteorological elements , 1955 .

[15]  Richard M. Vogel,et al.  PROBABILITY DISTRIBUTION OF ANNUAL MAXIMUM, MEAN, AND MINIMUM STREAMFLOWS IN THE UNITED STATES , 1996 .

[16]  J. Hüsler.  Maxima of normal random vectors: between independence and complete dependence , 1989 .

[17]  Donald W. Newton,et al.  Realistic Assessment of Maximum Flood Potentials , 1983 .

[18]  J. R. Wallis,et al.  Regional Frequency Analysis: An Approach Based on L-Moments , 1997 .

[19]  Ahiam I. Shalaby.  Estimating probable maximum flood probabilities , 1994 .

[20]  Lester B. Lave,et al.  Optimizing Spillway Capacity With an Estimated Distribution of Floods , 1987 .

[21]  A. Castellarin.  Probabilistic envelope curves for design flood estimation at ungauged sites , 2007 .