Probabilistic behavior of floods of record in the United States

Literature on the probability distribution function (PDF) of annual maximum flood discharges is extensive, yet the literature on the PDF of the flood of record (FOR) is sparse. This is partially due to two facts: (1) the PDF for record events is more complex than the PDF for annual maxima; and (2) data sets for observed FORs are much smaller than for the annual maximum flood series from which they derive. We show that, if annual floods arise from a generalized extreme values (GEV) distribution, then the FOR also arises from another GEV distribution, which we term GEV(max). We also derive the moments and L-moments for the PDF of GEV(max). Using record flood observations at over 1,500 basins in the United States, we compared theoretical and empirical properties of observed values of the FOR. We found that, at both regional and national scales, the FOR values are on average more extreme than would be expected if they occurred randomly, and that they tend to form spatial clusters.