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<br />. frequency should be applied to a detenninistic PMF estimate. Jarrett and Costa (1988) proposed using <br />regional flood-frequency estimates, which incorporated paleoflood infonnation. to estimate the recurrence <br />interval for selected PMF values for streams in Colorado. They found the recurrence interval was about <br />2,000 to 5,000 years for sites in eastem Colorado that are subject to extreme rainstonns to in excess of <br />10,000 years for streams above 7,500 ft Using similar methods to extrapolate site or regional flood- <br />frequency relations, the recurrence interval for the PMF varies from about 10,000 years to over 10 million <br />years (Jarrett and Waythomas, in press; Levish and others, 1994; Ostenaa and Levish, 1995; Jarrett and <br />others, in review; Jarrett, in review). Paleoflood data was used to extrapolate the regional flood-frequency <br />relation (Kircher and others, 1985) for Elkhead Creek at the dam. The recurrence interval for the PMF <br />ranges from about 50,000 years (figure 17d; Ayres) to in excess of a million years (figure 17d; this study). <br />Although such extrapolations of flood-frequency relations are not precise, they demonstrate: 1 ,} the PMF <br />has a wide range of risk associated for dam safety in the Rocky Mountain Region; and 2.} the risk of the <br />PMF in Elkhead Creek Basin is extremely small. <br /> <br />An assessment can be made of the likelihood that the PMF would not have occurred by chance in the <br />study area, Riggs (1961) shows the following equation to estimate the probability that a flood will not <br />occur: <br /> <br />P = [(l-lfT)N,]X <br /> <br />(1) <br /> <br />. <br /> <br />where P = the probability of a specific size flood having a recurrence interval of T-years and not occurring <br />in N years in X number of basins. Assuming the PMP covers 50 mi2, there are approximately 4 sub- <br />basins in Elkhead Creek Basin upstream from Elkhead Dam, The PMF is assumed to have a recurrence <br />interval (T) of 10,000 years and the paleoflood record (N) is at least 10,000 years. The probability that <br />the PMF would not have occurred in Elkhead Creek Basin in 10,000 years is 1, 183xl (}02; conversely, the <br />probability that the PMF would be expected to have occurred is 0,9817. The paleoflood study for <br />northwestem Colorado covered about 4,200 mi2, Thus, there are about 84 sub-basins having a size of <br />50 mi2 in the paleoflood-study area. The probability that the PMF would not have occurred in <br />northwestern Colorado in 10,000 years is 3,3x1Q-37; conversely, the probability that the PMF would be <br />expected to have occurred essentially is 1.0. These small probabilities help demonstrate that paleoflood <br />evidence for the PMF-sized floods should have been identified if not in Elkhead Creek Basin, then certainly <br />somewhere in northwestem Colorado. Thus, it raises further question as to the magnitude of the PMF <br />estimate for Elkhead Reservoir and provides regional support for the interpretation of maximum flood <br />potential in Elkhead Creek Basin. <br /> <br />. <br /> <br />The Interagency Advisory Committee on Water Data (1986) considers that a ratio of the maximum- <br />observed flood (envelope curve of known flOods) in a region of about 50 percent or more of the PMF is an <br />acceptable level of agreement. The maximum paleoflood in at least 10,000 years for Elkhead Creek at <br />Elkhead Reservoir is about 13 percent of the PMF estimate. Several recent paleoflood studies primarily <br />conducted by the U.S. Geological Survey and Bureau of Reclamation also demonstrate large differences <br /> <br />29 <br />