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<br />14 <br /> <br />From statistical principles, Langbein (1949) has shown that there is a def- <br />inite relationship between the values in the two series. The following table <br />shows comparative vaiues of recurrence intervals. <br /> <br />Recur rence intervals in years <br />Annual-flood series Partial-duration series <br />1.16 0.5 <br />1.58 1.0 <br />2.00 1.45 <br />2.54 2.0 <br />5.52 5.0 <br />10.5 10 <br />20.5 20 <br />50.5 50 <br />100.5 100 <br /> <br />For some purposes it is desirable to know how often, on the average a <br />stream will exceed a certain relatively minor flood such as for determining <br />how often a road fill will be inundated, and for other designs or studies of <br />damages invoiving low frequencies. The partiai-duration series is applicabie <br />to studies of that type. Adequate results may be obtained by converting the <br />curve based on the annual-flood series by use of the relation expressed in the <br />table presented above. <br /> <br />Plotting Positions <br /> <br />The annuai floods for each year of record were numbered in descending <br />order of magnitude. The next step was the computation of the appropriate re- <br />currence interval for each flood. In the method used by the Geological Survey, <br />recurrence intervals, in years, are computed by the formula (N+l)/ M, where N <br />equals the number of years of record and M is the relative order of magnitude <br />of the floods. In the case of available historical information, N is the number <br />of years during which it is known that the flood was of the order assigned. For <br />example, if reliable information indicates that the highest flood during a 40- <br />year period of record exceeded all floods for at ieast 25 years prior to the <br />beginning of record, N becomes 65 for this particular flood. The formula used <br />is simple to compute, is applicable to both the annual-flood and partiai-duration <br />series, and produces acceptable results conforming with some of the iatest <br />theories on computing piotting positions. <br />