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<br />00"_~ ~3 <br /> <br />19 <br /> <br />Adjustment to Base Period <br /> <br />Records, in order to be combined, must be reduced to a common time <br />basis, or base period. The longer the time basis, the more reliable is the <br />resulting frequency curve, Therefore, the base period should be as long as <br />feasible, and the period 1921- 56 was selected as the base for the analyses here- <br />in. Table 1 shows that the actual record for many stations is somewhat short- <br />er than the base period. The shorter records were extended to complete the <br />period by the following procedure. Using all available data, figures of annual <br />peak discharge were computed for the missing years by correlating with a <br />nearby long-term station. The computed figures were not used directly as <br />discharges but were used only to designate the likely order of magnitude of <br />the observed discharges. <br /> <br />Definition of Mean Annual Flood <br /> <br />According to the theory of extreme val ues as applied to floods by Gumbel <br />(1945), the arithmetical mean of the annual peak discharges in an infinitely <br />long series is equal to the discharge corresponding to the 2_..33 -y'e::).!:..r_e.currenc e <br />interval. This discharge is commonly, although ambiguously, referred to as <br />the "mean annual flood" and the term has been retained in this report. A more <br />rigorous expression would be "mean of the annual floods as defined graphically <br />on frequency-graph paper". By definition, the 2.33-year flood is considered <br />as the mean of such short flood series as are available in Kansas. <br /> <br />Annual flood data for all the gaging stations, adjusted to the base period, <br />were plotted on frequency-graph paper and smooth curves were drawn by vis- <br />ual methods to fit the data, giving less weight to the higher points. The mean <br />annual flood (Q2.33) was determined for each station as the discharge corres- <br />ponding to the intersection of the smooth curve with the 2.33-year recurrence <br />line. The position of the curve is fairly well defined in this range and is not <br />influenced by the erratic plotting of high points. Mean annual floods are listed <br />in table 1. <br /> <br />Test for Homo'geneity <br /> <br />A homogeneity test was applied to the individual station records in order <br />to ensure that the records combined are in a region of uniform frequency char- <br />acteristics. This is a statistical test on a 95 percent confidence level applied <br />to the slopes of the individual frequency graphs to determine whether deviations <br />from an average slope are such as may be due to chance alone. <br />