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20 " . . . ~ . > . "-- . . -- . . . . , . , . -- - . ./ , /' . / . . . ,. , '00 . .I . , > . ~ > . ,., " ,.. ,.. ,. 10 20 50 40 !lO EFFECTIVE LENGTH OF RECORD. IN YEARS Figure 6.-- Homogeneity test graph .. The ratio of the 10-year flood to the mean annual flood was determin- ed from the individual frequency graph for each station. The average ratio was multiplied by the mean an- n ual flood for the individual stations and the corresponding recurrence interval determined from the station frequency graph. These recurrence intervals were then plotted against the effective length of record on a test graph similar to that shown in figure 6, which is based on the theory of extreme values. The effective length of record is the number of an- nual floods defined plus one-half the number estimated to complete the base period. If points for all stations plot at random between the envelope curves of figure 6, the records are considered homogeneous. The test defined two homogen- eous flood regions in Kansas which are designated as regions A and B. Points for all stations in the two regions plotted between the envelope curves of figure 6, except for one out-of-State station which was not used in the subsequent development of the composite fre- quency curve, The regional boundary is shown in figure 7. Composite Frequency Curves Composite frequency curves were derived for the two flood regions by combining the frequency graphs for all stations in the respective regions. The data were converted to a comparable basis by expressing each annual flood, for the base period, as a ratio to the mean annual flood for the particular sta- tion. The flood ratios were arrayed in tabular form under their respective recurrence intervals and the medians of these ratios were determined for each recurrence interval. The median ratios were then plotted at their respective recurrence intervals to define the regional or composite frequency curves. The curves were well established below the recurrence interval of 10 years by the foregoing method. However, the median ratios obtained by this method for higher recur1'ence intervals were erroneous because they neither evaluated the period of knowledge of the maximum floods since 1921 nor included the weighted effect of other known floods prior tc 1921.