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G~)'~::.n~ 17 Length of record, in years, within the indicated percentage, required for a single station to define a flood 19 times in 20, is as follows: Magnitude of flood 2.33 -year flood 10 -year flood 25-year flood 50 - year flood 25 percent 12 18 31 39 10 percent 40 90 105 110 Although the figures in the above table are based on hypothetical rather than on actual flood events, they do give some indication of the considerable errors possible.. from chance alone, in frequency graphs based on short-term records for single stations. A comparison of the lengths of record available for Kansas streams (table 1) and those indicated by Benson suggests that very few records in the State are long enough to define reliable individual frequency graphs for floods of infrequent occurrence. Obviously some expanded treatment must be sought to define flood frequency. Analysis on a regional rather than on a site basis is a solution developed in a subsequent section of this report. Much work has been done by others on the problem of the best fit of a the- oretical frequency curve to the data at a single site, the ultimate purpose being to extrapolate the curve to a frequency beyond the range of the data. The fore- going paragraphs illustrate the futility of such endeavor. Only visually-fitted smooth curves were used in this analysis, with decreasing weight given to the higher values. Regional Flood Frequency The method of defining flood-frequency relations from data at a single gaging station has been described and shown to be generally inadequate if us ed alone. This section describes how these data have been combined into groups to provide a more reliable definition applicable to both gaged and ungaged sites. It can be proved statistically that the past sample of flood events combined for a group of homogeneous sites is a better criterion of future expectancy than that of a .sample at an individual site, In Ben30n's study (1952) it was shown that if 5 or more of his theoretical 10-year records were combined, the 50-year flood was defined within 7,8 percent of the long-term (l,OOO-year) value, A comparable improvement may be expected with actual homogeneous records, It is particularly desirable that some of the stations contained in a group have long records to define the long-term trends. The flood data for a group of stations are combined by two operations. In the first operation, the records are combined on the basis of a geometric sim- ilarity of the individual flood-frequency graphs. If all gaged streams within a certain region show frequency graphs of the same general shape and slope,