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16 Limitations of a Flood-Frequency Graph at a Gaging Station The 50-year flood is sometimes selected as a design criterion forhydrau- lic structures currently being constructed in Kansas. Table 1 shows that there are only 30 gaging stations in the State having 30 or more years of defined peak discharges, 14 stations having 40 or more years of defined peaks, and 3 stations having 50 or more years of defined peaks. Furthermore, the indi- cated plotting position for the greatest flood is not entirely dependable. Thus, the graph defining the 50-year flood might require extrapolation from the trend of the plotting positions of lesser floods. P'or a 30-year record, this would amount to an extrapolation from 15~ years or lower up to 50 years on the scale of the recurrence intervals. Although this lineal distance appears short on the graph, the error of the curve at its outer extremity could be considerable, regardless of the method of curve fitting or type of plotting paper used. Another and more serious limitation of flood-frequency graphs based on records at a single station arises from the random manner in whi ch flood events are distributed with respect to time. For example, a flood record of 100 years cannot be expected to include exactly one 100 -year flood, two 50-year floods, three 33.3-year floods, and so on. If the 100-year record is separated into two 50-year periods, one period might include several 50-year floods; the other none. Frequency graphs based on each of the two 50-year periods may be vastly different and neither may closely resemble the frequency graph derived from the 100-year record considered as a whole. Similarly, the frequency graph obtained from the 100 -year record could be appreciably different from that for a different time period of the same length, or for a longer period. Thus, the record of annual floods for a particular stream is a random sample which may define a frequency graph much different from one which would be derived from a record of infinite length. The maximum departure to be expected between flood magnitudes or fre- quencies computed from relatively short records and their true (long-term) values increases with the magnitude of the flood and decreases with the length of the record. The variation, owing to the chance factor alone, between the flood magnitudes computed from records of varying length and the long-term values has been studied by Benson (1952), who analyzed an array of 1,000 hypo- thetical annual floods distributed according to the theory of extreme values (Gumbel, 1945). In using statistical methods, the most favorable expectancy during 95 percent of the time, or 19 chances out of 20, is generally used as the criterion for dependable results. The following table, based on Benson's study, shows the length of record required to define the frequency of floods of various magnitudes by the records at a single site. .