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6 TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS efficients are statistically significant at the 1 percent level. The standard error of log Q,o is smaller than that of either log Q2 or log Q2" probably because the regression for log Q,o is based on only 10 stations whose records may be less independent than are the records for the 18 stations used in the other regressions. It should not be assumed that Q" can be esti- mated more closely than the others because it has the smallest standard error. Equations applied to a specific site to obtain discharges corresponding to several recur- rence intervals may not produce points that lie on a smooth curve. To check the equations for the Snohomish River example, assume a basin of 300 square miles with a mean annual precipitation of 150 inches. The 2-, 25-, and 50-year flood peaks computed by slide rule are 35,500, 83,000, and 97,600 cfs respectively. These are plotted in figure 3 along with results from a 300-square-mile basin having 50 inches of precipitation. The results appear to be con- sistent. A frequency curve could be drawn to aver- age the computed points, but this is usually not justified unless a set of equations produces a large-recurrence-interval flood which is small- er than one computed for a smaller recurrence interval. This condition does not appear pos- sible with the equations derived for this exam- ple, although it can occur with equations from some analyses. I I I I (; 100 - , - ~ " z """ ~z "0 Ou ,"w ~~ ~: .L w~ 10 - Ow 0 ~w ""~ 0 '"u u- ~.. -:> 0 "u ~ "" W L , 2 10 25 50 RECURRENCE tNHRVAl, IN YEAliS 3. Plol of computed floods for hypolfletical basins. The object of a regional study usually is to define the floods corresponding to two or three recurrence intervals at ungaged sites, not to define the entire frequency curve. The 2-year flood and the mean annual flood (2.33-yr) are of limited interest. . Regionalization of characteristics of the frequency distribution Both the index-flood method and the regres- sion method regionalize peak discharges at specific recurrence intervals; in the above example separate regressions were made for floods at the 2-, 25- and 50-year recurrence intervals. These discharges at individual sites , were selected from the station frequency curves which may be either graphically or analytically defined. If the station frequency curves are obtained by analytically fitting the same theoretical frequency distribution to data for each sta- tion, the differences among those frequency curves can be described by the differences in the computed parameters of the theoretical distribution. A two-parameter distribution can be described by its mean and variance (or standard deviation). A three-parameter dis- tribution will require an index of skewness in addition to the mean and variance. Then a regionalization procedure might consist of relating separately the mean, the variance, and the skewness to basin character- istics by the regression method. These three parameters, estimated from the regression equations for a specific site will define the regionalized frequency curve not only in the defined range but also beyond that range where its use is not justified. In practice, re- gressions are computed for the mean and for the standard deviation only. A mean value of skew is usually applied to a region of consid- erable size because the computed skew from an individual record is highly unreliable. Regionalization of parameters of the frequen- cy curve is described by Beard (1962, section 7). Fitting of station data to a Pearson Type III distribution is described in book 4, chapter A2 of "Techniques of Water Resources Inves- tigations" {Riggs 1968b) and by Water Re- sources Council (1967). , .,1 i' . ~ .