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<br />6
<br />
<br />TECHNIQUES OF W A TER.RESOURCES INVESTIGATIONS
<br />
<br />efficients are statistically significant at the 1
<br />percent leveL The standard error of log Q"" is
<br />smaller than that of either log Q, or log Q,.."
<br />probably because the regression for log Q"" is
<br />based on only 10 stations whose records may
<br />be less independent than are the records for
<br />the 18 stations used in the other regressions,
<br />It should not be assumed that Q"" can be esti. ,
<br />mated more closely than the others because it
<br />has the smallest standard error,
<br />Equations applied to a specific site to obtain
<br />discharges corresponding to several recur. !
<br />rence intervals may not produce points that
<br />lie on a smooth curve. To check the equations
<br />for the Snohomish River example, assume a
<br />basin of 300 square miles with a mean annual
<br />precipitation of 150 inches, The 2-, 25-, and
<br />50-year flood peaks computed by slide rule are
<br />35,500, 83,000, and 97,600 ds respectively,
<br />These are plotted in figure 3 along with results
<br />from a 300-square.mile basin having 50 inches
<br />of precipitation, The results appear to be con.
<br />sistent,
<br />A frequency curve could be drawn to aver.
<br />age the computed points, but this is usually not
<br />justified unless a set of equations produces a
<br />large-recurrence-interval flood which is small-
<br />er than one computed for a smaller recurrence
<br />intervaL This condition does not appear pos-
<br />sible with the equations derived for this exam-
<br />ple, although it can occur with equations from
<br />some analyses,
<br />
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<br />2' 10 2.5 SO
<br />RECURRENCE INTERVAL, IN YEARS
<br />
<br />3. Plol of computed Roods for hypolt,efical bosins.
<br />
<br />The obj ect of a regional study usually is to
<br />define the floods corresponding to two or three
<br />recurrence intervals at ungaged sites, not to
<br />define the entire frequency curve, The 2.year
<br />flood and the mean annual flood (2,33-yrl are
<br />of limited interest,
<br />
<br />Regionalization of characteristics of the
<br />frequency distribution
<br />
<br />Both the index-flood method and the regres-
<br />sion method regionalize peak discharges at
<br />specific recurrence intervals; in the above
<br />example separate regressions were made for
<br />floods at the 2., 25- and 50.year recurrence
<br />intervals, These discharges at individual sites
<br />were selected from the station frequency
<br />curves which may be either graphically or
<br />analytically defined,
<br />If the station frequency curves are obtained
<br />by analytically fitting the same theoretical
<br />frequency distribution to data for each sta-
<br />tion, the differences among those frequency
<br />curves can be described by the differences in
<br />the computed parameters of the theoretical
<br />distribution, A two. parameter distribution
<br />can be described by its mean and variance (or
<br />standard deviation), A three.parameter dis.
<br />tribution will require an index of skewness in
<br />addition to the mean and variance.
<br />Then a regionalization procedure might
<br />consist of relating separately the mean, the
<br />variance, and the skewness to basin character.
<br />istics by the regression method, These three
<br />parameters, estimated from the regression
<br />equations for a specific site will define the
<br />regionalized frequency curve not only in the
<br />defined range but also beyond that range
<br />where its use is not justified, In practice, reo
<br />gressions are computed for the mean and for
<br />the standard deviation only, A mean value of
<br />skew is usually applied to a region of consid-
<br />erable size because the computed skew from
<br />an individual record is highly unreliable.
<br />Regionalization of parameters of the frequen.
<br />cy curve is described by Beard (1962, section
<br />7), Fitting of station data to a Pearson Type
<br />III distribution is described in boo~( 4, chapter
<br />A2 of "Techniques of Water Resources Inves.
<br />tigations" (Riggs 1968b) and by Water Re-
<br />sources Council (1967),
<br />
<br />,.
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