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<br />REGIONAL ANALYSES OF ST'REAMFLOW CHARACTERISTICS <br /> <br />9 <br /> <br />. <br /> <br />frequency curves that requires less work. <br />, More commonly the short records in a re- <br />gion are not closely correlated with longer <br />ones; in practice few short records will be <br />found that meet the criterion for extension. <br />Thus a decision on whether to extend or not <br />to extend may be required only infrequently. <br />Frequency data for use in a regional analy- <br />sis are often based on records for a selected <br />period of years, called a base period. Adjust- <br />ment of all records to a base period requires <br />that parts of long records be discarded and <br />that short records be extended. The objective <br />of using a base period is to obtain a group of <br />records all affected by the same weather oc- <br />currences so that the differences among the <br />frequency characteristics are largely due to <br />differences in basin characteristics. This ob- <br />jective mayor may not be met depending on <br />the particular streamflow characteristic being <br />studied and on the size of the region consid- <br />ered. <br />The records for a base period should pro- <br />duce a regional regression relation with a <br />smaller standard error than would records <br />for periods of various lengths. However, the <br />purpose of a regionalization is to average the <br />variability due to random weather occur- <br />rences. The more samples (in time) used the <br />more likely will the average represent long- <br />term conditions. But use of a base period <br />minimizes the number of independent events <br />and thus may produce a biased result. <br />Ordinarily the flood-frequency characteris- <br />tics should be defined by all the record avail- <br />able at each site. If an extension of a record <br />is made to improve the definition of the fre- <br />quency curve, the extension should cover the <br />entire length of the longer record, not just a <br />part of it. <br />Lack of independence of flood occurrences <br />at the various sites used in a regional analy- <br />sis has two effects: (1) The variability of the <br />slope of the regression line is reduced, and <br />(2) the variability of the intercept is in- <br />creased; that is, the slope of the regional <br />relation is better defined because of a depend- <br />ence among stations but its position is less <br />well defined (Matalas and Benson, 1961). For <br />example, suppose that all the stations in ,a <br /> <br />. <br /> <br />. <br /> <br />region are affected by the same storms, that <br />the 20-year flood is defined at each station, <br />and that these 20-year floods are related to <br />basin characteristics. The resulting regres- <br />sion equation may describe very well the rela- <br />tive effects of the various basin characteris- <br />tics on flood magnitude, but we do not know <br />whether the magnitude is that of a 20-year <br />flood or of one having a very different recur- <br />rence interval because we have essentially <br />only one sample of flood experience. <br />In most parts of the United States, the <br />longer flood records can not be considered <br />homogeneous because of man-made changes <br />in the flow regimen. It has been proposed <br />that a hydrologic basin model be used to ad- <br />just the annual floods of record to undevel- <br />oped basin conditions. This would add con- <br />siderable information for use in a regional <br />analysis. Of course the results of the regional <br />analysis would not apply to that particular <br />stream under its existing pattern of regula- <br />tion. <br /> <br />Model and parameters <br /> <br />The regression model used in regional flood- <br />frequency analyses is of the form <br /> <br />Qn = a A 'B'G" . . . . <br /> <br />the log transform of which is linear. Selection <br />of suitable independent variables is often <br />made on a statistical basis; that is, many <br />variables are used in preliminary regressions <br />and those that lack statistical significance are <br />discarded. This practice occasionally results <br />in the retention of a variable whose effect in <br />the regression does not conform to known <br />hydrologic principles. Usually the effect of <br />such a variable on the result is trivial (a few <br />percent reduction in standard error). The <br />fact that the particular variable does not ap- <br />pear in regressions for other areas may indi- <br />cate that it does not exert an effect of prac- <br />tical significance. <br />It seems desirable to select in advance those <br />variables which are expected, on the basis of <br />previous work, to have practical significance. <br />However, some commonly used and widely <br />accepted variable may not prove significant <br />in a particular regression if the range in that <br />variable is small. For example, channel slope <br />