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<br />REGIONAL ANALYSES OF STREAMFLOW CHARACTERISTICS
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<br />equation can be applied to ungaged basins,
<br />Under these conditions the average is likely
<br />to be biased, On the other hand, if the records
<br />are independent and the chance variation is
<br />extremely large, the regression analysis
<br />should produce a good answer. but the quality
<br />of the results may not be recognized because
<br />of the large standard error. Thus the success
<br />of a regionalization procedure by regression
<br />analysis cannot be measured in terms of the
<br />standard error of regression alone.
<br />However, for a given set of data. the regres.
<br />sion equation with the smallest practical
<br />standard error should be used, Improvement
<br />of the regression equation not only reduces the
<br />standard error but reduces the portion of the
<br />standard error that is due to differences in
<br />basin characteristics,
<br />A regional regression having a large stand.
<br />ard error may prod de a good answer if most
<br />of that standard error is due to chance varia.
<br />tion, But since we have no way of knowing
<br />how well the regression describes the real dif-
<br />ferences among basins. we usually conclude
<br />that a relation with a large standard error has
<br />much room for improvement,
<br />A very small standard error of regression
<br />indicates little chance variation among the
<br />records used, The practice of reducing the
<br />residual variation to near Zero by assigning
<br />various coefficients to subareas of the total
<br />area represented by the regression must be
<br />
<br />based on the assumption that the residual
<br />variation is largely due to unexplained differ.
<br />ences in basin characteristics, and thus that
<br />the chance variation is small, This assumption
<br />does not seem iustified, More likely, the major
<br />part of the residual variation is due to chance,
<br />Benson (1962a, b, 1964) discusses and shows
<br />examples of the multiple. regression method of
<br />regional analysis of flood peaks, The following
<br />example outlines the procedure,
<br />Table 1 lists the 2-, 25., and 50. year floods.
<br />the drainage area, and the mean annual basin
<br />precipitation for gaging stations in Snohom.
<br />ish River basin, Washington (Collings, 1971).
<br />A graphical regression using these data is
<br />shown in figure 1 and the gage sites are shown
<br />in figure 2, See Riggs (1968a) for method of
<br />making a graphical multiple regression,
<br />This graphical step is preliminary and may
<br />be bypassed in an analysis, but it takes little
<br />time and usually clearly indicates the suitabil.
<br />ity (or lack of suitability) of the model to be
<br />used in the mathematical fitting, In figure 1
<br />the plotted points indicate the statistical sig.
<br />nificance of both independent variables.
<br />Standard errOr of the graphical regression
<br />can be estimated,
<br />Not all graphical regressions are as clear
<br />cut as that of figure 1. Consequently the re-
<br />gression is usually determined by mathemati.
<br />cal fitting, preferably by digital computer,
<br />The computer program produces the standard
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<br />T<ible 1._00to from Snoh<:lmish River basin, Washington
<br />
<br /> Annual flood peak (efs) Mean
<br /> at indicated recurrence interval (years) Drainage annual
<br />Station "ea , precipitation
<br /> (sq mil , (in.)
<br /> 2 25 50 I
<br />1330, S. F. Skykomish........... 22,600 54,400 63,300 355 116
<br />1335. Troublesome..u.....'"'' 920 2,760 - 10,6 , 176
<br />1345. Skykomish..u..u.....'" 36,100 87,800 102,000 535 119
<br />1350, Wallaco.....u.....""" 1,990 3,570 4,000 19,0 141
<br />1375, Sultan...._..........__... 16,700 35,200 39,600 74.5 151
<br />1410. Woods..u.....'u.u.... 1.210 2,300 2,580 56,4 59
<br />1415. M. F, Snoqualmie... ...." 12,500 27,100 - 169 127
<br />1420, N. F. Snoqualmie..__...... 7,440 16,600 19,100 64,0 139
<br />1440, S, F, Snoqualmie........_. 4,190 8,080 - 81.7 112
<br />1445. Snoqualmie_________un__ 26,500 63,500 - 375 118
<br />1460. Patteraon....u .....u"" 201 309 - 15.5 47
<br />1407. Griffin...u_......"'''''' 393 944 1,120 17.1 65
<br />1475, N, F, ToIL...nu........ 5,000 9,540 - 39,2 112
<br />1480. S, F. Tolt.........u..nu 3,450 6,700 - 19.7 123
<br />1485. Tolt...........__.....nu 7,780 16,100 17,900 81.4 I 105
<br />1490. Snoqualmie_ _ _ _ _ __ _ __ _ - - -- 28,200 59,400 67,400 603 102
<br />1525, Pilchuck....... n__....... 5,080 9,120 10,200 54.5 114
<br />1530, L. Pilchuck........___n.. 281 627 17,0 53
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