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2 TECHNIQUES OF WATER.RESOURCES INVESTIGATIONS Procedure for Flood Peaks Index-Aood method The index-flood method, described by Dal- rymple (1960), was used for most of the re- gional flood-frequency analyses made by the U,S, Geological Survey prior to 1965, It con- sists of two parts, The first part graphically relates mean an- nual flood to drainage area, and sometimes to other variables, Usually the plotted points define several different relations, On the basis of these preliminary relations, the geographic area being studied is divided into subareas such that a single relation of mean annual flood to drainage area applies to each, Thus the regionalization of the mean annual flood is attained, The second part of the regionalization proc. ess averages the individual frequency curves to provide a regional curve, This is accom- plished after expressing the flood magnitudes at selected recurrence intervals for each curve as ratios to the mean annual flood (the index flood). If some of the dimensionless individual curves are greatly different from others, the geographic area is subdivided so that each subdivision contains curves of similar shape, Then the curves in each subdivision are aver- aged, The subdivisions for this purpose are usually not coincident with the subareas de- fining the various relationships of mean an. , nual flood to drainage area. The index.f1ood method thus accomplishes the general purposes of a regionalization by relating the position of the frequency curve on the discharge scale to basin size, and by aver- aging the shapes of the individual curves, The method provides satisfactory results in many regions and is fairly simple to perform, The results are easy to apply to ungaged areas because usually only drainage area need be measured. Application of the method requires arbi- trary decisions as to the boundaries of sub. areas considered homogeneous with respect to mean annual flood or to shape of frequency curve, No subarea should be represented by fewer frequency curves than needed to define a meaningful regionalization, even though a close agreement among frequency character- istics in the subarea is not attained, A basic assumption of the index. flood meth. od is that the shape of the frequency curve in a homogeneous region is not related to drain. age.area size or to other basin characteristics, This assumption does not appear to be justi. fied on the basis of results from other types of analysis, Consequently, the variability in shape among dimensionless frequency curves from drainage areas of greatly differing size results both from chance and from real dif. ferences in the population frequency curves. Thus an average curve may obscure some real differences. A few published regional analyses have included suitable adjustments, Further evaluations of the index.f1ood method are de. scribed by Benson (1962a) and Cruff and Rantz (1965), No example of the index.f1ood method is given here because one is described by Dal- rymple (1960) and many others are available in published reports of the Geological Survey, Multiple.regression method Multiple regression is directly useful as a regionalization tool because the discharge for a given frequency level can be related to basin characteristics, leaving residuals that may be considered as due to chance, The regression line averages these residuals, Thus, in one operation, the effects of differing basin char. acteristics are preserved and the chance vari. ation is averaged, 1n practice, the interpretation of results from a regional regression analysis is not quite so straightforward. We know that we cannot describe all the variability due to basin characteristics by a regression, Therefore, the residuals contain both chance variation and variation due to basin characteristics, but we have no measure of the relative amounts of each, The chance variation among a group of rec- ords may be small if the records are for the same period of time and are responses to the same general weather events, Here a paradox arises, If the records are not independent, and consequently the chance variation is small, there is little to be gained by averaging the chance variation except that the regression ~