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10 TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS is a significant basin characteristic in some regional frequency analyses, but if all streams in a region have very similar slopes, the slope characteristic will not be significant, either statistically or practically. The significant variables found in 10 pub- lished regional flood-frequency regressions are shown in table 2. The four most common variables are drainage area, main-channel slope, percentage of basin area covered by lakes and swamps, and mean annual precipi- tation. Mean annual runoff appears only once; mean annual precipitation could have been substituted for it because the two are highly related. Only four of the 11 remaining vari- ables appear more than once. Because of the relatively high intercorre- lation among certain of the so-called inde- pendent variables and because most of these variables are only crude indexes of the char- acteristic being described, we may question whether the ones infrequently reported as significant are really so. Ordinarily the first four variables in table 2 will reduce the stand- ard error very close to the practical minimum. The regression model previously described was used for each of the 10 analyses referred to in table 2. However, that model is not ade- quate for semiarid regions of large relief. For example, consider a stream which rises in the high mountains and flows onto a plain. The 10-year flood will increase with drainage area to the base of the mountains and from that point on may decrease, or at least not increase at the same rate as in the upper part of the basin. If channel slope is included in a regression using data from such streams, the computed effect of drainage area will depend to some extent on the way channel slope is defined; the usual definition is not adequate to describe a major break in the channel pro- file. Thus a better model for regional analysis is needed for such regions. It is desirable practice to plot the residuals from a regional regression analysis on a map to check for possible geographical bias. Where a substantial bias is indicated by this test, a "geographical factor" is sometimes intro- duced into the regression equation to com- pensate for the bias. Before doing this, the analyst should realize that a geographical bias does not necessarily indicate that the re- gional relation is inadequate; there may have been much higher flood experience in one part of the region than in another during the pe- riod of record used. If possible one should identify the reasons for the bias and incorpo- rate them in the analysis rather than use a geographic factor. Regardless of the region being studied, the analyst should select his model and the rele- vant variables on the basis of knowledge of the system, leaving little of the selection proc- ess to be defined by the data. Snyder and Stall (1966) support this approach by writing: . . The extreme versatility of numerical methods and computing machines has sometimes led man into the pitfall of relying solely on these methods and ma- chines. This occurs when an analysis of a set of data is made without reference to past knowledge, under Variable Table 2.-lndependent varilJbles used in 10 regional f1ood-'frequency analyses 2 3 4 5 6 7 8 9 10 Drainage area___~_______________________________________________ x x x x x X x x x X Main-channel slope___________n_______nn_______n_____________ x x x x x u______unu__u__ Percentage of basin covered by lakes and swamps_ _ _ _ _ _ _ _ _ __ __ _ n _ n X X X ~ __ _ n __ nuX X u__ Mean annual precipitation_________u_____n__u__n_n___n____n____ x nnU_n___n__ X __n X X Mean annual runoff_ _ _ _ __ _ _ _"____ _ _ _ ___ ____ _ _ _ _ _ _ ~ __ ___ _ _ _ ______ __ _____ ___ _ _ ___ _ ___ _ _ _ _ _ __ _ _ _ x __ _ __ ___ T-year 24-hour rainfaIL_____u_unn______n__u__n__n________ x un X u__u ___n__n_u_____nn Average degrees below freezing in January_____n___n_~n~nu_____ X u__n _____~__n___nunnnnn__ Orographic factor _ _ _ _ _ _ ~_ _ ______~__ ___ _ __ _ _ ___ _ ___ _ ___ _ _ _ _ _ _ _ ___ x ___ __ ~ __ _ _ ~_ _ _ _ _ _ _ ___ ____ ____ Elevation_ _ __ ______________________________________________________ x _______ ___ _________________ x Number of thunderstorm days_ _ _ _u _ _ n _ __ _ _ n______ __ ___n _ __~__u _ _ x x _ _ _ _ _ _ _________ _____u Main-channellength__~_ _ _ _____ _ ____ ___ _ ____ ___ _ __ _ _____ __ _ _ __ _ ___ _ _ ___ _ _ x __ _ ___ _ __ _ _ _ _ __ ___ ____ _ _ ~ ~ __ Ratio of runoff to precipitatioll_______nu_nn_n_nununnn__n__u__ x nnnnn__n_n_nu__n__ Mean annual snowfaIL____nn_ _ n _ _ ___ _ __ ___________U__nu___n_u__ _ ___ _ _ x _. __n_ __u_n_ ___ _ _. n_ ~h~~f~~t~~~~~:-~~:~~~~~~~~a~~=============================================__~_-j(-================ Geographical factor __._____ ________ _ ________ __ _ _ _______ _ ____ __~___ __ ____ ___ _____ _______ _ __ _ _ _ X X ____ .