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<br />EM 1110--2-U08 <br />1 Much 1960 <br /> <br />By drawing straight lines between these discharges, hydrograph C is obtained and it represents the first <br />step hydrograph of the successive a\'erage-lag mcthod. In each successive subreach the midpoint <br />discharges of the preceding hydrographs ore connected with the result that the wave form flattens in its <br />downstream procession. A consideration of the geometrical properties inherent in the method is suffi- <br />cient to disclose that the crest and shape of the hydrograph at some distant downstream point varies <br />with the choice of the time increment of the successive steps. That is, the smaller the time increment, <br />the more nearly does the routed hydrograph retain the shape of the original hydrograph. <br />d. Comparison with Coefficient Method. A comparison of the successive average-lag method <br />with the coefficient method, by equating outflows of the first subreach, discloses that for K=Atj2 the <br />value of X is zero, <br />It may b( observed that the routing constants of this method, in plate No. 10, differ from those of <br />the coefficient method, in plate No, 2, for reaches of equivalent travel time, <br /> <br />5-03. PROGRESSIVE AVERAGE-LAG METHOD OF FLOOD ROUTING. In the progressive <br />average.Jag method, a numbe!' of inflow values .are averaged and the mean value then is lagged by the <br />time of travel of the flood wave to yield the discharge and tim~ of occurrence of one value of the outflow <br />hydrograph, The process is repeated for other outflow values until the outflow hydrograph is determined. <br />This method differs from' the suceessive average-lag method in two respects: (1) Equal rather than <br />variable weight is given each inflow value in deriving an outflow and (2) thelength of period for which <br />inflow \'alues are averaged to obtain an outflow value does not necessarily have any relation to the <br />flood.wav~ travel time, Generally the length of the inflow period is determined by trial until a satis- <br />factory agreement is obtained between the computed and actual peak outflows, The length of inflow <br />period is usually found to be in the range from three-fourths to twice the travel time, In the case re- <br />ported in the ~lissouri River "308" repo!'t" the length of inflow period was taken equal to the travel <br />time. Computations are facilitated by the selection of an odd number of inflow values to avoid the use <br />of fractional periods (or the lag period. In some cases it may be necessary to use a lag period somewhat <br />greater or less than the time of travel in order to obtain a satisfactory reproduction of a known outflow <br />hydrograph, The flexibility in the selection of inflow periods and lag periods emphasizes the approxi. <br />mate nature of this method.Gf routing, The use of the method in extrapolation to hydrographs differing <br />from those used as checks possibly is justified only if it is realized that in many applications the esti- <br />mates of travel time, hydrographs of historic or record floods, or hydrographs of design floods are no <br />more preCIse. <br />Generally the 'method is not readily compared with the coefficient method in terms of X, K, and I1t. <br />It is equivalent to the successive avcrage-lag method, and therefore to x=o and K=Atj2 of the coeffi- <br />cient method, in the single case wherein the number of inflow values bein~ averaged is two and the outflow <br />thus obtained occurs at the time of the second inflow value. <br />There are several ad vantages to using the progressive ave'rage-Iag method. The work necessary <br />to develop storage curves for some alternate methods of routing is not necessary for this method. The <br />principsl adnntage is the speed with which it can be used, It is useful to obtain hasty or preliminary <br />estimates of flood-control benefits on large watersheds for which a relatively small amount of hydro- <br />graphic and hydraulie information is available. Jvlodifying conditions, such as reservoir operation for <br />the control of floods, can readily be studied, and results from several proposed storage capacities or from <br />different. systems of reservoirs or from individual reservoirs of a system can be found conveniently. <br />The next paragraph indicates the manner of evaluating the effect of each reservoir of a system on control <br />of floods. <br /> <br />5-04. ROUTING OF RESERVOIR HOLDOUTS BY THE PROGRESSIVE AVERAGE-LAG <br />METHOD. The differences between a natural hydrograph.and one resulting from, say, modifieation <br />by re.,<;ervOlr storage may be routed downstream to determine the lowering of crest discharges resulting <br />from storage. This is generally simpler than routing.the modified hydrograph, with which tributary <br />inflow must be combined. The differences may be routed by any of the methods presented in this chap- <br /> <br />16 <br /> <br />c <br /> <br /> <br />( <br />'. <br /> <br />/ <br />, <br />i <br />