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<br />By drawing straight lines between these discharges, hydrograph C is obtained and it <br />represents the first step hydrograph of the successive average-lag method. In each <br />successi.ve sub reach the midpoint discharges of the preceding hydrographs are <br />connected with the result that the wave form flattens in its downstream procession. <br />A consideration of the geometrical properties inherent in the method is sufficient to <br />disclose that the crest and shape of the hydrograph at some distant downstream point <br />varies with the choice of the time increment of the successive steps. That is, the <br />smaller the time increment, the more nearly does the routed hydrograph retain the <br />shape of the original hydrograph. <br /> <br />4.7. COMPARISON WITH MUSKINGUM METHOD. A comparison of the <br />successive average-lag method with the Muskingum method, by equating outflows of <br />the first subreach, discloses that for K = Ilt/2 the value of X is zero. <br /> <br />It may be observed thatthe routing constants ofthis method <br />differ from those of the Muskingum method, for reaches of equivalent travel time. <br /> <br />5. STRADDLE-STAGGER METHOD. In the Straddle-Stagger method, sometimes <br />referred to as the progressive average-lag method, a number of inflow values are <br />averaged and the mean value then is lagged by the time of travel of the flood wave <br />to yield the discharge and time of occurrence of one value of the outflow hydrograph. <br />The process is repeated for other outflow values until the outflow hydrograph i <br />determined. This method was developed by the Kansas City District, Corps of <br />Engineers and was originally described in the Missouri River 308 report in 1935. <br /> <br />This method differs from the successive average-lag method in two <br />respects: (1) Equal rather than variable weight is given each inflow value in deriving <br />an outflow and (2) the length of period for which inflow values are averaged to obtain <br />an outflow value does not necessarily have any relation to the flood-wave travel time. <br />Generally the length of the inflow period is determined by trial until a satisfactory <br />agreement is obtained between the computed and actual peak outflows. The length <br />of inflow period is usually found to be in the range from three-fourths to twice the <br />travel time. In the case reported in the Missouri River "308" report the length of <br />inflow period was taken equal to the travel time. Computations are facilitated by the <br />selection of an odd number of inflow values to avoid the use of fractional periods for <br />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 <br />a known outflow hydrograph. the flexibility in the selection of inflow period and lag <br />periods emphasizes the approximate nature of this method of routing. The use of the <br />method in extrapolation to hydrographs differing from those used as checks possibly <br />is justified only if it is realized that in may applications the estimates of travel time, <br />hydrographs of historic or record floods, or hydrographs of design floods are not more <br />precise. <br /> <br />7-48 <br />