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<br />4. TATUM METHOD. This method was developed in the Rock Island District, Corps <br />of Engineers by Fred E. Tatum and is sometimes referred to as the successive average- <br />lag method. The premises upon which this method is based can be described as <br />follows: <br /> <br />4.1. The flow-storage relation, and with it the shape of the flood <br />hydrograph, tends to vary uniformly along a stream due to the flood way having <br />adapted itself to the discharges from the watershed. Tatum demonstrates, for <br />instance, that flood recession curves of some midwestern rivers retain the same <br />recession coefficient at successive gaging points in the stream. <br /> <br />4.2. The shape of the hydrograph reflects the cumulative effect of all the <br />storage factors of the valley above the point of measurement. <br /> <br />4.3. If I, and I 2 represent ordinates of the hydrograph at times t 1 and <br />t 2 at station A, there is some downstream station B where the discharge at times t <br />is equal to the mean flow, (I, + 12)/2, at A for the interval t , to t 2' It is assumed <br />that this relation between discharges at A and B applies to all time periods of the same <br />duration as the interval t 1 to t 2' <br /> <br />4.4. It is assumed that the hydrograph at B reflects in its altered shape <br />the changes due to storage conditions in the reach between A and B. therefore, the <br />process may be repeated for as many subreaches as desired in order to determine the <br />change in shape of the hydrograph as a result of routing through channel storage. It <br />is probable that the successive hydrographs obtained by this procedure are not, <br />necessarily, spaced at equal intervals along the stream, but that they are equally <br />spaced in time. For some subreaches the velocity of translation of the flood wave <br />may be greater or less than for others due to local variations in storage conditions. <br /> <br />4.5. ROUTING CONSTANTS AND ROUTING PROCEDURE. The ordinates <br />of a hydrograph routed successively through n subreaches may be expressed in terms <br />of the ordinates of the original hydrograph routed successively through n subreaches <br />may be expressed in terms of the ordinates of the original hydrograph. Thus if there <br />are two subreaches, the .ordinates are: <br /> <br />(18) <br /> <br />and if there are three subreaches: <br /> <br />(19) <br /> <br />If the inflow ordinates are I" I 2' 13 . . . . . .1 n + 1, and n is the number of subreaches, <br /> <br />(20) <br /> <br />7-46 <br />