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<br />EM 1110-:--1408 <br />1 Much 1~0 <br /> <br />CHAPTER 5 <br />FLOOD-ROUTING APPROXIMATIONS BY TIME DISPLACEMENT <br />OF AVERAGE INFLOW <br /> <br />5-01. GENERAL. Methods of flood routing by time displacement of average inflow are described in- <br />asmuch as they have bee'>. used by several field offices and because in some cases, they yield adequate <br />approximations of crests Or flood hydrographs for some USes. These methods generally We.re de'lieloped <br />from intuitive processes rather than mathematical equations of motion or storage. When tested by <br />applications to hydrographs they can be said to be empirical methods of flood routing. In practice, the <br />methods have been applied to long reaches, The shortcuts in computations for the long reaches obtained <br />by these methods constitute the principal advantage over the coefficient method. However, since these <br />methods do not recognize many factors affecting flood-wave movement their reliability and the number <br />of instsnces to .which the methods may be applied are limited. ' <br />The methods to be described are: <br />Successive Average-Lag Method. This method was d~veloped in the Rock Island District, Corps of <br />Engineers, by Fred E. Tatum." . <br />Progressive Averl1{Je-La.g Method. This method was used for the Missouri River "308" report,'" <br />and ha5 been used by the Tulsa and Kansas City Districts, Corps of Engineers. <br />Routing with either method will reproduce a flood recession of the exponential fotm. Reservoir <br />holdouts also ma'y be routed by either me',hod. <br /> <br />5-02. SUCCESSIVE AVERAGE-LAG METHOD. a. Premises. The premises upon which this <br />method is based can be stated subsG.ntially as follows: <br />(1) The flow-storage relation, and with it the shape of the flood hydrograph, tends to vary uniformlv <br />along a stream due to the f100dway ha,'ing adapted itself to the discharges from the watershed. <br />Tatum II demonstrates, for instance, that flood recession curves of some midwestern rivers retain <br />the same recession coefficient at successive gaging points in the stream. <br />(2) The shape of the hydrograph reflects the cumulative effect of all the storage factors of the valley <br />above the point of measurement. <br />(3) If I, and I, represent ordinates of the hydro graph at times t, and t, at station A, there is some <br />downstream station B where the discharge at time t, is equal to the mean flow, (1,+1,)/2, at A <br />for the interval t, to t,. It is assumed that this relation between discharges at A and B applies <br />to all time periods of the same duration as the interval tl to t" <br />(4) It is assumed that the hydrograph at B reflects in its altered shape the changes due to <br />storage conditions in the reach between A and B. Therefore, the process may be repeated <br />for as many subre8ches as desired in order to det.ermine the change in shape of the hydrograph <br />as a result of routing through channel storage. It is probable that the successive hydrographs <br />obtained by this procedure are not, necessarily, spaced at equal intervals along tbe stream, <br />but that they are equally spaced in time. . For some subreaches the velocity of translation of the <br />flood wave may be greater or less than for othel"> due to local variations in storage conditions. <br /> <br />b. Routing Constants and Routing Procedure. The ordinates of a hydrogl'aph routed successively <br />through n subreaches may be expressed in terms of the ordinates of the original hydrograph. Thus if <br />there are two subreaches, the. ordinates are <br /> <br />o =~[I,+I,+I,+I'J <br />"2 2 2 <br /> <br />1,+21,+13 _ _ _ _. _ _ _. _ __ _ _ _ _ _ _ _ __ _ _ __ _. (31) <br />4 <br /> <br />and if there are three subreaches <br /> <br />0, I, +31,+313+1,______ _ u _ u _ _ _ __ __ __ u_._ _.__u _ _ (32) <br />8 <br /> <br />11 <br /> <br />c <br /> <br />r <br />i <br /> <br />/ <br />, <br />, <br /> <br />-"-- <br />