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<br />Where: <br /> <br />I = The average inflow to the reach during dt <br />o = The average outflow from the reach during dt <br />dS = Change in storage, storage within the reach during dt <br />dt = Time interval <br /> <br />One of the simplest routing applications is the analysis of a flood wave that passes <br />through an unregulated reservoir. The inflow hydrograph is known, and it is desired to <br />compute the outflow hydrograph from the reservoir. Assuming that all gate and spillway <br />openings are fixed, a unique relationship between storage and outflow can be developed. <br /> <br />The equation defining storage routing, based on the principle of conservation of <br />mass, can be written in approximate form for a routing interval ",I. Assuming the subscripts <br />'1' and '2' denote th.a beginning and end of the routing interval, the equation is written as <br />follows: <br /> <br />Q 1 +02 =L.:tL-S .-S , <br />2 2 ",t <br /> <br />(2) <br /> <br />The known values in this equation are the inflow hydrograph, and the <br />storage and discharge at the end of the routing interval. With two unknowns (02 and S 2) <br />remaining, another relationship is required to obtain a solution. The storage-outflow <br />relationship is normally used as the second equation. How that relationship is derived is <br />what distinguishes various storage routing methods. <br /> <br />In applying hydrologic routing methods to a channel, the reach is subdivided into <br />a series of sub-reaches with each sub-reach routed through as if it was an Individual <br />reservoir. Each sub-reach is selected such that the average travel time through the sub- <br />reach is equal to the computation time Interval. <br /> <br />2. MODIFIED PULS ROUTING. Routing in natural rivers is complicated by the fact that <br />storage in a river rea.~h is not a function of outflow alone. The water surface in a channel, <br />during the paSSing 01' a flood wave, is not uniform. The storage and water surface slope <br />within a river reach, for a given outflow, is greater during the rising stages of a flood wave <br />than during the fallin!J. Therefore, the relationship between storage and discharge at the <br />outlet of a channel is: not a unique relationship, rather it is a looped relationship. <br /> <br />In order to apply the Modified Puis method to a channel routing problem, the <br />storage within the riv.ar reach is approximated with a series of cascading reservoirs. Each <br />reservoir is assumed to have a level pool, and therefore a unique storage-discharge <br />relationship. The cascading reservoir approach is capable of approximating the looped <br />storage-outflow effect when evaluating the river reach as a whole. The rising and falling <br />flood wave is simulated with different storage levels in the cascade of reservoirs, thus <br />producing a looped storage-outflow function for the total river reach. <br /> <br />2.1 DETERMINATION OF THE STORAGE-OUTFLOW RELATIONSHIP. <br />Determining the storage-outflow relationship for a river reach is a critical part of the <br /> <br />Colorado Flood <br />Hydrology Mallual <br /> <br />76.2 <br /> <br />fRIlFT <br />