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<br />Ell 1110-2.1416 <br />15 Oct 93 <br /> <br />the reasonableness of the boundary conditions for a <br />hypothetical event (because accuracy can seldom be <br />established) limits the quality of the conclusions. Fur- <br />thermore, the way that the boundary conditions are <br />applied can control the overall accuracy and consistency <br />of the model. <br /> <br />a. Ups/ream boundary conditions. The upstream <br />boundary condition defines an input 10 be routed through <br />the system. In most cases this is either a flow or stage <br />hydrograph. <br /> <br />(I) Flow hydrograph. A flow hydrograph is the <br />classic upstream boundary condition where the lime <br />varying discharge is routed downstream and the corre- <br />sponding stages are computed by the model at the <br />upstream boundary and elsewhere. If the flow hydro- <br />graph is at a gaging station, the location of the station <br />should be checked. If the station is on a stream with a <br />flat bed slope or with a highly mobile bed, a stage <br />boundary condition may be preferable for reproducing an <br />observed event. However, the flow boundary may be <br />acceptable if the upstream boundary is on a smaller tribu- <br />tary which only makes a minor contribution 10 the over- <br />all system. For this case any error would be lost in the <br />overall system. Be careful when using flows from a <br />slope station as an upstream boundary condition; t~ <br />values may not be accurate, resulting in an inability /0 <br />calibrate. <br /> <br />(2) Stage hydrograph. If a stage hydrograph lis used <br />as an upstream boundary, the corresponding/flow is <br />computed from the conveyance given by the/geometric <br />data. Because errors in stage data are less ttran errors in <br />flow data, the stage hydrograph may have substantial <br />advantages in accuracy over the flow hy~graph. The <br />stage hydrograph is used when a flow station is not avai- <br />lable or the quality of flow data is in question. Flow <br />computed from a stage boundary must always be verified <br />against reliable flow measurements, otherwise substantial <br />error in flow can result. If no flow measurements are <br />available, the stage hydrograph should only be used when <br />absolutely necessary and then with caution. Figure 5-4 <br />shows the reproduction of flow measurements at <br />Hickman from routing Cairo stages down the Mississippi <br />River. Figure 5-5 shows the reproduction of stage at <br />Memphis 200 miles downstream. <br /> <br />b. Downstream boundary condition. For subcritical <br />flow, the downstream boundary condition introduces the <br />effect of backwater into the model. Four types of <br /> <br />5-6 <br /> <br />downstream boundary conditinns are stage hydrograph, <br />flow hydrograph, rating curve, and Manning's equation. <br /> <br />e <br /> <br />(1) Stage hydrograph. The classic downstream <br />boundary is the stage hydrograph. The corresponding <br />flow is calculated by the model. Because the stage <br />hydrograph is observed, and therefore presumed accurate, <br />the downstream end of a study reach can be located at a <br />gage. <br /> <br />(2) Flow hydrograph. The flow hydrograph is a <br />special purpose downstream boundary condition which is <br />generally used to simulate a reservoir outflow or a pump- <br />ing station if accurate outflow is known. For the flow <br />hydrograph, the model calculates the corresponding <br />stages. The time series of computed stages is based on <br />an initial stage and will change with a differing initial <br />stage. The flow hydrograph must be used with great care <br />because the flow is leaving the system and negative <br />depths may be computed, in particular at pumping <br />stations. <br /> <br />. <br /> <br />~: <br /> <br />'L <br /> <br />(3) Rating curve. A single valued rating curve <br />describes a monotonic relationship between stage and <br />flow. The rating curve is accurate and useful for <br />describing a boundary condition at a free overfall, such <br />as a spillway or at a falls, or at a pump station whose <br />performance is defmed by a schedule. But the single <br />valued rating curve is often a poor downstream boundary <br />condition for a free flowing stream. Natural rivers dis- <br />play a looped rating curve; use of a single valued rating <br />curve, however, forces a monotonic relationship which <br />erroneously reflects waves upstream. For this reason, the <br />rating curve must be located well downstream of the <br />reach of interest in a free flowing stream to prevent <br />errors from propagating upstream into the area of inter- <br />est. This lack of sensitivity should be confirmed by <br />sensitivity tests. <br /> <br />e <br /> <br />(4) Manning's equation. Manning's equation can be <br />used as a downstream boundary condition for a free <br />flowing stream when no other boundary condition is <br />available. The model computes both stage and flow with <br />the stage being a function of the friction slope. Two <br />methods prevail for determining the friction slope. Fread <br />(1978, 1988) in DWOPER and DAMBRK assumes that <br />the friction slope is equal 10 the water surface slope. <br /> <br />. <br />~ <br /> <br />. <br /> <br />UNET (U.S. Army Corps of Engineers 1991b) uses the <br />friction slope at the last cross sectinn. These two <br />assumptions, which produce slightly different results, are <br /> <br />e <br />