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<br />included as a part of the input and used in the simulation. Unfortunately, <br />sediment rating data are rarely very reliable or simply not available. For <br />such cases, it is assuned that the river channel remains unchanged above the <br />study reach and sediment inflow rate is canputed at the upstream section at <br />each time step just like they are computed at other cross sections. For <br />this reason, the study reach should extend far enough upstream so that the <br />channel beyond may be considered basically stable. Factors that may induce <br />river channel changes must be included in the study reach. <br /> <br />Numerical Solution of continuity Equation for Sediment <br /> <br />Changes in cross-sectional area, due to longitudinal and transverse <br />imbalances in sediment discharge, are obtained based upon numerical solution <br />of continuity equations for sediment in the respective directions. First, <br />the continuity equation for sediment in the longitudinal direction is <br /> <br />dAt, dOs <br />(1 -,\) -~t + ""$5 - qg = 0 <br /> <br />(6) <br /> <br />where ^ is the porosity of bed material, At, is the cross-sectional area of <br />channel bed within sane arbitrary frame, Qs is the bed...rnaterial discharge, <br />and qs is the lateral inflow rate of sediment per unit length. According to <br />this equation, the time change of cross-sectional area ~Abiat is related to <br />the longitudinal gradient in sediment discharge dQs/oS and lateral sediment <br />inflow qg. In the absence of qg, longitudinal imbalance in Qs is absorbed <br />by channel adjustments toward establishing unifomity in Qs. <br /> <br />The change in cross-sectional area ~ At, for each section at each time <br />step is obtained through numerical solution of Eq. 6. This area change <br />will be applied to the bed and banks following correction techniques for <br />channel width and channel-bed profile. <br /> <br />From Eq. 6, the correction in cross-sectional area of channel bed for a <br />time increment can be written as <br /> <br />AAt, = _ _~=_ (dQ~ _ qg' <br />1->. dS ") <br /> <br />(7) <br /> <br />15 <br />