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At a section i, the lateral sediment inflow may be written as 1. . 1 ~. = -2 (~, + ~~ ) 111 (8) where superscripts j and j+l are the times at t and t + Llt, respectively. This model employs an upstream difference in s and a centered difference in t for the partial derivative, ~Qs/as, in Eg. 6, Le. (dQS! = __-=__ (_~~t ~:~ _ _~~i=L~~~~J.) (9) ~s Ji Llsi + Llsi_l 2 2 where .t.si is the distance between sections i and i+l, ASi_l is the distance between i-l and L With this upstream difference for dQs/us, the change' in bed area at a section i depends on sediment rates at this section and its upstream section i-l; it is independent of the sediment rate at the down- stream section. In other words, it is under upstream control. Contrary to this, the stage at a section in subcritical flow depends on the downstream stage and is independent of the upstream stage, Le., the stage is under downstream control in a subcritical flow. VIII. SIKJLATlal OF CIfAY;ES IN CiANND. WID'1H 'Ihe change in cross-sectional area AAb obtained in sediment routing represents the correction for a time increment t that needs to be applied to the bed and banks. With~AiJ being the total correction, it is possible for both the bed and banks to have deposition or erosion; it is also possible to have deposition along the banks but erosion in the bed and vice versa. The direction of width adjustment is detennined following the stream power approach and the rate of change is based upon bank erodibili ty and sediment transport described in the fOllowing. Direction of width Adjustment FOr a time step, width corrections at all cross sections are such that the stream power for the reach moves toward unifonnity; these corrections are subject to the physical constraint of rigid banks and limi ted by the 16