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employs a space-time domain in which the space domain is represented by the discrete cross sections along the river reach and the time domain is represented by discrete time steps. In water routing, the time and spatial variations of the discharge, stage, velocity, energy gradient, etc., along the reach are obtained by an iterative procedure. At each time step, sediment discharge at each cross section is computed; changes in channel width, channel-bed profile and lateral migration are obtained and applied to each cross section. The bed-material composition is up- dated at each time step. Water routing is assumed to be uncoupled from the sediment processes. The five components are described. Water Routing.-Basic equations for water routing include the conti- nuity and momentum equation of flow, these are aQ aA - + - - q = O. . . . .. . . . . . . .. . .. .. . .. , .. . .. .. , .. .. .. . . .. .. . . ... (1) ax at g aH + .!. aQ + .!.!.. (Q') + gS - Q, q = 0 ........................ (2) ax A at Aax A A in which Q = flow discharge; x = distance in the longitudinal or flow direction; A = cross-sectional area of flow; t = time; q = lateral inflow rate per unit channel length; g = gravitational acceleration; H = stage or water surface elevation; and 5 = energy gradient. Eqs. 1 and 2 con- stitute a system of partial differential equations; they may be written in finite difference form in the space-time domain. With the prescribed ini- tial and boundary conditions, time and spatial variations of Q and H along the reach may be obtained by an iterative procedure. This tech- nique for water routing can be found elsewhere (6). If the temporal terms in Eqs. 1 and 2 are ignored, water routing may be simplified by computing water-surface profiles at successive time steps. This option is available in the model. Computation of the water-surface profile at each time step is based upon the standard-step method using techniques similar to the HEC-2 computer model (9). For many cases, spatial variation in discharge due to channel storage is small and this technique produces closely similar results as the previous one. Sediment Routing.-The sediment routing component has three ma- jor features: (1) Numerical solution of the continuity equation for sedi- ment in the longitudinal direction; (2) computation of bed-material load using a formula suitable for the physical conditions; and (3) accounting of bed-material composition. The continuity equation for sediment in the longitudinal direction is aA" aQ, (1 - I.) - + ~ - q, = 0 ..'.........................,.......... (3) at ax in which I. = porosity of bed material; A" = cross-sectional area of chan- nel bed within some arbitrary frame; Q, = volumetric sediment rate; and q, = lateral inflow rate of sediment per unit length. The change in cross- sectional area 11A" for each section at each time step is obtained through numerical solution of Eq. 3. Techniques for numerical solution can be found in the literature (3,4). The area change AA" is applied to the bed and banks following the techniques of corrections of channel-bed profile 158 7