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Eq. 8 relates the direction of bed load movement to the direction of near-bed velocity and transverse bed slope azjar. As transverse velocity starts to move sediment away from the concave baok, it creates a trans- verse bed slope that counters the transverse sediment movement. An equilibrium is reached when the effects of these counteractive factors are in balance. Under this situation, the angle of deviation becomes zero. In this model, transverse bed profile evolution is related to the trans- verse variation in bed material load. Since bed material load, excluding wash load, is usually concentrated near the bed, it is assumed to follow the direction given by Eq. 8, i.e. q; = q, tan 8 . . . . . . . .. . . . . .. .. . .. .. .. . .. . .. . .. . .. . . .. . .. . . .. . .... (9) in which q; = transverse bed material load per unit channel length; and q, = longitudinal bed material load per unit channel width. Unsteady sediment transport is complicated by sediment sorting. Methods for estimating sediment rate by tracking variation in bed ma- terial composition and stream bed profile evolution have been devel- oped by Bennett and Nordin (4), Alonso et al. (1), and Borah et al. (5), among others, To treat this time-dependent sediment transport, bed ma- terials are divided into five size fractions, and the size for each fraction is represented by its geometric mean diameter. For each size fraction, sediment transport capacity is first computed using a sediment transport formula. Then the actual sediment rate is obtained by considering sed- iment material of all size fractions already in the flow and the exchange of sediment load with the bed using the method by Borah et al. (5). If the stream carries a load in excess of its capacity, it will deposit the ex- cess material on the bed. In the case of erosion, any size fraction avail- able for entrainment at the bed surface will be removed by the flow and added to the sediment already in transport. During sediment removal, the exchange between the flow and the bed is assumed to take place in the active layer at the surface. Thickness of the active layer is based upon the relation defined by Borah et al. (5). As a function of the material size and composition, this thickness also reflects the flow condition. During degradation, several of these layers may be scoured away, resulting in the coarsening of the bed material and formation of a armor coat. How- ever, new active layers may be deposited on the bed in the process of aggradation. These procedures for computing sediment rate and sedi- ment sorting are applied to the longitudinal and transverse direction. They are also coupled with stream bed prome changes described in the next section. Prediction of Stream Bed Profile Changes.-Changes in stream bed prome, at each time step, due to longitudinal and transverse variations in sediment load are simulated. Changes along the longitudinal direc- tion, i.e., aggradation or degradation, are computed using the continuity equation for sediment movement in the longitudinal direction. This is explained in Ref. 7. Changes in channel bed elevation at a point due to transverse load are computed using the continuity equation az 1 10 - +---(rq;) = 0...... ..... ....... .... ...,.... .... ... ... (to) at 1-~rar 648 26