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00625 . . . Modelling of sand depo5ilion in Colorado River 363 where d is grain diameter, T. is the ratio of the skin friction shear stress to the critical shear stress (T,flT,), and 0, is a constant (0, = 0.68). The coefficient 02 is a function of the grain size in centimetres: 02 = 0.0203S(ln(d))2 + 0.02203In(d) + 0.07090 (14.14) The boundary condition at the water surface is c = 0, which is consistent with equation (14.8). The evolution of the bed over time is calculated from the sediment continuity equation: 0., = _.l (aq, + aq,) at ct. ax ay (14.15) where TJ is the bed elevation. The sediment discharge, q" is the sum of the sand transported by bedload and in suspension. The suspended sand discharge is deter- mined by vertically integrating the product of the flow velocity and the sand concentration. The beclload is determined by applying the Meyer-Peter and Miiller (1948) for- mula modified with the critical shear stress of the given grain size in place of their constant of 0.047: '" = 8(T' - T.,)J/2 (14.16) where q, is the nondimensional bedload transport (q, = q/[(p,!p - l)g,/f"), T. is the nondimensional boundary shear stress (T' = T/[(p, - p)gdJ), and T., is the nondimen- sional critical shear stress (ro, = TcI[[(Po - p)gdj). The grain diameter is represented by d; d"" the median grain diameter, is used in the model results presented later. The density of the sand is represented by Po. The boundary shear stress used in equation (14.16) is the magnitude of the vector sum of the shear stress calculated from the flow equations and an apparent stress due to gravity. The apparent stress due to gravity is calculated with a method proposed by Nelson and Smith (1989a) in which sinf'ilTJ TO = T'sin <l>IVTJI (14.17) where TO is the apparent gravitational stress, e is the local maximum bed slope, and is the grain angle of repose. The x and y components of the bedload are determined from the respective components of the flow velocity and components of the local bed slope. The magnitude of TO is zero where the bed is horizontal, and approaches T, where deposition increases the bed slope to the grain angle of repose. A large fraction of the total shear stress at the bed is exerted as form drag on large roughness elements, such as the extreme irregularity of the bedrock channel, bed- forms. and boulder-size talus and bed material. This form drag must be deducted from the total shear stress to arrive at the skin friction portion of the total shear stress that transports sediment. Wiele el ai. (1996) calculated the fraction of the total shear stress active in transporting sediment in reaches of the Colorado River in the ,. -