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472 Topographic Response of a Oar , ~ 1 [-->- -->-] or = - Cb V . qs (2) where '1 is the bed elevation, q; is the volumetric vector sediment flux and ~ =....65 is the percentage of the bed made up of sediment (Le., unity minus the porosity). Using computed sediment fluxes, the rate of erosion is easily calculated from Equation (2). The erosion rate, in conjunction with an assumed time increment, predicts the modification to the bed in that interval. Thus, this equation may be employed in an iterative manner to predict temporal adjustment of the bed to flow conditions, as discussed below. The other way in which the channel may be modified is through changes in stage. Although this effect does not modify the actual bed topography (except through erosion and deposition, as discussed in the previous paragraph), it does have a profound effect on the planfonn and depth of the channel. For example, the centerline trace of a typical meandering stream is typically more sinuous at low flow than at bankfull; the centerline is defined as the locus of points midway between the two water edges. Similarly, the relative cross-sectional area at a given longitudinal location in the reach may change dramatically from low to high flow. TheSe effects may seem obvious or even trivial, but they play a major role in determining the difference in patterns of erosion and deposition at different stages in a given reach. The method used in developing low flow initial channels from bankfull topographic surveys is relatively straightforward. First, a comprehensive topographic map is constructed from surveyed points. In order to obtain approximate channel alignment and topography below bankfull elevation, the bankfuII channel is "sliced" along a surface parallel to the bankfull free surface. This surface is positioned at a distance below the bankfull free surface equivalent to the desired stage drop. Points below the plane are interpolated using a tensioned spline and resampled in a regular grid. The potential error in this approach arises from assuming that the pattern of superelevation in the free surface is relatively invariant with stage change. This approximation is never precisely correct, but the error incurred in the depths is typically very small. Furthermore, the size of the error can be calculated using the flow model, and a new free surface can be calculated iteratively to improve the estimated depth. For the Green River reach desj:ribed herein, the error was typically less than two or three centimeters. This is well ~ithin the uncertainty in the surveyed topography, and was assumed to be negligible. The technique described above also can be employed to predict variations in channel form due to stage change while erosion and deposition are taking place on the bed. In other words, the channel topography can be adjusted with each increment of time to account for both erosion and deposition and stage changes in a quasi~teady sense. This allows the investigation of the response of the channel topography in cases where the change in stage occurs over time scales which are short compared to the bed modification and in cases where discharge and stage vary slowly compared to the bed evolution. The Evolution Model The coupling of the various components of the full evolution model is shown in Figure 3. As shown, the inputs to the evolution model consist of the following: the initial planform and topography of the channel, the sediment size making up the bed, and the sta~e and discharge as a function of time. Using the specified channel geometry and iDltial discharge, the flow model described herein can be employed to calculate the spatial distribution of boundary shear stress. These values are inserted