10 Adjustment of the bed surface size distribution of gravel-bed rivers in response to cycled hydrographs

Mountain gravel-bed rivers typically display a surface layer that is armored. That is, the surface layer visible at low flow is coarser than both the substrate and mean annual bedload transported. The surface layer is difficult to sample at the high flows that transport most of the gravel. As a result, the question as to whether the surface layer remains armored at high flows is something of a mystery. The few measurements available suggest that some form of armoring may be in place at high flows as well. In lieu of more measurements, numerical modelling provides an avenue to explore this issue. Research results are presented using a 1D model of aggradation and degradation to mobile-bed equilibrium in gravel-bed streams. In the model, a hydrograph is cycled repeatedly so that water discharge goes up and down in time. The magnitude of the bedload feed rate and the size distribution of the feed material are, however, held constant at the upstream end of the reach. As a result, the final mobile-bed equilibrium attained is characterized by a bed at the upstream end of the reach that cyclically degrades and coarsens at high flow (when the sediment feed rate is not sufficient) and aggrades and becomes finer at low flow (when there is an excess of sediment feed). Only a short distance downstream, however, a remarkable tradeoff occurs. The bed adjusts so that over the great majority of the modelled reach the bed elevation and surface size distribution become invariant in time, hardly changing at all from low flow to high flow. The bedload transport rate and size distribution, however, fluctuate strongly with the hydrograph. That is, the higher flows support a higher transport rate of coarser material and the lower flows support a lower transport rate of finer material. The implication is that rivers subject to repeated hydrographs can evolve so that neither surface grain size distribution nor mean bed elevation (averaged over bars) need change much with flow, nearly all the variation being absorbed by the bedload. If this is true, it provides a most useful result; the surface grain size distribution seen at low flow may be very close to that seen at high flow. The results have been verified with two transport relations, that of Parker and that of Wilcock and Crowe. The reasons behind this simple result are explored in terms of a "hydrograph boundary layer," downstream of which the effect of the hydrograph on bed elevation and surface size distribution become negligible. The results of the numerical model also indicate that for a given hydrograph, the degree to which the surface is armored relative to the grain size distribution of the feed sediment decreases with increasing gravel feed rate.