Fluvial erosion, transport and deposition (continued)
In general alluvial channels are assumed to be at grade, that is the channel gradient is in equilibrium with long term average of sediment influx from upstream and effective discharge
Thus the previous equation is solved for gradient as a function of contributing area and sediment load imposed from slope and bedrock channel erosion
Notes:
In the Howard (1994) model the calculation of bed changes in alluvial channels utilized the simplifying assumption that the gradient is adjusted so that the channel is at grade -- that is, the gradient is adjusted to transport the sediment load contributed from upstream. The channel gradient is determined by rearranging the previous equation to give gradient as a function of the load imposed from slope and channel erosion upstream and the available discharge.