Abstract Bed-load channels tend to adjust their cross-sections so that given slope, roughness and sediment load, channel shape approaches the optimum for bed-load transport. The extent to which any one shape is the optimum varies with discharge, so four Cumberland Basin stream channels have been investigated to determine the discharges at which their present cross-sections represent the optimum for bed-load transport. These discharges have return periods ranging from 1.1 to 1.5 years on the annual series. The return periods closely correspond with return periods for the discharge at which, over a period of time, the most bed-load is transported. These return periods vary from 1.15 to 1.45 years when the same bed-load equation is used. The close correspondence between sets of return periods suggests that bed-load channels tend to adjust their cross-sections to become the optimum shape for bed-load transport at or close to the discharge at which the most bed-load transport is accomplished.
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