Channel Geometry Controls Downstream Lags in Sediment Rating Curves

In transport-limited alluvial streams, the suspended sediment concentration $C$ exhibits power functional relationships with the flow discharge $Q$ at a given station. Once the power-law $C\text{-}Q$ relationships at multiple stations along a stream are compiled, these relationships either systematically lag in the downstream direction (i.e., decreasing $C$ downstream for a constant $Q$) or overlap each other (i.e., similar $C$ for a constant $Q$ anywhere along the stream). It has been claimed that the mode of downstream $C\text{-}Q$ (lag or overlap) is associated with the downstream channel geometry. This poses a fundamental question as to whether different modes of downstream $C\text{-}Q$ relationships are the mechanistic consequences of channel hydraulics functions induced by different channel geometries or distinct channel geometries are the signatures of adaptation to the varying $C\text{-}Q$ relationships. This question is investigated in this study with theoretical streams by applying a numerical model which solves sediment flux and shallow water equations simultaneously. Simulation results are consistent with observations from natural rivers in many respects, such as power-law at-a-station and downstream hydraulic geometry relationships. Lagged $C\text{-}Q$ relationships are reproduced whereas the degree of a lag depends on the imposed channel geometry. This agrees with field observations and can be explained through the downstream increase rate in the bed shear stress. These findings imply that the downstream lag in $C\text{-}Q$ relationships is the resultant feature of a given channel geometry.