Engineered rivers are often prone to channel bed incision. This decreases the channel-floodplain connection, hampers navigation where nonerodible reaches increasingly protrude from the bed, and can destabilize structures. Here we inventorize causes and characteristics of channel incision measures. We elaborate on how channel bed incision is a transient channel response toward a new equilibrium channel state. Causes of incision comprise base level fall, channel narrowing (e.g., due to river training), channel shortening (bend cut-offs), an increased channel-forming discharge (e.g. due to climate change), and a decrease (or fining or coarsening) of the sediment flux from the upstream part of the basin. Finally, we discuss two measures that may mitigate channel bed incision: sediment nourishments and longitudinal training walls.

Engineering modifications of rivers, e.g., dams or groynes, often induce long-term riverbed erosion, which can be mitigated with sediment nourishments. Here, we consider nourishments to mitigate channel bed erosion induced by channel narrowing, as opposed to the more common application downstream of dams. Our objective is to assess and quantify how dumping location, grainsize, and volume are important for mitigation efficacy. Our results show that erosion can be mitigated if nourishments change the sediment flux such that the corresponding equilibrium channel slope is increased. This is achieved by coarsening the sediment flux throughout the reach, increasing magnitude of the sediment flux, or both. Flux is coarsened via additions of sediment at or coarser than the bed surface and nourished sediment should be distributed throughout the incising reach. The second option is nourishing a large volume of relatively fine sediment to increase the equilibrium channel slope. Additions of fine sediment in small volumes decrease the equilibrium channel slope and enhance erosion, because the fine sediment flux makes the gravel more mobile.

For upland ephemeral gullies, gully erosion is strongly related to the formation and migration of cyclic steps. It is necessary to provide insight into the process of cyclic step development to accurately predict the pace of landscape evolution and soil loss. Information on the geometry of cyclic steps in subaerial environments is limited, and, to our knowledge, no model of cyclic step development considers plunge pool erosion. In this study, we analyze the geometric features and controlling factors of erosional cyclic steps through meta-analysis of measured data including new measurements in the Loess Plateau, China. We focus on cyclic step dynamics of fluvial beds controlled by bed shear stress and local plunge pool erosion. We develop a new theory to incorporate plunge pool erosion through adapting existing cyclic step and plunge pool models. Our method agrees with measured data, showing that a larger flow rate leads to larger step length L_d and height H_d and increasing erodibility increases step aspect ratio L_d/H_d. The method is also able to predict how the step length, height, and aspect ratio change with the average channel slope. Our results indicate that plunge pool erosion is an important mechanism of cyclic step evolution. However, plunge pool development alone is not sufficient to explain the wide range of L_d/H_d in the measured data. The posed theory relates to equilibrium conditions and thus cannot consider temporal adjustments in step geometry.

An engineered alluvial river (i.e., a fixed-width channel) has constrained planform but is free to adjust channel slope and bed surface texture. These features are subject to controls: the hydrograph, sediment flux, and downstream base level. If the controls are sustained (or change slowly relative to the timescale of channel response), the channel ultimately achieves an equilibrium (or quasi-equilibrium) state. For brevity, we use the term “quasi-equilibrium” as a shorthand for both states. This quasi-equilibrium state is characterized by quasi-static and dynamic components, which define the characteristic timescale at which the dynamics of bed level average out. Although analytical models of quasi-equilibrium channel geometry in quasi-normal flow segments exist, rapid methods for determining the quasi-equilibrium geometry in backwater-dominated segments are still lacking. We show that, irrespective of its dynamics, the bed slope of a backwater or quasi-normal flow segment can be approximated as quasi-static (i.e., the static slope approximation). This approximation enables us to derive a rapid numerical space-marching solution of the quasi-static component for quasi-equilibrium channel geometry in both backwater and quasi-normal flow segments. A space-marching method means that the solution is found by stepping through space without the necessity of computing the transient phase. An additional numerical time stepping model describes the dynamic component of the quasi-equilibrium channel geometry. Tests of the two models against a backwater-Exner model confirm their validity. Our analysis validates previous studies in showing that the flow duration curve determines the quasi-static equilibrium profile, whereas the flow rate sequence governs the dynamic fluctuations.