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Lateral movements of alluvial river channels control the extent and reworking rates of alluvial fans, floodplains, deltas, and alluvial sections of bedrock rivers. These lateral movements can occur by gradual channel migration or by sudden changes in channel position (avulsions). Whereas models exist for rates of river avulsion, we lack a detailed understanding of the rates of lateral channel migration on the scale of a channel belt. In a two-step process, we develop here an expression for the lateral migration rate of braided channel systems in coarse, non-cohesive sediment. On the basis of photographic and topographic data from laboratory experiments of braided channels performed under constant external boundary conditions, we first explore the impact of autogenic variations of the channel-system geometry (i.e. channel-bank heights, water depths, channel-system width, and channel slope) on channel-migration rates. In agreement with theoretical expectations, we find that, under such constant boundary conditions, the laterally reworked volume of sediment is constant and lateral channel-migration rates scale inversely with the channel-bank height. Furthermore, when channel-bank heights are accounted for, lateral migration rates are independent of the remaining channel geometry parameters. These constraints allow us, in a second step, to derive two alternative expressions for lateral channel-migration rates under different boundary conditions using dimensional analysis. Fits of a compilation of laboratory experiments to these expressions suggest that, for a given channel bank-height, migration rates are strongly sensitive to water discharges and more weakly sensitive to sediment discharges. In addition, external perturbations, such as changes in sediment and water discharges or base level fall, can indirectly affect lateral channel-migration rates by modulating channel-bank heights.
Alluvial and transport-limited bedrock rivers constitute the majority of fluvial systems on Earth. Their long profiles hold clues to their present state and past evolution. We currently possess first-principles-based governing equations for flow, sediment transport, and channel morphodynamics in these systems, which we lack for detachment-limited bedrock rivers. Here we formally couple these equations for transport-limited gravel-bed river long-profile evolution. The result is a new predictive relationship whose functional form and parameters are grounded in theory and defined through experimental data. From this, we produce a power-law analytical solution and a finite-difference numerical solution to long-profile evolution. Steady-state channel concavity and steepness are diagnostic of external drivers: concavity decreases with increasing uplift rate, and steepness increases with an increasing sediment-to-water supply ratio. Constraining free parameters explains common observations of river form: to match observed channel concavities, gravel-sized sediments must weather and fine - typically rapidly - and valleys typically should widen gradually. To match the empirical square-root width-discharge scaling in equilibrium-width gravel-bed rivers, downstream fining must occur. The ability to assign a cause to such observations is the direct result of a deductive approach to developing equations for landscape evolution.