Response times of fixed-width rivers to changes in boundary conditions: Incision vs Aggradation

Long profiles of alluvial rivers are sensitive to changes in water discharge (Qw) and sediment supply (Qs), both of which depend on local climatic and tectonic conditions. Consequently, changes in prevailing environmental boundary conditions impact the adjustment of river long profiles. Rivers respond through modifications in channel slope, either by steepening via sediment deposition supplied from upstream or by lowering through bed incision driven by sediment entrainment.  The time of river long-profile adjustment is commonly estimated using a range of equations derived from models of river evolution. While these formulations are widely applied, they do not distinguish between incision and aggradation and hence predict similar response times, despite these adjustments being governed by different physical processes. As a result, it remains unclear whether incision and aggradation operate on different characteristic timescales of slope adjustment. Given the increasing number of rivers with artificially fixed channel width due to anthropogenic activities, we focus here on the response of fixed-width rivers to changes in boundary conditions. Based data from analogue flume experiments, we investigate how the type of adjustment, i.e., incision or aggradation, affects the response time of slope adjustment of fixed-width rivers to changes in water discharge (Qw) and sediment supply (Qs). Across the experiments, we systematically vary water discharge (Qw), sediment supply (Qs) and grain size, while continuously recording the evolution of the channel slope. Response times are quantified using e-folding fits. We further explore the potential of estimating response times using an Ornstein—Uhlenbeck framework. While both approaches assume exponentially fast adjustment towards new boundary conditions, the Ornstein--Uhlenbeck formulation explicitly incorporates stochastic variability, accounting for model uncertainty and natural slope fluctuations. This makes it a robust alternative for characterizing slope adjustment dynamics. Preliminary results indicate a power-law relationship between steady-state channel slope in and the Qs/Qw ratio, consistent with previous studies. Moreover, the time of slope adjustments increases with the volume of material that has to be eroded or deposited to reach the new long profile. Furthermore, both water discharge (Qw) and sediment supply (Qs) seem to act as catalyst, exerting a primary control on the rate of the slope adjustment in the sense that for fixed Qs/Qw ratio the rate scales positively with an increase in (Qw), implying an increase in (Qs) to retain the ratio Qs/Qw, and vice versa an increase in (Qs). Fluvial systems shape our landscapes. Consequently, characterizing the time of river long-profile adjustment allows for accurate predictions of landscape evolutions, and we expect our results to provide new meaningful insights in that regard.