Evolution of channel belts, flood plains and fluvial valleys

Channel belts, floodplains and fluvial valleys form by the mobilization and deposition of sediments during the lateral migration of rivers. The width of these surfaces is determined by the speed of lateral migration and the average time that the channel migrates laterally before switching direction. Here, we introduce a recent physics-based model of channel-belt width and explore its consequences for transient channel-belt evolution. The model builds on the assumption that the switching of the direction of lateral migration of a channel can be described by a Poisson process, with a constant rate parameter related to channel hydraulics. As such, the lateral migration of the channel can be viewed as a non-standard random walk. We derive an exponential equation to describe the mean approach to the steady state channel belt or valley width. Further, we exploit the properties of random walks to obtain equations for the increase of area visited by the channel (squareroot scaling), the “safe” distance from a channel that is unlikely to be inundated in a given time interval (law of the iterated logarithm), and the mean lateral drift speed of steady state unconstrained floodplains as well as constrained fluvial valleys in uplifting landscapes. All of these equations can be directly framed in terms of the channel hydraulic properties. The results are compared to experimental observations of the inundated area in a large-scale sand box. Finally, we show that the distribution of floodplain ages follows a power law scaling with a scaling exponent of -1.5, close to what has been observed in natural systems. This observation implies that the mean and variance of floodplain ages are infinite, with implications for storage times and chemical alteration of floodplain sediments.