Steady-state valley width revealed by alluvial terrace sequences

Lateral erosion by rivers drives valley widening and controls valley-bottom width. The current lack of a comprehensive valley-widening model complicates the reproduction of the full range of valley shapes that we find in nature as well as the prediction of valley evolution under different climatic and tectonic boundary conditions. Field data have shown that water discharge and valley wall lithology control lateral erosion rates. However, order-of magnitude variations in valley width formed in uniform lithology and under similar discharge conditions suggest additional, so far unquantified controls on valley width.

Fluvial terrace sequences offer an opportunity to study valley-width evolution under comparable discharge and lithologic conditions. Alluvial terraces are composed of flat surfaces and steep walls carved into previously deposited river sediments. They form where a river alternates between phases of lateral valley widening by lateral planation and vertical incision and terrace formation. In order to form an entire terrace staircase, such alternations have to repeat and many Quaternary terrace staircases are interpreted to be driven by cyclic climate changes. Because Quaternary climate cycles have had comparable amplitudes and durations, individual surfaces in paired climate-driven terrace sequences preserve the widths of valleys that have formed under similar discharge conditions, lithologies and over comparable time-intervals. We use a global compilation of 16 climatically formed alluvial terrace sequences to investigate controls on valley width.

Between 90 and 99% of the variance in valley width can be explained by a linear relationship of the width with the total valley depth. Hence, at least one of the missing controls on valley width must scale (close to) linearly with valley depth. Ruling-out a preservation bias and a number of parameters that are unrelated to valley depth, we propose a model that relates valley width to a competition between the sediment supplied from valley walls and the river’s capacity to rework sediment, such that a lateral sediment-flux steady state is reached. According to our model the valley width-depth relationship is controlled by (1) the horizontal hillslope-erosion rate, (2) the lateral sediment-transport capacity of the river and (3) the valley-width which forms in the absence of lateral-sediment input. Hence, the model allows to predict valley width when all of the above parameters are quantified in the field. Alternatively, any of the three parameters can be predicted when valley width is measured. The new model is able to reproduce the first-order trend observed in terrace-derived valley widths and it can explain the evolution of paired terrace sequences, which has so far been a major challenge.