Threshold constraints on the size, shape and stability of alluvial rivers

The geometry of alluvial river channels both controls and adjusts to the flow of water and sediment within them. This feedback between flow and form modulates flood risk, and the impacts of climate and land-use change. Considering widely varying hydro-climates, sediment supply, geology and vegetation, it is surprising that rivers follow remarkably consistent hydraulic geometry scaling relations. In this Perspective, we explore the factors governing river channel geometry, specifically how the threshold of sediment motion constrains the size and shape of channels. We highlight the utility of the near-threshold channel model as a suitable framework to explain the average size and stability of river channels, and show how deviations relate to complex higher-order behaviours. Further characterization of the sediment transport threshold and channel adjustment timescales, coupled with probabilistic descriptions of river geometry, promise the development of future models capable of capturing rivers' natural complexity.