Self-consistently matching sediment supply, water discharge, and channel slope: Lane's balance at the catchment scale

Abstract:

Rivers are self-adjusting mass-transport engines, varying their slopes and planform geometries to send incoming sediment downvalley using the available water. According to Lane's balance, increasing sediment supply and/or decreasing water supply increase channel slope, whereas the opposite inputs decrease channel slope. This model describes the behavior of transport-limited rivers, whose rates of long-profile evolution are limited by their ability to export supplied sediment. Therefore, their form should reflect the balance between catchment hydrology, sediment additions from hillslopes, and sediment removal due to weathering and in-channel abrasion.

Here we apply a mass-balance framework to route sediment through a linked hillslope–channel network, compute downstream-fining rates from field data, and evaluate the impacts of sediment addition and removal on river long-profile geometry. Our prototype site is the intermontane drainage basin of the gravel-bed Río Rosario, Salta Province, Argentina. We calculate the hillslope and fluvial transport pathways of material with distinct lithologies from every point in the catchment to the drainage-basin outlet. We connect bundles of these pathways that lie upbasin of 32 in-channel locations, at each of which we measured the lithology and b-axis diameter of 100 fluvially transported gravel clasts. By comparing source areas and transport pathways to distributions of field-measured samples, we optimize a lossy mixing model to find best-fitting parameters for relative hillslope sediment production rates and exponential (Sternberg's law) gravel removal due to downstream fining. This procedure allows us to compute proportions of gravel lithologies and grain-size statistics throughout the tributary network, which we convert to an absolute gravel supply using catchment-mean denudation rates. We then estimate spatially distributed river discharge by combining Global Precipitation Mission time series with local rainfall and stream-gauge data. By comparing spatially variable sediment and water supply to channel slope, we test the internal consistency of our knowledge about individual components of the coupled geomorphic system and build a unified framework for addressing catchment-wide sediment dynamics.