Stage-Slope-Discharge Relationships Upstream of River Confluences Revealed by Satellite Altimetry

With increasing coverage, density, and accuracy of the global inland water altimetry record, remote sensing observations of water surface elevation (WSE) and water surface slope (WSS) are becoming available for the world's rivers. In steady, uniform flows, WSS is invariable, while there is a unique one-to-one relationship between WSE and discharge, the rating curve. While the assumptions of steady uniform flow are appropriate for many rivers, they are violated upstream of river confluences. We present a simple analytical hydraulic model of river confluences using the theory of steady, gradually varied flow. We apply the model to four river confluences in the Mississippi-Missouri river system. We determine the spatial extent of the backwater-affected zones and map WSE-discharge and WSS-discharge relationships. We show that coincident measurements of WSE and WSS from new satellite altimetry missions effectively constrain discharge estimates from space in the backwater-affected zones upstream of river confluences. New satellite altimetry missions monitor water levels in global rivers at unprecedented spatio-temporal resolution and accuracy. One principal objective of this monitoring effort is to map river flow in space and time, understand the impacts of climatic change on river flows, and provide river flow estimates for practical water resources applications. In many locations and situations, there is a one-to-one relationship between river flow and river water level. This so-called rating curve can be used to directly translate water level observations into river flow estimates. However, the concept of the rating curve breaks down whenever the flow in the river is significantly different from steady uniform flow, which is the flow occurring in a long and uniform river reach with constant boundary inflow. Upstream of river confluences, conditions are often non-uniform, because high flow in one tributary can coincide with low flow in the other, leading to significant backwater effects in both tributaries. This study models water level and water surface slope dynamics upstream of river junctions and highlights the value that data sets from new satellite missions provide for understanding the hydraulics around river confluences and for estimating flow upstream of river confluences from space. The classic stage-discharge rating curve concept fails upstream of river confluences because of backwater effectsHydraulic modeling confirms that unique stage-slope-discharge relationships exist upstream of river confluencesNew satellite altimetry observations of river stage and slope reveal stage-slope-discharge relationships for selected river confluences