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.