Estimation of River Depth from Remotely Sensed Hydraulic Relationships
The Surface Water and Ocean Topography (SWOT) radar interferometer satellite mission will provide unprecedented global measurements of water surface elevation (WSE) for inland water bodies. However, like most remote-sensing technologies SWOT will not observe river channel bathymetry below the water surface, thus limiting its value for estimating river discharge. This study explores the possibility of using remotely sensed observations of river flow width and WSE alone to estimate this unmeasured flow depth. Synthetic values of WSE and either cross-sectional flow width (w) or effective width (We, inundated area divided by reach length) are extracted from 1,495 surveyed channel cross-sections and 62 km of continuously acquired sonar data for the Upper Mississippi, Illinois, Rio Grande, and Ganges-Brahmaputra river systems. A method is presented which uses extrapolation of low-flow width-WSE relationships to estimate d, at locations where two distinct hydraulic relationships, one for moderate-to-high flows and one for low-flows, are identified (called the "Slope-break Method," owing to detection of two clearly different linear trends in width-WSE relationships at these locations). These slope-break relationships represent a subset of "optimal" locations where river flow width and WSE co-vary with relative predictably. Slope-breaks were discovered in all four river systems at 6 (.04%) to 242 (16%) of the 1,495 studied cross-sections for channel bathymetric exposures ranging from 20% to 95%, respectively. Depth estimates generated by the Slope-break Method produced root mean squared errors (RMSE) of less than 20% (relative to bankfull mean depth) for the Upper Mississippi, Illinois, Rio Grande, and Ganges-Brahmaputra river systems when channel exposure was >25%, >50%, >75%, and >75%, respectively. HEC-RAS modeling for the Upper Mississippi and Rio Grande rivers suggests that these channel exposures occur at least ~25% and ~42% of the time, respectively, based on historic discharge records and steady-state discharge simulations. "Reach-averaging" (spatial averaging) of retrieved hydraulic variables reduces both RMSE and longitudinal variability in the derived depth estimates, especially at reach lengths of ~1000-2000 m. The findings presented here have positive implications for SWOT and other sensors attempting to estimate river flow depth and/or discharge solely from incomplete, remotely sensed hydraulic variables, and suggest that useful depth retrievals can be obtained even given the spatial and temporal constraints of spaceborne observations.