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 (h) for inland water bodies. However, like most remote sensing technologies SWOT will not observe river channel bathymetry below the lowest observed water surface, thus limiting its value for estimating river depth and/or discharge. This study explores if remotely sensed observations of river inundation width and h alone, when accumulated over time, may be used to estimate this unmeasurable flow depth. To test this possibility, synthetic values of h and either cross-sectional flow width (w) or effectivewidth (We, inundation area divided by reach length) are extracted from 1495 previously surveyed channel cross-sections for the Upper Mississippi, Illinois, Rio Grande, and Ganges-Brahmaputra river systems, and from 62 km of continuously acquired sonar data for the Upper Mississippi. Two proposed methods (called Linear and Slope-Break) are tested that seek to identify a small subset of geomorphically optimal locations where w or We covary strongly with h, such that they may be usefully extrapolated to estimate mean cross-sectional flow depth (d). While the simplest Linear Method is found to have considerable uncertainty, the Slope-Break Method, identifying locations where two distinct hydraulic relationships are identified (one for moderate to high flows and one for low flows), holds promise. Useful slope breaks were discovered in all four river systems, ranging from 6 (0.04%) to 242 (16%) of the 1495 studied cross-sections, assuming channel bathymetric exposures ranging from 20% to 95% of bankfull conditions, respectively. For all four rivers, the derived depth estimates from the Slope-Break Method have root mean squared errors (RMSEs) of <20% (relative to bankfull mean depth) assuming at least one channel bathymetry exposure of similar to 25% or greater. Based on historic discharge records and HEC-RAS hydraulic modeling, the Upper Mississippi and Rio Grande rivers experience adequate channel exposures at least similar to 60% and similar to 42% of the time, respectively. For the Upper Mississippi, so-called reach-averaging (spatial averaging along some predetermined river length) of native-resolution h and We values reduces both RMSE and longitudinal variability in the derived depth estimates, especially at reach-averaging lengths of similar to 1000-2000 m. These findings 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 within the spatial and temporal constraints of satellite observations.