River Discharge and Bathymetry Estimation from Inversion of Surface Currents and Water Surface Elevation Observations

Abstract

We developed an approach for estimating river discharge and water depth from measurements of surfacevelocity and water surface elevation, based on analytical velocity–depth and velocity–slope relationships derived from the steady gravity–friction momentum balance and mass conservation. A key component in this approach is specifying the influence of bottom friction on the modeled depth-averaged flow. Accordingly, we considered two commonly used bottom friction parameterizations—a depth-independent Darcy friction coefficient and a depth-dependent friction coefficient based on the Manning’s roughness parameter. As- suming that the bottom friction coefficient is known, the unknown discharge was determined by minimizing the difference between the measured total head profile and the one determined from the velocity–slope relationship. The model performance and its sensitivity to key assumptions were evaluated using existing bathymetry data, and surface velocity and elevation observations obtained during field experiments on the Kootenai River near Bonners Ferry, Idaho, and the Hanford reach of the Columbia River. We found that the Manning’s friction parameterization provided superior depth and discharge estimates, compared to the Darcy friction law. For both steady and moderately unsteady flow, inversions based on the Manning’s friction provided discharge and thalweg depth estimates with relative errors not exceeding 5% and 12%, respectively.