Estimating River Bathymetry from Surface Velocity Observations Using Variational Inverse Modeling

Abstract

Accurate river bathymetry characterization is important to understanding all aspects of the riparian environment and provides crucial information for ensuring the safe passage of vessels and guiding channel maintenance operations. Verified models based on readily collected physical data facilitate accurate predictions of changes to a riverbed caused by traffic, weather, and other influences. This paper presents a methodology for estimating river bathymetry from surface velocity data by applying variational inverse modeling to the shallow-water equations. We describe the mathematical framework for the methodology and the algorithm, and the numerical tools we developed to test the methodology. The hydrodynamic modeling uses 2D depth-averaged solvers (under the hydrostatic assumption) and applies a standard empirical correlation that relates depth-averaged velocity to surface velocity. We tested the application of the bathymetry estimation algorithm to water-surface velocity data on a 95 km reach of the Columbia River in Washington State. The root mean square error (RMSE) of the estimated bathymetry field relative to the ground truth data is approximately two meters over the entire reach. The results of the test case indicate that our approach can be used to estimate river bathymetry to a close approximation based on the bank-to-bank surface velocity data on the reach of interest.