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

Abstract:

We developed an inversion model for river bathymetry and discharge estimation based on measurements of surface currents, water surface elevation and shoreline coordinates. The model uses a simplification of the 2D depth-averaged steady shallow water equations based on a streamline following system of coordinates and assumes spatially uniform bed friction coefficient and eddy viscosity. The spatial resolution of the predicted bathymetry is related to the resolution of the surface currents measurements. The discharge is determined by minimizing the difference between the predicted and the measured streamwise variation of the total head. The inversion model was tested using in situ and remote sensing measurements of the Kootenai River east of Bonners Ferry, ID. The measurements were obtained in August 2010 when the discharge was about 223 m³/s and the maximum river depth was about 6.5 m. Surface currents covering a 10 km reach with 8 m spatial resolution were estimated from airborne infrared video and were converted to depth-averaged currents using acoustic Doppler current profiler (ADCP) measurements along eight cross-stream transects. The streamwise profile of the water surface elevation was measured using real-time kinematic GPS from a drifting platform. The value of the friction coefficient was obtained from forward calibration simulations that minimized the difference between the predicted and measured velocity and water level along the river thalweg. The predicted along/cross-channel water depth variation was compared to the depth measured with a multibeam echo sounder. The rms error between the measured and predicted depth along the thalweg was found to be about 60cm and the estimated discharge was 5% smaller than the discharge measured by the ADCP.