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

Abstract:

We developed a finite difference model for deterministic prediction of river depth and discharge from measurements of surface currents, water surface elevation slope and shoreline coordinates. The model is based on the inversion of the Reynolds-averaged depth-averaged steady shallow water equations in streamline curvilinear coordinates and assumes a quadratic bottom drag law with a known spatially-uniform friction coefficient. Iterative techniques are used to invert the discretized algebraic system relating the water depth to local gradients of the depth-averaged velocity and the water surface elevation. Inversion tests with in situ measurements of water surface elevations and surface currents from a 2010 field experiment on the Kootenai River (ID) showed encouraging agreement between the measured and predicted bathymetry. In situ measurements of velocity depth profiles obtained with an acoustic Doppler current profiler are used to relate the measured surface currents to the depth-averaged velocity used in the 2D hydraulic model. The shorelines were extracted from video imagery and the surface currents were estimated from remotely sensed infrared imagery or measured in situ from drifters. The value of the friction coefficient was obtained from previous calibration simulations with a forward hydraulic model that minimized the difference between the predicted and measured velocity and water level on a set of points along the river channel.