One-dimensional bathymetry based on velocity measurements

Abstract

Modelling the hydrodynamics of open channel flows requires the prior knowledge of the channel bed topography in order to accurately determine the flow features. As an alternative to measure the bed topography either by direct or airborne optical measurement, a numerical technique which uses the measured flow velocity to infer the channel bed topography is presented. The depth-averaged one-dimensional shallow water equations along with an empirical relationship between the free-surface and the depth-averaged velocities are used for the inverse problem analysis. It is shown that after a series of algebraic manipulation and integration, the equation governing the inverse problem simplifies to a simple integral equation. The proposed method is tested on a range of analytical and experimental benchmark test cases and the results confirm that, within the given assumptions, it is possible to reconstruct the river bed topography from a known velocity distribution (either free-surface velocity or depth-averaged velocity).