Bottom Topography Mapping via Nonlinear Data Assimilation

Abstract

Abstract A variational data assimilation method is described for bottom topography mapping in rivers and estuaries using remotely sensed observations of water surface currents. The velocity field and bottom topography are related by the vertically integrated momentum and continuity equations, leading to a nonlinear inverse problem for bottom topography, which is solved using a Picard iteration strategy combined with a nonlinear line search. An illustration of the method is shown for Haverstraw Bay, in the Hudson River, where the known bottom topography is well reconstructed. Once the topography has been estimated, currents and water levels may be forecast. The method makes feasible 1) the estimation of bottom topography in regions where in situ data collection may be impossible, dangerous, or expensive, and 2) the calibration of barotropic shallow-water models via control of the bottom topography.