Recent Developments in Bottom Topography Mapping Using Inverse Methods

Abstract

The problem of identification and mapping of underwater topography , in the form of river channel depth, littoral zone depth profiles, and spatially-resolved river, estuary , and ocean bottom topography, has received attention in recent years in tandem with the increasing availability of remotely-sensed data for hydrologic and hydrodynamic modeling. A variety of inverse methods have been successfully applied in order to estimate the bottom topography from diverse data, typically by using variants of the ensemble extended Kalman filter , but variational methods and non-parametric filters have also been used. The types of measurements used include remotely-sensed and in situ water level, surface currents, surface wave celerity, and measurements of surface wave direction and wave breaking. The dynamics employed to relate bottom depth to the measured variables have, to date, been based on the vertically integrated shallow equations, the Saint-Venant equations , with either Chézy or Manning frictional representation; and coastal zone applications have additionally coupled these dynamics with the wave radiation stress and dissipation from models of phase-averaged surface waves. The relevance of three-dimensional dynamics associated with vertical shear and baroclinicity are recognized but not yet incorporated into inverse methods for topographic estimation. A scale analysis of the shallow water equations is proposed as a guide to understanding how the dynamics, spatial correlation scales, and data types are related to length and time scales of the given application.