Open Ocean Modeling as an Inverse Problem: Tidal Theory

Abstract

Classical models of tides in open coastal regions employ ad hoc conditions on the open boundaries instead of reliable sea level data on the coastline in order to achieve a well-posed problem. A weighted variational formulation is described here, employing both the open boundary conditions and the coastal data and also any flow or sea level data at isolated deep water locations. The procedure for solving, the equations of the first variation is an infinite-dimensional generalisation of the least-squares inverse theory for finite-dimensional systems. The classical solution is obtained as the variational solution in the limit of vanishing data weights. A more rational choice of weights may be made, based on known errors in the dynamics, boundary conditions and data. The variational formulation provides a procedure for the design of observational arrays.