The assimilation of altimetric data into the barotropic mode of a rigid lid ocean model

Abstract

Some aspects of the computation of the barotropic mode of a primitive equations, rigid lid, global ocean model are reviewed in the perspective of data assimilation. It is shown that “blending” the surface pressure predicted by the model and that obtained from altimetry is impracticable, since mass conservation must be enforced. By relaxing the momentum equation, however, it is possible to take the measurements into account. A variational method, requiring that the perturbation to the momentum equation be minimal, is suggested. A Poisson equation is obtained for the streamfunction—allowing evaluation of the transport—for which a noniterative solution method is derived. The difference between the curl of the assimilated transport and that ensuing from the model unconstrained by data is investigated, pointing to the role of the bathymetry and that of the “implicitness” in the evaluation of the Coriolis acceleration. Finally, implications for altimetric data assimilation of the elliptic nature of the rigid lid equations are presented, and a comparison with the hyperbolic equations of a free surface model is outlined.