Time-dependent assimilation of CTD data to an open ocean Rossby wave model

Abstract

For two CTD surveys taken two months apart during the 1981 Ocean Tomography experiment southwest of Bermuda, a time-dependent ocean state is estimated that evolves from the first to the second survey. The mesoscale motions are modelled by quasi-geostrophic dynamics, and the ocean model state is represented by freely propagating Rossby waves in the 1st and 2nd baroclinic modes whose time-dependent amplitudes are fit to the data at the two survey times. First the linear dispersion relation is used to evolve the waves in time, then the weak nonlinear interactions between the waves are incorporated into the model. The wave-wave interactions enable the waves in the barotropic mode to enter into the model state evolution as an unknown control variable. Three techniques from optimal control theory are developed and applied to this problem: the Kalman filter / smoother, the adjoint method and dynamic programming. These methods allow the barotropic component of the flow, which is indeterminate from the CTD data, to be estimated.