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.
