Source: Dissertation Abstracts International, Volume: 53-04, Section: B, page: 1763.

Adviser: George Veronis.

An inverse problem to obtain velocities and diffusion coefficients from tracer distributions has been studied. Developed models have been tested by a feasibility study and have been applied to real data. The method of total least squares (TLS), which is a linear parameter estimation technique used when errors occur in both the coefficient matrix and the data vector, has been introduced. This method has been successfully applied to a problem with a null data vector using the invariability of the TLS solutions to a transformation of unknowns.

A feasibility study has been carried out with artificially generated data in a two- and a three-dimensional channel. The inversion recovers the correct velocities and diffusivities with perfect data when the system is overdetermined. With imperfect data, the results deteriorate with increases in truncation error, structure in the original flow field, or the noise level in the input data. However, a certain level of noise has less effect when truncation error is significant. Approximate treatments of the velocity and diffusion coefficient which reduce the required amount of input data have yielded generally good results.

The inversion has been also applied to data from the middle of the thermohaline staircase east of Barbados. The derived vertical diffusivities from the tracer equations are positive, and the fluxes and the ratio of diffusivities are qualitatively consistent with values measured in laboratory experiments on salt fingers. This indicates that salt-fingering is present in the interface of the staircase. It is found that this sub-grid-scale process is consistently parameterized by a Fickian formulation. When the tracer system is constrained by geostrophy, the velocity field is similar to the one from geostrophic balance alone and the vertical velocity and vertical diffusivities are no longer consistent with those from the tracer inversion. The results imply that velocities determined by tracers are fundamentally different from those obtained from geostrophic dynamics.