Variational Interpolation of Circulation with Nonlinear, Advective Smoothing*

Abstract

A modified variational algorithm, previously proposed in meteorology, is presented for the interpolation of oceanic hydrographic and velocity data. The technique is anisotropic and involves a variational approach that allows revealing of the spatial structure in its application. Being a part of the variational family of algorithms, the method is quite general in that it allows one to set dynamical constraints, and weighting functions, applicable to the problem of interest. This flexibility is illustrated by using the nonlinear terms of momentum balance equation as constraints. The inclusion of these constraints appears to assist in the resolution of narrow jets in the flow fields. The method is applied to data from two different regions of the ocean: Lagrangian drifter data from the northwest Pacific and hydrographic data from the Scotian Shelf. Each dataset presents quite different scales, physical processes, and data types. The resulting flow fields are compared with results determined from traditional optimal interpolation, and advantages of the proposed method are discussed.