The calculation of the dynamic sea surface topography and the associated flow field from altimetry data : A characteristic function method

The quasi-stationary sea surface topography (QSST) and associated oceanic circulation is determined by means of a characteristic function technique. The method was originally implemented in an ideal simplified case. The present application involves a 4 degree x 4 degree grid in spherical coordinates approximating the boundaries of the main ocean basins. The data field is provided by the first year of altimetric data from the TOPEX/POSEIDON mission. The method requires the numerical determination of the eigenfunctions spanning the streamfunction field and the associated characteristic functions from the balance equation. The former yields the flow field and the latter the surface height distribution, or QSST. These functions are determined by the geometry and topography of the ocean basins and satisfy the linear steady-state dynamical equations. They are defined within the basins only and avoid the problems encountered when using functions defined over the entire sphere. The velocity field can be computed over the entire ocean area, including the equatorial regions. The coefficients of the height functions have been determined by fitting the surface height field provided by TOPEX altimetry. Seasonal variations have been computed by subtracting a 32-cycle solution from each of the four 8-cycle seasonal solutions.