A new method to determine the mean sea surface dynamic topography from satellite altimeter observations

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Abstract
A method is presented to calculate mean sea surface dynamic topography from satellite altimeter observations of its temporal variability. Time averaging of a simplified version of the quasi‐geostrophic potential vorticity equation for the upper ocean layer results in a differential equation for the averaged relative vorticity in which the mean divergence of the eddy vorticity fluxes acts as a source or sink. The essential part is that these eddy fluxes can be determined from the altimeter observations. Consequently, no parameterisations appear in the averaged vorticity equation. From the average vorticity field, surface geostrophic velocities and related mean dynamic sea surface topography can then simply be derived. The usefulness of the method is established using “perfect” data, namely numerical output from the United Kingdom Fine Resolution Antarctic Model. The method appears applicable to areas of the ocean with strong enough mesoscale variability such as the major western boundary currents and their extensions and to frontal regions of the Antarctic Circumpolar Current. Quite realistic results are presented for active regions of the world ocean. Results are compared with hydrographic observations for the major western boundary current extensions of the Southern Ocean. An important application is to combine the newly derived averaged flow field with the observed eddy field to derive the total time‐varying geostrophic surface velocity field. As a striking example this is applied to the Agulhas Current retroflection, where the repeated shedding of large rings can now be synoptically reconstructed as a continuous process.