An optimal filter for geostrophic mesoscale currents from along-track satellite altimetry

An optimal difference operator is derived for smoothing along-track sea surface height measurements from satellite altimeters and computing geostrophic surface currents at or below ocean mesoscale wavelengths with second-order approximation accuracy. The difference operator minimizes the white noise of the height measurements to find a compact difference formula for the sea surface height derivative and a residual noise estimate for the surface geostrophic velocity. This compact, optimal operator has fine along-track spatial resolution ideal for studies in areas of shallow water, near landfall, and at high latitudes where the first-baroclinic Rossby radius of deformation becomes small. Accurate extraequatorial geostrophic velocities are determined by varying the filter window to maintain accuracy and resolution, which will benefit global mesoscale studies from the tandem Jason-1 and TOPEX/Poseidon missions and, particularly, the proposed wide-swath altimetry mission.