The accuracy of altimetric surfaces

Estimates of the shape of the sea surface as determined from satellite altimeters have become of increasing importance in geophysics, geodesy and physical oceanography. The most effective error reduction procedures used in producing these surfaces have been some version of a crossing-arc analysis. The problem with this procedure is the absence of an easy means of evaluating the noise structure of the final result. By recasting the problem as one of objective mapping (optimal estimation) the error reduction is optimized and an explicit estimate is obtained of the wave-number structure of the final altimetric surface. Examples, suitable to a small computer, have been generated to show that the error reduction along the sub-satellite tracks is very great, with most of the residual lying in long wavelengths.