In the radar altimeter measurement of the satellite height above the instantaneous sea surface, radial orbit errors are “mapped” on the earth with the spacecraft motion. In many geophysical and oceanographical applications of satellite altimetry, a precise knowledge of the mapped error features is necessary to estimate sea (or ice sheet) surface topographies and to assess their absolute accuracies. So we derive a general formulation to infer from any a priori time spectrum of orbit errors the characteristic wavelengths of the mapped error biasing the recovery of a sea surface topography. Because of commensurability between the satellite motion and earth rotation, radial orbit errors at the nodal or orbital periods and their harmonics are mapped into smooth long-wavelength surfaces and fully aliased in the steady surface topography. As this phenomenon presents a close relationship with the resonance of the orbit perturbations, we suggest naming it the mapped orbit error resonance. Our formulation also provides an explicit account of both time and space sampling effects on the correlation of the mean sea surface, oceanic tides, and orbit errors. For instance, the typical wavelength of a resonant mapped error is scattered by the land gaps in all the near wavelengths of an oceanic surface. The derived mapping function also seems to indicate that the statistics of the crossover differences are unable to estimate the absolute precision of altimetric surfaces because a nonnegligible portion of radial orbit errors falls into the steady component of the sea surface.
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