Spectral characteristics of time‐dependent orbit errors in altimeter height measurements

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Abstract
A mean reference surface and time‐dependent orbit errors are estimated simultaneously for each exact‐repeat ground track from the first two years of Geosat sea level estimates based on the Goddard Earth model (GEM)‐T2 orbits. Motivated by orbit theory and empirical analysis of Geosat data, the time‐dependent orbit errors are modeled as 1 cycle per revolution (cpr) sinusoids with slowly varying amplitude and phase. The method recovers the known “bow tie effect” introduced by the existence of force model errors within the precision orbit determination (POD) procedure used to generate the GEM‐T2 orbits. The bow tie pattern of 1‐cpr orbit errors is characterized by small amplitudes near the middle and larger amplitudes (up to 160 cm in the 2 years of data considered here) near the ends of each 5‐ to 6‐day orbit arc over which the POD force model is integrated. A detailed examination of these bow tie patterns reveals the existence of daily modulations of the amplitudes of the 1‐cpr sinusoid orbit errors with typical and maximum peak‐to‐peak ranges of about 14 cm and 30 cm, respectively. The method also identifies a daily variation in the mean orbit error with typical and maximum peak‐to‐peak ranges of about 6 cm and 30 cm, respectively, that is unrelated to the predominant 1‐cpr orbit error. It is suggested that the two daily signals arise from daily adjustments of the drag coefficient in the GEM‐T2 POD procedure. Application of the simultaneous solution method to the much less accurate Geosat height estimates based on the Naval Astronautics Group orbits concludes that the accuracy of POD is not important for collinear altimetric studies of time‐dependent mesoscale variability (wavelengths shorter than 1000 km), as long as the time‐dependent orbit errors are dominated by 1‐cpr variability and a long‐arc (several orbital periods) orbit error estimation scheme such as that presented here is used. The accuracy of POD becomes more important for studies of larger‐scale variability.