Adjustment, interpolation, and smoothing of GEOS 3 altimeter data

A rapid computational scheme has been developed to construct a local or regional murine geoid by adjusting the GEOS 3 altimeter data. The principle of adjustment is to remove the data's inconsistencies by minimizing the difference of measured sea surface height values at the intersection of two crossing satellite tracks. A total of 91,230 crossover points between 1216 ascending and 1199 descending tracks in the latitude range between 60°S and 60°N were computed and listed. The numerical procedure consists of a least squares adjustment of single‐track data that is iterated until the rms crossover residual becomes stationary. The method is, in essence, equivalent to the solution of least squares normal equation, but the corrections' absolute values are indeterminate. The ambiguity was removed by imposing a condition that the errors in the altimeter measurements are mostly random so that their average must be null. The validity of the assumption was confirmed by comparing the local geoid constructed by this method with a standard model such as GEM 10. Numerical examples show that, for an area not larger than 30° longitude by 30° latitude, the crossover rms residual is reduced from more than 5 m to less than 50 cm by making adjustment for the data's erroneous bias and tilt. It enabled us to contour the geoid map with an interval of l m and to locate and delineate geoid anomalies of a few meters in magnitude. In marine geophysical studies it is often necessary to compare the geoid with other marine geophysical data that are usually recorded continually along the ship's track. A formula was derived for projecting the adjusted GEOS 3 data onto a ship's track using the data's autocovariance. The formula's filtering characteristics showed that the use of data distributed within 500 km of the ship's track is effective in profiling a geoid height variation in the wavelength range between 700 and 1000 km, but details with the scale length shorter than 200 km are totally smoothed out. To construct a finer profile, use must be made of the data more localized near the center of projection, provided that the distribution of data is dense enough to warrent a statistical treatment.