Recomputation of EGM96 Spherical Harmonic Coefficients Using Fast Spherical Collocation
Abstract
The abundance of data expected to be collected by GOCE does not permit the direct use of least- squares collocation, which require that as many equations as unknowns must be solved. However if the data is gridded equidistantly in longitude, and an isotropic covariance function is used, the systems of equations will have a repetitive structure which will reduce the computational effort considerably. The method of fast spherical collocation which is based on work by O.Colombo from 1979, has been designed to take advantage of this. This method may use data on non-equidistant parallels, which furthermore for different parallels do not need to be of the same data type or have the same distance from the origin. The method has been tested using the 0.5 degree mean gravity anomalies used when developing the EGM96 model. A covariance function with degree-variances put equal to zero for the degree larger than 720 was used. The result agree with the EGM96 coefficients within their error bounds. However, when using the coefficients to degree 360 for the calculation of 0.5 degree mean values the differences with respect to the original data become considerable larger than when using EGM96. The large discrepancies occur over large sea-mounts and in mountainous areas. If one consider that collocation gives an exact agreement between data and predictions (for noise-free data) then this discrepancy is an indication that the procedure used to determine the EGM96 coefficients has forced low order coefficients to carry higher order gravity anomaly information. This may explain some of the long wavelength errors seen when using EGM96 for geoid determination.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2001
- Bibcode:
- 2001AGUFM.G41C..10T
- Keywords:
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- 1214 Geopotential theory and determination