Error Propagation with Geographic Specificity for Very High Degree Geopotential Models
Users of high-resolution global gravitational models require geographically specific estimates of the error associated with various gravitational functionals (e.g., Δg N, ξ, η) computed from the model parameters. These estimates are composed of the commission and the omission error implied by the specific model. Rigorous computation of the commission error implied by any model requires the complete error covariance matrix of its estimated parameters. Given this matrix, one can compute the commission error of various model-derived functionals, using covariance propagation. The error covariance matrix of a spherical harmonic model complete to degree and order 2160 has dimension ∼4.7 million. Because the computation of such a matrix is beyond the existing computing technology, an alternative method is presented here which is capable of producing geographically specific estimates of a model’s commission error, without the need to form, invert, and propagate such large matrices. The method presented here uses integral formulas and requires as input the error variances of the gravity anomaly data that are used in the development of the gravitational model.
KeywordsGeopotential high-degree spherical harmonic models error propagation convolution
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- Haagmans, R., E. de Min, M. Van Gelderen (1993). Fast evaluation of convolution integrals on the sphere using 1D FFT, and a comparison with existing methods for Stokes’ integral. manusc. geod., 18, 227–241.Google Scholar
- Haagmans, R.H.N., M. Van Gelderen (1991). Error variances-covariances of GEM-T1: Their characteristics and implications in geoid computation. J. Geophys. Res., 96(B12), 20011–20022.Google Scholar
- Heiskanen, W.A. and H. Moritz (1967). Physical Geodesy. W.H. Freeman, San Francisco.Google Scholar
- Jekeli, C. (1981). Alternative Methods to Smooth the Earth’s Gravity Field. Rep. 327, Dept. of Geod. Sci. and Surv., The Ohio State University, Columbus, Ohio.Google Scholar
- Wong, L. and R. Gore (1969). Accuracy of Geoid Heights from Modified Stokes Kernels. Geophys. J.R. Astr. Soc., 18, 81–91.Google Scholar