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Efficient propagation of error covariance matrices of gravitational models: application to GRACE and GOCE

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Abstract

We have applied efficient methods for computing variances and covariances of functions of a global gravity field model expanded in spherical harmonics, using the full variance–covariance matrix of the coefficients. Examples are given with recent models derived from GRACE (up to degree and order 150), and with simulated GOCE derived solutions (up to degree and order 200).

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References

  • Abrikosov O, Foerste C, Rothacher M, Bruinsma S, Marty JC, Balmino G (2006) Gravity Field Recovery with Simulated GOCE Observations, EGU, Vienna (A), Session G8

  • Balmino G (1994) Gravitational potential harmonics from the shape of an homogeneous body. Cel Mech Dyn Astr 60(3): 331–364. doi:10.1007/BF00691901

    Article  Google Scholar 

  • Bosch W (1983) Effiziente Algorithmen zur Berechnung von Raster-Punkwerten von Kugelfunktionsentwicklungen, Memorandum, D.G.F.I., Munich

  • Foerste C, Schmidt R, Stubenvoll R, Flechtner F, Meyer U, Konig R, Neumayer H, Biancale R, Lemoine JM, Bruinsma S, Loyer S, Barthelmes F, Esselborn S (2007) The GFZ/GRGS Satellite-Only and Combined Gravity Field Models: EIGEN-GL04S1 and EIGEN-GL04C. J Geod. doi:10.1007/s00190-007-0183-8

  • Gerstl M (1980) On the recursive computation of the integrals of the associated Legendre functions. Manuscr Geod 5: 181–199

    Google Scholar 

  • Haagmans RHN, van Gelderen M (1991) Error variances–covariances of GEM-T1: their characteristics and implications in geoid computation. J Geophys Res 96(B12):20, 011–20, 022. doi:10.1029/91JB01971

  • Holmes SA, Featherstone WE (2002) A unified approach to the Clenshaw summation and the recursive computation of very high degree and order normalised associated Legendre functions. J Geod 76: 279–299. doi:10.1007/s00190-002-0216-2

    Article  Google Scholar 

  • Jekeli C (1981) Alternative methods to smooth the Earth’s gravity field, Rep 310, Department of Geodetic Science and Surveying, Ohio State University, Columbus

  • Sneeuw N, Bun R (1996) Global spherical harmonic computation by two-dimensional Fourier methods. J Geod 70: 224–232

    Google Scholar 

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Authors and Affiliations

  1. C.N.E.S., Groupe de Recherches de Geodesie Spatiale, Observatoire Midi-Pyrenees, 14 Avenue Edouard Belin, 31400, Toulouse, France

    Georges Balmino

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  1. Georges Balmino
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Correspondence to Georges Balmino.

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Balmino, G. Efficient propagation of error covariance matrices of gravitational models: application to GRACE and GOCE. J Geod 83, 989–995 (2009). https://doi.org/10.1007/s00190-009-0317-2

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  • DOI: https://doi.org/10.1007/s00190-009-0317-2

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