Sideris, M. G.

Sneeuw, N.

Weigelt, Matthias

Open Repository and Bibliography - Luxembourg

Summary The poster describes the local gravity field determination for high-latitude areas by means of the energy integral approach. Point-wise data is interpolated by least-squares prediction at satellite height and the results are on the same level as a global solution for good and poor ground coverage. A local solution including downward continuation by least-squares collocation yields same accuracy for good ground coverage as a global solution and improved results for months with poor groundtrack. Acknowledgements • Chen Xu, University of Calgary, Canada • GeoForschungsZentrum (GFZ) Potsdam, Germany • Institute for Astronomical and Physical Geodesy (IAPG), TU Munich, Germany • GEOIDE Network of Centers of Excellence, Canada • Werner Graupe International Fellowship in Engineering, University of Calgary, Canada Conclusion • Least-squares collocation yields consistent local monthly solutions which are nearly independent of the groundtrack pattern • Monthly solutions with good ground coverage are on the same level as the global solution, but local LS-collocation for high-latitude areas clearly yields an improvement for a monthly solution with a poor ground coverage • Results at satellite height are at the cm-level. LS-prediction is an excellent tool for gridding Future work • Improvement in the data selection in order to stabilize the covariance matrix of the observations • Investigation of the dependence on the regularization parameter • Testing of covariance functions from global geopotential models • Derivation of local covariance functions • Transfer procedure to other areas, e.g., Canada, Antarctica, …  Researchers: High-latitude local gravity field recovery  from CHAMP with least-squares collocation Matthias Weigelt, mlbweige@ucalgary.ca, Department of Geomatics Engineering University of Calgary, Canada Dr. Michael Sideris, Department of Geomatics Engineering, University of Calgary, Canada Dr. Nico Sneeuw, Geodetic Institute, University of Stuttgart, Germany Least-squares prediction at satellite height • Vertical interpolation to mean orbit radius • Basic formula for least-squares prediction:   • Covariance model for Csl and Cll: Tscherning-Rapp  Comparison of geoid heights: monthly CHAMP solution vs. GGM02s          • Errors are at the cm-level and less pronounced than in a global solution, i.e., LS-prediction is an excellent tool for gridding, e.g., as initial step for a spherical harmonic analysis by FFT Least-squares collocation • LS-prediction + downward continuation  Least-squares collocation • Regularization due to ill-conditioning of the covariance matrix of the observations necessary Comparison of geoid heights: monthly CHAMP solution vs. GGM02s                • Groundtrack effect is considerably smaller in local solution • Downward continuation causes loss of accuracy • Regularization enables solution but is strongly dependent on the regularization parameter Method The energy integral approach connects position, velocity and accelerometry to the disturbing potential:                             Introduction • Determination of monthly gravity field solutions from the CHAMP satellite mission • Principle of high-low satellite-to-satellite tracking • Pointwise determination enables 1.global solutions, e.g., by spherical harmonic analysis on the  sphere or on the torus 2. local solutions, e.g., by least-squares prediction/collocation • Importance of the geoid: it serves as a reference surface for many applications Motivation for local geoid determination in   high-latitude areas  • Groundtrack changes constantly since satellite is slowly decaying →top figure shows example of good ground coverage in January 2003 →middle figure shows poor ground coverage in June 2003 • Global gravity field solution is influenced by groundtrack pattern since a global spherical harmonic analysis is limited by the equatorial data spacing. →Bottom figure shows degree RMS  spectra of the difference between a monthly CHAMP solution and GGM02s and reveals the impact on the accuracy of the monthly solution due to the groundtrack • Due to a near polar orbit the data density is higher in polar areas and a  local gravity field determination can make use of the full potential of the measurements in these areas. lCCs llsl1Local LS-prediction Global SH-analysis January 2003 June 2003 January 2003 June 2003 Local LS-collocation Global SH-analysis January 2003 June 2003                  RMS = 3.9 cm RMS = 6.0 cm RMS = 3.4 cm RMS = 7.4 cm RMS = 1.582 m RMS = 1.463 m RMS = 2.893 m RMS = 1.635 m 

High-latitude local gravity field recovery from CHAMP with least-squares collocation

http://orbilu.uni.lu/bitstream/10993/14406/1/Weigelt2006a.pdf

High-latitude local gravity field recovery from CHAMP with least-squares collocation

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