Advertisement

Accuracy Analysis of External Reference Data for GOCE Evaluation in Space and Frequency Domain

  • K.I Wolf
  • J Müller
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 133)

abstract

With the upcoming Esa satellite mission Goce, all components of the gravitational tensor (2nd derivatives of the Earth’s gravitational potential) will be measured globally except of the polar gaps. The highest accuracy level within the measurement bandwidth (Mbw, 5–100 mHz) is 11 mE/√Hz for the diagonal components of the tensor (1 mE = 10-121/s^2). To meet this accuracy level, the gradiometer will be calibrated and evaluated internally as well as externally. One strategy of an external evaluation includes the use of a global geopotential model in combination with ground gravity data upward continued to satellite altitude

In this study an error estimation for the external reference data is carried out (a) statistically by applying least-squares collocation and (b) empirically in a synthetic environment including (correlated and uncorrelated) noise. The use of synthetic data permits a closed-loop validation in all points. The spectral combination method based on integral formulas with a modified kernel function is applied to compute all components of the tensor. The closed-loop differences are analysed in the space and in the frequency domain. The dependency of the prediction error on the characteristics of the input data (noise level, area size and resolution) is shown. An accuracy below the required level of 11 mE/√Hz can be reached combining gravity anomalies with a noise level of 1 mGal and current global geopotential models

Keywords

Satellite gradiometry Spectral combination Synthetic Earth model 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arabelos, D. and Tscherning, C. C. (1998). Calibration of satellite gradiometer data aided by ground gravity data. J. Geod, 72:2–625Google Scholar
  2. Arabelos, D., Tscherning, C. C. and Veicherts, M. (2007). External calibration of GOCE SGG data with terrestrial gravity data: a simulation study. In Proc Joint IAG/IAPSO/IABO Assembly “Dynamics Planet”, Cairns, Australia, Aug. 22–26, 2005, Vol 130, IAG Symp, pp. 337–344. Springer, Berlin HeidelbergGoogle Scholar
  3. Benner, P., Mehrmann, V., Sima, V., Van Huffel, S. and Varga, A. (1999). SLICOT – a subroutine library in systems and control theory. NICONET T Rep 97-3Google Scholar
  4. Bouman, J. and Koop, R. (2003). Calibration of GOCE SGG data combining terrestrial gravity data and global gravity field models. In I. N. Tziavos, (Eds.), Proc IAG Int Symp “Gravity and Geoid”, Thessaloniki, Greece, Aug. 26–30, 2002, pp. 275–280. Zeta PublGoogle Scholar
  5. Bouman, J., Koop, R., Haagmans, R., Müller, J., Sneeuw, N., Tscherning, C. C. and Visser, P. N. A. M. (2005). Calibration and validation of GOCE gravity gradients. In F. Sansö, (Eds.), A Window on the Future of Geodesy, Proc 36th IAG General Assembly, 23rd IUGG General Assembly, Sapporo, Japan, 2003, Vol 128, IAG Symp, pp. 265–270. Springer, BerlinGoogle Scholar
  6. Denker, H. (2003). Computation of gravity gradients over Europe for calibration/validation of GOCE data. In I. N. Tziavos, (Eds.), Proc IAG Int Symp “Gravity and Geoid”, Thessaloniki, Greece, Aug. 26–30, 2002, pp. 287–292. Zeta PublGoogle Scholar
  7. Denker, H. and Torge, W. (1998). The European gravimetric quasigeoid EGG97 – an IAG supported continental enterprise. In R. Forsberg, M. Feissel, and R. Dietrich, (Eds.), Proc IAG Scientific Assembly “Geodesy on the Move – Gravity Geoid, Geodynamics, and Antartica”, Rio de Janeiro, Brazil, Sept. 3–9, 1997, Vol 119, IAG Symp, pp. 249–254. Springer, BerlinGoogle Scholar
  8. Drinkwater, M. and Kern, M. (2006). Calibration and Validation Plan for L1b Data Products. Technical Report EOP-SM/1363/MD-md, ESA ESTEC, Noordwijk, The Netherlands, hhtp://www.esa.int/ esaLP/ESAJJL1VMOC_LPgoce_0.htmlGoogle Scholar
  9. GFZ (2006). Combined Gravity Field Model EIGEN-GL04C, http://www.gfz-potsdam.de/GRACE/results/grav/g005_eign-gl04c.html (25.10.2006)
  10. Haagmans, R., de Min, E. and van Gelderen, M. (1993). Fast evaluation of convolution integrals on the sphere using 1D FFT, and a comparison with existing methods for Stokes’ integral. Man Geod, 18:2–241Google Scholar
  11. Kern, M. and Haagmans, R. (2005). Determination of gravity gradients from the terrestrial gravity data for calibration and validation of gradiometric GOCE data. In C. Jekeli, L. Bastos, and J. Fernandes, (Eds.), Proc IAG Int Symp “Gravity, Geoid and Space Missions”, Porto, Portugal, Aug. 30–Sept. 3, 2004, Vol 129, IAG Symp, pp. 95–100. Springer, Berlin HeidelbergGoogle Scholar
  12. Knudsen, P. (1987). Estimation and modelling of the local empirical covariance function using gravity and satellite altimeter data. Bull Géod, 61(2):145–160Google Scholar
  13. Lemoine, F. G., Kenyon, S. C., Factor, J. K., Trimmer, R. G., Pavlis, N. K., Chinn, D. S., Cox, C. M., Klosko, S. M., Luthcke, S. B., Torrence, M. H., Wang, Y. M., Williamson, R. G., Pavlis, E. C., Rapp, R. H. and Olson, T. R. (1998). The development of the joint NASA GSFC and NIMA geopotential model EGM96, NASA/TP-1998-206861. Technical Report, NASA, Greenbelt, MarylandGoogle Scholar
  14. Moritz, H. (1980). Advanced Physical Geodesy. Herbert Wichmann Verlag, KarlsruheGoogle Scholar
  15. Pail, R. (2003). Local gravity field continuation for the purpose of in-orbit calibration of GOCE SGG observations. Advances in Geosciences, 1:2–18Google Scholar
  16. Pail, R. (2004). GOCE Data Archiving and Processing Center (DAPC) Graz, Austrian Space Application Programme, Bridging Phase, Final Report. Technical Report, Technische Universität Graz, Austria, http://www.inas. tugraz.at/forschung/DAPC/projectIb.html Google Scholar
  17. Reigber, C., Schmidt, R., Flechtner, F., König, R., Meyer, U., Neumayer, K.-H., Schwintzer, P. and Zhu, S. Y. (2005). An earth gravity field model complete to degree and order 150 from GRACE: EIGEN-GRACE02S. Journal of Geodynamics, 39(1):1–10Google Scholar
  18. SCVII (2000). Simulation Scenarios for Current Satellite Missions. IAG Special Commission VII, http://www. geod.uni-bonn.de/apmg/lehrstuhl/simulationsszenarien/sc7/ satellitenmissionen.php (13.07.2006)
  19. Tscherning, C. C. (1976). Computation of the second-order derivatives of the normal potential based on the representation by a Legendre series. Man Geod, 1:2–92Google Scholar
  20. Tscherning, C. C. and Rapp, R. H. (1974). Closed Covariance Expressions for Gravity Anomalies, Geoid Undulations, and Deflections of the Vertical Implied by Anomaly Degree Variance Models. OSU Rep 208Google Scholar
  21. Weber, G. and Wenzel, H.-G. (1983). Error covariance functions of sea gravity data and implications for geoid determination. Marine Geodesy, 75(1–4):199–226CrossRefGoogle Scholar
  22. Wenzel, H.-G. (1982). Geoid computation by least-squares spectral combination using integral kernels. In Proc General Meeting of the IAG, Tokyo, May 7–15, 1982, pp. 438–453, Berlin Heidelberg. SpringerGoogle Scholar
  23. Wenzel, H.-G. (1999). Schwerefeldmodellierung durch ultra hochauflösende Kugelfunktionsmodelle. Zeitschrift für Vermessungswesen, 124(5):144–154Google Scholar
  24. Wolf, K. I. (2006). Considering coloured noise of ground data in an error study for external GOCE calibration/validation. In P. Knudsen, J. Johannessen, T. Gruber, S. Stammer, and T. van Dam, (Eds.), Proc GOCINA Workshop, April, 13–15, 2005, Vol 25, Cahiers du Centre Européen de Géodynamics et de Séismologie, pp. 85–92. LuxembourgGoogle Scholar
  25. Wolf, K. I. (2007). Kombination globaler Potentialmodelle mit terrestrischen Schweredaten für die Berechnung der zweiten Ableitungen des Gravitationspotentials in Satellitenbahnhöhe. Ph.D. thesis, Deutsche Geodätische Kommission, Reihe C, Nr. 603, www.dgk.badw.deGoogle Scholar
  26. Wolf, K. I. and Denker, H. (2005). Upward continuation of ground data for GOCE calibration/validation purposes. In C. Jekeli, L. Bastos, and J. Fernandes, (Eds.), Proc IAG Int Symp “Gravity, Geoid and Space Missions”, Porto, Portugal, Aug. 30–Sept. 3, 2004, Vol 129, IAG Symp, pp. 60–65. Springer, Berlin HeidelbergGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • K.I Wolf
    • 1
  • J Müller
    • 2
  1. 1.Institut für ErdmessungLeibniz Universität HannoverSchneiderberg 50Germany
  2. 2.Institut für ErdmessungLeibniz Universität HannoverSchneiderberg 50Germany

Personalised recommendations