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M. Herceg and C.C.Tscherning, University of Copenhagen Evaluation of Least-Squares Collocation and the Reduced Point Mass method using the International.

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Presentation on theme: "M. Herceg and C.C.Tscherning, University of Copenhagen Evaluation of Least-Squares Collocation and the Reduced Point Mass method using the International."— Presentation transcript:

1 M. Herceg and C.C.Tscherning, University of Copenhagen Evaluation of Least-Squares Collocation and the Reduced Point Mass method using the International Association of Geodesy, Joint Study Group 0.3 test data. EGU 2014

2 Least-Squares collocation (LSC) and Reduced point masses (RPM) EGU 2014

3

4 Reproducing kernel determination / Covariance fitting: EGU 2014 Covariance functions with N=241 and N=37 estimated in the two test areas and used to determine analytic representation as a reproducing kernel. Fitting difficult in Pacific area due to extreme values. (In practice, residual topographic effects would have been used to smooth values).

5 Empirical covariances and Reproducing kernel model: EGU 2014

6 RPM grid and depth selection: EGU 2014 For RPM we have to fix the position Grid spacing: 0.25° x 0.50° Depth of the sources (Bjerhammer sphere) is 20km

7 EGU 2014

8 EuropeLSCRPMPacificLSCRPM ”obs”DiffErrorDiff”obs”DiffErrorDiff Mean-0.01-0.030.800.07-0.13-0.060.79-0.40 St.dev4.080.821.444.820.242.94

9 EGU 2014 Difference (Obs - RPM prediction) Difference (Obs - Col prediction) Observations (contribution up do d/o 240 is subtracted)

10 EGU 2014 Europe (LSC)Pacific (LSC) ObsDifErrObsDiffErr Mean-0.112.97-0.13-0.081.65 St.dev4.082.734.821.92

11 EGU 2014 Europe (LSC)RPMPacific (LSC)RPM ObsDiffErrDiffObsDiffErrDiff Mean-0.11-0.266.800.064.62-0.188.41-0.74 St.dev32.556.035.7849.076.666.92 Difference (Obs - RPM prediction) Difference (Obs - Col prediction)

12 EGU 2014 From GRACE potential differences, and EGM08 to 36 : Europe (LSC)Pacific (LSC) ObsDifErrObsDiffErr Mean-0.11-1.7628.754.620.1924.64 St.dev32.5519.1549.0718.75

13 Conclusion (1) EGU 2014 Good agreement between differences and error- estimates for LSC. Errors large at borders to lower resolution data. Results unbiased considering error estimates. Good agreement for LSC and RPM Results in Europe of 8 cm, Pacific 2 cm excellent, but Pacific error-estimate larger.

14 Conclusion (2) EGU 2014 Improvement in results if Topography or observations of EGM08 coefficients to higher degree was used (JSG decision) RPM must be further developed 1.in order to use potential differences (GRACE) defined by JSG 0.3. 2.to account for errors in EGM used. RPM experiments with grid point selection needed.

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