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M. Herceg and C.C.Tscherning , University of Copenhagen

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. Least-Squares collocation (LSC) and Reduced point masses (RPM).

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M. Herceg and C.C.Tscherning , University of Copenhagen

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  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) • Both methodsuse radial base functions for constructingapproximations to T=W-U: • LSC: ReproducingKernels (in all obs. Points) • RPM: Reduced point masspotentials in grid • M EGU 2014

  3. Approximation of anomalous potential, . • , harmonicfunction = linear combination of base-functions on which the observation functional has beenappliedwrt. Q. • Requires global data-coverage, but JSG 0.3 data are regional, so egm2008 coefficients up to degree N used as observations. • Equivalent to EGM is subtracted and lateradded. EGM96error-degreevariancesused to represent the error (arbitrarychoice). EGU 2014

  4. Reproducing kernel determination / Covariance fitting: • Covariancefunctions with N=241 and N=37 estimated in the two test areas and used to determineanalyticrepresentation as a reproducingkernel. • Fitting difficult in Pacific area due to extremevalues. (In practice, residualtopographiceffectswould have beenused to smoothvalues). EGU 2014

  5. Empirical covariances and Reproducing kernel model: EGU 2014

  6. RPM grid and depth selection: • For RPM we have to fix the position • Grid spacing:0.25° x0.50° • Depth of the sources(Bjerhammersphere) is 20km EGU 2014

  7. Calculations/estimations of : • Low and high resolution ground data used (11335 values). • Airborne data used at altitude (as only source) • ”GOCE” data used at satellite positions • ”GRACE” δT valuesused at satellite position • Groundcomputed from ”GRACE” and ”GOCE” data – results not shown. • Detailled resultsavailableat http://cct.gfy.ku.dk/jsg03.htm EGU 2014

  8. Results: Differences prediction from of – T “observed”, EGU 2014

  9. Results: Differences prediction from of – T “observed”, Observations (contribution up do d/o 240 is subtracted) Difference (Obs - RPM prediction) Difference (Obs - Colprediction) EGU 2014

  10. Differences prediction of ): From Airborne, EGM2008 to 240 subtracted: EGU 2014

  11. Differences prediction of ): From GOCE , and EGM08 to 36: Difference (Obs - Colprediction) Difference (Obs - RPM prediction) EGU 2014

  12. Differences prediction of ): From GRACE potential differences, and EGM08 to 36: EGU 2014

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

  14. Conclusion (2) • Improvementin results if Topography or observations of EGM08 coefficients to higherdegreewasused(JSG decision) • RPM must befurtherdeveloped • in order to use potential differences (GRACE) defined by JSG 0.3. • to account for errors in EGM used. • RPM experiments with grid point selectionneeded. EGU 2014

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