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New accurate atmospheric correction of SLR observations Dudy D. Wijaya and Fritz K. Brunner

16 th International Workshop on Laser Ranging 13–17 October 2008, Poznan-Poland. New accurate atmospheric correction of SLR observations Dudy D. Wijaya and Fritz K. Brunner Institute of Engineering Geodesy and Measurement Systems Graz University of Technology. Motivation.

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New accurate atmospheric correction of SLR observations Dudy D. Wijaya and Fritz K. Brunner

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  1. 16th International Workshop on Laser Ranging 13–17 October 2008, Poznan-Poland New accurate atmospheric correction of SLR observations Dudy D. Wijaya and Fritz K. Brunner Institute of Engineering Geodesy and Measurement Systems Graz University of Technology Engineering Geodesy and Measurement Systems Graz University of Technology

  2. Motivation • Contribution to Refraction Study Group (RSG) of ILRS : • Accuracy goal was set to achieve sS1mm • Provide an accurate atmospheric correction formula for two frequency observations : • Two frequency SLR & Co-located SLR-GPS • New formula has been developed based on the theory of two frequency range correction (Gu and Brunner, 1990) Engineering Geodesy and Measurement Systems Graz University of Technology

  3. Original paths Satellite ds2 Path projection using perturbation technique ds1 S (chord) R2 : reference path P21 R1 eo • Calculations along two different paths Ground station Ground station • Calculations along the reference path 1. Theoretical basis : optical path length equations R1 & R2 Projection of the second optical path R2(l2) onto the first path R1(l1) Accepted assumption: - Geometrical optics formulation is applicable - Atmospheric dispersion & no turbulence Engineering Geodesy and Measurement Systems Graz University of Technology

  4. R1 = S + 10-6Ng(r1,l1) ds1+ K1 p1 p1 R2 = S + 10-6Ng(r2,l2) ds2+ K2 p2 • Equations after path projection R1 = S + 10-6Ng(r1,l1) ds1+ K1 R2 = S + 10-6Ng(r1,l2) ds1+ K1+ P21 (Calculated along the path p1) p1 1. Theoretical basis : optical path length equations R1 & R2 • Equations for original paths Ki : Arc-to-chord correction P21 : Propagation correction Ng : the group refractivity r1, r2 : vector of position l1,l2 : wavelength Engineering Geodesy and Measurement Systems Graz University of Technology

  5. p1 p1 p1 p1 p1 • Substituting Ng yields: rtds1 R1 = S + 10-6 D(l1) rtds1 + 10-6W(l1) rvds1+ K1 R2 = S + 10-6 D(l2) rtds1 + 10-6W(l2) rvds1+ K1 + P21 Now including the gradients can rigorously be eliminated 1. Theoretical basis : the refractivity Ng & elimination of the density rt • The refractivity model (Separation of density from dispersion effect) rt , rv : the total/vapour density of air D, W : the dispersion factors for dry and wet air Engineering Geodesy and Measurement Systems Graz University of Technology

  6. T1: dispersion T2: curvature T3: water vapour • Applications: • Two frequency SLR observations • Co-located observations of two frequency SLR and GPS 1. Theoretical basis : new atmospheric correction formula S = R1 + nx(R2 - R1) - (nP21 + K1) + HxSIWV • The derivation considers all propagation effects, except turbulence Engineering Geodesy and Measurement Systems Graz University of Technology

  7. Mean values T1 10 3 T2 10 -3 T3 2. Application : Two frequency SLR observations (Graz station) S = RSLR-1 + nx(RSLR-2 – RSLR-1) - (nP21 + K1) + HxSIWV T3 T2 T1 • Simulation method: • 2D Ray tracing technique • SLR Station : • Graz • Frequency: • l1= 0.532 mm &l2= 1.0684mm • Meteorological data: • ECMWF in Jan-March 2006 Engineering Geodesy and Measurement Systems Graz University of Technology

  8. Error (Model – Ray tracing) 2. Application : Two frequency SLR observations (Graz station) S = RSLR-1 + nx(RSLR-2 – RSLR-1) - (nP21 + K1) + HxSIWV • Dispersion term: • n= 65.86 • Humidity term: • H = 1.5 x 10-4 m3/kg • Curvature term: • K1 >> n x P21 Engineering Geodesy and Measurement Systems Graz University of Technology

  9. Mean values T1 10 3 T2 10 -3 T3 2. Application : Two frequency SLR observations (TIGO-Wettzell) S = RSLR-1 + nx(RSLR-2 – RSLR-1) - (nP21 + K1) + HxSIWV T3 T2 T1 • SLR Station : • TIGO Wettzell • Frequency: • l1= 0.4235 mm &l2= 0.8470mm • Dispersion term: • n = 41.25 • Humidity factor: • H = 1.4 x 10-4 m3/Kg Engineering Geodesy and Measurement Systems Graz University of Technology

  10. The dispersion factor • Typical values for n : 20 – 300 3. Critical issues (1) : SLR observations RSLR S = RSLR-1 + nx(RSLR-2 – RSLR-1) - (nP21 + K1) + HxSIWV • Requirement for the observation accuracy • Accuracy for SLR observations : ~ 0.03 mm • Hard to achieve using the current SLR systems. Engineering Geodesy and Measurement Systems Graz University of Technology

  11. Formulae and values for K1 and P21 K1 nxP21 • Accuracy requirement sK1  1 mm sP21 0.03 mm 3. Critical issues (2) : Curvature K1 and propagation terms nP21 S = RSLR-1 + nx(RSLR-2 – RSLR-1) - (nP21 + K1) + HxSIWV Engineering Geodesy and Measurement Systems Graz University of Technology

  12. Calculation for humidity factor H • Typical values: 1.4 x 10-4 m3/kg • Dispersion formula of Ciddor (1996) 3. Critical issues (3) : Slant integrated water vapour SIWV and humidity factor H S = RSLR-1 + nx(RSLR-2 – RSLR-1) - (nP21 + K1) + HxSIWV • SIWVestimation • Accuracy requirement : 5 Kg/m2 of SIWV ( ~ 5 cm Slant Wet Delay) • GPS is very useful and readily available technique Engineering Geodesy and Measurement Systems Graz University of Technology

  13. Ideal conditions • SLR telescope and GPS receiver are very close to each other • SLR and GPS signals travel through the same atmospheric condition Assumption for the computation:SLR and GPS receiver positions are identical • Microwave refractivity for Non-hydrostatic part k3,5 : refractivity constants Rv : gas constant Approximation by the mean temperature, T  Tm 3. Critical issues (3) : Water vapour estimation by GPS Co-located observations of two frequency SLR and GPS • Purpose: • Elimination of the vapour density effects in two frequency SLR observations by GPS Engineering Geodesy and Measurement Systems Graz University of Technology

  14. Two observation scenarios: 1. SLR and GPS observations to GPS satellites equipped with retroreflector SWD is calculated from GPS-35/36 signals 2. SLR observations to the other retroreflectors SWD is calculated by interpolation from all GPS signals 3. Critical issues (3) : Water vapour estimation by GPS • GPS Slant wet delay (SWD): • T3 correction term: T3 = Hswd x SWD  0.02 Engineering Geodesy and Measurement Systems Graz University of Technology

  15. 4. Summary • Rigorous derivation of atmospheric corrections • The total density effects and their gradients are eliminated • Curvature and propagation terms are considered • Water vapour effects and their gradients can be calculated from GPS • Potential accuracy of the range correction is better than 1 mm Engineering Geodesy and Measurement Systems Graz University of Technology

  16. Next development: Averaging technique could help to improve precision of the results 5. Closing remarks Advantage: The systematic effects in SLR observations are eliminated Remaining problem: Very high accuracy requirement for SLR observations Thank you for your attentions…!!!! Engineering Geodesy and Measurement Systems Graz University of Technology

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