Height system unification in Europe

Transcription

1 Height system unification in Europe Axel Rülke, Gunter Liebsch, Martina Sacher, Uwe Schäfer, Uwe Schirmer, Johannes Ihde Federal Agency for Cartography and Geodesy International Symposium on Gravity, Geoid and Height Systems GGHS 2012 October 9-12, 2012, Venice, Italy

2 Approaches for height reference frame unification Spirit leveling approach Common adjustment of potential differences and observed cross-border connections. Observation across water (UK, Fennoscandia) is difficult. Susceptible to systematic errors (low redundancy of leveling networks) Example: EVRF2007 (Sacher et al. 2009) 10/10/2012 2

3 Approaches for height reference frame unification Spirit leveling approach Common adjustment of potential differences and observed cross-border connections. Observation across water (UK, Fennoscandia) is difficult. Susceptible to systematic errors (low redundancy of leveling networks) Example: EVRF2007 (Sacher et al. 2009) Gravity field (GF) approach Combination of ellipsoidal heights (GNSS), physical heights (national height reference frame) and gravity field model No direct observations between national height reference frames needed 10/10/2012 3

4 Approaches for height reference frame unification Spirit leveling approach Common adjustment of potential differences and observed cross-border connections. Observation across water (UK, Fennoscandia) is difficult. Susceptible to systematic errors (low redundancy of leveling networks) Example: EVRF2007 (Sacher et al. 2009) Gravity field (GF) approach Combination of ellipsoidal heights (GNSS), physical heights (national height reference frame) and gravity field model No direct observations between national height reference frames needed Ocean leveling approach (last talk by P. Woodworth) 10/10/2012 4

5 Spirit leveling Approach EVRF2007 Rülke et al. Height system unification in Europe. 10/10/ International Symposium on Gravity, Geoid and Height Systems

6 Method GF approach Observed height anomaly in zero-tide system ζ z iobs a h b = h + δ ( H δ i a z i + H b z ) 10/10/2012 6

7 Method GF approach Observed height anomaly in zero-tide system ζ z iobs a h b = h + δ ( H δ i a z i + H b z ) tidal corrections 10/10/2012 7

8 Method GF approach Observed height anomaly in zero-tide system ζ z iobs a h b = h + δ ( H δ i a z i + H b z ) tidal corrections Related to modeled height anomaly from gravity field model in zero-tide system ζ z i = ζ z iobs ζ z imod 10/10/2012 8

9 Method GF approach Observed height anomaly in zero-tide system ζ z iobs a h b = h + δ ( H δ i a z i + H b z ) tidal corrections Related to modeled height anomaly from gravity field model in zero-tide system ζ z i = ζ z iobs ζ z imod Offset estimation (observation equation) z ζ i = m1 e 10/10/2012 9

10 Method GF approach Observed height anomaly in zero-tide system ζ z iobs a h b = h + δ ( H δ i a z i + H b z ) tidal corrections Related to modeled height anomaly from gravity field model in zero-tide system ζ z i = ζ z iobs ζ z imod Plane Offset estimation (observation equation) with ζ z i = m [ m M ϕ ϕ ) + m N ( λ )] 1 e + 2 0( i i λ0 m 2, m 3 ϕ 0,λ 0 M 0, N 0 tilt (North-South, West-East)] Coordinates of reference point P 0 radius of curvature in meridian and perpendicular to the meridian in P 0 10/10/

11 Data sets 10/10/

12 Data sets Satellite-only gravity field models GOCE TIM R3 d/o 250 (Pail et al. 2011) GOCO03S d/o 250 (Mayer-Gürr et al. 2012, this morning) 10/10/

13 Data sets Satellite-only gravity field models GOCE TIM R3 d/o 250 (Pail et al. 2011) GOCO03S d/o 250 (Mayer-Gürr et al. 2012, this morning) High resolution gravity field models EGM2008 d/o 2190 (Pavlis et al., JGR, 2012) EGG2008 grid 1 x1 (H. Denker, IfE Hannover) 10/10/

14 Data sets Satellite-only gravity field models GOCE TIM R3 d/o 250 (Pail et al. 2011) GOCO03S d/o 250 (Mayer-Gürr et al. 2012, this morning) High resolution gravity field models EGM2008 d/o 2190 (Pavlis et al., JGR, 2012) EGG2008 grid 1 x1 (H. Denker, IfE Hannover) National physical heights ( points of the EUVN_DA dataset, given in the national height system, tidal system of 23 European countries (Kenyeres et al., IAG Symposia 135, 2010) 10/10/

15 Data sets Satellite-only gravity field models GOCE TIM R3 d/o 250 (Pail et al. 2011) GOCO03S d/o 250 (Mayer-Gürr et al. 2012, this morning) High resolution gravity field models EGM2008 d/o 2190 (Pavlis et al., JGR, 2012) EGG2008 grid 1 x1 (H. Denker, IfE Hannover) National physical heights ( points of the EUVN_DA dataset, given in the national height system, tidal system of 23 European countries (Kenyeres et al., IAG Symposia 135, 2010) Ellipsoidal heights ETRS89, zero-tide 10/10/

16 Satellite-only GGMs vs. high resolution models Rülke et al. Height system unification in Europe. 10/10/ International Symposium on Gravity, Geoid and Height Systems

17 Satellite-only GGMs vs. high resolution models The spatial resolution of satellite-only GGMs is limited. How does this limitation influence the offset estimation? How does GOCE improve the results? Rülke et al. Height system unification in Europe. 10/10/ International Symposium on Gravity, Geoid and Height Systems

18 Satellite-only GGMs vs. high resolution models The spatial resolution of satellite-only GGMs is limited. How does this limitation influence the offset estimation? How does GOCE improve the results? Comparison with results based on high resolution models. Combination of GOCE GGMs and high resolution gravity field model Rülke et al. Height system unification in Europe. 10/10/ International Symposium on Gravity, Geoid and Height Systems

19 Combination of gravity field models 10/10/

20 Combination of gravity field models Catenation of spherical harmonic series (shc-combined models) GOCE TIM R3 d/o EGM2008 d/o GOCO03S d/o EGM2008 d/o /10/

21 Combination of gravity field models Catenation of spherical harmonic series (shc-combined models) GOCE TIM R3 d/o EGM2008 d/o GOCO03S d/o EGM2008 d/o Combination by Gaussian filtering (filter-combined models) Synthesis of satellite-only GGM and regional GM on grid low pass filter of satellite-only GGM high pass filter of regional GM summation of both parts G 2πσf 1 6 = e with σ b = 10/10/

22 Gravity field models vs. GNSS/leveling data in Germany 954 GNSS/leveling points ellipsoidal heights: ETRS89 physical heights: DHHN92 10/10/

23 Gravity field models vs. GNSS/leveling data in Germany 954 GNSS/leveling points ellipsoidal heights: ETRS89 physical heights: DHHN92 2.8cm 2.6cm 10/10/

24 Gravity field models vs. GNSS/leveling data in Germany 954 GNSS/leveling points ellipsoidal heights: ETRS89 physical heights: DHHN92 4.7cm 4.2cm 2.8cm 2.6cm 10/10/

25 Gravity field models vs. GNSS/leveling data in Germany 954 GNSS/leveling points ellipsoidal heights: ETRS89 physical heights: DHHN92 4.7cm 4.2cm 2.8cm 2.6cm 10/10/

26 Results different gravity field models 10/10/

27 Results different gravity field models 10/10/

28 GF vs. Spirit leveling approach 10/10/

29 Residuals (GOCO03S+EGG2008, filter-combined) 10/10/

30 Residuals (GOCO03S+EGG2008, filter-combined) vs. EUVN_DA vs. D954 10/10/

31 Example: English Channel H Folkestone - H Coquelles Observed (leveling through Tunnel) 40cm +- 2cm (Greaves et al. 2007) Spirit leveling approach 47.2cm GF approach 33.8cm ê = ˆ ζ ζ GF approach with considered regional residual pattern 33.8cm + ~4cm (residual England) + ~2cm (residual France) = ~40cm 10/10/

32 Conclusions 10/10/

33 Conclusions GF approach is a suitable approach to unify European height system realizations. 10/10/

34 Conclusions GF approach is a suitable approach to unify European height system realizations. The combination of satellite-only GGM and EGM2008 shc-series decreases the accuracy of the combined model in comparison to the pure EGM /10/

35 Conclusions GF approach is a suitable approach to unify European height system realizations. The combination of satellite-only GGM and EGM2008 shc-series decreases the accuracy of the combined model in comparison to the pure EGM2008. A simple combination based on filter technique using Gaussian filter gives better results. In comparison to a German GNSS/leveling data set, standard deviations of 2.1cm (GOCE TIM R3) and 2.4cm (GOCO03S) are obtained for combinations with EGG /10/

36 Conclusions GF approach is a suitable approach to unify European height system realizations. The combination of satellite-only GGM and EGM2008 shc-series decreases the accuracy of the combined model in comparison to the pure EGM2008. A simple combination based on filter technique using Gaussian filter gives better results. In comparison to a German GNSS/leveling data set, standard deviations of 2.1cm (GOCE TIM R3) and 2.4cm (GOCO03S) are obtained for combinations with EGG2008. Further improvement can be reached by a combination of satellite observations and terrestrial data. 10/10/

37 Conclusions 10/10/

38 Conclusions Satellite-only GGMs (100km spatial resolution) already give satisfactory results for height reference frame unification in Europe. 10/10/

39 Conclusions Satellite-only GGMs (100km spatial resolution) already give satisfactory results for height reference frame unification in Europe. In comparison to high resolution gravity field models and to the spirit leveling approach results, differences on the level of 5cm occur for the most cases. 10/10/

40 Conclusions Satellite-only GGMs (100km spatial resolution) already give satisfactory results for height reference frame unification in Europe. In comparison to high resolution gravity field models and to the spirit leveling approach results, differences on the level of 5cm occur for the most cases. In areas with a rough gravity field, satellite-only GGMs give larger differences up to 15cm. 10/10/

41 Conclusions Satellite-only GGMs (100km spatial resolution) already give satisfactory results for height reference frame unification in Europe. In comparison to high resolution gravity field models and to the spirit leveling approach results, differences on the level of 5cm occur for the most cases. In areas with a rough gravity field, satellite-only GGMs give larger differences up to 15cm. There is no clear evidence for a dependency of the error from the country size. 10/10/

42 Conclusions Satellite-only GGMs (100km spatial resolution) already give satisfactory results for height reference frame unification in Europe. In comparison to high resolution gravity field models and to the spirit leveling approach results, differences on the level of 5cm occur for the most cases. In areas with a rough gravity field, satellite-only GGMs give larger differences up to 15cm. There is no clear evidence for a dependency of the error from the country size. The GF approach can be applied globally and is the preferred method for the realization of a World Height System. 10/10/