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Toward new geoid solution in Slovenia

Toward new geoid solution in Slovenia. Miran Kuhar UL, Faculty of Civil and Geodetic Engineering. Workshop: Overview of subproject Geodetic Reference Frame (GRF) Ljubljana, October 1-3, 2014. The shape of geoid surface in Slovenia. Geodet ic r eferen ce surfaces (1).

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Toward new geoid solution in Slovenia

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  1. Toward new geoid solution in Slovenia Miran Kuhar UL, Faculty of Civil and Geodetic Engineering Workshop: Overview of subproject Geodetic Reference Frame (GRF) Ljubljana, October 1-3, 2014

  2. The shape of geoid surface in Slovenia

  3. Geodeticreferencesurfaces (1) Geoid is not an analitical surface; it's a "mathematical figure of the Earth" (C.F. Gauss), equipotential surface of the Earth's gravity field. It is not suitable for geodetic computations, therefore it is substituted by a rotational ellipsoid. geoid elipsoid ocean Rotational ellipsoid is the mathematical approximation of the figure of the Earth; it is suitable for geodetic computation and positioning.

  4. Geodeticreferencesurfaces (2) • Geoid determination requires that observables be reduced down to the geoid. • Use of observables without any reductions (as they were measured on the Earth's surface) gives quasigeoid. geoid quaigeoid ellipsoid ocean

  5. The relationship between surfaces h = H +N h = HN +z mean-sea-level heights (H, HN) reckoned from the geoid or quasigeoid ("orthometric" or "normal" heights) HN H h quasigeoid geoid z geoid height – difference between the ellipsoid and the geoid N height anomaly – difference between the ellipsoid and the quasigeoid ellipsoid

  6. Height reference surface • What we really use in practice is: • Height reference surface (height conversion surface). •  surface adjusted to the local vertical datum. • All the errors in the geoid, GNSS-heightsandlevelling are somehow assimilated into this surface. • Minimizing all the influences (errors), one could determine the optimal surface for performing GNSS-levelling.

  7. Brief history of Geoid research in Slovenia • Prof. A. Muminagić (1974), astrogeodetic solution (Bessel ellipsoid):

  8. Prof. dr. T. Bašić, (GF Zagreb), 1993 • Astrogeodetic solution (Bessel ellipsoid):

  9. Official solution (year 2000) • Prof. Pribičević (GF Zagreb), combined solution by LS collocation (ellipsoid GRS-80):

  10. Properties of the geoid solution from 2000 • Geoid surface is fitted (adjusted) to the set of GPS/levelling points consisted of 163 points, unequally distributed across Slovenia. • Mean-sea-level (MSL) heights of these GPS/leveling points originate from the time before the recomputation of the Vertical reference network of Slovenia was performed (in the year 2000). • Unhomogenous accuracy of the determination of ellipsoidal and mean-sea-level (MSL) heights as well. • Residuals, computed from the interpolated values and "measured" geoid heights (N=h-H): • between +20,3 cm and – 28,0 cm; • average residual: -11,3 cm • Included in the software package SITRA (SlovenIan TRAnsformation).

  11. Geoid 2000: residuals on the GNSS/levelling points -1

  12. Geoid 2000: residuals on the GNSS/levelling points -2

  13. Statistics of the residuals

  14. Tasks perfomed in the frame of the new Geoid project • Gravimetric, levelling and GNSS-measurements on the "control" points: • over 1400 new g-values, (since 2000), • ~ 800 GNSS/levelling points (since 1995). • Determination of two new DEM (Digital Elevation Model) for the broad and narrow area of computation, grid coordinates in ETRS89 system, for the first time in Slovenia! • Evaluation of the existing data: • test computation indicates the presence of gross errors (blunders)! • Acquirement and evaluation of new data; neighbouring countries: Austria, Italy Hungary! • Test computation...

  15. Current data - measured gravity values

  16. Current data – components of the deflection of the vertical

  17. Current data used – GPS/levelling points

  18. Results of the test computations (1) • Test computations performed at STATENS KARTVERK, Hønefoss, during november 2010. • Gravimetric method: only gravity values used. • Computed geoid surface adjusted to the 23 GNSS/levelling points  height reference surface. • Acuracy estimation performed at 347 GNSS/levelling control points.

  19. Results of the test computations (2) • Statistics of residuals:

  20. Test computation – figure 1

  21. Test computation – figure 2

  22. Comparison: solution 2000 vs. solution 2010 • Comparison of grids: • solution 2000 (1'1,5'); solution 2010 (30"45").

  23. Comparison: solution 2000 vs. solution 2010

  24. Current work (1) • Aim: determination of "cm" geoid at the whole area of Slovenia! • Regional gravity survey in western part of Slovenia: • app. 500 – 600 new gravity points. • Computed (quasi)geoid surface is to be adjusted (fitted) to as many as possible very accurate GNSS/levelling points ( Collocation points), evenly distributed across Slovenia: • 43 points at the moment. • To perform accuracy estimation of the "height reference surface" on GNNS/levelling control points, evenly distributed across Slovenia: • almost 800 GNSS/levelling control points.

  25. Current work (2) Naslov • Careful examination and evaluation of all data and eliminate gross errors (blunders). • Computation of the geoid with all existing data. • Use different computation methods

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