Improved Determination of Elevations from the Global Positioning System (Gps)

Geoid and Geoid-type Surface Determination

IMPROVED DETERMINATION OF HEIGHTS FROM THE GLOBAL POSITIONING SYSTEM (GPS)

Background

Over the last decade, there has been an increased interest in the determination of the (quasi)geoid. This is mainly due to the demands for height transformation from users of GPS (Global Positioning System). This procedure replaces costly conventional levelling operations with quicker and cheaper GPS surveys, as long as the (quasi)geoidal height has been computed to a high accuracy. Therefore, there is a common goal among geodesists to determine “the 1-cm (quasi)geoid model”. This study focuses on the determination of a precise quasigeoid over Norway and fitting it to GPS-levelling data to obtain a geoid-type surface which enhances the accuracy of levelling by GPS. The impact of different modification of Stokes’s formula and Global Geopotential Models (GGM) is considered. It is shown that the quasigeoid model computed by Vaníček-Kleusberg solution (one of the modification models considered), provides the smallest residuals (with standard deviation of ±12.8 cm) compared with GPS-levelling data. The recent GGM model (GGM02S) obtained from GRACE (Gravity Recovery and Climate Experiment) twin-satellite mission is used here. The optimum degree of 90 for modification of Stokes’s formula is selected based on the results. The required corrections for computing a precise (quasi)geoid like direct and indirect topographic corrections, atmospheric correction and ellipsoidal correction are considered here. As topographic correction is the main correction in (quasi)geoid determination, both the classic and the recent developed formulas are employed and the classic formulas are used according to the results.

In addition to land, marine and airborne gravity data, satellite altimetry-derived gravity anomalies are also computed over sea areas (North Sea, the Norwegian Sea and the Barents Sea). The available Levitus climatology model is used to correct data for MDT (Mean Dynamic Topography). Deflections of the vertical are computed from along track gradients and then they are converted to Free Air Anomaly (FAA) by applying inverse Vening-Meinesz formula.

The combination of the gravimetric quasigeoid model with GPS-levelling data using the Least squares Collocation (LSC) and Second-Generation Wavelets (SGW) is then considered. The new surface derived from this combination is called a geoid-type surface here. Since results from LSC are sensitive to the selection of the trend and covariance model, different models are employed and results are evaluated. Results show that using the 3rd order or trigonometric trend model and exponential covariance model provide better results compared with GPS-levelling data (standard deviations of ±2.9 cm and 0.15 ppm achieved in absolute and relative sense, respectively). Second-generation wavelets and their associated lifting scheme, which do not require regularly spaced data, are also used to combine gravimetric quasigeoid model and GPS-levelling data over Norway. The wavelet-based results are also evaluated with GPS-levelling data and standard deviations of ±3.3 cm and 0.12 ppm achieved in absolute and relative sense respectively. Comparison with the solutions from LSC merging shows that using LSC provides smaller standard deviation in absolute sense. But, in relative sense, the SGW solution with smaller standard deviation is preferred. Employing the SGW solution as a trend model in LSC is led to a combined method called SGW-LSC here. The solution using this combined method provides better results both in the absolute (±2.8 cm) and relative (0.11 ppm) sense.

Selected Publications: Nahavandchi, Hossein; Soltanpour, Ali. Impact of the New GRACE Global Geopotential Model to the Geoidal Height Modeling over Norway [Poster]. IAG International Symposium-Gravity, Geoid and Space Missions - GGSM2004; 30.08.2004 - 03.09.2004. Published in: Proceedings GGSM2004

Nahavandchi, Hossein; Soltanpour, Ali; Nyrnes, Erik. A New Gravimetric Geoidal Height Model over Norway Computed by the Least-Squares Modification Parameters. In: Gravity, Geoid, and Space Missions. Berlin: Springer Publishing Company 2004. ISBN 3-540-26930-4. pp. 191-196

Nahavandchi, Hossein; Soltanpour, Ali. Adjustment of the Surface of the Gravimetric Geoidal Height Model between Constrained GPS-levelling Stations [Poster]. IAG International Symposium- Gravity, Geoid and Space Missions - GGSM2004; 30.08.2004 - 03.09.2004. Published in: Proceedings GGSM2004 (Poster)

Soltanpour A., Nahavandchi H., Featherstone W.E. (2005) On the use of second-generation wavelets to combine a gravimetric geoid model with GPS-levelling data. Journal of Geodesy 80: 82-93.

Nahavandchi H., Soltanpour A. (2005) Improved Determination of Heights Using a Conversion Surface by Combining Gravimetric Quasi/Geoid and GPS-levelling Height Differences. Studia Geophysica et Geodaetica 50: 165-180.

A. Soltanpour, H. Nahavandchi, K. Ghazavi (2006) Recovery of marine gravity anomaly from ERS2 and ENVISAT data and its contribution to the geoid of Norway [Poster]. European Geosciences Union, General Assembly, Vienna, Austria 02 – 07 April 2006

A. Soltanpour, H. Nahavandchi (2006) A new high-resolution geoid for Iran with emphasise on different modification procedures and new GRACE geopotential model. [Poster]. European Geosciences Union, General Assembly, Vienna, Austria 02 – 07 April 2006

A. Soltanpour, H. Nahavandchi, W.E. Featherstone (2006) Geoid-type surface determination using wavelet-based combination of gravimetric quasi/geoid and GPS-levelling data [Scientific Oral Presentation]. European Geosciences Union, General Assembly, Vienna, Austria 02 – 07 April 2006