Methodology for local correction of the heights of global geoid models to improve the accuracy of GNSS leveling

At present,one of the methods used to determine the height of points on the Earth’s surface is Global Navigation Satellite System(GNSS)leveling.It is possible to determine the orthometric or normal height by this method only if there is a geoid or quasi-geoid height model available.This paper proposes the methodology for local correction of the heights of high-order global geoid models such as EGM08,EIGEN-6C4,GECO,and XGM2019e_2159.This methodology was tested in different areas of the research field,covering various relief forms.The dependence of the change in corrected height accuracy on the input data was analyzed,and the correction was also conducted for model heights in three tidal systems:"tide free","mean tide",and"zero tide".The results show that the heights of EIGEN-6C4 model can be corrected with an accuracy of up to 1 cm for flat and foothill terrains with the dimensionality of 1°×1°,2°×2°,and 3°×3°.The EGM08 model presents an almost identical result.The EIGEN-6C4 model is best suited for mountainous relief and provides an accuracy of 1.5 cm on the 1°×1°area.The height correction accuracy of GECO and XGM2019e_2159 models is slightly poor,which has fuzziness in terms of numerical fluctuation.

Performance evaluation of high/ultra-high-degree global geopotential models over Vietnam using GNSS/leveling data

The availability of many high-degree Global Geopotential Models(GGMs), namely EGM2008, EIGEN-6C4,GECO, SGG-UGM-1, SGG-UGM-2, XGM2019e_2159, and GGMPlus, challenges users regarding which model is best for Vietnam. This study, therefore, evaluates their performance by comparing them with GNSS/leveling data over Vietnam. Results show that their absolute and relative performances are largely independent of topographic conditions and geographical location and can be ranked into three classes:(1)XGM2019e_2159 has the highest accuracy,(2) the models EIGEN-6C4, GECO, SGG-UGM-1, SGG-UGM-2, and GGMPlus, have a very similar level of medium accuracy, while(3) EGM2008 is found to be the least accurate. In an absolute sense, the differences between GNSS/leveling and EGM2008-based height anomalies have a standard deviation(STD) of 0.290 ± 0.010 m, whereas, for XGM2019e_2159, this is 0.156 ± 0.006 m.All other models have STDs of(0.18-0.19) ± 0.007 m. Regarding relative performance without fitting, all GGMs have comparable accuracies for baseline length of 5-20 km, while for baselines longer than 20 km,the STD of XGM2019e_2159 is 1.5 ppm-0.5 ppm(approximately 19%-40%) lower compared with EGM2008, and 0.5 ppm-0.25 ppm(approximately 7%-36%) lower compared with EIGEN6C4, GECO,SGG-UGM-1, SGG-UGM-2, and GGMPlus. In addition, the STDs decrease significantly from 20 to 12 ppm in the range of 5-10 km, slightly from 12 to 6 ppm for 10-35 km, very slightly from 6 to 2.5 ppm for35-200 km, and then remain almost unchanged for longer baselines. After fitting, the relative accuracies of all GGMs are at the same level with negligible STD/RMSE values. Furthermore, only EGM2008 experiences significant regional differences, while other GGMs show more homogeneous spatial variation of absolute accuracy over Vietnam. These findings can contribute to the development of local quasigeoid models in Vietnam and may be helpful with the improvement of GGMs in the future.

Assessment of hybrid geoids in Chile and Spain,combining GGM and GNSS/Leveling observations

This research presents the results for analyses done to five geopotential global models(GGM),comparing them with ground data from GNSS and leveling in heterogenic zones from the geodetic perspective,in Chile and Spain.While the official and complete implementation of the International Height Reference Frame(IHRF)has not yet been established,the vertical geodetic system of many countries is not calculated on a global scale;instead,it is calculated by the variation of relative heights between one or more local tide gauges,such as in the case of Spain and Chile.This aspect creates regional and specific altimetry data,which disables the use of GGM to directly obtain the orthometric height of the vertical reference system(VRS)from the GNSS heights.Global models currently reach centimetric precision due to their high resolution but are directly incompatible for a local level.To solve this,we expose in this article the contrast between geometric geoidal undulation(ellipsoidal heights and orthometric data from the leveling networks in Spain and Chile)with the geoidal undulation in more recent models and higher resolution:Earth Gravitational Model 2008(EGM08),European Improved Gravity model of the Earth by New techniques(EIGEN6 C4),Gravity Observation Combination(GOCO05 C),Experimental Gravity Field Model(XGM2016),and Ultra-High Resolution Global Geopotential Model(SGG-UGM),adjusting the residual between both referential heights by different parametric models and polynomials of determined order.Once evaluated,their geoidal undulations are combined with GNSS/leveling data from the corresponding VRS to generate a correcting surface,which is also known as a hybrid geoid,resulting in a model of optimal adjustment for the combination of five parameters of the EIGEN-6 C4 with orthometric heights and ellipsoids of both Chile and Spain.The results show 2-3 cm precisions,which were statistically analyzed to determine the suitability for use.The final products are three grids of independent hybrid geoids,one for northern Spain and two for Chile(central and north),which allow continuous access to the VRS of each country using the GNSS’s full potential until the IHRF is available and ready for use.

Revisiting the determination of Mount Olympus Height(Greece)

The present study deals with the determination of Mount Olympus summit(Mytikas),exploiting modern observations such as Global Navigation Satellite Systems(GNSS)and existing geodetic information.The last official Olympus height determination goes back 102 years by the Swiss surveyor M.Kurz.Since then,only unofficial measurement campaigns have taken place.There is a variety of released heights,which range from 2917 to 2919 meters.In September and October of 2022,we conducted a GNSS campaign,focusing on the area of highest Olympus peaks.Employing precise GNSS measurements(accuracy of 1-3 cm),in conjunction with height information from Greece’s National Triangulation Network(5-10 cm accuracy)and an appropriate,recent geoid model(5-6 cm accuracy),we estimate through the so-called GNSS-levelling,the height of Olympus to 2917.727 m with respect to Greece’s officially accepted mean sea level and 2918.390 m with respect to the global vertical datum.Our estimation of Olympus highest peak shows remarkable consistency at the level of 12.8 cm to that of M.Kurz in 1921.

Local geoid modeling in the central part of Java, Indonesia, using terrestrial-based gravity observations

The Global Navigation Satellite System(GNSS)positioning method has been significantly developed in geodetic surveying.However,the height obtained through GNSS observations is given in a geodetic height system that needs to be converted to orthometric height for engineering applications.Information on geoid height,which can be calculated using the global geopotential mode,is required to convert such GNSS observations into orthometric height.However,its accuracy is still insufficient for most engineering purposes.Therefore,a reliable geoid model is essential,especially in areas growing fast,e.g.,the central part of Java,Indonesia.In this study,we modeled the local geoid model in the central part of Java,Indonesia,using terrestrial-based gravity observations.The Stokes'formula with the second Helmert's condensation method under the Remove-Compute-Restore approach was implemented to model the geoid.The comparison between our best-performing geoid model and GNSS/leveling observations showed that the standard deviation of the geoid height differences was estimated to be 4.4 cm.This geoid result outperformed the commonly adopted global model of EGM2008 with the estimated standard deviation of geoid height differences of 10.7 cm.

Regional Evaluation of GOCE-Based GGMs with Ground-Based Gravity and GPS/Levelling Data over Egypt

The gravity field and steady-state ocean circulation explorer (GOCE) satellite mission has provided numerous Global Geopotential Models (GGMs) with different processing methodologies and model accuracies. In the current contribution, the latest releases of GOCE-based GGMs are evaluated on the regional scale using the available terrestrial GPS/Levelling and gravity data collected over Egypt. To overcome the spectral inconsistency between the GOCE-based GGMs and the ground-based data, the spectral enhancement method (SEM) is applied. Five of GOCE-based GGMs have been used, namely GOSG01S, IGGT_R1, IfE_GOCE05s_ GO_CONS_GCF_2_SPW_R5 (SPW_R5 in the following) and NULP-02. The evaluation process of GOCE-based GGMs with the available ground data over Egypt considering the SEM method shows remarkable improvements obtained from the SPW_R5 model. The model provides lower differences of the standard deviations with respect to the EGM2008 and the other applied geopotential gravity models as well as the applied ground-based gravity and GPS/Levelling data. The findings regarding the ground-based data show obvious reductions of about 15.16% and 32.22% achieved by the GOCE-based model in term of standard deviations differences of gravity anomalies and geoid heights, respectively. Therefore, the SPW_R5 model is recommended to be applied as a reference model for compensating the long-to-short wavelength (up to spherical harmonics degree/order 280) components when modelling the gravimetric geoid over Egypt.