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...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.展开更多
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...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.展开更多
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 met...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.展开更多
A method is proposed to fuse the velocity data of the global navigation satellite system(GNSS) and leveling height via combined adjustment with constraints. First, stable GNSS-leveling points are uniformly selected, a...A method is proposed to fuse the velocity data of the global navigation satellite system(GNSS) and leveling height via combined adjustment with constraints. First, stable GNSS-leveling points are uniformly selected, and the constraints of the geodetic height change velocity and normal height change velocity are given. Then, the GNSS vertical velocities and leveling height difference are used as observations of combined adjustment, and robust least-squares estimation are used to estimate the velocities of the unknown points. Finally, a vertical movement model is established with the GNSS vertical velocities and leveling vertical velocities obtained via combined adjustment. Data from the second-order leveling network and GNSS control points in Shandong Province are taken as test data, and eight calculation schemes are used for discussion. One of the schemes, the bifactor robust combined adjustment method based on variance component estimation with two kinds of vertical velocity constraints achieves the optimal results. The method applied in the scheme can be recommended for data fusion of GNSS and leveling, further improving the reliability of vertical crustal movement in Shandong Province.展开更多
文摘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.
基金financial support for the Chilean part of the project from the Scientific and Technological Research Department of USACH(DICYT in Spanish)through the project DICYT-Regular 091612TM。
文摘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.
基金the International Center for Global Earth Models(ICGEM)for the height anomaly and gravity anomaly data and Bureau Gravimetrique International(BGI)for free-air gravity anomaly data from the World Gravity Map project(WGM2012)The authors are grateful to Głowny Urza˛d Geodezji i Kartografii of Poland for the height anomaly data of the quasi-geoid PL-geoid2021.
文摘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.
基金supported by the National Natural Science Foundation of China(41774004,41904040)the Technological Innovation of SHASG(SCK2020-11).
文摘A method is proposed to fuse the velocity data of the global navigation satellite system(GNSS) and leveling height via combined adjustment with constraints. First, stable GNSS-leveling points are uniformly selected, and the constraints of the geodetic height change velocity and normal height change velocity are given. Then, the GNSS vertical velocities and leveling height difference are used as observations of combined adjustment, and robust least-squares estimation are used to estimate the velocities of the unknown points. Finally, a vertical movement model is established with the GNSS vertical velocities and leveling vertical velocities obtained via combined adjustment. Data from the second-order leveling network and GNSS control points in Shandong Province are taken as test data, and eight calculation schemes are used for discussion. One of the schemes, the bifactor robust combined adjustment method based on variance component estimation with two kinds of vertical velocity constraints achieves the optimal results. The method applied in the scheme can be recommended for data fusion of GNSS and leveling, further improving the reliability of vertical crustal movement in Shandong Province.
