The Global Geopotential Models (GGMs) of GOCE (Gravity Recovery and steady- state Ocean Circulation Explorer) differ globally as well as regionally in their accuracy and resolution based on the maximum degree and orde...The Global Geopotential Models (GGMs) of GOCE (Gravity Recovery and steady- state Ocean Circulation Explorer) differ globally as well as regionally in their accuracy and resolution based on the maximum degree and order (d/o) of the fully normalized spherical harmonic (SH) coefficients, which express each GGM. The main idea of this study is to compare the free-air gravity anomalies and quasi geoid heights determined from several recent GOCE-based GGMs with the corresponding ones from the Earth Gravitational Model 2008 (EGM2008) over Egypt on the one hand and with ground-based measurements on the other hand. The results regarding to the comparison of GOCE-based GGMs with terrestrial gravity and GPS/levelling data provide better improvement with respect to EGM2008. The 4th release GOCE-based GGM developed with the use of space-wise solution strategy (SPW_R4) approximates the gravity field well over the Egyptian region. The SPW_R4 model is accordingly suggested as a reference model for recovering the long wavelength (up to SH d/o 200) components of quasi geoid heights when modelling the gravimetric quasi-geoid over the Egypt. Finally, three types of transformation models: Four-, Five- and Seven-parameter transformations have been applied to reduce the data biases and to provide a better fitting of quasi geoid heights obtained from the studied GOCE-based GGMs to those from GPS/levelling data. These models reveal that the standard deviation of vertical datum over Egypt is at the level of about 32 cm.展开更多
The main objective of this study is to improve the geoid by GPS/leveling data in Egypt.Comparisons of the gravimetric geoid with GPS/leveling data have been performed.On the basis of a gravimetric geoid fitted to GPS/...The main objective of this study is to improve the geoid by GPS/leveling data in Egypt.Comparisons of the gravimetric geoid with GPS/leveling data have been performed.On the basis of a gravimetric geoid fitted to GPS/leveling by the least square method,a smoothed geoid was obtained.A high_resolution geoid in Egypt was computed with a 2.5′×2.5′ grid by combining the data set of 2 600 original point gravity values,30″×30″ resolution Digital Terrain Model (DTM) grid and the spherical harmonic model EGM96.The method of computation involved the strict evaluation of the Stokes integral with 1D_FFT.The standard deviation of the difference between the gravimetric and the GPS/leveling geoid heights is ±0.47 m.The standard deviation after fitting of the gravimetric geoid to the GPS/leveling points is better than ±13 cm.In the future we will try to improve our geoid results in Egypt by increasing the density of gravimetric coverage.展开更多
The aim of this investigation is to study how to use a gravimetric (quasi) geoid for levelling by GPS data in an optimal way.The advent of precise geodetic GPS has made the use of a technique possible,which might be c...The aim of this investigation is to study how to use a gravimetric (quasi) geoid for levelling by GPS data in an optimal way.The advent of precise geodetic GPS has made the use of a technique possible,which might be called GPS_ gravimetric geoid determination.In this approach,GPS heights above the reference ellipsoid are determined for points whose levelled (orthometric) height H is above sea level people have already surveyed;for these points,we thus have the values of the geoid undulation N .These values are then used to constrain the geoid undulations N′ obtained from the gravimetric solution.展开更多
This paper first develops the approaches to determine the geopotential of the local mean sea level,and then investigates the offset of the 1985 vertical datum surface defined by the mean sea level of Yellow Sea at the...This paper first develops the approaches to determine the geopotential of the local mean sea level,and then investigates the offset of the 1985 vertical datum surface defined by the mean sea level of Yellow Sea at the Dagang Tide Gauge in Qingdao city using the developed approaches and GPS/leveling data.It shows that the geopotential of the local mean sea level at the tide gauge is equal to 62 636 853.5±0.2 m2·s -2 and that the 1985 vertical datum surface is 24.6±5.4 cm above the geoid realized by the geopotential W 0= 62 636 856.0±0.5 m2·s -2.展开更多
Determining the altitude of mountains is one of the most fundamental challenges for humankind.Therefore,the main objective of the study is to determine the altitudes of the three main summits in Ecuador through GNSS p...Determining the altitude of mountains is one of the most fundamental challenges for humankind.Therefore,the main objective of the study is to determine the altitudes of the three main summits in Ecuador through GNSS positioning,referring to the official vertical datum of Ecuador and the geo-potential surface(W_(o)).The three peaks are active volcanoes named Chimborazo,Cotopaxi and Cayambe,all of which are known to be over 5700 m above sea level.Positioning GNSS was performed on the summit of the volcanoes,and the GPS leveling method was applied on nearby plates.At these summits,the correction of the potential difference between the mean sea level and W_(o) was used.The altitudes referred to the mean sea level were compared with other registered heights,and the results are more accurate than previous geodetic missions.展开更多
Digital Elevation Models(DEMs)contain topographic relief data that are vital for many geoscience applications.This study relies on the vertical accuracy of publicly available latest high-resolution(30 m)global DEMs ov...Digital Elevation Models(DEMs)contain topographic relief data that are vital for many geoscience applications.This study relies on the vertical accuracy of publicly available latest high-resolution(30 m)global DEMs over Cameroon.These models are(1)the ALOS World 3D-30 m(AW3D30),(2)the Shuttle Radar Topography Mission 1 Arc-Second CBand Global DEM(SRTM 1)and(3)the Advanced Spaceborne Thermal Emission and Reflection Global DEM Version 2(ASTER GDEM 2).After matching their coordinate systems and datums,the horizontal positional accuracy evaluation was carried out and it shows that geolocation errors significantly influence the vertical accuracy of global DEMs.After this,the three models are compared among them,in order to access random and systematic effects in the elevation data each of them contains.Further,heights from 555 GPS/leveling points distributed all over Cameroon are compared to each DEM,for their vertical accuracy determination.Traditional and robust statistical measures,normality test,outlier detection and removal were used to describe the vertical quality of the DEMs.The test of the normality rejected the hypothesis of normal distribution for all tested global DEMs.Overall vertical accuracies obtained for the three models after georeferencing and gross error removal in terms of Root Mean Square(RMS)and Normalized Median Absolute Deviation(NMAD)are:AW3D30(13.06 m and 7.75 m),SRTM 1(13.25 m and 7.41 m)and ASTER GDEM 2(18.87 m and 13.30 m).Other accuracy measures(MED,68.3% quantile,95% quantile)supply some evidence of the good quality of AW3D30 over Cameroon.Further,the effect of land cover and slope on DEM vertical accuracy was also analyzed.All models have proved to be worse in the areas dominated by forests and shrubs areas.SRTM 1 and AW3D30 are more resilient to the effects of the scattering objects respectively in forests and cultivated areas.The dependency of DEMs accuracy on the terrain roughness is evident.In all slope intervals,AW3D30 is performing better than SRTM 1 and ASTER GDEM 2 over Cameroon.AW3D30 is more representative of the external topography over Cameroon in comparison with two others datasets and SRTM 1 can be a serious alternative to AW3D30 for a range of DEM applications in Cameroon.展开更多
Estimation of the zero-height geopotential value W_0^（LVD） for the CVD（China Vertical Datum） plays a fundamental role in the connection of traditional height reference systems into a global height system.Estimatio...Estimation of the zero-height geopotential value W_0^（LVD） for the CVD（China Vertical Datum） plays a fundamental role in the connection of traditional height reference systems into a global height system.Estimation the W_0^（LVD） of China is based on the computation of the mean geopotential offset between the value W_0= 62636856.0 m^2 s^（-2）, selected as reference in this study, and the unknown geopotential value W_0^（LVD）. This estimation is based on the combination of ellipsoidal heights, levelled heights（referring to the CVD）, and some physical parameters, such as geopotential values, gravity values, and geoid undulations.The geoid undulations derived from the GGM（Global Geopotential Models）. This combination is performed through three approaches： The first one is based on the theory of Molodensky, and the second one compares levelled heights and geopotential values derived from the GGMs, while the third one analyses the differences between GPS/Levelling and GGMs geoid undulations. The approaches are evaluated at 65 benchmarks（BMs） covered around Qingdao where the tide gauge is used to observe the local mean sea level of China. The results from three approaches are very similar. Furthermore, the W_0^（LVD）determined for the China local vertical datum was 62636852.9462 m^2 s^（-2）, indicates a bias of about3.0538 m^2/s^（-2） compared to the conventional value of 62636856.0 m^2 s^（-2）.展开更多
The orthometric heights can be obtained without levelling by means of the ellipsoidal and geoidal heights. For engineering purposes, these orthometric heights must be determined with high accuracy. For this reason, th...The orthometric heights can be obtained without levelling by means of the ellipsoidal and geoidal heights. For engineering purposes, these orthometric heights must be determined with high accuracy. For this reason, the determination of a high-resolution geoid is necessary. In Andalusia (South Spain) a new geopotential model (EIGEN-GL04C) has been available since the publication of a more recent regional geoid. As a consequence, these new data bring about improvements that ought to be included in a new regional geoid of Andalusia. With this aim in mind, a new gravimetric geoid determination has been carried out, in which these new data have been included. Thus, a new geoid is provided as a data grid distributed for the South Spain area from 36 to 39 degrees of latitude and –7 to –1 degrees of longitude (extending to 3 × 6 degrees), in a 120 × 240 regular grid with a mesh size of 1.5’ × 1.5’ and 28800 points in the GRS80 reference system. This calculated geoid and previous geoids are compared to the geoid undulations obtained for 262 GPS/levelling points, distributed within the study area. The new geoid shows an improvement in accuracy and reliability, fitting the geoidal heights determined for these GPS-levelling points better than any previous geoid.展开更多
Earth＇s gravity model（EGM） helps people better determine the figure of Earth, which is generally represented by a global geoid. For a considerable amount of practical applications, people use quasi-geoid to approxi...Earth＇s gravity model（EGM） helps people better determine the figure of Earth, which is generally represented by a global geoid. For a considerable amount of practical applications, people use quasi-geoid to approximate the geoid, thus the quasi-geoid is also treated as an important height datum. In this study we revisit the method to directly determine regional quasi-geoid using EGM and digital elevation model（DEM）, on the basis of Molodensky theory. According to the method we obtain a 50 50quasi-geoid for China's Mainland and its vicinity areas, based on the EGM2008 gravitational potential model and the Shuttle Radar Topography Mission（SRTM） DEM model. By comparing height anomalies derived from EGM2008 with observations at 70 GPS/leveling points in areas including northwest,mid-west, mid-east and southeast of China, we find that the 50 50EGM2008 quasi-geoid well fits the GPS/leveling results, with average deviations less than 10 cm for the selected areas in east China（with mainly plain topography） and ~20 cm for the selected areas in west China（highland or mountainous areas）. We also discuss a few technical issues for directly determining height anomalies based on EGM and DEM, under the frame of Molodensky theory.展开更多
Developing the Nabucco engineering infrastructure was the most challenging task imaginable and required state-of-the-art technologies.For this purpose,a NabuccoGlobal Positioning System(GPS)Network was established.It...Developing the Nabucco engineering infrastructure was the most challenging task imaginable and required state-of-the-art technologies.For this purpose,a NabuccoGlobal Positioning System(GPS)Network was established.It is 762 km long.Nine-hundred and two ground control unit points were established.In order to provide the relationship with ITRF96 datum,it was surrounded by TFNGN(Turkish Fundamental National GPS Network)and TNVCN(Turkish National Vertical Control Network)checkpoints.GPS observations were evaluated in the form of a unique network.After being reduced to projection segments,coordinates in ED50 datum were provided between datums by 2D-Helmert Transformation.Orthometric heights related to the GPS Network were obtained by the improvement of TG-03 data based on a GPS/leveling procedure.The objective of the study is to present the results of a comprehensive engineering project which involved many geodetic considerations including GPS,orthometric heights,and geoid undulations and gives insight into the accuracy and precision of such large projects in terms of recent geodetic practice.In this study,a Global Navigation Satellite System(GNSS)-based geodetic infrastructure is presented,methods to obtain the necessary precision requirements are provided,and experience is shared in order to provide an example of a large-scale pipeline project,and to provide insight into the planning necessary for future similar engineering projects.展开更多
文摘The Global Geopotential Models (GGMs) of GOCE (Gravity Recovery and steady- state Ocean Circulation Explorer) differ globally as well as regionally in their accuracy and resolution based on the maximum degree and order (d/o) of the fully normalized spherical harmonic (SH) coefficients, which express each GGM. The main idea of this study is to compare the free-air gravity anomalies and quasi geoid heights determined from several recent GOCE-based GGMs with the corresponding ones from the Earth Gravitational Model 2008 (EGM2008) over Egypt on the one hand and with ground-based measurements on the other hand. The results regarding to the comparison of GOCE-based GGMs with terrestrial gravity and GPS/levelling data provide better improvement with respect to EGM2008. The 4th release GOCE-based GGM developed with the use of space-wise solution strategy (SPW_R4) approximates the gravity field well over the Egyptian region. The SPW_R4 model is accordingly suggested as a reference model for recovering the long wavelength (up to SH d/o 200) components of quasi geoid heights when modelling the gravimetric quasi-geoid over the Egypt. Finally, three types of transformation models: Four-, Five- and Seven-parameter transformations have been applied to reduce the data biases and to provide a better fitting of quasi geoid heights obtained from the studied GOCE-based GGMs to those from GPS/levelling data. These models reveal that the standard deviation of vertical datum over Egypt is at the level of about 32 cm.
文摘The main objective of this study is to improve the geoid by GPS/leveling data in Egypt.Comparisons of the gravimetric geoid with GPS/leveling data have been performed.On the basis of a gravimetric geoid fitted to GPS/leveling by the least square method,a smoothed geoid was obtained.A high_resolution geoid in Egypt was computed with a 2.5′×2.5′ grid by combining the data set of 2 600 original point gravity values,30″×30″ resolution Digital Terrain Model (DTM) grid and the spherical harmonic model EGM96.The method of computation involved the strict evaluation of the Stokes integral with 1D_FFT.The standard deviation of the difference between the gravimetric and the GPS/leveling geoid heights is ±0.47 m.The standard deviation after fitting of the gravimetric geoid to the GPS/leveling points is better than ±13 cm.In the future we will try to improve our geoid results in Egypt by increasing the density of gravimetric coverage.
文摘The aim of this investigation is to study how to use a gravimetric (quasi) geoid for levelling by GPS data in an optimal way.The advent of precise geodetic GPS has made the use of a technique possible,which might be called GPS_ gravimetric geoid determination.In this approach,GPS heights above the reference ellipsoid are determined for points whose levelled (orthometric) height H is above sea level people have already surveyed;for these points,we thus have the values of the geoid undulation N .These values are then used to constrain the geoid undulations N′ obtained from the gravimetric solution.
文摘This paper first develops the approaches to determine the geopotential of the local mean sea level,and then investigates the offset of the 1985 vertical datum surface defined by the mean sea level of Yellow Sea at the Dagang Tide Gauge in Qingdao city using the developed approaches and GPS/leveling data.It shows that the geopotential of the local mean sea level at the tide gauge is equal to 62 636 853.5±0.2 m2·s -2 and that the 1985 vertical datum surface is 24.6±5.4 cm above the geoid realized by the geopotential W 0= 62 636 856.0±0.5 m2·s -2.
文摘Determining the altitude of mountains is one of the most fundamental challenges for humankind.Therefore,the main objective of the study is to determine the altitudes of the three main summits in Ecuador through GNSS positioning,referring to the official vertical datum of Ecuador and the geo-potential surface(W_(o)).The three peaks are active volcanoes named Chimborazo,Cotopaxi and Cayambe,all of which are known to be over 5700 m above sea level.Positioning GNSS was performed on the summit of the volcanoes,and the GPS leveling method was applied on nearby plates.At these summits,the correction of the potential difference between the mean sea level and W_(o) was used.The altitudes referred to the mean sea level were compared with other registered heights,and the results are more accurate than previous geodetic missions.
文摘Digital Elevation Models(DEMs)contain topographic relief data that are vital for many geoscience applications.This study relies on the vertical accuracy of publicly available latest high-resolution(30 m)global DEMs over Cameroon.These models are(1)the ALOS World 3D-30 m(AW3D30),(2)the Shuttle Radar Topography Mission 1 Arc-Second CBand Global DEM(SRTM 1)and(3)the Advanced Spaceborne Thermal Emission and Reflection Global DEM Version 2(ASTER GDEM 2).After matching their coordinate systems and datums,the horizontal positional accuracy evaluation was carried out and it shows that geolocation errors significantly influence the vertical accuracy of global DEMs.After this,the three models are compared among them,in order to access random and systematic effects in the elevation data each of them contains.Further,heights from 555 GPS/leveling points distributed all over Cameroon are compared to each DEM,for their vertical accuracy determination.Traditional and robust statistical measures,normality test,outlier detection and removal were used to describe the vertical quality of the DEMs.The test of the normality rejected the hypothesis of normal distribution for all tested global DEMs.Overall vertical accuracies obtained for the three models after georeferencing and gross error removal in terms of Root Mean Square(RMS)and Normalized Median Absolute Deviation(NMAD)are:AW3D30(13.06 m and 7.75 m),SRTM 1(13.25 m and 7.41 m)and ASTER GDEM 2(18.87 m and 13.30 m).Other accuracy measures(MED,68.3% quantile,95% quantile)supply some evidence of the good quality of AW3D30 over Cameroon.Further,the effect of land cover and slope on DEM vertical accuracy was also analyzed.All models have proved to be worse in the areas dominated by forests and shrubs areas.SRTM 1 and AW3D30 are more resilient to the effects of the scattering objects respectively in forests and cultivated areas.The dependency of DEMs accuracy on the terrain roughness is evident.In all slope intervals,AW3D30 is performing better than SRTM 1 and ASTER GDEM 2 over Cameroon.AW3D30 is more representative of the external topography over Cameroon in comparison with two others datasets and SRTM 1 can be a serious alternative to AW3D30 for a range of DEM applications in Cameroon.
文摘Estimation of the zero-height geopotential value W_0^（LVD） for the CVD（China Vertical Datum） plays a fundamental role in the connection of traditional height reference systems into a global height system.Estimation the W_0^（LVD） of China is based on the computation of the mean geopotential offset between the value W_0= 62636856.0 m^2 s^（-2）, selected as reference in this study, and the unknown geopotential value W_0^（LVD）. This estimation is based on the combination of ellipsoidal heights, levelled heights（referring to the CVD）, and some physical parameters, such as geopotential values, gravity values, and geoid undulations.The geoid undulations derived from the GGM（Global Geopotential Models）. This combination is performed through three approaches： The first one is based on the theory of Molodensky, and the second one compares levelled heights and geopotential values derived from the GGMs, while the third one analyses the differences between GPS/Levelling and GGMs geoid undulations. The approaches are evaluated at 65 benchmarks（BMs） covered around Qingdao where the tide gauge is used to observe the local mean sea level of China. The results from three approaches are very similar. Furthermore, the W_0^（LVD）determined for the China local vertical datum was 62636852.9462 m^2 s^（-2）, indicates a bias of about3.0538 m^2/s^（-2） compared to the conventional value of 62636856.0 m^2 s^（-2）.
文摘The orthometric heights can be obtained without levelling by means of the ellipsoidal and geoidal heights. For engineering purposes, these orthometric heights must be determined with high accuracy. For this reason, the determination of a high-resolution geoid is necessary. In Andalusia (South Spain) a new geopotential model (EIGEN-GL04C) has been available since the publication of a more recent regional geoid. As a consequence, these new data bring about improvements that ought to be included in a new regional geoid of Andalusia. With this aim in mind, a new gravimetric geoid determination has been carried out, in which these new data have been included. Thus, a new geoid is provided as a data grid distributed for the South Spain area from 36 to 39 degrees of latitude and –7 to –1 degrees of longitude (extending to 3 × 6 degrees), in a 120 × 240 regular grid with a mesh size of 1.5’ × 1.5’ and 28800 points in the GRS80 reference system. This calculated geoid and previous geoids are compared to the geoid undulations obtained for 262 GPS/levelling points, distributed within the study area. The new geoid shows an improvement in accuracy and reliability, fitting the geoidal heights determined for these GPS-levelling points better than any previous geoid.
基金supported by the National 973 Project of China(2013CB733301)the Natural Science Foundation of China(41204017,11173049,41429401 and 41228004)+1 种基金the Shanghai Postdoctoral Sustentation Fund(13R21417900)the Special Program Fund of Shanghai Astronomical Observatory(Y196591009)
文摘Earth＇s gravity model（EGM） helps people better determine the figure of Earth, which is generally represented by a global geoid. For a considerable amount of practical applications, people use quasi-geoid to approximate the geoid, thus the quasi-geoid is also treated as an important height datum. In this study we revisit the method to directly determine regional quasi-geoid using EGM and digital elevation model（DEM）, on the basis of Molodensky theory. According to the method we obtain a 50 50quasi-geoid for China's Mainland and its vicinity areas, based on the EGM2008 gravitational potential model and the Shuttle Radar Topography Mission（SRTM） DEM model. By comparing height anomalies derived from EGM2008 with observations at 70 GPS/leveling points in areas including northwest,mid-west, mid-east and southeast of China, we find that the 50 50EGM2008 quasi-geoid well fits the GPS/leveling results, with average deviations less than 10 cm for the selected areas in east China（with mainly plain topography） and ~20 cm for the selected areas in west China（highland or mountainous areas）. We also discuss a few technical issues for directly determining height anomalies based on EGM and DEM, under the frame of Molodensky theory.
文摘Developing the Nabucco engineering infrastructure was the most challenging task imaginable and required state-of-the-art technologies.For this purpose,a NabuccoGlobal Positioning System(GPS)Network was established.It is 762 km long.Nine-hundred and two ground control unit points were established.In order to provide the relationship with ITRF96 datum,it was surrounded by TFNGN(Turkish Fundamental National GPS Network)and TNVCN(Turkish National Vertical Control Network)checkpoints.GPS observations were evaluated in the form of a unique network.After being reduced to projection segments,coordinates in ED50 datum were provided between datums by 2D-Helmert Transformation.Orthometric heights related to the GPS Network were obtained by the improvement of TG-03 data based on a GPS/leveling procedure.The objective of the study is to present the results of a comprehensive engineering project which involved many geodetic considerations including GPS,orthometric heights,and geoid undulations and gives insight into the accuracy and precision of such large projects in terms of recent geodetic practice.In this study,a Global Navigation Satellite System(GNSS)-based geodetic infrastructure is presented,methods to obtain the necessary precision requirements are provided,and experience is shared in order to provide an example of a large-scale pipeline project,and to provide insight into the planning necessary for future similar engineering projects.
