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Table 6: Statistics of GNSS-Levelling Data In Johor2020

Table 6 Statistics of GNSS-Levelling Data In Johor2020

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Figure 1: Location of Data in the State of Johor: Red Triangles Indicate the Fiducial Points of the Regional Ellipsoid, Green Dots Are the Gravity Stations, While the Magenta Circle Contains the GNSS-Levelling Test Points
Figure 1: Location of Data in the State of Johor: Red Triangles Indicate the Fiducial Points of the Regional Ellipsoid, Green Dots Are the Gravity Stations, While the Magenta Circle Contains the GNSS-Levelling Test Points
Copyright © GLOBAL ACADEMIC EXCELLENCE (M) SDN BHD - All rights reserved Volume 6 Issue 24 (December 2021) PP. 226-242 DOI: 10.35631/JISTM.624022
Copyright © GLOBAL ACADEMIC EXCELLENCE (M) SDN BHD - All rights reserved Volume 6 Issue 24 (December 2021) PP. 226-242 DOI: 10.35631/JISTM.624022
where GM is the geocentric gravitational constant of the Earth. The term J2, are the zonal harmonic coefficients which are expressed as:- Computation of Geoid Undulation
where GM is the geocentric gravitational constant of the Earth. The term J2, are the zonal harmonic coefficients which are expressed as:- Computation of Geoid Undulation
Similar equations may be written for the normal potential (Barthelmes, 2013; Kosarev et al., 2018):-
Similar equations may be written for the normal potential (Barthelmes, 2013; Kosarev et al., 2018):-
+. Two sets of gravity field functionals were computed for comparison. The first set was computed from the observed ellipsoidal heights, orthometric heights and gravity accelerations of the test data, having been first converted into the respective ellipsoidal systems (i.e. WGS84, GRS80 and Johor2020) as explained above. Observed geoid undulations were computed at the 18 GNSS-levelling test points from their known ellipsoidal and orthometric heights, while the observed gravity disturbances and gravity anomalies were computed from 30 randomly selected gravity stations in the gravity accelerations data set. The second set involved the synthesis of the same points using the spherical harmonic coefficients of the EGM2008 model and the parameters of the three ellipsoids. Ignoring the topographic effects, which are functions of the orthometric height and therefore equal for all the ellipsoid systems, residual quantities were computed by subtracting the synthesized quantities from the observed ones. Table 12 through Table 20 show the statistics of the observed and synthesized geoid undulations, as well as the statistics of the residual geoid for the three ellipsoids. Copyright © GLOBAL ACADEMIC EXCELLENCE (M) SDN BHD - All rights reserved Comparison of Gravity Field Functionals
+. Two sets of gravity field functionals were computed for comparison. The first set was computed from the observed ellipsoidal heights, orthometric heights and gravity accelerations of the test data, having been first converted into the respective ellipsoidal systems (i.e. WGS84, GRS80 and Johor2020) as explained above. Observed geoid undulations were computed at the 18 GNSS-levelling test points from their known ellipsoidal and orthometric heights, while the observed gravity disturbances and gravity anomalies were computed from 30 randomly selected gravity stations in the gravity accelerations data set. The second set involved the synthesis of the same points using the spherical harmonic coefficients of the EGM2008 model and the parameters of the three ellipsoids. Ignoring the topographic effects, which are functions of the orthometric height and therefore equal for all the ellipsoid systems, residual quantities were computed by subtracting the synthesized quantities from the observed ones. Table 12 through Table 20 show the statistics of the observed and synthesized geoid undulations, as well as the statistics of the residual geoid for the three ellipsoids. Copyright © GLOBAL ACADEMIC EXCELLENCE (M) SDN BHD - All rights reserved Comparison of Gravity Field Functionals
Conclusion Conciusion Based on the initial studies that have been carried out, regional level ellipsoids may be used alongside global geopotential models to compute gravity field functionals, provided the respective zero-degree spherical harmonics are taken into account. Statistical comparisons of the observed gravity field functionals with those obtained by harmonic synthesis using the three llipsoids reveal that the regional normal ellipsoid, Johor2020, performed quite well in recovering the gravity field functionals. For observed undulations, Johor2020 obtained a mean of 1.02m compared to 7.91m for both WGS84 and GRS80. For synthesized undulations, an average of 0.20m was obtained for Johor2020 against 7.07m for the global ellipsoids. There was little difference amongst the three ellipsoids in the values of the residual geoid and residual sravity anomalies, although Johor2020 showed some slight advantage. For the residual gravity disturbances, Johor2020 obtained a mean of -7.38mgals, respectively, which were smaller in magnitude than those obtained by both global ellipsoids; -9.49mgals and -9.35mgals, respectively, for WGS84 and GRS80. Comparing the synthesized undulations obtained with selected GGMs, it was found that the GGMOSG provided the smallest mean of -0.091m. This shows that a best-fitting regional level ellipsoid, together with a suitable geopotential model, san yield geoid undulations with zero expectation values. If the vertical datum bias is known, orthometric heights can be derived from observed ellipsoidal heights alone. In the absence of 1 vertical datum bias, ellipsoidal heights derived with regional level ellipsoids would equal the orthometric heights.
Conclusion Conciusion Based on the initial studies that have been carried out, regional level ellipsoids may be used alongside global geopotential models to compute gravity field functionals, provided the respective zero-degree spherical harmonics are taken into account. Statistical comparisons of the observed gravity field functionals with those obtained by harmonic synthesis using the three llipsoids reveal that the regional normal ellipsoid, Johor2020, performed quite well in recovering the gravity field functionals. For observed undulations, Johor2020 obtained a mean of 1.02m compared to 7.91m for both WGS84 and GRS80. For synthesized undulations, an average of 0.20m was obtained for Johor2020 against 7.07m for the global ellipsoids. There was little difference amongst the three ellipsoids in the values of the residual geoid and residual sravity anomalies, although Johor2020 showed some slight advantage. For the residual gravity disturbances, Johor2020 obtained a mean of -7.38mgals, respectively, which were smaller in magnitude than those obtained by both global ellipsoids; -9.49mgals and -9.35mgals, respectively, for WGS84 and GRS80. Comparing the synthesized undulations obtained with selected GGMs, it was found that the GGMOSG provided the smallest mean of -0.091m. This shows that a best-fitting regional level ellipsoid, together with a suitable geopotential model, san yield geoid undulations with zero expectation values. If the vertical datum bias is known, orthometric heights can be derived from observed ellipsoidal heights alone. In the absence of 1 vertical datum bias, ellipsoidal heights derived with regional level ellipsoids would equal the orthometric heights.
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