The Uruguayan gravimetric geoid model UruGeoide110 was calculated by the Military Geographic Institute (IGM) in 2023. The extent is from 29.5° S to 35.5° S in latitude, and 52.5° W to 59.5° W in longitude, covering parts of Argentina and Brazil, with a grid resolution of 1´ x 1´. The geodetic reference system is SIRGAS ROU-98 (the reference ellipsoid is GRS80). The model is a combination of the EIGEN-6C4 geopotential model up to degree and order of 720, 10,429 land gravimetric stations plus 10,089 free air gravity anomalies in marine areas, based on the DTU13 model. The terrain data at the final 90 m resolution was taken from a 2017 Lidar survey in Uruguay with a 2.5 m initial resolution and SRTM (V2) for the external terrestrial data. The DT18 bathymetry model was used for the marine areas. Due to the total terrain data points (about 104 million), the overall area was divided into 4 overlapped blocks in the framework of the remove-compute-restore procedure. The reduced height anomalies were computed from the reduced gravity anomalies with Stokes 1D FFT and Wong Gore´s kernel modification (170-180 degrees). After adding back the residual terrain model effects and the contribution of the global geopotential model, the obtained quasi-geoid was transformed into a geoid model via Bouguer anomalies, even if the difference between the two models is just a few mm. A comparison with 51 GNSS/levelling stations shows a standard deviation of 10 cm. The geoid model is provided in ISG format 2.0 (ISG Format Specifications), while the file in its original data format is available at the model ISG webpage.
The Uruguayan gravimetric quasi-geoid model UruQGeoide110 was calculated by the Military Geographic Institute (IGM) in 2023. The extent is from 29.5° S to 35.5° S in latitude, and 52.5° W to 59.5° W in longitude, covering parts of Argentina and Brazil, with a grid resolution of 1´ x 1´. The geodetic reference system is SIRGAS ROU-98 (the reference ellipsoid is GRS80). The model is a combination of the EIGEN-6C4 geopotential model up to degree and order of 720, 10,429 land gravimetric stations plus 10,089 free air gravity anomalies in marine areas, based on the DTU13 model. The terrain data at the final 90 m resolution was taken from a 2017 Lidar survey in Uruguay with a 2.5 m initial resolution and SRTM (V2) for the external terrestrial data. The DT18 bathymetry model was used for the marine areas. Due to the total terrain data points (about 104 million), the overall area was divided into 4 overlapped blocks in the framework of the remove-compute-restore procedure. The reduced height anomalies were computed from the reduced gravity anomalies with Stokes 1D FFT and Wong Gore´s kernel modification (170-180 degrees) and the quasi-geoid model was finally obtained by adding back the residual terrain model effects and the contribution of the global geopotential model. The geoid model is provided in ISG format 2.0 (ISG Format Specifications), while the file in its original data format is available at the model ISG webpage.
The Uruguayan gravimetric geoid model UruGeoide2007 was calculated by the Military Geographic Service (SGM) in 2007. The extent is from 29° S to 36° S in latitude and 52° W to 60° W in longitude, with a grid resolution of 1´ x 1´. The geodetic reference system is WGS84. The computation was based on the remove-restore procedure, using 8433 gravity observations from stations in Argentina, Brasil and Uruguay, 9172 marine free-air gravity anomalies from the KMS02 model, the GGM02C geopotential model, the SRTM terrain model and the DNSC05 bathymetric model. The reduced height anomalies were computed from the reduced gravity anomalies by Stokes integration via spherical Fast Fourier Transform. After adding back the residual terrain model effects and the contribution of the global geopotential model, the obtained quasi-geoid was transformed into a geoid model by using a Bouguer anomaly grid, even if the difference between the two models is 1 cm at most. The geoid model is provided in ISG format 2.0 (ISG Format Specifications), while the file in its original data format is available at the model ISG webpage.
The geoid model of São Paulo State was computed using the updated and filtered gravimetric data and the new system of the normal height of the 2018 Brazilian Vertical Reference Frame (BVRF). For the ocean area, gravity anomalies of the DTU13 model with a resolution of 1’ were used. To quantify the terrain effects through the Residual Terrain Model procedure, the SRTM15+ DTM was used. The computation of the quasi-geoid model was performed by numerical integration through the Fast Fourier Transform (FFT). The Molodensky gravity anomaly was determined in a 5’x5’ grid and reduced and restored using the Residual Terrain Model (RTM) technique and the XGM2019e global gravity model truncated at degree and order 720. The geoid model was derived from the Bouguer gravity anomalies. The zero-order degree term was added in the final computation. The validation for the quasi-geoid model based on 291 GPS measurements in the leveling network has shown 18 cm RMS difference. The geoid model is provided in ISG format 2.0 (ISG Format Specifications), while the file in its original data format is available at the model ISG webpage.
The geoid model of São Paulo State was computed using the updated and filtered gravimetric data and the new system of the normal height of the 2018 Brazilian Vertical Reference Frame (BVRF). For the ocean area, gravity anomalies of the DTU13 model with a resolution of 1’ were used. To quantify the terrain effects through the Residual Terrain Model procedure, the SRTM15+ DTM was used. The computation of the quasi-geoid model was performed by numerical integration through the Fast Fourier Transform (FFT). The Molodensky gravity anomaly was determined in a 5’x5’ grid and reduced and restored using the Residual Terrain Model (RTM) technique and the XGM2019e global gravity model truncated at degree and order 250. The geoid model was derived from the Bouguer gravity anomalies. The zero-order degree term was added in the final computation. The validation for the quasi-geoid model based on 291 GPS measurements in the leveling network has shown 18 cm RMS difference. The geoid model is provided in ISG format 2.0 (ISG Format Specifications), while the file in its original data format is available at the model ISG webpage.
UruGeoide2000 is a hybrid geoid model for Uruguay computed in 2000. The extent is from 29° S to 36° S in latitude and 52° W to 60° W in longitude, however the model is valid in the Uruguayan territory only. The grid resolution is 1´ × 1´. The geodetic reference system is SIRGAS ROU-98 (the reference ellipsoid is GRS80). A gravimetric model was initially computed through the remove-restore procedure, using 5873 ground gravity observations, 9987 marine free-air gravity anomalies from the GMGA9706 model and the EGM96 geopotential model. The topographic data were compiled from the 2 km × 2 km SGM digital terrain model, the 2.5' × 2.5' USP model and from the GTOPO30 global topographic model. The external masses to the geoid was considered with the second Helmert condensation method, taking in account the indirect effect. The gravimetric contribution was calculated using residual free-air anomalies in the spherical Stokes formula, evaluated with 1D-FFT. The resulting gravimetric geoid was finally adapted by a bias and a tilt to the national vertical system, Cabildo 1948, by fitting GPS/levelling observations, with a resulting accuracy of 13 cm. The UruGeoide2000 model was adopted by the Military Geographic Service (SGM) and it was the official Uruguayan geoid model for height conversion until the computation of an updated model in 2007. The geoid model is provided in ISG format 2.0 (ISG Format Specifications), while the file in its original data format is available at the model ISG webpage.
The geoid model for Taiwan, including the Kinmen and Matzu islands, covers the area 118°E–125°E and 21°N–27°N with a grid resolution of 30" x 30". The gravimetric model is based on land, shipborne and airborne gravity data, as well as marine gravity derived from satellite altimetry. After merging data by least-squares collocation, a remove-restore procedure is applied. First height anomalies are computed by 1D FFT with Wong-Gore modification of the Stokes kernel and then they are converted into the geoid heights. The reference global gravity model is EGM2008 up to degree and order 2190. The used digital terrain model is derived from several photogrammetric surveys at a resolution of 3"×3" and 9"×9" for the inner and outer zone, respectively. The gravimetric model is finally adapted to GPS/levelling data at more than 2000 benchmarks. To this aim, an interpolation based on the minimum curvature principle (GMT command) is adopted. The resulting hybrid geoid model provides the transformation surface between the conventional Taiwan Vertical Datum (TWVD2001) and Taiwan Datum 97 (TWD97). The gravimetric model fits the GPS/levelling control points with a standard deviation of 7.9 cm (and a mean difference of 21.9 cm), while the hybrid solution fits them with a standard deviation of 3.6 cm (and a mean difference of -0.9 cm). The geoid model is provided in ISG format 2.0 (ISG Format Specifications), while the file in its original data format is available at the model ISG webpage.
The Brazilian geoid model MAPGEO2010 is limited by 6°N and 35°S in latitude and 30°W and 75°W in longitude with a 5' resolution. The terrestrial gravity data for the continent have been updated by surveys in Brazil and in the neighbour countries until 2010. The complete Bouguer and Helmert gravity anomalies have been derived through the Canadian package SHGEO. The short wavelength component was estimated via FFT. The geopotential model EGM2008 was used as a reference field restricted to degree and order 150. The geoid height was corrected from the zero-order term, -0.41 meter, for compatibility with the GRS80 ellipsoid, used by SIRGAS2000. The RMS difference associated with the MAPGEO2010 model was ±0.28 meter, determined from the comparison of IBGE GPS/levelling points. The geoid model is provided in ISG format 2.0 (ISG Format Specifications), while the file in its original data format is available at the model ISG webpage.
The quasi-geoid model of São Paulo State was computed using the updated and filtered gravimetric data and the new system of the normal height of the 2018 Brazilian Vertical Reference Frame (BVRF). For the ocean area, gravity anomalies of the DTU13 model with a resolution of 1’ were used. To quantify the terrain effects through the Residual Terrain Model procedure, the SRTM15+ DTM was used. The computation of the quasi-geoid model was performed by numerical integration through the Fast Fourier Transform (FFT). The Molodensky gravity anomaly was determined in a 5’x5’ grid and reduced and restored using the Residual Terrain Model (RTM) technique and the XGM2019e global gravity model truncated at degree and order 720. The zero-order degree term was added in the final computation. The validation for the quasi-geoid model based on 291 GPS measurements in the leveling network has shown 18 cm RMS difference. The geoid model is provided in ISG format 2.0 (ISG Format Specifications), while the file in its original data format is available at the model ISG webpage.
The quasi-geoid model of São Paulo State was computed using the updated and filtered gravimetric data and the new system of the normal height of the 2018 Brazilian Vertical Reference Frame (BVRF). For the ocean area, gravity anomalies of the DTU13 model with a resolution of 1’ were used. To quantify the terrain effects through the Residual Terrain Model procedure, the SRTM15+ DTM was used. The computation of the quasi-geoid model was performed by numerical integration through the Fast Fourier Transform (FFT). The Molodensky gravity anomaly was determined in a 5’x5’ grid and reduced and restored using the Residual Terrain Model (RTM) technique and the XGM2019e global gravity model truncated at degree and order 250. The zero-order degree term was added in the final computation. The validation for the quasi-geoid model based on 291 GPS measurements in the leveling network has shown 18 cm RMS difference. The geoid model is provided in ISG format 2.0 (ISG Format Specifications), while the file in its original data format is available at the model ISG webpage.
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