RIO2QG_FFT_2025 is a local, high-precision, high-resolution, pure-gravimetric quasigeoid model developed for the area surrounding RIO2, an International Height Reference Frame (IHRF) station located in the Province of Tierra del Fuego, Argentina, covering latitudes 56°S to 51°S and longitudes 71°W to 64°W, with a 0.03° grid resolution. The purpose of the model is to determine the IHRF vertical coordinate at this station. Its computation followed Molodensky’s formulation of the Geodetic Boundary Value Problem (GBVP) and employed the remove–compute–restore (RCR) strategy. Long-wavelength components were modeled using the XGM2019e Global Geopotential Model (GGM) up to degree and order 700. Topographic contributions were modeled via Residual Terrain Modeling (RTM) using the SRTM v4.1 Digital Elevation Model (DEM). Residual height anomalies were calculated with the 1D-FFT technique incorporating the Wong-Gore modification to Stokes’ kernel. All computational steps were performed with the GRAVSOFT software package. Validation against 41 GNSS/leveling points yielded an estimated precision of 0.061 m after applying a four-parameter fit. 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.
UNSAQG_FFT_2025 is a local, high-precision, high-resolution, pure-gravimetric quasigeoid model developed for the area surrounding UNSA, an International Height Reference Frame (IHRF) station located in the Province of Salta, Argentina, covering latitudes 26.5°S to 24.5°S and longitudes 66°W to 64°W, with a 0.03° grid resolution. The purpose of the model is to determine the IHRF vertical coordinate at this station. Its computation followed Molodensky’s formulation of the Geodetic Boundary Value Problem (GBVP) and employed the remove–compute–restore (RCR) strategy. Long-wavelength components were modeled using the XGM2019e Global Geopotential Model (GGM) up to degree and order 800. Topographic contributions were modeled via Residual Terrain Modeling (RTM) using the SRTM v4.1 Digital Elevation Model (DEM). Residual height anomalies were calculated with the 1D-FFT technique incorporating the Wong-Gore modification of Stokes’ kernel. All computational steps were performed with the GRAVSOFT software package. Validation against 51 GNSS/leveling points yielded an estimated precision of 0.124 m after applying a four-parameter fit. 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.
OAFAQG_FFT_2025 is a local, high-precision, high-resolution, pure-gravimetric quasigeoid model developed for the area surrounding OAFA and UNSJ, two International Height Reference Frame (IHRF) stations located in the Province of San Juan, Argentina, covering latitudes 34°S to 30°S and longitudes 70.5°W to 65.5°W, with a 0.03° grid resolution. The purpose of the model is to determine the IHRF vertical coordinate at these stations. Its computation followed Molodensky’s formulation of the Geodetic Boundary Value Problem (GBVP) and employed the remove–compute–restore (RCR) strategy. Long-wavelength components were modeled using the XGM2019e Global Geopotential Model (GGM) up to degree and order 840. Topographic contributions were modeled via Residual Terrain Modeling (RTM) using the SRTM v4.1 Digital Elevation Model (DEM). Residual height anomalies were calculated with the 1D-FFT technique incorporating the Wong-Gore modification of Stokes’ kernel. All computational steps were performed with the GRAVSOFT software package. Validation against 188 GNSS/leveling points yielded an estimated precision of 0.170 m after applying a four-parameter fit. 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.
UNPAQG_FFT_2025 is a local, high-precision, high-resolution, pure-gravimetric quasigeoid model developed for the area surrounding UNPA, an International Height Reference Frame (IHRF) station located in the Province of Santa Cruz, Argentina, covering latitudes 54°S to 50°S and longitudes 72°W to 66°W, with a 0.03° grid resolution. The purpose of the model is to determine the IHRF vertical coordinate at this station. Its computation followed Molodensky’s formulation of the Geodetic Boundary Value Problem (GBVP) and employed the remove–compute–restore (RCR) strategy. Long-wavelength components were modeled using the XGM2019e Global Geopotential Model (GGM) up to degree and order 740. Topographic contributions were modeled via Residual Terrain Modeling (RTM) using the SRTM v4.1 Digital Elevation Model (DEM). Residual height anomalies were calculated with the 1D-FFT technique incorporating the Wong-Gore modification of Stokes’ kernel. All computational steps were performed with the GRAVSOFT software package. Validation against 81 GNSS/leveling points yielded an estimated precision of 0.092 m after applying a four-parameter fit. 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.
AGGOQG_FFT_2025 is a local, high-precision, high-resolution, pure-gravimetric quasigeoid model developed for the area surrounding AGGO and LPGS, two International Height Reference Frame (IHRF) stations located in the Province of Buenos Aires, Argentina, covering latitudes 36°S to 31°S and longitudes 61°W to 55°W, with a 0.03° grid resolution. The purpose of the modelis to determine the IHRF vertical coordinate at these stations. Its computation followed Molodensky’s formulation of the Geodetic Boundary Value Problem (GBVP) and employed the remove–compute–restore (RCR) strategy. Long-wavelength components were modeled using the XGM2019e Global Geopotential Model (GGM) up to degree and order 600. Topographic contributions were modeled via Residual Terrain Modeling (RTM) using the SRTM v4.1 Digital Elevation Model (DEM). Residual height anomalies were calculated with the 1D-FFT technique incorporating the Wong-Gore modification of Stokes’ kernel. All computational steps were performed with the GRAVSOFT software package. Validation against 111 GNSS/leveling points yielded an estimated precision of 0.063 m after applying a four-parameter fit. 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 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 official Uruguayan geoid model, called IGM110, was calculated by the Military Geographic Institute (IGM) in 2023 and consists of a grid of 1´ x 1´ geoidal undulations with a total of 151,981 points. The geodetic reference system is SIRGAS ROU-98 (the reference ellipsoid is GRS80). 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. 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 resulting geoid was also adapted by a bias and a tilt to the national vertical system, Cabildo 1948, by fitting GNSS/levelling observations, with a mean of 1 cm and a standard deviation of 7 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 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.
The MK_HREF2022 quasi-geoid model is a height reference surface for North Macedonia, referred to the GRS80 ellipsoid. It was computed by the Agency for Real Estate Cadastre of the Republic of North Macedonia, in cooperation with the Norwegian Mapping Authority (Kartverket), and it is given in the form of a regular grid, with resolution of 0.01° × 0.01°, within the limits of 40.8° < latitude < 42.4° and 20.4° < longitude < 23.1°. The model is based on a set of relatively new gravity data measured in 2014 (along the high accuracy levelling lines and in the frame of the regional gravimetric survey), in total 2470 points in mean-tide system. Stokes/Molodensky equations and the Fast Fourier transform technique were applied in the calculations, with use of the global geopotential model EGM2008. The computed quasi-geoid surface was fitted to 77 high quality GNSS/levelling points, fairly distributed throughout the territory of the country. The resulting height reference surface allows the conversion between ellipsoidal heights (ETRS89, epoch 1989.0) and heights in the official national height system (NVT1, datum Trieste 1875.0, normal orthometric heights). The inner accuracy of the calculated quasi-geoid model is 4.0 cm, while the outer accuracy (based on 1035 control GNSS/levelling measurements along levelling lines) is up to 10 cm. MK_HREF2022 is the official quasi-geoid model for North Macedonia since November 28, 2025. 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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