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 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 gravimetric geoid model xGGM23 was computed at the University of New Brunswick, Canada, with the aim to update the national geoid for Mexico, as well as to contribute to the construction of the regional geoid for North and Central America. Terrestrial gravimetry collected up to year 2020 was processed in spectral combination with the satellite-derived geopotential model GOCO06s (up to degree and order 230) using the UNB’s Stokes-Helmert technique. The geoid model is purely gravimetric, corresponds to the regional standard reference gravity potential for North America (Wo=6263656.0 m2/s2), tide-free gravity concept, and covers latitudes from 10° N to 40° N and longitudes from 125° W to 80° W, with a grid resolution of 2.5 arc minutes. This resolution is coherent with the densification of terrestrial gravity data collected inside Mexico. The accuracy of geoidal height is estimated as 10 cm inside Mexico and 5 cm in the southern US. 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 South American gravimetric geoid model, named GEOID2021, was computed thanks to a collaboration of several institutions, companies and universities of South America. The model covers the area between 15°N and 60°S in latitude and 100°W and 30°W in longitude, with a grid resolution of 5' x 5'. It is based on 959,404 terrestrial gravimetric points, the XGM2019 global geopotential model up to degree and order 200 and the SRTMv3 digital terrain model. The short wavelengths of the solution were estimated via Fast Fourier Transform (FFT) with the modified Stokes kernel proposed by Vaníček and Kleusberg (1987). On the other hand, long and medium wavelengths were removed and replaced in the framework of a remove-compute-restore procedure. Regions without gravimetric observations were completed using XGM2019 to its full degree. The calculation of the geoid model was performed by the Canadian package SHGEO (Stokes-Helmert Geoid Software). The comparison between the estimated geoid heights and GPS/levelling data at 4464 points in Argentina, Chile, Colombia, Ecuador and Venezuela (2931, 176, 464, 703 and 190 points, respectively) shows differences with an RMS ranging from 34 cm for Argentina to 92 cm for Ecuador. 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-MACAS2021 model for the urban area of the Macas City in Ecuadorian Amazon was computed with a non-conventional technique, such as Cokriging (Goovaerts, 1997), through the combination of GPS data/differential leveling and a densely sampled auxiliary variable. The GPS satellite positioning was performed using the Static Differential method through dual-frequency receivers in each point; regarding the level heights they were obtained by first-order differential leveling and the GPS leveling technique. A total of 17 geoid undulation data were used for the computation, while the geoid undulation from the EGM2008 model with a spatial resolution of 1 arc-min was proposed as an auxiliary variable for the interpolation (Odera & Fukuda, 2015). The ordinary Cokriging predictor was used for the study. In order to check the fit of the resulting geoid model, a cross-validation was carried out using the “leave one out” principle, obtained an RMSE of 5.3 cm. In addition, a validation was performed with external GPS/leveling data, reaching an accuracy of 2.1 cm RMSE. This model presents auspicious results for engineering applications, for obtaining level heights quickly and accurately. 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 ColLSMHA2021 geoid gravimetric model has been computed by the Gravity Research Group of the Department of Geomatics Engineering, Istanbul Technical University (ITU-GRG). This is an updated solution with respect to the ColLSMSA2020 geoid model, that has been computed in the frame of the International Association of Geodesy Joint Working Group 2.2.2 "The 1 cm geoid experiment". The area covered by the model is 109°W ≤ longitude ≤ 103°W, 36°N ≤ latitude ≤ 39°N with a grid spacing of 2' in both latitude and in longitude. The computation is based on the Least Squares Modification of Hotine Integral with Additive Corrections (LSMHA). In the computation, the XGM2016 global geopotential model up to degree/order 719 is used. Integration radius for Hotine integral is chosen as 0.5°. The error degree variance of gravity anomalies is constructed using a bandlimited white noise model where standard deviation is taken as 3 mGal. The input gravity data include terrestrial and airborne data combined using 3D Least-Squares Collocation (LSC). The accuracy of the geoid model over GSVS17 GPS/leveling is 2.7 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 ETH-GM21 model is a gravimetric geoid of 2'x2' spatial resolution developed over Ethiopia. This model has been computed using terrestrial and airborne gravity data together with the EIGEN-6C4 GGM and the SRTM3 digital elevation model. The ETH-GM21 model has been determined by using the remove-compute-restore procedure and the least-squares collocation method, obtaining geoid undulations referred to WGS84. With the use of geometric geoid heights obtained from 46 GNSS/levelling data distributed over Ethiopia, the accuracy of the ETH-GM21 gravimetric geoid model has been estimated to ±13 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 ColLSMHA2021 quasi-geoid gravimetric model has been computed by the Gravity Research Group of the Department of Geomatics Engineering, Istanbul Technical University (ITU-GRG). This is an updated solution with respect to the ColLSMSA2020 quasi-geoid model, that has been computed in the frame of the International Association of Geodesy Joint Working Group 2.2.2 "The 1 cm geoid experiment". The area covered by the model is 109°W ≤ longitude ≤ 103°W, 36°N ≤ latitude ≤ 39°N with a grid spacing of 2' in both latitude and in longitude. The computation is based on the Least Squares Modification of Hotine Integral with Additive Corrections (LSMHA). In the computation, the XGM2016 global geopotential model up to degree/order 719 is used. Integration radius for Hotine integral is chosen as 0.5°. The error degree variance of gravity anomalies is constructed using a bandlimited white noise model where standard deviation is taken as 3 mGal. The input gravity data include terrestrial and airborne data combined using 3D Least-Squares Collocation (LSC). The accuracy of the quasi-geoid model over GSVS17 GPS/leveling is 2.6 cm. The quasi-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 IndGG-LSMSA2021 is the Indian Gravimetric Geoid model developed using the Royal Institute of Technology (KTH) method of Least Squares Modification of the Stokes formula with Additive corrections (LSMSA). The method was used to calculate the quasigeoid model, which was converted to the geoid model by applying the geoid-quasigeoid separation term calculated using the method by Flury and Rummel (2009). Data used are terrestrial gravity anomalies from GETECH, satellite-altimeter derived marine gravity anomalies, MERIT digital elevation model, EGM2008 and GO_CONS_GCF_2_DIR_R5 global geopotential models. The LSMSA method was used with various combinations of modification degree and integration radius. This gravimetric geoid model was obtained with the modification degree of 300 and an integration radius of 1°. The IndGG-LSMSA2021 model extends from 7° N to 37° N latitude and 68° E to 98° E longitude with a grid spacing of 0.02°×0.02° and it is referred to the GRS80 ellipsoid. On validation with the available GNSS/levelling data, mean±STD (in m) for India is -0.14±0.43. However, on cluster-wise validation in the four regions of the country, Uttar Pradesh West, Uttar Pradesh East, Hyderabad, and Bangalore, mean±STD (in m) are -0.58±0.13, -0.49±0.10, 0.14±0.16, and 0.79±0.03, respectively. 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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