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The DRUKGEOID2015 model is a geoid of Bhutan, covering the area from 88.5°E to 92.5°E in longitude and from 26.5°N to 28.5°N with a grid resolution of 0.02°. It is referred to the GRS80 ellipsoid and it is based on a set of 255 points with both GNSS and gravity, collected in the framework of this project. Gravity observations were observed by the National Land Commission (NCL) using two CG5 gravimeters. As for the GNSS observations, the positions were computed using the differential GNSS approach for points in the proximity of Permanent Reference Stations (PRS). The Precise Point Positioning (PPP) technique were employed. The DRUKGEOID2015 model was computed by applying the remove-restore procedure, where the used global geopotential model was EIGEN-6C4 and the topography information was taken from the Shuttle Radar Topography Mission (SRTM) model. After the removal step, gravity residual were converted into residual height anomalies using the Least-Squares Collocation (LSC) approach. After the restoring step, height anomalies were converted into geoid undulations using the algorithm by Flury and Rummel (2009) and the SRTM topography. It was decided to fix the resulting gravimetric geoid to the fundamental benchmark at NLC headquarters in Thimphu (TH01). At this point the GNSS ellipsoidal height with respect to the DRUKREF03 system (ITRF2000 at epoch 2003.87) minus the geoid undulation is equal to the official orthometric height. Comparison of 27 GNSS/levelling benchmarks with DRUKGEOID15 showed a standard deviation of 0.55 m. 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 Austrian Geoid 2008 is the official geoid model for Austria provided by the Austrian Federal Office for Metrology and Surveying (BEV). This model describes the transformation surface (EPSG:9276) between ellipsoidal heights w.r.t. the GRS80 ellipsoid (EPSG:4937) and orthometric heights (EVRF2000 Austrian, EPSG:9274). The grid is defined in ETRS89 (EPSG:4258), covering the area within 46.3° < latitude < 49.1° and 9.5° < longitude < 17.3°, with a spacing of 1.5' in latitude and 2.5' in longitude. The model is based on 14001 gravity anomaly values, 672 deflections of the vertical and 170 GPS/levelling observations. The computation was performed in the framework of a remove-restore procedure, modelling the long wavelengths of the gravity field by the EIGEN-GL04S global model, and the short wavelengths by the Airy-Heiskanen model with a standard density of 2670 kg/m3. A digital terrain model with a resolution of 44 x 49 m was assembled as a combination of regional Austrian and Swiss models, as well as SRTM for the neighboring countries. The Least Squares Collocation (LSC) technique was used for the geoid computation, interpolating the empirical covariance of the residual quantities by the Tscherning-Rapp analytic covariance model. Special care was devoted to the optimal relative weighting of the input data, namely to the noise covariance models, especially concerning the GPS/levelling observations. The resulting hybrid geoid model was assessed by comparing it with independent GPS/levelling information, leading to an estimated accuracy of the order of 2-3 cm over the whole Austrian territory. The model is also available at the BEV open data portal, and more information about it can be found on the BEV website. 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 Austrian Geoid 2008 is the official geoid model for Austria provided by the Austrian Federal Office for Metrology and Surveying (BEV). This model describes the transformation surface (EPSG:9277) between ellipsoidal heights w.r.t. the Bessel ellipsoid (datum MGI, EPSG:9267) and orthometric heights (EVRF2000 Austrian, EPSG:9274). The grid is defined in MGI (EPSG:4312), covering the area within 46.3° < latitude < 49.1° and 9.5° < longitude < 17.3°, with a spacing of 1.5' in latitude and 2.5' in longitude. The model is based on 14001 gravity anomaly values, 672 deflections of the vertical and 170 GPS/levelling observations. The computation was performed in the framework of a remove-restore procedure, modelling the long wavelengths of the gravity field by the EIGEN-GL04S global model, and the short wavelengths by the Airy-Heiskanen model with a standard density of 2670 kg/m3. A digital terrain model with a resolution of 44 x 49 m was assembled as a combination of regional Austrian and Swiss models, as well as SRTM for the neighboring countries. The Least Squares Collocation (LSC) technique was used for the geoid computation, interpolating the empirical covariance of the residual quantities by the Tscherning-Rapp analytic covariance model. Special care was devoted to the optimal relative weighting of the input data, namely to the noise covariance models, especially concerning the GPS/levelling observations. The resulting hybrid geoid model was assessed by comparing it with independent GPS/levelling information, leading to an estimated accuracy of the order of 2-3 cm over the whole Austrian territory. The model is also available at the BEV open data portal, and more information about it can be found on the BEV website. 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.
DRUKGEOID2022 is the official geoid model of Bhutan, covering the area from 88.5°E to 92.5°E in longitude and from 26.5°N to 28.5°N in latitude with a grid resolution of 0.02°. It is an update of the previous DRUKGEOID2015 model, that was changed by a bias of 0.8761 m. This update was due to the change of the reference benchmark from the TH01 station at NLC headquarters to the more reliable THIZ station belonging to the national zero-order GNSS/levelling network. In this way, the resulting geoid can be used for the conversion from ellipsoidal heights in the DRUKREF03 system (ITRF2000 at epoch 2003.87) to orthometric heights in the national vertical datum, which is in turns connected to the Indian mean sea level through the neighboring benchmarks in the Indian states of West Bengal and Assam. Comparison of 27 GNSS/levelling benchmarks with DRUKGEOID2022 showed a standard deviation of 0.55 m. 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.
IGGT_R1 is a static gravity field model based on the second invariant of the GOCE gravitational gradient tensor, up to degree and order 240. Based on tensor theory, three invariants of the gravitational gradient tensor (IGGT) are independent of the gradiometer reference frame (GRF). Compared to traditional methods for calculation of gravity field models based on GOCE data, which are affected by errors in the attitude indicator, using IGGT and least squares method avoids the problem of inaccurate rotation matrices. IGGT_R1 is the first experiment to use this method to build a real gravity field model by using GOCE gravitational gradients.This new model has been developed by Wuhan University (WHU), GFZ German Research Centre for Geosciences (GFZ), Technical University of Berlin (TUB), Huazhong University of Science and Technology (HUST) and Zhengzhou Information Engineering University (IEU). More details about the gravity field model IGGT_R1 is given in our paper “The gravity field model IGGT_R1 based on the second invariant of the GOCE gravitational gradient tensor” (Lu et al., 2017, http://doi.org/10.1007/s00190-017-1089-8).This work is supported by the Chinese Scholarship Council (No. 201506270158), the Natural Science Foundation of China (Nos. 41104014, 41131067, 41374023, 41474019 and 41504013) and the Key Laboratory of Geospace Environment and Geodesy, Ministry Education, Wuhan University (No. 16-02-07).
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 ColLSMSA2020 gravimetric geoid model has been computed by the Gravity Research Group of the Department of Geomatics Engineering, Istanbul Technical University (ITU-GRG). The model 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 Stokes Integral with Additive Corrections (LSMSA). In the computation, the XGM2016 global geopotential model up to degree/order 719 is used. Integration radius for Stokes 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 2.9 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 ColWLSC2020 geoid model is a gravimetric model and has been computed by Department of Civil and Environmental Engineering (DICA), Politecnico di Milano. The model has been computed in the frame of the International Association of Geodesy Joint Working Group 2.2.2 "The 1 cm geoid experiment" and the so called "Colorado experiment". The area covered by the models is 108.5°E ≤ longitude ≤ 103.5°E, 36.5°N ≤ latitude ≤ 38°N with a grid spacing of 2' in both latitude and in longitude. The computation is based on the remove-compute-restore technique with XGM2106 being used as a reference field. The topographic effects were treated using a Residual Terrain Correction (RTC) by solving the spectral filter problem of RTC using Earth2014 and ERTM2160 models. The input gravity data include terrestrial and airborne data combined using Least-Squares Collocation (LSC). The final estimation was carried out using Windowed LSC (WLSC). The mean accuracy of the geoid model, when compared against GSVS17 GPS/leveling, is at 3.9 cm level. 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 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.
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