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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.
The gravimetric quasi-geoid model for the State of Minas Gerais covers the longitude range of -38º to -53º and the latitude range of -12º to -25º, with a resolution of 5 arc minutes. A total of 49,067 terrestrial gravity values were utilized to compute Molodenski's gravity anomalies. The quasi-geoid model was computed by the Least Squares Collocation method. The XGM2019 geopotential model up to degree and order 300 was employed to represent the long-wavelengths of the gravity field. The digital terrain model SRTM15+ was selected for the RTM computation, while the DTU17 gravity field model was used in oceanic areas. The quasi-geoid model was validated against 136 GNSS/leveling stations, yielding a bias of 23 cm and a standard deviation of 11 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 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 local geoid for Madeira was computed using strapdown airborne gravimetry measurements taken on 27 and 31 August 2010 as part of the GEOMAD campaign. The inertial measurements were acquired with an iXsea IMU. The observations made during the turns of the aircraft were disregarded and a decimation to a 50 second sampling was applied. The geoid determination was based on the standard remove-restore technique with EGM2008 as reference global geopotential model and SRTM for the computation of the residual terrain correction. The Least-Squares Collocation approach was used to convert the residual gravity disturbances at flight level into height anomalies at sea level. The subsequent conversion of height anomalies into geoid undulations was based on the corrections provided with the EGM2008 model. The datum of the local geoid model is WGS84, given in the tide-free system. According to the Least-Squares Collocation procedure the errors are around 5 cm, however a more realistic estimate of the uncertainty is of the order 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.
This gravimetric geoid model of São Paulo State, Brazil, has been computed by remove-restore technique using Least Squares Collocation (LSC). The reference geopotential model is GO_CONS_GCF_2_DIR_R3 up to degree and order 150. The SAM3s_v2 DTM has been used for the computation of terrain correction and other topographic and atmospheric effects. The mean free-air gravity anomaly (FA) in a 5'x5' grid over continent has been derived from the complete Bouguer anomalies (FA over the ocean has been obtained from the DTU10 satellite gravity model). Geoidal heights, referred to the GRS80 ellipsoid, have been computed on a grid of 5'x5' covering the area from 17°S to 28°S in latitude and from 56°W to 42°W in longitude. The resulting model has been verified by comparing them with 363 GPS/leveling points distributed all over the area, showing differences with a root mean square of 0.20 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 Sudanese SUD-GM2014 gravimetric geoid model has been computed from the available terrestrial mean free-air gravity anomalies, the TIM-R4 GOCE-only global geopotential model, and the high-resolution SRTM30_PLUS global digital elevation model. The computation has been performed by using the remove-compute-restore procedure and the least squares collocation method. Thereafter, the SUD-GM2014 model has been evaluated by using geoid heights at 19 GNSS/levelling points distributed over the country, showing an overall accuracy of 30 cm. However, this estimate of the geoid model quality could not be fully representative due to the low accuracy, very limited number and inhomogeneous distribution of the used GNSS/levelling control points. The SUD-GM2014 model has been recommended as reference for GNSS heighting in Sudan. 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.
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