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The Indian gravimetric geoid model based on the KTH method of Least Squares modification of the Stokes formula with additive corrections: IndGG-LSMSA2021

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.

The ITU geoid based on Least Squares modification of Stokes integral with additive corrections for the Colorado Experiment: ColLSMSA2020

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 ITU quasi-geoid based on Least Squares modification of Stokes integral with additive corrections for the Colorado Experiment: ColLSMSA2020

The ColLSMSA2020 gravimetric quasi-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 quasi-geoid model over GSVS17 GPS/leveling is 2.7 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 Turkish hybrid geoid: TG-20

The Turkish Geoid Model-2020 (TG-20) is currently the official geoid model for Turkey computed by the General Directorate of Mapping, the national mapping agency. It is a hybrid model extending from 35°N to 43°N and from 25°E to 45°E. It was determined using more than 265,000 point gravity data, as well as the GOCO06S global geopotential model and a digital elevation model of 7.2 arc-second resolution based on SRTM V4.1. Free-air gravity anomalies over marine areas and neighboring countries at 1’×1’ resolution were computed using the XGM2019e model up to degree and order 5399. The computation was based on the Least-Squares Modification of Stokes’ Formula with Additive Corrections (LSMSA) method using the LSMS-GEOLAB scientific software. The transformation of the gravimetric model was carried out via 4-parameter fit to 182 historical and homogenously distributed GPS/levelling data. Absolute validation of the resulting hybrid model with 278 recent GPS/levelling data yielded standard deviations ranging from 1.2 cm to 6.3 cm (below 2 cm at almost every test profile) which brought about considerable improvement over the previous official geoid models. TG-20 with 5 arc-min spatial resolution is freely available to the public. 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 KTH geoid based on Least Squares modification of Stokes integral with additive corrections for the Colorado Experiment: ColLSMSA-KTH2019

The ColLSMSA-KTH2019 gravimetric geoid model has been computed by the University of Gävle, the Lantmäteriet and the Royal Institute of Technology (KTH) in Sweden. The model has been worked out 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 model is 251°E ≤ longitude ≤ 257°E, 36°N ≤ latitude ≤ 39°N with a grid spacing of 1' in both latitude and in longitude. The quasi-geoid is computed using a two-step procedure. First, the terrestrial and de-biased airborne gravity anomalies are gridded using a Remove-Compute-Restore technique and three-dimensional Least Squares Collocation (LSC) with spherical Tscherning and Rapp (1974) type of covariance functions. This step achieves downward continuation of the airborne gravity data and combination with the terrestrial observations. In the second step, the resulting surface gravity anomaly grid is used to compute height anomalies by using Least Squares Modification of Stokes’ formula with Additive corrections (LSMSA or KTH method). The GEOID17RefB global gravity model up to degree 2190 is used in the first gridding step, while the satellite-only GOCO05S model up to degree 240 is used in the second step. Finally, the classical formula by Heiskanen and Moritz (1967) is used for quasi-geoid to geoid conversion. The accuracy of the geoid model, when compared against GSVS17 GPS/leveling, is equal to 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 KTH quasi-geoid based on Least Squares modification of Stokes integral with additive corrections for the Colorado Experiment: ColLSMSA-KTH2019

The ColLSMSA-KTH2019 gravimetric quasi-geoid model has been computed by the University of Gävle, the Lantmäteriet and the Royal Institute of Technology (KTH) in Sweden. The model has been worked out 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 model is 251°E ≤ longitude ≤ 257°E, 36°N ≤ latitude ≤ 39°N with a grid spacing of 1' in both latitude and in longitude. The quasi-geoid is computed using a two-step procedure. First, the terrestrial and de-biased airborne gravity anomalies are gridded using a Remove-Compute-Restore technique and three-dimensional Least Squares Collocation (LSC) with spherical Tscherning and Rapp (1974) type of covariance functions. This step achieves downward continuation of the airborne gravity data and combination with the terrestrial observations. In the second step, the resulting surface gravity anomaly grid is used to compute height anomalies by using Least Squares Modification of Stokes’ formula with Additive corrections (LSMSA or KTH method). The GEOID17RefB global gravity model up to degree 2190 is used in the first gridding step, while the satellite-only GOCO05S model up to degree 240 is used in the second step. The accuracy of the quasi-geoid model, when compared against GSVS17 GPS/leveling, is equal to 2.8 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 GEOF-NTIS geoid based on Least Squares modification of Stokes integral with additive corrections for the Colorado Experiment: ColLSMSA-GEOF2019

The ColLSMSA-GEOF2019 gravimetric geoid model has been computed by the Faculty of Geodesy, University of Zagreb (GEOF) in cooperation with the New technologies for the Information Society, University of West Bohemia (NTIS). It has been worked out 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 model is 251°E ≤ longitude ≤ 257°E, 36°N ≤ latitude ≤ 39°N with a grid spacing of 1' in both latitude and in longitude. The geoid is computed using a two-step procedure. First, the terrestrial and airborne gravity data are gridded by Least Squares Collocation (LSC) with a planar logarithmic covariance model in the framework of a remove-compute-restore procedure. Long wavelengths are modelled by XGM2016 up to degree and order 500, while short wavelengths are taken from the topographic gravity effect. In the second step, the resulting 1'x1' grid of Molodensky-type free-air gravity anomalies is used to compute geoidal heights by using Least Squares Modification of Stokes’ formula with Additive corrections (LSMSA). In particular, the geoidal heights are obtained by using a biased modification of the Stokes kernel (0.5° spherical cap size integration) and then by adding four corrections, namely topographic, downward continuation, atmospheric and ellipsoidal corrections. The accuracy of the geoid model, when compared against GSVS17 GPS/leveling, is equal to 3.9 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 GEOF-NTIS quasi-geoid based on Least Squares modification of Stokes integral with additive corrections for the Colorado Experiment: ColLSMSA-GEOF2019

The ColLSMSA-GEOF2019 gravimetric quasi-geoid model has been computed by the Faculty of Geodesy, University of Zagreb (GEOF) in cooperation with the New technologies for the Information Society, University of West Bohemia (NTIS). It has been worked out 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 model is 251°E ≤ longitude ≤ 257°E, 36°N ≤ latitude ≤ 39°N with a grid spacing of 1' in both latitude and in longitude. The geoid is computed using a two-step procedure. First, the terrestrial and airborne gravity data are gridded by Least Squares Collocation (LSC) with a planar logarithmic covariance model in the framework of a remove-compute-restore procedure. Long wavelengths are modelled by XGM2016 up to degree and order 500, while short wavelengths are taken from the topographic gravity effect. In the second step, the resulting 1'x1' grid of Molodensky-type free-air gravity anomalies is used to compute geoidal heights by using Least Squares Modification of Stokes’ formula with Additive corrections (LSMSA). In particular, the geoidal heights are obtained by using a biased modification of the Stokes kernel (0.5° spherical cap size integration) and then by adding four corrections, namely topographic, downward continuation, atmospheric and ellipsoidal corrections. Finally, the conversion from geoid to quasi-geoid is computed only approximately using the formula by Heiskanen and Moritz (1967). The accuracy of the quasi-geoid model, when compared against GSVS17 GPS/leveling, is equal to 3.6 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.

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