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The Colombian gravimetric quasi-geoid: QgeoidCOL2023

QgeoidCOL2023 is a gravimetric quasi-geoid model for Colombia, computed by the Deutsches Geodätisches Forschungsinstitut (DGFI), Technical University of Munich. The area covered by the model is located from 4.8°S to 12.8°N in latitude and from 79.3°W to 66.7°W in longitude, with a grid spacing of 5' in both latitude and longitude. The input data include terrestrial and airborne gravity data, provided by the Instituto Geográfico Agustín Codazzi (IGAC), as well as satellite altimetry data derived from the DTU21Gra model, all used at their original observation locations. A bias estimation for the airborne gravity surveys was performed using spherical radial basis functions (SRBFs), by comparing the data with the SaTop model up to degree and order 719 (Zingerle, 2022), since the surveys were conducted at different times and by different companies. The quasi-geoid computation is performed in the framework of a remove-compute-restore procedure, using the XGM2019 (Zingerle et al. 2020) as the gravity background model and the Earth2014 (Rexer et al. 2016) / ERTM2160 (Hirt et al. 2014) for the topographic gravity effects. The computation method is based on spherical radial basis functions (SRBFs), using the Shannon function and the Cubic Polynomial (CuP) function for the terrestrial and airborne data, respectively. The terrestrial, airborne, satellite altimetry and topography data observations were combined within a parameter estimation procedure, and the relative weights among them were determined by the method of variance component estimation (VCE). The comparison of the QgeoidCOL2023 quasi-geoid model against GPS/leveling shows differences with a standard deviation of about 16 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 quasi-geoid of Paracel Islands: PIGEOID2021

PIGEOID2021 is a purely gravimetric quasi-geoid model covering the whole Paracel Islands in the northwestern South China Sea. The quasi-geoid is referred to the GRS80 ellipsoid and extends from 15.27°N to 18.23°N and from 110.59°E to 113.30°E with a grid spacing of 30" in both the latitudinal and longitudinal directions. PIGEOID2021 is computed using localised airborne gravity anomalies (with an accuracy of 1.44 mGal at a resolution of 3 km) under the framework of the remove-compute-restore method, where XGM2019e_2159 (truncated to d/o 1080) is used as the reference model and the residual terrain model is applied for smoothing local gravity field at very short scales (< 3 km). The residual gravity field is parameterized using Poisson wavelets by assuming white noise of observations. Comparisons with altimeter-derived geometric quasi-geoid heights retrieved from Jason-2, CryoSat-2, and SARAL show the misfits of PIGEOID2021 are within 5 cm. Further analysis shows PIGEOID2021 reduces the bubble-like errors over island areas by a magnitude exceeding 6 cm compared to existing global geopotential models. 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 DGFI geoid based on spherical radial basis functions for the Colorado Experiment: ColSRBF-DGFI2019

The ColSRBF-DGFI2019 gravimetric geoid model has been computed by the Deutsches Geodätisches Forschungsinstitut (DGFI), Technical University of Munich (TUM). 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. Input data include terrestrial and airborne gravity observations, both used with their original observation sites. The computation method is based on spherical radial basis functions (SRBFs), using the Shannon function and the Cubic Polynomial (CuP) function for the terrestrial and airborne data, respectively. The computation is performed in the framework of a remove-compute-restore procedure, taking XGM2016 as global gravity model and Earth2014 / ERTM2160 for the topographic gravity effects. The terrestrial and airborne observations are combined within a parameter estimation procedure, and the relative weight between these two types of observations are determined by the method of variance component estimation (VCE). 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 3.0 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 DGFI quasi-geoid based on spherical radial basis functions for the Colorado Experiment: ColSRBF-DGFI2019

The ColSRBF-DGFI2019 gravimetric quasi-geoid model has been computed by the Deutsches Geodätisches Forschungsinstitut (DGFI), Technical University of Munich (TUM). 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. Input data include terrestrial and airborne gravity observations, both used with their original observation sites. The computation method is based on spherical radial basis functions (SRBFs), using the Shannon function and the Cubic Polynomial (CuP) function for the terrestrial and airborne data, respectively. The computation is performed in the framework of a remove-compute-restore procedure, taking XGM2016 as global gravity model and Earth2014 / ERTM2160 for the topographic gravity effects. The terrestrial and airborne observations are combined within a parameter estimation procedure, and the relative weight between these two types of observations are determined by the method of variance component estimation (VCE). The accuracy of the quasi-geoid model, when compared against GSVS17 GPS/leveling, is equal to 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 Belgian hybrid quasi-geoid: hBG18

hBG2018 is the hybrid quasi-geoid model for Belgium, including both the Belgian mainland and the Exclusive Economic Zone. The hBG18 quasi-geoid heights are referred to the ETRS89/GRS80 ellipsoid. It is computed using radar altimetry data, terrestrial gravity anomalies, airborne gravity disturbances, and shipboard gravity anomalies. The quasi-geoid computation is based on the remove-compute-restore procedure. The long-wavelength signal content in the data is reduced by removing the contribution of the GOCO05S global gravity field model complete to degree 280. At the very short wavelengths, residual terrain modelling (RTM) is applied to the shipboard, terrestrial and airborne gravity datasets using EuroDEM as input data. The residual disturbing potential is parameterized over the target area using Spherical Radial Basis Functions (SRBF). The SRBF coefficients and bias parameters for the sets of gravity anomalies and disturbances are estimated using weighted least-squares with regularization, assuming white noise. To support the exploitation of the hBG2018 gravimetric quasi-geoid for the conversion of GNSS derived heights to the TAW/DNG height system, several post-processing steps were applied. First, as the TAW/DNG height system is a mean-tide height system (i.e., mean-tide crust = zero crust over mean-tide geoid) the quasi-geoid was transformed from the zero-tide to the mean tide system. Thereafter, a corrector surface (also called 'innovation function') has been estimated from the differences between the geometric quasi-geoid at 3707 GNSS/leveling points and the gravimetric quasi-geoid. This surface also accounts for the difference between the fictitious datum point of the gravimetric hBG18 and the datum point of the TAW/DNG. Finally, the transformation from the tide-free permanent tide system adopted in the GNSS community and the mean-tide system adopted in TAW/DNG, has been applied. hBG18 replaces hBG03 as the official Belgian model since August 1, 2018. 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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