We present results from an airborne gravity campaign conducted in Norway during December 2024 by DTU Space on behalf of the Norwegian Mapping Authority (NMA). One part of the campaign covered the southwestern coast, mapping the marginal land-sea zone to support the realisation of one common future height system for land and sea areas. The second part covered Jostedalsbreen, a region experiencing large gravity variations due to rough topography including high mountains, glaciers and deep fjords. Root-mean-square-error estimates of crossover points show 1.63 mGal and 1.35 mGal, after modelling residual temperature errors in the iMAR system, in the coastal zone and Jostedalsbreen, respectively. Optimum full-width-half-maximum filtering length is found as 70 and 40 s for the two regions, respectively. Comparison with existing (DTU15 and DTU21) global altimetry-derived gravity in the sea area shows standard deviations in the order of 3.69–3.24 mGal. Comparison with a preliminary DTU26 altimetry model, including two years of data from the Surface Water and Ocean Topography (SWOT) mission, shows a standard deviation of 2.56 mGal. Outliers in marine gravity data are detected based on comparison with the airborne gravity data and DTU26. The long-wavelength pattern of the residuals between altimetry and marine gravity data coincides with existing questionable geostrophic currents based on geodetic mean dynamic topography models. This indicates erroneous long-wavelength signal in the underlying gravimetric geoids.
Mission Genesis of the European Space Agency has been approved for launch in 2028. Its primary goal is the enhancement of the terrestrial reference frame by establishing a space tie on the Genesis satellite between all space geodetic techniques used for the determination of the frame. The satellite will be equipped with a dedicated Very Long Baseline Interferometry (VLBI) transmitter for geodesy. In this work, simulation studies with a global 20-station VLBI network are carried out to assess the impact of errors related to the VLBI transmitter on the terrestrial reference frame, more precisely on station coordinates derived from VLBI observations to Genesis. Our findings indicate that the calibration of the position of the VLBI transmitter on Genesis is critical for the success of the mission. Errors in the position at the one-centimeter-level will cause station coordinate errors of several millimeters. In particular, the tangential and cross-track components do have a significant influence. The precision of the VLBI group delays, however, is not as critical. Simulating white noise for the group delays of 40 ps does still yield station coordinate accuracies at the millimeter level, if estimated in a global solution from weekly 24-h sessions over five years. Considering the investigated aspects, the simulations confirm that the VLBI-related goals of Genesis can be achieved, if stringent requirements with the VLBI transmitter are fulfilled.
GRACE/GRACE-FO missions recover gravity field from orbits observed by GPS and variations in inter-satellite distances obtained by the inter-satellite ranging systems. Compared to GRACE, GRACE-FO is also equipped with a laser ranging interferometer (LRI), a more precise inter-satellite ranging technology and the preferred choice for future gravity missions. While the majority of studies predominantly focus on stochastic errors, this research highlights the critical role of non-stochastic biases, specifically the range scale factor for the K-Band ranging (KBR) and LRI data, and baseline biases in GPS observations, i.e., offsets over the 200 km separation. The effects of range scale factor and baseline biases on the gravity field spherical harmonic coefficients (SHCs) are evaluated through simplified bias models (SBM). We demonstrate that baseline biases exert an influence on the SHCs in a manner analogous to that of the range scale factor. At low SH degrees (2–8), range scale factor and baseline biases impact SHCs approximately proportional to the static gravity field coefficients. The SBM agrees well with error-free simulations, but deviations appear at higher degrees (8–60) when background model errors are included and scale biases are below 1 ppm. Additionally, the effectiveness of the SBM is validated using real GRACE-FO data. A strong correspondence was observed between the scale factor corrections and the C20 relative errors, which provides a practical basis for error budgeting in future missions. These findings indicate the significant impact of scale factors and baseline biases on gravity missions, which can be effectively evaluated using the SBM presented here.
The rapid improvement in the accuracy and resolution of satellite mission products requires a detailed modelling of the topographic masses near gravity stations, in order to represent the regional gravity signal as precise as possible. Motivated by the upcoming Next Generation Gravity Mission (NGGM) and Mass change And Geosciences International Constellation (MAGIC) satellite missions, different approaches to perform terrain modelling are evaluated. Up till today, the terrain surface is typically approximated using right rectangular prisms. Here, we implement general polyhedra and tesseroids to represent the topographic surface near twelve selected International Height Reference Frame (IHRF) stations. Especially for the station AUT1 located in Thessaloniki, Greece, both modelling techniques are compared against the classical prismatic approximation. For all applied algorithms, the surface elevation is obtained by the Copernicus Global Digital Elevation Model (DEM) at 30 m resolution. The calculated topographic effects and terrain corrections prove the superiority of a polyhedral representation, which can lead to differences in geoid height definition at the level of 1 m compared to prismatic modelling and 1 cm with respect to tesseroids. The latter are of special interest to the realization of the IHRF in view of the forthcoming NGGM/MAGIC missions, which will offer improved spatial and temporal representations of the Earth’s potential.
When investigating the gravitational field (e.g., gravitational potential, gravitational vector, gravitational gradient tensor, and gravitational curvature) in the spherical coordinate system, there are currently three benchmarks: a spherical shell, a spherical zonal band, and a spherical prism. To obtain simple analytical formulas similar to those of a spherical shell and to reduce computation time with respect to a spherical zonal band, we introduce a spherical longitudinal sector as a new benchmark. It is defined geometrically as the part of a spherical shell confined between two meridians. Alternatively, one can consider the spherical longitudinal sector to be a spherical prism without latitude restrictions, i.e., extending from pole to pole. Based on the relationship with a spherical prism, we derive analytical expressions for the gravitational potential, gravitational vector, gravitational gradient tensor, and gravitational curvature of a homogeneous spherical longitudinal sector when the computation point is on the polar axis. The effectiveness of this proposed benchmark of a spherical longitudinal sector discretized into spherical prisms has been validated through numerical experiments. Numerical results indicate that, compared to a spherical zonal band discretized into spherical prisms, a spherical longitudinal sector improves computational efficiency by a factor of 2, corresponding to a 50
