We present an iterative approach for solving the nonlinear satellite-fixed geodetic boundary value problem (NSFGBVP) by the finite element method that is applied for a determination of local quasigeoid in Himalayas and Andes. At first, we formulate the NSFGBVP that consists of the Laplace equation holding in the 3D bounded domain outside the Earth, the nonlinear boundary condition (BC) prescribed on the disretized Earth's surface, and the Dirichlet BC given on a spherical boundary placed approximately at the altitude of chosen satellite mission and additional four side boundaries. Then the iterative approach is based on determining the direction of actual gravity vector together with the value of the disturbing potential. Such a concept leads to the first iteration where the oblique derivative boundary value problem is solved, and the last iteration represents the approximation of the actual disturbing potential and the direction of gravity vector. As a numerical method for our approach, we have implemented the finite element method with triangular prisms. Finally, we present a high-resolution numerical experiment dealing with the local gravity field modelling in Himalayas and Andes.

How to cite: Macák, M., Minarechová, Z., Čunderlík, R., and Mikula, K.: A local quasigeoid determination by solving the nonlinear satellite-fixed geodetic boundary value problem, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-13000, https://doi.org/10.5194/egusphere-egu23-13000, 2023.

Spherical harmonic expansions are routinely used to represent the gravitational potential and its higher-order spatial derivatives in global geodetic, geophysical, and planetary science applications. The convergence domain of external spherical harmonic expansions is the space outside the minimum Brillouin sphere (the smallest sphere containing all masses of the planetary body). Nevertheless, these expansions are commonly employed inside this bounding surface without any corrections. Justification of this procedure has been debated for several decades, but conclusions among scholars are indefinite and even contradictory.

In this contribution, we examine the use of external spherical harmonic expansions for the gravitational field modelling inside the minimum Brillouin sphere. We employ the most recent lunar topographic LOLA (Lunar Orbiter Laser Altimeter) products and the measurements of the lunar gravitational field by the GRAIL (Gravity Recovery and Interior Laboratory) satellite mission. We analyse selected quantities calculated from the most recent GRAIL-derived gravitational field models and forward-modelled (topography-inferred) quantities synthesised by internal/external spherical harmonic expansions. The comparison is performed in the spectral domain (in terms of degree variances depending on the spherical harmonic degree) and in the spatial domain (in terms of spatial maps). To our knowledge, GRAIL is the first gravitational sensor ever, which helped to resolve the long-lasting convergence/divergence problem for the analytical downward continuation of the external spherical harmonic expansions, see (Šprlák and Han, 2021).

References

Šprlák M, Han S-C (2021) On the Use of Spherical Harmonic Series Inside the Minimum Brillouin Sphere: Theoretical Review and Evaluation by GRAIL and LOLA Satellite Data. Earth-Science Reviews, 222, 103739, https://doi.org/10.1016/j.earscirev.2021.103739.

How to cite: Šprlák, M., Han, S.-C., Pitoňák, M., and Novák, P.: Evaluation of external spherical harmonic series inside the minimum Brillouin sphere: examples for the lunar gravitational field, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-3913, https://doi.org/10.5194/egusphere-egu23-3913, 2023.

In this contribution, we will discuss a problem of regional gravitational field modelling by the spectral combination of spaceborne first-, second- and third-order radial derivatives of the gravitational potential at the mean altitude of 250 km. Some of the mentioned measurements are not observable yet, so we will synthesize them from a global geopotential model over a test area. The main goal of a numerical experiment is to compute the gravitational field in a regional area from spatially restricted higher-order radial derivatives of disturbing potential, and two problems arise. The first is how to estimate local spectral properties, i.e., degree-order variances of local data, and the second is the effect of the omitted distant zone data, i.e., (spatial) truncation error. The spherical harmonic power spectrum from local data will be recovered by 2D-DFT, and the truncation error will be calculated from a global geopotential model. For this purpose, a mathematical model based on the spectral combination method of heterogeneous gravity field data and a global geopotential model is developed. The correctness of derived spectral weights suitable for spectral downward continuation will be verified by a closed-loop test and by direct comparison with the global solution. Moreover, different sizes of a data area (area covered by simulated satellite measurements) to minimize the truncation error and various truncation degrees of a global geopotential model will be tested.

How to cite: Pitoňák, M., Šprlák, M., and Novák, P.: Regional gravitational field modelling by the spectral combination of satellite higher-order radial derivatives of the gravitational potential and a global geopotential model, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-2718, https://doi.org/10.5194/egusphere-egu23-2718, 2023.

In recent years, high-order gravitational potential gradients and variable density models are the potential research topics in gravity field modeling. This paper focuses on the variable density model for gravitational curvatures (or gravity curvatures, third-order derivatives of gravitational potential) of a tesseroid and spherical shell in the spatial domain of gravity field modeling. In this contribution, the general formula of the gravitational curvatures of a tesseroid with arbitrary order polynomial density is derived. The general expressions for gravitational effects up to the gravitational curvatures of a spherical shell with arbitrary order polynomial density are derived when the computation point is located above, inside, and below the spherical shell. The influence of the computation point's height and latitude on gravitational curvatures with the polynomial density up to fourth order is numerically investigated using tesseroids to discretize a spherical shell. Numerical results reveal that the near-zone problem exists for the fourth-order polynomial density of the gravitational curvatures, i.e., relative errors in log10 scale of gravitational curvatures are large than 0 below the height of about 50 km by a grid size of 15'x15'. The polar-singularity problem does not occur for the gravitational curvatures with polynomial density up to fourth order because of the Cartesian integral kernels of the tesseroid. The density variation can be revealed in the absolute errors as the superposition effects of Laplace parameters of gravitational curvatures other than the relative errors. The derived expressions are examples of the high-order gravitational potential gradients of the mass body with variable density in the spatial domain, which will provide the theoretical basis for future applications of gravity field modeling in geodesy and geophysics. This study is supported by the Alexander von Humboldt Foundation in Germany.

How to cite: Deng, X.-L.: Gravitational curvatures for a tesseroid and spherical shell with arbitrary order polynomial density, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-3881, https://doi.org/10.5194/egusphere-egu23-3881, 2023.

Abstract: Global Navigation Satellite System-Reflectometry (GNSS-R) technique has been used to obtain sea surface height (SSH) since the 1990s. Due to the short wavelengths and low power of GNSS signals, the continuously tracked carrier phase measurements of reflected signals are usually unavailable for sea surfaces with big roughness, varying over space and time. Under high sea states, the phase difference cannot be well retrieved from carrier phase measurements, especially for the signals with high elevation angles. To overcome these shortcomings related to temporal incoherence, we propose an improved algorithm to extract the combined interferometric phase difference measurements between direct and reflected signals. We improve the configuration of GNSS-R altimetry software-defined receiver (SDR) by reconstructing ‘clean’ direct signals to compute phase differences between direct and reflected signals. The interferometric phase differences are combined in the complex domain and the resulting interferometric signal is refined through open-loop tracking with 60-s coherent integration before the phase difference measurements are extracted, without tracking their respective carrier phase measurements in advance.  In order to verify our method, a coastal experiment under different sea conditions was conducted. Raw intermediate frequency data of Quasi-Zenith Satellite System were collected and processed by SDR to compute the path delay measurements of L1 and L5. Under high sea states, the phase delay measurements of L1 and L5 were random over time, while phase delay can still be well recovered based on the proposed method even in the case of high elevation angles. The altimetry solutions were compared with the in situ observations from a radar altimeter instrument. The results show that centimeter-level altimetry accuracy can be achieved under high sea states using the proposed method The same SDR and method are applied in the shipborne altimetry experiment, the interferometric phase observations are successfully extracted on both ship motion and statics. Also, the integer ambiguity in the interferometric phase observations is well estimated. The differences in the SSH measurements between different satellites is at centimeter level. The coastal and shipborne experiments demonstrate that the dual-antenna GNSS-R phase altimetry technique can be used for low-cost tide gauges on different platforms to monitor sea levels.

Acknowledgments: This work was supported by Natural Science Foundation of China (42192534) and Key Research and Development Program of Shandong Province (Major Technological Innovation Project, 2021ZDSYS01).

How to cite: Xu, T., He, Y., Gao, F., and Meng, X.: High-precision GNSS-R Altimetry based on Carrier Phase Measurement Combination, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-4062, https://doi.org/10.5194/egusphere-egu23-4062, 2023.

The physics-informed neural networks (PINN) are emerging as a new tool for gravity field modeling. In some scenarios, such as near-source gravitational fields representation, PINN may have greater potential than traditional spherical/ellipsoidal harmonics solutions, as the latter suffers from both theoretical and numerical divergence problems for sources with complex geometry. By incorporating observational, geometrical and statistical density information into the neural network, we aim to reduce the non-uniqueness of the solution space, therefore obtaining improved accuracy in representing gravity fields, especially near the source body. By transforming the trained gravitational potential into density distribution through Poisson's equation, we also provide a new perspective to observe the evolution of the neural network for gravity field modeling as "redistribution of equivalent density sources". The influence of multiple parameters of the neural network on the performance of the PINN gravity modeling, including its size and shape, distribution of Laplacian and Poisson collocation points, and balance between loss functions of the multiple constraints applied, are also investigated. Numerical results are illustrated using the EROS asteroid model and a regional DEM model of Colorado Geoid Experiment area.

How to cite: Wu, L., Chen, L., Livermore, P., de Ridder, S., and Zhang, C.: Physics-Informed neural networks for gravity field modeling incorporating observation, geometry and density constraints, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-8952, https://doi.org/10.5194/egusphere-egu23-8952, 2023.

In several geodetic studies, the triaxiality of the Earth has been proven beyond a reasonable doubt, thus a triaxial ellipsoid is a better approximation and a more natural reference surface. As opposed to geodesics, plane curves on this surface are relatively easy to solve. These curves are produced by the intersection of a central ellipsoid and a plane and it is proved that they are in general ellipses. Therefore, we study the problems of the computation of an arc length of an ellipse and the determination of a point after a given length on an ellipse, using either a numerical or an approximate analytical method. Also, all the required transformations of the coordinates from the plane of the section to 3D space and conversely, are given. Subsequently, five types of planes of the ellipsoidal sections are determined: the central section, two normal sections, and two mean normal sections. Furthermore, the algorithms that solve the direct and inverse problems for these plane curves on a triaxial ellipsoid are described. Extended numerical experiments demonstrate the workability of the presented method which can also be applied to other celestial bodies. All developments in the literature assume the presence of an oblate spheroid and include an iterative scheme to solve the aforementioned problems. Alternatively, in this work, we provide the most general solutions to these problems applicable and for an oblate spheroid and all types of sections, without iterations.

How to cite: Filaretou, C. and Panou, G.: Plane curves on the Earth’s triaxial ellipsoid, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-1219, https://doi.org/10.5194/egusphere-egu23-1219, 2023.

The North American Vertical Datum of 1988 (NAVD88) was established by the minimum-constrain adjustment of geodetic levelling observations in Canada, USA, and Mexico. It held fixed the height of the primary tidal benchmark at Rimouski, Quebec, Canada. The NAVD88 datum was never officially adapted in Canada due its large east-west tilt of 1.5 m from the Atlantic to Pacific coast (Hayden et al., 2012). Also, a large systematic difference (ranging from -20 cm to +130 cm) was found between NAVD88 and the pure geoid gravimetric models. Using Factor Analysis it was discovered that one of the factors, which can explain the tilt of the NAVD88, is the terrain, i.e. small in the flat states but large in the mountainous areas such as in the Rockies and the Appalachians (Li, 2012). A possible reason for the tilt of the NAVD88 might be the weights used into adjustment of the network. In this study the data of two precise national levelling networks are used, e.g. the Second Levelling of Finland and the Third Levelling of Bulgaria, in order to support the above hypothesis. An iterative procedure based on the Inverse Absolute Height Weighting (IAHW) is applied. The core of this procedure is to find this value of the power parameter (p) of the weights w=H^p, where H is the absolute elevation difference of the terminals in the levelling lines, that minimize the mean of the mean squared errors (MSE) of the nodal bench marks (NBM) in both networks. It has been found that p=1 and p=4.3 for the Bulgarian and the Finnish networks, respectively. Also, a similar iterative procedure based on the Inverse Distance Weighting (IDW) is performed and the best decisions for the Finnish and the Bulgarian networks are obtained. It has been found that the weights w=L^-5.9 and w=L^-1.6, where L is the length of the levelling line, lead to the minimal MSE of the NBM for the Finnish and the Bulgarian networks, respectively. The results of both the IDW and the IAHW procedures are compared. It has been revealed that the IAHW based adjustments lead to significantly less MSE of the NBM than all variants of the IDW. It has also been shown that concerning the Bulgarian and the Finnish analyzed here data, the IAHD approach leads to physically lower adjusted heights than the IDW. In some cases these differences are more than 1.5-2 times greater than the MSE of the corresponding bench marks.

How to cite: Cvetkov, V. and Gospodinov, S.: Inverse Absolute Height Weighting in the Highest Order Levelling Networks, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-4219, https://doi.org/10.5194/egusphere-egu23-4219, 2023.

Geodesy defines a physical height as the shortest distance of a point to a height reference surface in the Riemannian physical space. Two types of physical heights are most commonly used in science and applications, namely orthometric and normal heights. Both heights use the same reference surface (geoid) but differ in metrics associated with either the real (in case of orthometric heights) or model (for normal heights) gravity field. Orthometric heights correspond to the classical concept of physical heights introduced in the 19th century by Gauss, Stokes and Helmert. The main reason for introducing normal heights in the mid-20th century by Vignal and Molodensky, was related to a fact that the metric for orthometric heights (or corresponding gravity corrections to levelled height differences) could be estimated only approximately as they depend on the topographic mass density. Consequentially, normal heights have been introduced in many countries worldwide. However, their concept is sometimes misunderstood as the quasi-geoid is incorrectly referred to as their reference surface. Physical heights and corresponding height systems were discussed at the 10th Hotine-Marussi Symposium held in Milan, June 2022. A motion was proposed and discussed at the symposium that acknowledged reported problems of the quasi-geoid and its improper use as a height reference surface in geodesy. This presentation summarizes main arguments that were used to forge the motion. 

How to cite: Novak, P. and Sansò, F.: On the correct definition and use of normal heights in geodesy  , EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-17520, https://doi.org/10.5194/egusphere-egu23-17520, 2023.

The “non-harmonicity” problem, as one of the main problems in the residual terrain modelling (RTM) method, would involve more than 200 mGal errors in the gravity field determination over the Himalaya area. To deal with it, there are five main harmonic correction (HC) methods, i.e., the condensation method, regularized downward continuation method with Taylor series expansions (TS), regularized downward continuation method with spherical harmonics (SH), complete HC method, and Kadlec's method, being provided in previous studies. However, their performances in gravity field determination are not studied nor compared directly yet. In this study, all these five HC methods are completely reviewed and evaluated, especially their performances in regional geoid determination. The expressions of HCs under various approximations are derived, and the Kadlec’s method is proved to be equivalent to the condensation method when adopting the same approximation for Bouguer masses. For the continuation methods, the HC associated with the complete method shows large differences compared to the HC associated with TS and SH methods. This is caused by the fact that the continuation process within the complete method is implemented in the situation of the Earth’s masses being changed. To cope with this problem, we promote a new three-step approach for computing the HC which is proved to be equivalent to the HC using the TS method. Then the HCs with various methods are completely considered and evaluated in the Colorado geoid determination using the remove-compute-restore technique. The best performance is achieved when the SH method is adopted for computing the RTM corrections to gravity anomaly in the removal procedure. The accuracy of the calculated geoid height is ~1.62 cm. Involving HCs for geoid height in the restore procedure would slightly improve the results to an accuracy of ~1.56 cm.

How to cite: Yang, M., Li, X., Lin, M., Feng, W., and Zhong, M.: Harmonic Correction in Regional Gravity Field Determination, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-6403, https://doi.org/10.5194/egusphere-egu23-6403, 2023.

In local and regional quasi-geoid modeling, the residual terrain modeling (RTM) method is often used to remove the short-wavelength gravity field signals from the measured gravity both on the ground and up in the air, in order to obtain the regularized and smooth gravity field which is suited for field interpolation and modeling. Accurate computation of RTM corrections requires a set of fine-tuned parameters in terms of the gravity forward modeling technique, digital elevation model (DEM), reference topography, and integration radius for the inner zone and outer zone. To our limited knowledge, this has not been systematically documented, albeit its importance is obvious. This work aims to clearly investigate the impact of these factors on the RTM correction computation and their effects on the quasi-geoid modeling so to provide practical guidelines for real applications. Two gravity forward modeling techniques, i.e., the prismatic approach and the tesseroidal approach, are employed to investigate the following issues existing in the practical use of the RTM method: ① can a combination of a high-resolution DEM and a DEM with a lower resolution replace the use of a single high-resolution DEM for the RTM correction computation without loss of accuracy? ② how to properly choose the integration radius for the inner zone and outer zone while costing less time and keeping the accuracy? ③ what are the performances of using the reference topographies obtained by the direct averaging, the moving averaging, and the spherical harmonic analysis and synthesis on the RTM correction computation and quasi-geoid determination? For obtaining objective findings, two research regions are selected for this investigation. One is the Colorado area (USA) having quite rugged terrains and the other is the Auvergne area (France) with moderate terrains. The numerical results show that, in the computation of RTM corrections to gravity anomaly and height anomaly, the combination of a dense DEM and a coarse DEM can replace the use of a single dense DEM without loss of accuracy. The increasing and decreasing of the integration radius for the inner zone and outer zone do not influence the RTM correction computation much. The recommended values are 10 km for the inner zone and 111 km for the outer zone. The use of different reference topographies changes RTM corrections, however, the final quasi-geoid models are at the similar accuracy level.

How to cite: Lin, M., Li, X., and Yang, M.: Numerical experiences on using the RTM method in quasi-geoid modeling, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-4935, https://doi.org/10.5194/egusphere-egu23-4935, 2023.

The official national height reference systems in use, apply different definitions of the height and the zero levels refer to different tide gauges and epochs. Additionally, the treatment of the permanent tide is not entirely consistent. This causes differences at the decimetre scale, which also vary along the national borders. The "European Alps Geoid Project" (EAlpG) aims to harmonize the basis for height determination in the Alpine region, including the neighbouring lowlands and the computation of a uniform geoid model according to European standards for height and positioning.

The project is based on the experiences and findings of the predecessor "D-A-CH geoid" project, which covered a test area around Lake Constance. It was a joint initiative of the federal and state authorities responsible for land surveying in Germany, Austria and Switzerland.

First steps of the EAlpG project were the conclusion of the Memorandum of Understanding in May 2022 as well as the initiation of the exchange of gravity and height data. The ambitions of the initiative are therefore to intensify the cooperation’s between the partners in regional gravity field modelling and to provide better information on the transformations between the national height systems. The following activities are planned:

1. Improved cross-border regional geoid model of the Alpine area:

• Revision and harmonization of the base data for the calculation of the geoid models: gravity data, digital elevation models, control points for validation
• Cross-border gravity measurements, e.g. Austria, France, Germany, Italy, Switzerland
• Comparative studies on geoid modeling in high mountains

2. Improved height transformation between the Alpine countries:

• Extensive comparative investigations and validation between the national height reference surfaces (geoid models and other height transformation grids) and the national and European heights along the borders
• Derivation of consistent height transformation models accurate to a few centimeters
• Development of a corresponding web application

The outcomes of the project will support (non-)geodetic users in there cross-border height applications, e.g. ground water level investigations, flood protection. Other important applications for cross-border height standardisation are engineering projects such as tunnels, bridges, supply lines, etc.

The results will be embedded in a pan-European geoid initiative within EUREF. Contributing to the upcoming EUREF Working Group “European Height Reference Surface”, the European Alps Geoid will be one of many cornerstones to build an official EVRS height reference surface.

The EAlpG project is a joint initiative of the national authorities and organization responsible for or involved in the integrated geodetic spatial reference of Austria, Czech Republic, France, Germany, Hungary, Italy, Slovakia, Slovenia and Switzerland. The scientific work is supported by various universities in the Alp area.

How to cite: Bauer, T. and Schwabe, J. and the The European Alps Geoid group: The European Alps Geoid (EAlpG) Project – a joint initiative for improved cross-border regional geoid modelling and height transformation, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-7431, https://doi.org/10.5194/egusphere-egu23-7431, 2023.

This research introduces the formation of a Geoid model that is based on terrestrial gravity measurements in Israel and its surroundings, together with shipborne gravity measurements and altimetry data over the Mediterranean Sea, using the EIGEN-6C4 as the reference earth gravity model – the first of a kind effort done in Israel to construct such a model. A challenging aspect for establishing this model for this area - that does not exist elsewhere in the world - is that approximately 20% of Israel's land area is located below sea level, some of which is minus 430 meters, mainly along the Dead Sea Rift. This unique topography requires new and challenging computation theories for gravimetric Geoid determination.

The results yield a standard deviation value of the gravimetric Geoid of 5.7 cm. The model is also successfully calculated in areas with a negative orthometric altitude, which proves for the first time the potential of the developed methodology of obtaining an accurate geoid model. The hybrid Geoid model significantly improves these values, where the standard deviation value is reduced to 2 cm with an error range of 22 cm. The hybrid Geoid model retains the orthometric datum of the control points while relying on gravimetric data to provide better gradient information about the area. The high accuracy of the hybrid Geoid model will allow the integration of the official national Geoid model and the new gravimetric Geoid model to support precise GNSS measurements used for precise infrastructure engineering projects. The gravimetric geoid can recreate a role with other local gravity models developed by countries surrounding Israel.

How to cite: Sarid, H., Dalyot, S., and Wang, Y.-M.: The first Gravity Geoid Model for Israel, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-9678, https://doi.org/10.5194/egusphere-egu23-9678, 2023.

Within the GeoNetGNSS project, funded by the European Union and National Funds through the Region of Central Macedonia (RCM), the main goal is to establish a dense network of Continuously Operating Reference Stations (CORS) in Northern Greece. Accuracy, reliability, wide coverage, ease of use and cost effectiveness are among the main advantages of differential positioning supporting mapping, surveying, geodetic, and large infrastructure projects. However, as ellipsoidal heights from GNSS measurements have no physical meaning, they should be transformed to orthometric heights. This transformation requires an accurate gravimetric geoid model to be readily available, in order to carry-out the so-called GNSS/Leveling, i.e., the determination of orthometric heights without the need to carry out levelling. With that in mind, a regional gravimetric geoid was determined based on historical and newly acquired high-accuracy and density gravity data that have been collected through dedicated gravity campaigns. These were focused not only around the CORS stations but also targeted the entire area of RCM. The gravity observations have been carried out with the CG5 gravity meter relative to absolute gravity stations established using the A10 (#027) absolute gravity meter. The development of the geoid was based in the classical Remove-Compute-Restore (RCR) technique and an FFT-evaluation of Stokes’ integral. The long and short wavelengths of the gravity field spectrum were removed from the available input gravity data, then prediction of the residual geoid was carried out and finally the effects removed have been restored to derive the final model. To model the long-wavelength part of the spectrum, XGM2019e has been used as reference while the topographic effects were evaluated based on a spherical harmonics expansion of the Earth’s potential and ultra-high resolution residual terrain correction (RTC) effects from a global model. The prediction of the geoid model was carried out using the classical 1d-FFT spherical Stokes convolution with the Wong-Gore modification for the Stokes kernel and 100% zero-padding in all directions. Various tests against available collocated GNSS/Leveling observations have been performed to find the optimal cut-off degree while the evaluation of the model was carried out over 533 geodetic benchmarks in the entire study area, where accurate static GNSS observations and orthometric heights from the Hellenic Military Geographic Service (HMGS) were available.

How to cite: Vergos, G. S., Natsiopoulos, D. A., Tzanou, E. A., Mamagiannou, E. G., Triantafyllou, A. I., Tziavos, I. N., Ramnalis, D., and Polychronos, V.: A regional gravimetric geoid model in support of the GeoNetGNSS CORS network, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-13423, https://doi.org/10.5194/egusphere-egu23-13423, 2023.