Poster session
Within this concept, we seek contributions concerning problems of reference frames, gravity field, geodynamics, and positioning, but also studies surpassing the frontiers of these topics. We invite presentations discussing analytical and numerical methods in solving geodetic problems, advances in mathematical modelling and statistical concepts, or the use of high-performance facilities. Demonstrations of mathematical and physical research directly motivated by geodetic practice and ties to other disciplines are welcome. In parallel to theory-oriented results, examinations of novel data-processing methods in various branches of geodetic science and practice are also acceptable.
Posters on site: Wed, 6 May, 16:15–18:00 | Hall X1
The least-squares method is commonly used to estimate the parameters of a known mathematical model with a single functional form. However, in many applications, the underlying behavior is better approximated by piecewise functions composed of multiple segments. Such problems are usually addressed by empirically selecting the breakpoints and then applying a constrained least-squares method. This manual selection, nevertheless, does not always guarantee a globally optimal solution. In this work, a methodology for the simultaneous estimation of the function parameters and their breakpoints is developed. The proposed approach combines the method of indirect measurements with constraints and the Newton–Raphson method. Specifically, the breakpoints are treated as unknowns in the Newton–Raphson procedure and as parameters in the least-squares formulation. As the breakpoint estimates converge, the least-squares solution is progressively guided toward the optimal solution. Furthermore, all measurement equations retain a fixed functional structure that is piecewise-defined, enabling automatic partitioning of the measurements within the least-squares procedure. Finally, numerical examples are presented to demonstrate the proposed methodology.
How to cite: Koci, J. and Panou, G.: Least-squares fitting of piecewise curves, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-3790, https://doi.org/10.5194/egusphere-egu26-3790, 2026.
Solar system bodies such as planets, asteroids, and comets are increasingly becoming targets of satellite missions. These bodies typically exhibit irregular shapes, and generating shape models using spherical harmonics can be valuable for studying their physical properties. Beyond geodesy, spherical harmonic modeling is widely used in other scientific fields, including physics, geophysics, climate and weather science, medical imaging, chemistry, and engineering. In this work, we present two methods for generating shape models, a process commonly referred to as spherical harmonic analysis and synthesis. First, the classical least-squares method is introduced, both in its basic formulation and in combination with auxiliary algebraic techniques. Second, the well-known Neumann method is employed to compute the spherical harmonic coefficients. The aim of this study is to evaluate and compare these methods in terms of precision, computational efficiency, and simplicity. Finally, the performance of both approaches is demonstrated through numerical applications to celestial bodies.
How to cite: Panou, G., Koci, J., and Pappa, A.: Generation of a shape model in terms of spherical harmonics, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-5612, https://doi.org/10.5194/egusphere-egu26-5612, 2026.
Airborne gravimetry plays a critical role in local gravity field determination but remains costly and operationally constrained. In current practice, gravity data collected during takeoff, landing, and turning (collectively referred to as preparing time) are routinely discarded due to sensor degradation under dynamic motion. These phases, however, constitute a substantial fraction of total flight time and represent a largely untapped data source. This study investigates the potential benefits of incorporating gravity observations from the entire flight trajectory to enhance local gravity field modeling.
Numerical simulations were first conducted to evaluate the impact of using full-flight gravity data under varying noise conditions and spectral bandwidths. Gravity disturbances synthesized from EGM2008 were downward continued using radial basis functions. Results show that including preparing-time data improves modeling precision by up to 67% within the spherical harmonic degree band [200, 1080] and up to 61% when extending the bandwidth to [200, 2160], consistently across different noise scenarios. The feasibility of this approach was further demonstrated using real scalar gravimeter data from the GRAV-D survey. Preliminary results of incorporating these recovered observations into an airborne-only local quasi-geoid model shows promising geoid model improvements when compared with GNSS/Leveling bench marks.
In addition to the completed work, ongoing research is exploring the integration of onboard inertial measurement unit (IMU) data, to which access has recently been obtained. Preliminary analyses reveal strongly correlated error patterns in the preparing-time gravity observations that appear closely linked to aircraft attitude variations. The availability of roll and pitch measurements from the IMU opens the possibility of analytically mitigating these errors through physical modeling, potentially reducing reliance on purely data-driven approaches.
Additional simulations indicate that achieving 1 mGal-level gravity precision during dynamic flight requires roll and pitch angle accuracies better than 5 arc-minutes, underscoring the importance of accurate attitude information. Overall, the results highlight significant untapped potential in airborne gravimetry and suggest a paradigm shift toward exploiting full flight trajectories. As emerging technologies such as vector gravimetry, cold-atom sensors, and advanced inertial systems continue to mature, the systematic integration of dynamic-flight data is expected to further enhance the accuracy and efficiency of future airborne gravity surveys.
How to cite: Li, X.: Exploiting Full Flight Trajectories in Airborne Gravimetry: From Simulation to Real-World Validation, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-22219, https://doi.org/10.5194/egusphere-egu26-22219, 2026.
Within the window remove-restore technique (Abd-Elmotaal and Kühtreiber, 2003), the effect of the topographic-isostatic masses is removed from the source free-air gravity anomalies using high-resolution Digital Terrain Models (DTMs) and a terrain correction software, e.g., TC-program (Forsberg, 1984). A harmonic analysis of the topographic-isostatic masses is then applied to compute the effect of the topographic-isostatic masses over the data window to adapt the used geopotential model, in order to avoid a double consideration of their contribution. In this study, it is intended to use only the topographic masses in the window remove-restore technique and to compare the results with the case of using the topographic-isostatic masses. This comparison allows estimating the effect of the isostatic masses in the framework of the window remove-restore technique. The quantification of the effect is done for two mountainous regions, the Alps in Austria and the Rocky Mountains region in Colorado. The comparison is performed at two levels: reduced anomalies and computed geoidal heights. The results demonstrate the impact of the isostatic masses in window remove-restore technique and are discussed in detail.
How to cite: Abd-Elmotaal, H. and Kühtreiber, N.: Effect of Isostatic Masses in the Framework of the Window Remove-Restore Technique, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-3074, https://doi.org/10.5194/egusphere-egu26-3074, 2026.
The mathematical apparatus of integral transformations is often used for gravitational field modelling. A basic assumption of these integrals is the knowledge of relatively accurate data available globally. Practically, however, global data coverage is rarely achieved, and measurement errors always contaminate data. Therefore, integral transformations are appropriately modified and practical integral estimators are formulated and further employed in numerical experiments. In addition, corresponding statistical characteristics are often desired to indicate the quality of calculated gravitational fields.
In this contribution, we systematically formulate practical integral estimators and their respective errors. We present the practical integral estimators in two forms: combined (i.e., combining the restricted integrals for near-zone effects and the truncated spherical harmonic series for far-zone effects) and as a spherical harmonic series. The practical integral estimators form a theoretical basis for an accurate gravitational field modelling, e.g. when solving upward or downward continuation. By employing a unified notation, the mathematical formulas are derived to an unprecedented extent for a broad class of quantities. Namely, the theoretical formulations connect four types of boundary conditions with twenty computed quantities. Point-wise errors and global mean square counterparts complement the practical integral estimators. The point errors can be calculated from the errors of the near-zone and far-zone boundary values, the position of the computational point, the size of the integration radius, and the maximum spherical harmonic degree of the far-zone effects. The number of variables is reduced for the global mean square errors, as they are invariant with respect to the horizontal position of computational points. Both statistical characteristics may also be employed in optimisation problems and experimental designs. The basic principles and formulations presented here can be applied to related problems in other potential fields, such as electrostatics or magnetism.
How to cite: Šprlák, M., Belinger, J., Pitoňák, M., and Novák, P.: Practical Integral Estimators for Gravitational Field Modelling: Basic Formulations and Statistical Characteristics, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-7879, https://doi.org/10.5194/egusphere-egu26-7879, 2026.
The determination of gravitational fields generated by planetary bodies represents a fundamental task in modern geodesy. To facilitate the computation of gravitational field functionals, we approximate the shapes of individual planetary bodies. The spherical approximation is the most popular, as it conveniently employs numerous symmetries of the sphere. Generally, however, planetary bodies are flattened at the poles or even at equators. Therefore, a conceptual framework on the spheroidal approximation should be analysed.
In this contribution, we develop a new mathematical theory for modelling gravitational fields generated by irregular bodies. Specifically, the gravitational potential, the components of the gravitational gradient and the second- and third-order gravitational tensor components are parametrised using spheroidal harmonic functions defined within the minimal Brillouin spheroid.
To enable global calculation, especially near the poles, the original spheroidal harmonic expansions are transformed into their non-singular counterparts. Additionally, we investigate selected numerical aspects of the Legendre functions of the first and second kind. Numerical experiments are performed to validate the proposed approach. Both singular and non-singular formulations are systematically evaluated.
How to cite: Belinger, J., Dohnalová, V., Pitoňák, M., Šprlák, M., and Novák, P.: Numerical aspects of gravitational field modelling using spheroidal harmonic functions, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-16758, https://doi.org/10.5194/egusphere-egu26-16758, 2026.
Integral transformations derived from boundary-value problems (BVPs) of potential theory constitute the core mathematical apparatus of physical geodesy and gravity-field modelling. Classical Green’s function solutions of the Dirichlet, Neumann, and Stokes problems generate a complete family of integral transformations that relate the disturbing gravitational potential and its directional derivatives. In the spherical approximation, this framework—summarised by the Meissl scheme—has reached a high level of completeness and currently provides mutual transformations among all components of the gravitational-gradient tensors up to the third order. These tools underpin the processing of heterogeneous gravity observations acquired by terrestrial, airborne, and satellite sensors.
Increasing accuracy requirements and the geometric proximity of the Earth to a rotational ellipsoid, however, necessitate a transition from spherical to spheroidal formulations. Although analytical solutions of the three fundamental BVPs on an oblate spheroid have been derived and several corresponding integral equations have been proposed, the spheroidal analogue of the Meissl scheme remains incomplete.
In this contribution, we derive spheroidal integral formulas for computing the disturbing gravitational potential and its first-, second-, and third-order directional derivatives from the disturbing potential and its vertical and horizontal derivatives. The correctness of the newly derived integral formulas is verified by closed-loop tests using data from a global geopotential model.
How to cite: Pitonak, M., Belinger, J., Novak, P., and Sprlak, M.: Spheroidal integral formulas for computing the disturbing gravitational potential and its first-, second- and third-order directional derivatives from disturbing gravitational potential and its vertical and horizontal derivatives , EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-16392, https://doi.org/10.5194/egusphere-egu26-16392, 2026.
The poster presents the modeling of the gravitational field of the near-earth asteroid 101955 Bennu using two spectral-domain methods based on spherical harmonics and two numerical spatial-domain approaches. Due to its irregular shape, accurate gravitational field modeling represents a challenging task that is essential for precise orbit determination and spacecraft navigation. A mutual comparison of spectral- and spatial-domain methods is therefore vital. The spherical harmonic methods rely on two distinctive approaches. The first one is known as spectral gravity-forward modelling and produces a spherical harmonic series that is valid only outside the smallest sphere completely encompassing bennu. The second approach estimates an external spherical harmonic series from surface gravitational data using the least-squares method, making the series valid everywhere on and above the surface of bennu. Opposed to the spherical harmonic methods, two numerical approaches based on the finite element method are considered: the first solves the exterior boundary value problem (BVP) for the Laplace equation, while the second addresses a coupled interior–exterior BVP for the Poisson equation. Constant mass density is assumed in all experiments.
In the theoretical part of the poster, the fundamental principles of all applied methods are introduced. These approaches are subsequently implemented and tested in a series of numerical experiments. In the first experiment, gravitational acceleration evaluated on an approximated surface of the asteroid by spatial-domain gravity-forward modeling is prescribed as a boundary condition.
The convergence of the numerical solution toward the reference solution obtained from spherical harmonic functions is then analyzed. In the second experiment, a triangulated surface representation of the asteroid bennu is employed in order to assess the performance of the numerical methods on a more realistic geometry. The comparison focuses on the convergence rate, computational efficiency, and memory requirements of the individual approaches, providing insight into their applicability for gravitational field modeling of irregular small bodies.
How to cite: Minarechová, Z., Bucha, B., and Macák, M.: A comparative study of gravitational field modeling for 101955 Bennu, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-9207, https://doi.org/10.5194/egusphere-egu26-9207, 2026.
This study presents high-resolution global gravity field modelling using the boundary element method (BEM), method of fundamental solutions (MFS) and singular boundary method (SBM). All three methods are applied to get numerical solutions of the fixed gravimetric boundary-value problem (FGBVP) which represents an exterior oblique derivative problem for the Laplace equation. In case of BEM, its direct formulation is applied to get the boundary integral equations that are numerically discretized using the collocation with linear basis functions. It involves a triangulated discretization of the Earth's surface considering its complicated topography.
MFS is a mesh-free method which avoids a numerical integration of the singular fundamental solution introducing a fictitious boundary outside the domain, i.e. below the Earth's surface, where the source points are located. In MFS, the fundamental solution of the Laplace equation plays the role of its basis functions. We present how a depth of the fictitious boundary influences accuracy of the obtained MFS solution on the Earth's surface. In case that the source points are located directly on the Earth's surface, the ideas of SBM are applied to isolate singularities of the fundamental solution and its derivatives.
Numerical experiments present high-resolution global gravity field modelling using BEM, MFS and SBM. All three methods are applied to reconstruct a harmonic function, namely the EGM2008 model up to degree 2160. At first, EGM2008 is reconstructed on the reference ellipsoid, and then on the discretized Earth’s surface. In all cases, the colocation/observation points are located with the same high-resolution of 0.075 deg. Comparisons of the obtained numerical solutions show that all three methods provide almost the same results when reconstructing EGM2008 on the ellipsoid. When solving FGBVP on the discretized Earth’s surface, the BEM numerical solution gives the best result, then SBM and finally MFS. In all cases, the largest residuals are in high mountains of Himalayas and Andes, however, they are much smaller in the BEM solution due to a special treatment of the oblique derivative problem.
How to cite: Čunderlík, R. and Minarechová, Z.: BEM, MFS and SBM applied for global gravity field modelling – comparison of their numerical solutions on an ellipsoid and the discretized Earth’s surface, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-6710, https://doi.org/10.5194/egusphere-egu26-6710, 2026.
This poster presents a numerical scheme based on the Discrete Duality Finite Volume (DDFV) method for solving boundary value problems with oblique derivative boundary conditions. Such problems arise in various engineering applications where the boundary behavior of the solution is prescribed in a non-normal direction. The formulation of the boundary value problem and the proposed scheme are described, and the main theoretical properties of the method are discussed. The performance of the method is then investigated using two theoretical two-dimensional numerical experiments. In the first experiment, the oblique derivative vector is generated solely by translation, while in the second experiment it is generated by a combination of translation and rotation. These test cases are designed to verify the accuracy and reliability of the proposed numerical scheme. In the future, the method can be naturally extended to three-dimensional problems, making it particularly suitable for modeling the local and global Earth’s gravity field.
How to cite: Macák, M., Minarechová, Z., and Mikula, K.: A DDFV-Based Approach to Oblique Derivative Boundary Value Problems with Applications in Geodesy, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-3741, https://doi.org/10.5194/egusphere-egu26-3741, 2026.
Gravitational data from satellites in Earth’s orbit can be used to reconstruct secular and
periodic mass movements at the Earth’s surface. These include tidal effects caused by the
Moon, seasonal variations in rainfall, and the melting of glacial ice at the poles.
Such mass transports not only lead to variations in the observed gravitational signal, but
also act as surface loads that induce elastic deformation of the Earth on short timescales.
In this talk, we present a method for calculating these deformations using the finite element
method (FEM), along with some numerical examples. Finally, we outline directions for future
research, in particular the inverse problem of reconstructing surface mass distributions from
GRACE data while explicitly accounting for deformational effects.
How to cite: Peter, T.-J., Michel, V., and Suttmeier, F.-T.: Elastic deformation of the Earth due to surface loading: finite element modelling and implications for inverse gravimetry, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-1803, https://doi.org/10.5194/egusphere-egu26-1803, 2026.
How to cite: Abbasi, M. A.: Surface Variations in Earth's Time Variable Gravity Field Modelled by the Finite Element Method, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-9360, https://doi.org/10.5194/egusphere-egu26-9360, 2026.
The structure of the Laplace operator is relatively simple when expressed in terms of spherical or ellipsoidal coordinates. The physical surface of the Earth, however, substantially differs from a sphere or an oblate ellipsoid of revolution, even if optimally fitted. The same holds true for the solution domain and the exterior of a sphere or of an oblate ellipsoid of revolution. The situation is more convenient in a system of general curvilinear coordinates such that the physical surface of the Earth (smoothed to a certain degree) is embedded in the family of coordinate surfaces. Therefore, a transformation of coordinates is applied in treating the gravimetric boundary value problem. The transformation contains also an attenuation function. Tensor calculus and its rules are used and the Laplace operator is expressed in the new coordinates. Its structure becomes more complicated now. Nevertheless, in a sense it represents the topography of the physical surface of the Earth. Subsequently the Green’s function method is used together with the method of successive approximations in the solution of the gravimetric boundary value problem expressed in terms of the new coordinates.
How to cite: Holota, P.: Laplace’s operator with a structure reflecting the solution domain geometry and its use in the determination of the disturbing potential by a convergent series of successive approximations, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-14574, https://doi.org/10.5194/egusphere-egu26-14574, 2026.
The precise determination of the Earth's gravity field and geoid represents a fundamental challenge in physical geodesy, with direct implications for navigation, mapping, and geodynamic studies. Geostatistical simulation provides a rigorous methodological framework for addressing the spatial heterogeneity of gravimetric data and quantifying uncertainties associated with geodetic models. This study presents geostatistical applications in physical geodesy along three main axes: optimal interpolation of gravity anomalies through kriging and its variants, geostatistical simulation for probabilistic gravity anomalies modeling, and geodetic network optimization for geoid calculation. Geostatistical methods are distinguished by their ability to explicitly model spatial correlation through the variogram and rigorously quantify spatial uncertainty. Practical applications demonstrate effectiveness in integrating multi-source data with heterogeneous precision and resolution (terrestrial, airborne, and satellite measurements), propagating uncertainty in derived quantities, and optimizing the positioning of new gravimetric stations according to objective statistical criteria. Current challenges include processing very large datasets requiring high-performance algorithms and low-rank approximations, modeling anisotropy and non-stationarity of the gravity field, and extending to spatio-temporal approaches to capture temporal variations. Promising perspectives lie in hybridization with machine learning for automatic estimation of complex variograms while preserving the theoretical rigor of geostatistics, establishing this approach as an indispensable complement to classical methods in physical geodesy.
Keywords: gravity field, physical geodesy problems, geostatistical simulation, spatial interpolation, uncertainty quantification.
How to cite: Benikhlef, I.: Application of geostatistical simulation to gravity field modeling and physical geodesy problems, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-16144, https://doi.org/10.5194/egusphere-egu26-16144, 2026.
Besides the widely used Taylor expansion for analytical functions there is more complex form to represent some different expansions using the rational function [PL/QM] in the form of relation of the two polynomials P and Q of degrees L for numerator and M for denominator.
The convergence rate of such an approximation is faster than of the ordinary Taylor expansion, while the coefficients of Padé approximation are calculated based on the Taylor expansion.
For example, let show the possibilities of the Padé approximations for expansion of the elliptical integrals, let's consider the well-known length X of an meridian arc from equator to geodetic latitude B on the reference ellipsoid with semi-major axis a and eccentricity e.
After standard Taylor expansion and integration we obtain expansion up to 11th degree:
The corresponding Padé approximation:
Regardless of the coefficients in front of the powers of the cosine of the latitude,
we can see that the maximum order of the cosine of the latitude reaches only 4.
Taking for example the ellipsoid WGS-84 we get the length of meridian arc form equator to latitude 89 degrees:
precise (numerical integration): 9890270.31374637 m,
by formula (*): 9890270.31374637 m,
by formula (**): 9890270.31374636 m.
We see that using of the two polynomials of lower degree (max 4) provide the same accuracy than the usual expansion up to 11 degree!
There are possibility to develop the method using special type of Padé approximations for the
- orthogonal functions, and in particular
- orthogonal polynomials.
In physical geodesy the Padé approximations could be used in the
- representing of the normal field characteristics, expanded into Taylor series, e.g. length of the coordinate line of the spheroidal system used in normal height calculation,
- gravity field modelling using Padé approximations with orthogonal functions,
- solving of the integral Fredholm equation of the second type by successive approximations.
The deficiencies of this method are related to the poles - points where the denominator turns into zero.
Literature:
G.A. Baker, P. Graves-Morris. Padé approximations. Part 1: Basic theory. Encyclopedia of Mathematics and its applications, Addison-Wesley, Reading, 1981.
How to cite: Popadyev, V., Dergileva, A., and Rakhmonov, S.: Using of Padé approximations in mathematical and physical geodesy, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-12401, https://doi.org/10.5194/egusphere-egu26-12401, 2026.
Global gravity fields are traditionally represented using linear combinations of spherical harmonic basis functions, whose coefficients encode the geophysical signal. While this formulation is theoretically well-founded and guarantees universal approximation on the sphere, achieving high accuracy for high-frequency features requires spherical harmonics of very high degree, leading to a rapidly increasing number of parameters and substantial computational cost. As an alternative, recent works have shown that neural networks and numerical methods can represent gravity fields by learning coordinate-to-field mappings directly, often achieving competitive accuracy with fewer parameters.
In this work, we investigate storing the gravity field implicitly as neural network weights, using spherical harmonic expansions as input to sinusoidal representation networks (SIRENs), enabling a nonlinear mapping of gravity field components. Unlike classical linear spherical harmonic models, this hybrid approach does not rely on the full harmonic basis for field reconstruction; instead, it achieves accurate representations using fewer spherical harmonics, with the network’s nonlinearity compensating for the reduced expansion. Thus, the aim of this research is to compare the performance and efficiency of this hybrid approach versus the classical spherical harmonics expansion with respect to the Earth’s gravity modeling problem.
To create a reference ground truth to approximate, we generate high-resolution acceleration data from the EGM2008 gravity model, sampling 5,000,000 points on an equal area grid for training, and 250,000 points on a Fibonacci grid for testing; both at EGM’s reference sphere. We remove the contribution associated with planetary oblateness to isolate higher-degree features. Using this dataset, we systematically evaluate a range of model complexities.
Results show that, for lower total parameter counts, the hybrid approach achieves a lower approximation error than the standard spherical harmonic expansion. Beyond a certain model complexity, a crossover behavior is observed, after which the standard spherical harmonic expansion surpasses the hybrid representation. This is consistent with increasing representational redundancy in the nonlinear network at high model complexity, whereas the classical spherical harmonic expansion allocates parameters efficiently through its orthogonal basis functions.
The location of this break-even point is strongly influenced by the number of input spherical harmonics. In particular, a hybrid configuration using spherical harmonics up to degree L = 15 in the first layer combined with a six-layer SIREN consistently achieves lower approximation error in the test dataset than purely linear spherical harmonic models for parameter counts up to approximately 200,000, corresponding to a linear expansion up to degree 446. For inference on 250,000 samples, the equivalent linear spherical harmonic model takes 205.872 s, while the hybrid approach requires only 0.028 s, highlighting the computational efficiency of the method.
Compared to purely coordinate-based neural networks, the hybrid model achieves better accuracy for similar parameter budgets. These results suggest that hybrid spherical harmonic–neural models offer an attractive trade-off between accuracy, parameter efficiency, and computational cost for global gravity field modeling. This study considered only 2-dimensional fields without an explicit radial component. Extending the hybrid representation to upward continuation and evaluation of functionals in 3D space is a direction for future work.
How to cite: Restrepo Berrío, J. D., Kusche, J., Springer, A., and Rußwurm, M.: Investigating Hybrid Spherical Harmonic–Neural Network Models for Efficient Functional Approximation of the Global Gravity Field Representation, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-14971, https://doi.org/10.5194/egusphere-egu26-14971, 2026.
Posters virtual: Thu, 7 May, 14:00–18:00 | vPoster spot 3
EGU26-16148 | Posters virtual | VPS25
Geodetic degree-based Models for Robust Regional Geoid RefinementThu, 07 May, 14:15–14:18 (CEST) vPoster spot 3
Accurate geoid models are essential for converting GNSS-derived heights into physically meaningful elevations and for ensuring consistency in modern height reference systems. This study presents a unified geodetic framework for refining gravimetric geoids using GNSS/leveling residuals through physically interpretable fitting models. Five correction representations are evaluated, ranging from local Cartesian planar surfaces to geodetically consistent spherical formulations of increasing degree. The analysis demonstrates that low-order models effectively remove regional bias and tilt but show limited predictive stability. To enhance robustness, iteratively reweighted least squares is applied to mitigate the influence of outliers while preserving deterministic structure. Higher-order geodetic models are stabilized using ridge regularization, with the regularization strength selected objectively through leave-one-out cross-validation. This strategy ensures numerical conditioning while directly optimizing predictive performance. Results show that the full degree-2 geodetic model offers the best balance among accuracy, stability, and physical interpretability. It reduces long-wavelength distortions while maintaining consistent in-sample and cross-validated performance. The proposed approach supports reliable GNSS-based height determination in modern vertical datum realization and height modernization efforts.
How to cite: Abdalla, A. and Dwira, C.: Geodetic degree-based Models for Robust Regional Geoid Refinement, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-16148, https://doi.org/10.5194/egusphere-egu26-16148, 2026.
