EGU General Assembly 2024  

The precision and accuracy of GPS/GNSS positioning has improved by considerably more than an order of magnitude over the course of my career, and the amount of data readily available (GNSS sites) has increased by several orders of magnitude. Over the last 40 years, geodesists have exploited this dramatic (and still continuing) increase in measurement capability to discover and study an ever-increasing set of phenomena. In the 1980s and early 1990s, the GPS satellite constellation was incomplete and there was only a sparse global tracking network. As a result, measurement noise limited rate accuracy to a few to several mm/yr, whereas today we are approaching accuracies of a few tenths of 1 mm/yr for long-term rates, and likely approaching the limit at which variability in surface loading makes motions fundamentally non-linear.

In this talk I will take a historical perspective, highlighting the improvement in measurement capabilities and our understanding of tectonic and other earth processes. At the beginning of my career, we focused on estimating rates of steady processes like rigid plate motions, the distribution of strain across rapidly-deforming plate boundary zones, or the displacements due to large earthquakes. We thought that over most of the Earth, motion and deformation mostly occurred linearly with time. The noise level in position solutions at that time was very high, and most non-linear variations in observed time series were considered to be noise either due to positioning error or to unstable geodetic monuments. While the deformation due to changing surface loads was recognized as a physical signal, knowledge of the changing loads was rudimentary and the signal was below the noise level in most cases. Today we recognize a wide variety of signals that produce a mix of linear and non-linear motions of the Earth, and positioning geodesy has become the essential tool for studying most of them. I have had the good fortune to work on measuring and understanding many of these processes, and I will discuss some of the highlights of the evolutionary path of positioning geodesy along with future perspectives. We have reached, or nearly reached, the point at which the approximation of linear motion breaks down because the measurement precision is now comparable to or smaller than the non-linear surface loading deformation over most of the planet. The coming years should see more exciting discoveries, but we must think broadly about the full range of geophysical signals that are contained within our data.

How to cite: Freymueller, J.: The Evolution of Positioning Accuracy and Linear vs. Non-linear Motions of the Earth, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-4118, https://doi.org/10.5194/egusphere-egu24-4118, 2024.

The Gravity Recovery and Climate Experiment Satellite mission has provided estimates of spatiotemporal changes in the Earth’s gravity field, which represents mass transport near the surface of the Earth. This unique satellite mission has been used to study groundwater depletion, lake volume changes, sea level rise, and the viscoelastic response of solid Earth to glacial cycles; glacial isostatic adjustment. In this talk, I will share my experiences: published, unpublished, and even incomplete, in using GRACE data for Earth system science and emphasize the power and limitations of this unique satellite mission. 

How to cite: Vishwakarma, B. D.: GRACE for Earth system science: novel insights into hydrology, sea level rise, and solid Earth uplift, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-11422, https://doi.org/10.5194/egusphere-egu24-11422, 2024.

A multitude of basis functions is available for modelling the gravitational field based on satellite data. The Regularized Functional Matching Pursuit (RFMP) algorithm, which has been developed by the Geomathematics Group Siegen, proved to be able to combine different sets of such trial functions. For this purpose, a dictionary is built as a redundant union of different established basis systems (such as spherical harmonics, radial basis functions and Slepian functions). In an iterative scheme, a best basis is selected by minimizing a Tikhonov-Phillips functional. In a recent add-on (the LRFMP), the dictionary does not have to be discretely predefined but can be learned as part of the algorithm. This is implemented as a non-linear optimization problem. The LRFMP has several benefits, which will be demonstrated in the presentation, where we show numerical tests regarding the inversion of noisy gravity data on real satellite orbits.

References:

N. Schneider, V. Michel and N. Sneeuw, High-dimensional experiments for the downward continuation using the LRFMP algorithm, preprint available at http://arxiv.org/abs/2308.04167, 2023.

N. Schneider, V. Michel: A dictionary learning add-on for spherical downward continuation, Journal of Geodesy, 96 (2022), article 21 (22pp). 

Source Code:

N. Schneider, (L)IPMP source code for gravitational field modelling, v2-dc-2023. Zenodo. https://doi.org/10.5281/zenodo.8223771, 2023. 

How to cite: Michel, V., Schneider, N., and Sneeuw, N.: Dictionary learning for downward continuation of gravity data, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-1903, https://doi.org/10.5194/egusphere-egu24-1903, 2024.

Integral transformations are a useful mathematical apparatus for modelling the gravitational field. They represent the mathematical basis for the formulation of integral estimators of gravity field values, including error propagation. The theoretical and practical aspects of integral transformations traditionally used for the calculation of geoid/quasi-geoid heights in geodesy, such as Stokes’ and Hotine’s integral transformations, have already been studied. However, theoretical and practical concepts regarding other integral transformations, including non-isotropic (azimuth-dependent) transformations, have not yet been explored. One of the basic assumptions of integral transformations is global data coverage. However, the availability of ground measurements is frequently limited. In practice, the global integral is divided into two complementary regions, namely the near and far zones. Non-negligible systematic effects of data in the far zone require accurate evaluation. For this purpose, a new software library entitled FarZone4IT is being created in the MATLAB environment to calculate far-zone effects in integral transformations for gravitational potential gradients up to the third order. The library contains scripts for the calculation of integral kernels, error kernels, truncation error coefficients, and far zone effects for a selected set of input parameters. This contribution concerns the implementation of theoretical equations defining far zone effects and the subsequent numerical testing of the library functionality. Closed-loop tests were carried out using gravitational potential functionals generated from a synthetic model of the Earth's gravity field.

How to cite: Pitonak, M., Trnka, P., Belinger, J., Novák, P., and Sprlak, M.: FarZone4IT: A new software for the calculation of far–zone effects for spherical integral, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-2824, https://doi.org/10.5194/egusphere-egu24-2824, 2024.

The numerical integration method has been routinely used by major institutions worldwide (for example, NASA Goddard Space Flight Center and GFZ) to produce global gravitational models from satellite tracking measurements. Such Earth’s gravitational products have found widest possible multidisciplinary applications. The method is essentially implemented by solving the differential equations of the partial derivatives of the orbit of a satellite with respect to the unknown force parameters under the zero initial conditions. From the statistical point of view, satellite gravimetry from satellite tracking is essentially to estimate the unknown parameters in the Newton’s nonlinear differential equations from satellite tracking measurements --- the mathematical foundation for satellite gravimetry from tracking. From this perspective, it is rather trivial to prove that the numerical integration method, originating from Gronwall on Ann Math almost 100 years ago and currently implemented and used in mathematics/statistics, chemistry/physics, and satellite gravimetry, is groundless, even though, up to this moment, many researchers in the geoscientific community still have problems in understanding this side point of my research. In this talk, we focus on presenting three different methods to derive local solutions to the Newton’s nonlinear differential equations of motion of satellites, given unknown initial values and unknown force parameters. They are mathematically correct and can be used to estimate unknown differential equation parameters, with applications in gravitational modelling from satellite tracking measurements as a typical example in geodesy. These solution methods are generally applicable to any differential equations with unknown parameters. More precisely, we develop the measurement-based perturbation theory and construct global uniformly convergent solutions to the Newton’s nonlinear differential equations of motion of satellites, given unknown initial values and unknown force parameters. From the physical point of view, the global uniform convergence of the solutions implies that they are able to exploit the complete/full advantages of unprecedented high accuracy and continuity of satellite orbits of arbitrary length and thus will automatically guarantee theoretically the production of a high-precision high-resolution global standard gravitational models from satellite tracking measurements of any types. Finally, we develop an alternative method by reformulating the problem of estimating unknown differential equation parameters, or the mixed initial-boundary value problem of satellite gravimetry with unknown initial values and unknown force parameters as a standard condition adjustment model with unknown parameters.
Xu P (2018) Measurement-based perturbation theory and differential equation parameter estimation with applications to satellite gravimetry. Commun Nonlinear Sci Numer Simulat, 59, 515-543. DOI 10.1016/j.cnsns.2017.11.021
Xu P (2008) Position and velocity perturbations for the determination of geopotential from space geodetic measurements. Celest Mech Dyn Astr, 100, 231–249.
Xu P (2009) Zero initial partial derivatives of satellite orbits with respect to force parameters violate the physics of motion of celestial bodies. Sci China Ser D, 52, 562–566.
Xu P (2012) Mathematical challenges arising from earth-space observation: mixed integer linear models, measurement-based perturbation theory and data assimilation for ill-posed problems. Invited talk, joint mathematical meeting of American mathematical society, Boston, January 4–7.

How to cite: Xu, P.: Statistical estimation of differential equation parameters: the mathematical foundation for satellite gravimetry from tracking, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-3550, https://doi.org/10.5194/egusphere-egu24-3550, 2024.

Integral transformations of the gravitational field gradients are defined over the entire solid angle on the surface of the sphere. Despite the indisputable progress in satellite gravimetry and gradiometry, gravity field focused satellite missions allow accurate determination of the gravity field with a spatial resolution of 100 km, i.e. only in its long-wavelength part. However, there is also a need for high-resolution gravity field models at regional, national or continental scales, especially concerning the determination of the quasi-geoid or geoid. On the other hand, potential weakness of ground-based data is the long-wavelength gravity field accuracy and limited availability due to several constraints (e.g. deserts, lakes and large rivers, forests, or lack of goodwill between neighboring countries to share sensitive data). The ideal scenario combines ground and satellite data that complement each other.

In this contribution, relations defining the estimation of the global root mean square errors of selected gravitational field functionals using integral transformations will be derived and presented. For practical calculation, knowledge about the accuracy of measured terrestrial data and formal errors of global satellite models of the Earth's gravity field will be utilized.

How to cite: Belinger, J., Pitonak, M., Trnka, P., Novak, P., and Sprlak, M.: Estimation of the Global Root Mean Square Error of Selected Gravitational Field Functionals Calculated by Integral Transforms, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-4098, https://doi.org/10.5194/egusphere-egu24-4098, 2024.

The need for the determination of the parameters of an equipotential rotational ellipsoid of revolution that approximates closer and closer to the Earth requires analysis of the most currently available data. The main objective of this study is to examine such new data and to perform an adjustment technique to estimate the parameters and their standard deviations of the mean Earth ellipsoid. The parameters considered are the geocentric gravitational constant, the angular velocity, the geoidal potential, the dynamical form factor, and the major and minor semi-axes. A-priori estimates of these quantities, which may be determined independently, are treated as “observations” and their adjusted values from a weighted least-squares procedure are presented. Since a level ellipsoid of revolution and its gravity field are completely determined by four constants, we use two non-linear condition equations to relate the six parameters for performing the adjustment. Among the products of the adjustment is the correlation matrix of the adjusted values of parameters, which helps us in the selection of a consistent set of four parameters for the definition of a new Geodetic Reference System (GRS). After the selection of the four parameters, we compute by Newton’s method the two derived parameters and estimate their standard deviations by applying the law of propagation of variances. Furthermore, all the derived geometric and physical constants are computed from the defining constants of a GRS, by means of closed formulas. Finally, in order to yield numerical results of high precision, all computations are executed in computer algebra system software using variable precision floating point numbers.

How to cite: Panou, G. and Marti, U.: Current adjustment of the mean Earth ellipsoid parameters, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-4313, https://doi.org/10.5194/egusphere-egu24-4313, 2024.

It is widely known that the geodetic networks (both terrestrial and space) suffer from the so-called rank deficiency. This is the algebraic expression of the weakness of the observations to sense all the necessary information for the reference system definition (in terms of origin scale and orientation). For example, the SLR technique is sensitive to the origin and scale, while the orientation can be only externally defined. On the other hand, the traditional quasar-based VLBI does not sense either origin and orientation but only scale.

In general, the rank deficiency is remedied by the use of the so-called constraints. The constraints can be divided into two major categories: a. The minimum constraints, where they just treat the rank deficiency problem (as the word minimum dictates) and do not interfere with the shape of the network, and b. the over-constraints, which do not only solve the rank deficiency but alter the shape of the geodetic network.

While the minimum constraint solutions are widely discussed in the geodetic literature, regarding their nature, the over-constraints' physical meaning is not so clear (if not vague). The present study aims to provide a physical meaning of the over-constraints solution, under the prism of its stochastic interpretation.

How to cite: Ampatzidis, D., Balidakis, K., and Tsimerikas, A.: On the physical meaning of geodetic networks’ over-constraints solutions, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-5214, https://doi.org/10.5194/egusphere-egu24-5214, 2024.

The study presents along-track nonlinear diffusion filtering of the airborne gravity data. At first, the provided airborne gravity disturbances from the GRAV-D campaign are transformed into the airborne complete Bouguer disturbances (CBD). This aims to reduce a correlation of the filtered data with the topography. Then the nonlinear diffusion filtering in 1D based on the Perona-Malik model is applied. In this model, a diffusivity coefficient depends on the edge detector, which allows reducing noise while preserving important gradients in the filtered data. As a numerical method we use the finite volume method (FVM). The derived semi-implicit numerical scheme leads to a three-diagonal system matrix that is solved in every iterative step. Here the diffusivity coefficients are updated in every step by new values of the edge detector recomputed from the previous solution.

The numerical experiment presents the along-track nonlinear filtering of the airborne CBD in high mountainous area of the ‘Colorado geoid experiment’. Afterwards, the along-track filtered data are gridded into a 2D map of the airborne CBD. The obtained results show that an appropriate choice of a sensitivity parameter of the diffusivity coefficient can better detect significant structures in the airborne CBD, especially their edges that are usually smoothed by the Gaussian filtering. Finally, the filtered and gridded airborne CBD are backward transformed into the airborne gravity disturbances.

How to cite: Cunderlik, R., Zahorec, P., and Papčo, J.: Along-track nonlinear filtering of airborne gravity data from the GRAV-D campaign: case study for the ‘Colorado geoid experiment’, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-5215, https://doi.org/10.5194/egusphere-egu24-5215, 2024.

Gravity field modelling of irregularly shaped bodies such as the Earth's Moon is a challenging task that can reveal both the strong and weak points of each modelling technique. In our approach we will develop a numerical approach based on the finite element method (FEM) and compare the obtained solutions with the solution by the spectral approach that relies on spherical harmonics. In this way, we aim to study whether the numerical methods such as FEM can overcome the limitations of the spherical-harmonic-based approaches, namely their divergence in the vicinity of the gravitating body. We hope that the presented developed approach could form a valuable alternative to the spherical harmonics.

How to cite: Macak, M., Šprlák, M., and Minarechová, Z.: Modelling gravity field of irregularly shaped bodies by numerical methods, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-5272, https://doi.org/10.5194/egusphere-egu24-5272, 2024.

Studying the gravitational effects of the Earth's topography and crustal layers is a fundamental topic in gravity field modeling in geodesy and geophysics. The introduction of gravitational curvatures (GC), which are the third-order derivatives of the gravitational potential (GP), has recently broadened theoretical research on gravitational effects. Using tensor analysis, this paper comes up with a general formula for the physical parts of the third-order tensor of the potential in cylindrical coordinates. Then, the expressions for the GC of a vertical cylindrical prism are accordingly derived in cylindrical coordinates. Based on the relation among the vertical cylindrical prism, cylindrical shell, and cylinder, the analytical expressions for gravitational effects up to the GC of a vertical cylindrical shell and a cylinder are derived when the computation point is located on the Z-axis no matter whether it is situated below, inside, or above the cylindrical shell and cylinder. Laplace's equation has been adopted to confirm the correctness of the newly derived formulas of the GC. In addition, a benchmark of a cylindrical shell discretized into cylindrical prisms is proposed to reveal the numerical properties of derived GC formulas with the computation point located on the Z-axis. Numerical results reveal that when the computation point's height increases, the relative and absolute errors of the GP, gravitational vector (GV), gravitational gradient tensor (GGT), and GC decrease, in which the relative errors in log₁₀ scale of the nonzero GP, GV, GGT, and GC components are approximately less than -2 when the computation is located below, inside, and above the cylindrical shell. These newly derived formulas lay the theoretical foundation for the GC in cylindrical coordinates and help to investigate the potential applications of the GC in geodesy and geophysics. This new benchmark can become the standard for testing the correctness of the gravitational effects of the cylindrical prism using different numerical algorithms in cylindrical coordinates in practical applications.

How to cite: Deng, X.: A benchmark for gravitational potential up to its third-order derivatives of a vertical cylindrical shell discretized into cylindrical prisms, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-5992, https://doi.org/10.5194/egusphere-egu24-5992, 2024.

Atmospheric refraction is the main source of deviations for laser-based sensors. Having a profound understanding of refraction, and the knowledge of the geometry of the line of sight, assists in identifying an accurate model to correct this error. The height of the point, similar to two other planar coordinates, is also impacted as a result of the refracted beam line. The height can be obtained through numerous geodetic measurement approaches such as spirit levelling or trigonometric levelling. An empirical refraction model was proposed in 1984 to better quantify the observations of trigonometric levelling. In this research, we propose a developed empirical model for the La Valette Landslide (Southeast French Alps) to determine the height of the target benchmarks in a landslide zone. The landslide is located in the Ubaye Valley, where the thrust fault of clay-shale sediments at the bottom and sandstone and limestone competent rocks at the top, control the occurrence of landsliding in this region. The deformation is attributed to the low resistance of the slope material and the increase in pore-fluid pressure resulting from the different hydraulic conductivities of the two geological units. The landslide has been monitored over many years, with several remote sensing techniques, and the task is undertaken as a part of the French Landslide Observation Service - OMIV. Since September 2019, an automated total station Long-Range Trimble S9 has been monitoring 54 reflectors’ positions every 1 to 3 hours with respect to three reference control points. The targets have been uniformly distributed over the landslides at distance from 350m to 2300m from the monitoring station, and at elevations varying from 1300m to 2100m. The research determined the point heights using the empirical trigonometric levelling model with the addition of an improved refraction model incorporating the development refraction correction for the observed angles of the control points.

How to cite: Sabzali, M., Ferhat, G., Pilgrim, L., Khaki, M., and Malet, J.-P.: Developed empirical refraction model for precise trigonometric levelling of the La Valette Landslide, France, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-6872, https://doi.org/10.5194/egusphere-egu24-6872, 2024.

The numerical approach for solving the nonlinear geodetic boundary value problem based on the finite element method with mapped infinite elements and itterative procedure is developed and implemented. In this approach, the 3D semi-infinite domain outside the Earth is bounded only by the triangular discretization of the whole Earth's surface and extends to infinity. Then the BVP consists of the Laplace equation for unknown disturbing potential which holds in the domain, the nonlinear boundary condition given directly at computational nodes on the Earth's surface, and regularity of the disturbing potential at infinity. In experiments, a convergence of the proposed numerical scheme to the exact solution is tested and then the numerical study is focused on a reconstruction of the harmonic function above the Earth's topography.

How to cite: Minarechová, Z., Macák, M., Čunderlík, R., and Mikula, K.: On solving the nonlinear geodetic boundary value problem using mapped infinite elements, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-7346, https://doi.org/10.5194/egusphere-egu24-7346, 2024.

Tesseroid and radial columns decomposition of the undersea relief strategies have been considered to recover the seafloor topography by Kalman Filter (KF) inversion of gravity data in the case of the Great Meteor seamount located in the North Atlantic ocean. These both modeling approaches are shown to be equivalent at high grid sampling rate (<1'). Different types of gravity data functionals for geoid height anomaly, vertical gravity component and gravity gradient (or tensor) are analyzed by spectral decomposition and combined to retrieve most detailed 3-D seafloor topography solutions, as gravity gradient data provide short-wavelength information to have access to high-resolution details. Besides only the vertical gravity tensor Vzz is usually inverted in previous field-related studies, considering up to six components of the gravity gradient is tested for improving the accuracy of the KF solution. The iterative KF scheme has been optimized and parallelized using C++ Armadillo software to accelerate the determination of a very large number of juxtaposed topographic heights.

How to cite: fuseau, D., Seoane, L., Ramillien, G., Darrozes, J., Plazolles, B., Rouxel, D., Schmitt, T., and Salaün, C.: Seafloor topography recovery improved by combination of different gravity data functionals, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-7800, https://doi.org/10.5194/egusphere-egu24-7800, 2024.

The Earth’s system is warming due to natural and human driven climate change. Observing, analyzing and understanding the associated geophysical processes is important in order to improve prediction of future changes and mitigate impacts on society and infrastructure. Investigating individual climate processes, such as sea level change, often requires partitioning of the total signal for identifying sub-signals and drivers; in the sea level example these could be trend and seasonal signals or impacts from the El Niño Southern Oscillation (ENSO).

A commonly applied method is the (real) Principal Component Analysis (PCA), which factorizes a given input dataset into time-invariant Empirical Orthogonal Functions (EOF), i.e. spatial patterns, and time-variable Principal Components (PC) based on the most dominant eigenvalues. However, this real-EOF analysis assumes more or less static patterns over time and, thus, lacks the ability to capture temporal variations in the patterns. This can be circumvented by the application of complex or Hermitian EOF analysis, which also enables capturing phase shifts or in other words allows for time-varying spatial patterns.

Here, we present first results from a novel approach utilizing dynamic time warping (DTW) for extracting dominant modes in the form of spatially distributed amplitudes and lags with respect to a ‘base curve’. While classic PCA methods are sensitive to outlier influence on the partitioning, our approach represents a robust alternative. Furthermore, base curves are computed that represent spatial modes via traversal matrices, which act as extensions of the base curves to capture individual lag. We introduce our new approach, compare to complex/Hermitian EOF, explain the numerical scheme, and present some first results based on gridded sea level change data.

How to cite: Uebbing, B., Höckendorff, J., Jungheim, C., Driemel, A., Sohler, C., and Kusche, J.: An alternative to PCA utilizing Dynamic Time Warping, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-8993, https://doi.org/10.5194/egusphere-egu24-8993, 2024.

During the last decades, several inversion approaches have been proposed to derive sea floor topography from satellite-based gravity data. Unfortunately, the most accurate non linear ones are based on iterative schemes that remain very time-consuming, especially if the number of topographic heights to be fitted is very important, e.g. when the oceanic domain is large and/or the gravity data is geographically dense and thus the maximum grid resolution to be accessible is high. Our strategy of computation is to decompose the total area into geographical cells that are overlapped to cancel the edge effects. The reference ocean depth given by GEBCO and the elastic thickness for regional compensation in function of the square root of the age of the oceanic crust are assumed to be constant in each cell. The initial inversion code has been translated into C++ and optimized using Armadillo software and LAPACK library to obtain a gain of speed of 1000 for a large region such as the complete North Atlantic Ocean (-54,-26,18,37). Post-fit and absolute errors are typically less than 200 m and 50 m r.m.s. respectively. These new detailed maps of bathymetry represent a precious source of information for geophysical applications. 

How to cite: Seoane, L., Fuseau, D., Ramillien, G., Darrozes, J., Plazolles, B., Rouxel, D., Salaün, C., and Schmitt, T.: Fast seafloor topography mapping of large oceanic provinces by optimization/parallelization, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-9318, https://doi.org/10.5194/egusphere-egu24-9318, 2024.

Although centralized coordinates are applied in geodetic coordinate transformations implicitly or explicitly, the centering strategy has not been comprehensively investigated from the theoretical perspective. We rigorously model and extend the empirically used three center strategies based on different models:

• Original model: Based on the partition representations of the solution, we propose a modified iteration policy, which reduces the parameter number and improves numerical stability during iteration. Also, its simplified version is analyzed when the cofactor matrix has the Kronecker product structures. It can be regarded as the extension of the work of Teunissen, since we essentially follow the same idea of partitioning the transformation parameters and the translation parameters, but more general covariance matrix structures are investigated in our consideration.
• Shifting model: With the partitioned solution forms, we prove the estimated transformation matrix and the residual vector are translational invariant. For iteration, with the classical iteration policy, the shifts should be chosen properly; with the modified iteration policy, there is no restriction since it is numerically equivalent to the original model. In addition, this model shows the feasibility of conducting the adjustment with the centralized coordinates and the original stochastic model.
• Translation elimination model: By multiplying the transformation relation with a specific matrix from both sides, we formulate the translation elimination model with the coordinates centralized and the translation parameters eliminated. With this model reduction, the covariance matrix has also been transformed since the observation equations are comprised of coordinate combinations. In addition, Leick’s model reduction strategy is a special case of this model, which is conducted by subtracting one particular observation equation from the remaining equations. 

Test computations with different weight structures show the validity of these strategies.

How to cite: Zhan, W., Fang, X., and Zeng, W.: Center strategies for universal geodetic transformations: modified iteration policy and two alternative models, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-13902, https://doi.org/10.5194/egusphere-egu24-13902, 2024.

The geoid model over dry land areas is determined from data observed at or above the Earth’s surface. Observable quantities include various functional of the disturbing potential defined as the difference between the real and model (normal) gravity potential. Transformation of the measured data into the sought-after, but directly unobservable gravity potential is often carried out using mathematical tools of the potential theory. An example of such a transformation is the well-known Hotine integral transform that transforms disturbing gravity, i.e., the first-order vertical gradient of the disturbing potential (Stokes formula is applied to anomalous gravity which is still often encountered in geodesy). Higher-order gradients of the Earth's gravitational potential have been collected by sensors on board aircraft or low-orbiting satellites. This advancement in data availability has resulted in the formulation of new tools based on Green's integral transforms and equations. Associated deterministic models have been well developed, tested, and successfully implemented. However, stochastic models for estimating uncertainties in sought values have only been partially developed. These uncertainties should reflect the inevitable implementation and approximation errors, the propagation of formal errors, as well as external accuracy estimation if relevant independent reference values are available. This contribution discusses mathematical models that can be used to estimate various types of uncertainties related to integral-based transformations of the measured potential gradients into the disturbing potential.

How to cite: Novak, P., Eshagh, M., and Pitoňák, M.: Uncertainties associated with integral-based transforms of measured potential gradients, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-15596, https://doi.org/10.5194/egusphere-egu24-15596, 2024.

The problem of determining the anomalous potential T on the earth's surface can be solved on the basis of various initial available data: gravity anomalies Δg and gravity disturbances δg, their vertical derivatives ∂(Δg)/∂H, ∂(δg)/∂H, gravity gradient anomalies Δ(∂g/∂H) etc. Existing methods of such BVP solution use the integral kernels, elaborated for the sphere and ellipsoid. The attempts to determine the real geoid are closely related to the direct problems of the potential theory, when the mass distribution is assumed to be approximately known (in Molodensky's theory the earth's crust density is used in topographic reductions only for better anomalies interpolation).

Using of the two tipes of related gravity data could be considered as a control, e.g., the anomalous potential T from the gravity anomalies Δg can be used to obtain the gravity disturbances δg, from which we must also get the same anomalous potential T. For the real Earth's surface more flexible is the method of integral equations.

(The prime sign indicates a point on the telluroid.)

Molodensky's integral equation for the simple layer density (distributed on the Earth's surface) using the gravity disturbances (1) and gravity anomalies (2) is known, but is usually solved indirectly with an introduction of the small parameter (the Molodensky's parameter k or/and ellipsoid eccentricity e), that lead to the series solution with the well-known integrals. Being the Fredholm equation, the Molodensky's integral equation itself can be solved directly by successive approximations in the ellipsoidal coordinate systems as well as in the spherical one. The integration procedure is probably longer, but any step is of the same type. Then the anomalous potential can be calculated by integration in the form (3).

Figure 1. Simple layers distributed with densities φ on the Earth’s surface S (green). Auxiliary simple layer density χ is distributed on the mean Earth’s sphere Ω  with radius R. In general case, the normal n to the surface, inclination angle α and the radius-vector ρ are slightly different in the two cases. E - reference ellipsoid (blue), the telluroid Σ (red), g - plumb-line.

Some real estimates are possible on the surface and gravity field models. In this study we use the Earth's model in the form of mascons for the surface and gravity field, see Fig. 2. We know all the elements of the anomalous field, the precise coordinates of the points with data and so we can estimate the real theoretical accuracy of the formulas and the number of iterations.

Figure 2. The scheme of the mass forming the anomalous field

In case of gravity anomalies the integration procedure can be considered as an integration over the successively refined  boundary surface. It is enough to find the density distribution of a simple layer on a smoothed surface constructed from the heights of points in the form of the sum of the normal height (from leveling) and the height anomaly from the Stokes approximation.

How to cite: Popadyev, V. and Sermiagin, R.: Control of the accuracy of the Molodensky's integral equation for the gravity anomalies and disturbances on the Earth's models, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-18996, https://doi.org/10.5194/egusphere-egu24-18996, 2024.

Current theory of integer inference, which is key to many carrier-phase driven observing systems, consists of a rich variety of different estimation principles, each with their own optimality and statistical properties. The various estimators can be classified into different classes of estimators, of which the integer estimation class is the smallest and the integer equivariant class the largest. Although the estimation theory for mixed integer models has matured significantly, there are still some important identifiable open unsolved problems. One of those concerns the way in which in practice the integer-equivariant baseline maximizer of the carrier-phase integer ambiguity function is resolved. Most of the methods employed in practice use rather ad hoc, brute-force grid search techniques, whereby proper considerations of the intrinsic properties of the objective function are lacking. As a result none of the available techniques have a demonstrated proven guarantee of global convergence. In this contribution we will present a novel algorithm for the numerical maximization of the multivariate carrier-phase integer ambiguity function. Our proposed method, which has finite termination with a guaranteed user-defined tolerance, is developed from combining the branch-and-bound principle with the projected-gradient-descent methodology, for which a special continuous differentiable convex-relaxation of the critical elements of the ambiguity objective function is constructed. The methodology of these three constituents is described in an integrated manner and numerical results are provided to illustrate the theory.

How to cite: Massarweh, L. and Teunissen, P.: A novel globally convergent maximizer for the multivariate carrier-phase integer ambiguity function, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-19367, https://doi.org/10.5194/egusphere-egu24-19367, 2024.

Digital Elevation Models (DEMs) are fundamental components in geodetic computations, serving as key inputs in geoid modelling processes. Mostly, the freely available DEMs are used for geoid modelling without considering its impact on the developed geoid. Considering the criticality of terrain and downward continuation corrections calculated from DEMs, this research work explores the sensitivity of geoid models to variations in DEMs, aiming to elucidate the impact of different DEMs on the accuracy and precision of geoid modelling. The study aims at a comprehensive sensitivity analysis framework to assess the influence of DEM resolution, terrain representation, and fitting methods on regional geoid modelling in India. The selected study area consists of three states of India (Haryana, Punjab, and Himachal Pradesh) bounding approximately 169,500 km² of the area (73.5≤λ≤77.5 and 29≤ϕ≤33 of longitude and latitude, respectively) of vast topography including Indo-Gangetic Plain, Shivalik Hills, lofty hills, deep valleys, and verdant forests. This study employs Least Squares Modification of Stokes formula with Additive Corrections (LSMSAC) method developed by the Royal Institute of Technology, Sweden and evaluates four DEMs, Cartosat, Merit, Palsar and SRTM. For surface correction (fitting), 24 GNSS points are used with 4,5 & 7 parameter fitting models which is validated with 15 other GNSS point based on elementary statistics. This investigation offers insights into selection of an optimal DEM by obtaining RMSE between developed geoid using various DEMs and 15 GNSS points. Based on the obtained results by considering above-mentioned DEMs with various fitting models, the Cartosat DEM outperformed other DEMs by obtaining lowest RMSE (0.078603m) with 7 parameter fitting model. Surprisingly, the lowest RMSE (0.064557m) is obtained by Cartosat DEM with 4 parameter model which could be because of Cartosat DEM being an India specific DEM. While comparing the efficacy of developed geoid between globally available DEM, Merit performed best with lowest RMSE (0.078657m). Out of 90 combinations of each DEM for various sets of Degree/order of Global Geopotential model (GGM), integration cap size; the best result is obtained by 180 degree of GGM and 0.8 integration cap size for each DEM. Presented study improved our understanding in assessing the sensitivity of geoid models to various DEMs. This research aids geodesists, geophysicists, and remote sensing specialists in making informed decisions while selecting a suitable DEM for geoid computations. The findings presented in this paper contribute to the ongoing efforts to enhance the precision and reliability of geoid modelling techniques, ultimately improving our understanding of Earth's gravity field.

How to cite: Kumar, A., maurya, V., and dwivedi, R.: Sensitivity Analysis of Digital Elevation Models in Geoid Modelling for Indian region, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-1087, https://doi.org/10.5194/egusphere-egu24-1087, 2024.

Numerical methods like the Finite Element Methods (FEM) or Finite Element Methods (FVM) are widely used in many engineering applications to solve boundary value problems that are hard to find rigorous analytical solutions. These numerical methods have been also applied in geodesy in many previous studies regardless of its huge computation demands. They have arisen due to the fact that the upper boundary condition was usually set up at the satellite orbit level, hundreds of kilometers above the Earth. The relatively large distances between the bottom boundary Earth' s surface, and the upper boundary even exacerbates the computation loads because of the required discretization in between. Considering that many areas such as the US have uniformly distributed airborne gravity data that are just a few kilometers above the topography, we propose to move the upper boundary from the satellite orbit level to the mean flight level of the airborne gravimetry. The significant reduction in altitudes, dramatically saves the large computation demands in previous FEM or FVM computations. This paper demonstrates this benefit by using FVM for both simulated data and real data in the target area. In the simulated case, the FVM numerical results show that about an order of magnitude precision improvement can be obtained when moving the upper boundary from 250km to 10km, the maximum altitude of GRAV-D. For the real data sets, 2-3 cm level of accurate quasi geoid model can be obtained depending on different schemes used to model the topographic mass. The paper also demonstrates how to find the upper layer in case no airborne data is available. Last but not the least, this study provides a 3D representation of the entire local gravity field instead of a single 2D surface, the (quasi) geoid.

How to cite: Li, X., Cunderlik, R., Lin, M., Macak, M., Zahorec, P., Papco, J., Minarechova, Z., Krcmaric, J., and Roman, D.: FVM: A Good Match to Airborne Gravimetry?, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-1346, https://doi.org/10.5194/egusphere-egu24-1346, 2024.

This groundbreaking study addresses the imperative to comprehend gravity shifts resulting from Groundwater Storage (GWS) variations in the Arabian Peninsula. Despite the critical importance of water resource sustainability and its relationship with gravity, limited research emphasizes the need for expanded exploration. The investigation explores the impact of GWS extraction on the gravity field, utilizing Gravity Recovery and Climate Experiment (GRACE) and Global Land Data Assimilation System (GLDAS) data in addition to validation using WaterGAP Global Hydrology Model (WGHM). Spanning April 2002 to June 2023, the study predicts GWS trends over the next decade using the Seasonal Autoregressive Integrated Moving Average (SARIMA) model.  The comprehensive time-series Analysis reveals a huge GRACE-derived GWS trend about -4.90±0.32 mm/year during the period of study. This significantly influences the gravity anomaly GA values, demonstrating a corresponding fluctuation in GWS time series. The projected GWS indicates a depletion rate of 14.51 km³/year over the next decade. The correlation between GWS and GA is substantial at 0.80, while GA and rainfall correlation is negligible due to low precipitation rates. Employing multiple linear regression explains 80.61% of the variance in gravity anomaly due to GWS, precipitation, and evapotranspiration. The study investigates climate change factors—precipitation, temperature, and evapotranspiration—providing a holistic understanding of forces shaping GWS variations. Precipitation and evapotranspiration exhibit nearly equal values, limiting GWS replenishment opportunities. This research holds significance in studying extensive GWS withdrawal in the Arabian Peninsula, particularly concerning crust mass stability. Integrating GRACE and hydrological models’ datasets furnishes a comprehensive understanding, contributing valuable foresight into the future trajectory of GWS. The results illuminate intricate relationships between GWS, gravity anomalies, and climate factors, presenting a robust framework for sustainable water resource management. 

How to cite: Mohasseb, H. A., Shen, W., Abd-Elmotaal, H. A., and Jiao, J.: Assessing Groundwater Sustainability in the Arabian Peninsula and its Impact on Gravity Fields through GRACE Measurements , EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-2185, https://doi.org/10.5194/egusphere-egu24-2185, 2024.

Although machine learning has become increasingly important in geodesy related fields such as geophysics, seismology and remote sensing, its applications in geodesy, especially in physical geodesy, are still in its early stages. The main reason for this can be attributed to the black box nature of pure data-driven machine learning, which lacks physical interpretability and credibility, making it difficult for machine learning approaches to be used in physical geodesy that takes reliability and accuracy as its core criteria. Physics-Informed Neural Networks (PINNs) is a class of deep learning algorithms aims to seamlessly integrate data and physical prior knowledge including ordinary or partial differential equations, it can yield more physically interpretable machine learning models that provide robust and accurate predictions. We present the PINN approach for gravimetric geoid modeling from Earth gravity model, terrestrial and airborne gravity datasets. A convolutional neural network (CNN) deep learning architecture is used, gravity measurements and physical laws are integrated by embedding the Laplace’s equation of disturbing potential and the fundamental equation of gravity anomaly into the loss function of the neural network using automatic differentiation. The PINN based geoid computation approach is tested in the area of the Colorado 1-cm geoid experiment. Simulated gravity observations and GNSS leveling derived geoid heights based on EIGEN-6C4 are used to validate the theoretical correctness and validity of the proposed PINN approach, and its performance on precise geoid modeling in this challenging area is evaluated using the actual terrestrial and airborne gravity observations, GNSS leveling measured geoid heights and high resolution DEM provided by NGS/NOAA.

How to cite: Jiang, T., Tu, Z., and Dang, Y.: Physics-Informed Neural Networks for geoid modeling: preliminary results in Colorado, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-4068, https://doi.org/10.5194/egusphere-egu24-4068, 2024.

The coverage of the gravity data plays an important role in the geoid determination process. Still some parts in the world have poor gravity data coverage, with sometimes, large data gaps, e.g., Africa. In this paper we study the effect of implementing Moho depths on the gravity interpolation at large data gaps. For this reason, and in order to qualify that effect, an artificial data gap has been made in the gravity data set of Austria (originally with perfect gravity data coverage). The outcome of the present study is essential for the IAG sub-commission on the gravity and geoid in Africa in order to determine the African geoid from the available data sets with the best possible precision. The gravity interpolation has been made at the original omitted data points at the data gap with and without the Moho information. The interpolated gravity has thus been compared to the original omitted data values for both cases to determine the effect of using Moho depths on gravity interpolation. The results are shown and comprehensively discussed.

How to cite: Abd-Elmotaal, H. and Kühtreiber, N.: Effect of Implementing Moho Depths on Gravity Interpolation at Large Data Gaps , EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-4477, https://doi.org/10.5194/egusphere-egu24-4477, 2024.

The combination of satellite positioning techniques (e.g., GPS) and high-resolution geoid or quasi-geoid models provides an alternative to the expensive and time-consuming spirit leveling for the determination of physical heights. The reliability of the physical heights thus undergoes the same accuracy limitations of the (quasi-) geoid models. However, in many regions, especially developing or newly industrializing countries, there is no reliable regional gravity model, due to the low availability or quality of surface gravity data. This study tackles such challenges in a case study in the northwestern part of South America and provides the first up-to-date high-resolution Colombian quasi-geoid model.

This region is a challenging study area with coastlines on both the Pacific and the Atlantic Ocean and rugged topography with high elevation reaching more than 5,000 m. Available terrestrial and airborne data were collected during the last eight decades, which frequently contain systematic errors and biases and the corresponding metadata is missing. We develop approaches to validate and improve the quality of old gravity datasets. They are then combined with a global gravity model (GGM) and topography models, which play an important role in mountainous areas, within the remove-compute-restore (RCR) procedure. In the offshore area, satellite altimetry-derived gravity data are additionally incorporated, which are obtained from the latest release of the DTU (Technical University of Denmark) gravity anomaly grid, DTU21GRA.

The computed quasi-geoid model is thoroughly validated with independent GPS/leveling data. It delivers an STD of 15.76 cm in comparison to the GPS/leveling data, which is 36% smaller than that obtained from the latest South American quasi-geoid model QGEIOD2021 (24.51 cm). Five recent high-resolution GGMs, namely EGM2008, EIGEN6C4, GECO, SGG-UGM-1, and XGM2019 are also validated using the same GPS/leveling data. They deliver STD values of 28.09 cm, 21.10 cm, 20.39 cm, 20.93 cm, and 17.86 cm, respectively, which are averagely 38% larger than that of our computation.

How to cite: Liu, Q., Schmidt, M., and Sánchez, L.: Methods for geoid determination in regions with challenging data quality and coverage, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-5383, https://doi.org/10.5194/egusphere-egu24-5383, 2024.

We have analysed the digital elevation models (DEMs) published in recent years and merged them to create a new elevation grid together with complementary Earth’s relief model for bedrock, surface, bathymetry, ice surface, and ice thickness. Although each model is unique in its own, the merged grid is able to provide seamless elevation information based on a common reference surface globally with high spatial resolution as required for various geoscience applications. We present how the merging procedure was carried out, how the accuracy of the model was evaluated and for which application areas it is intended. Our aim is to disseminate the use of a homogeneous and a consistent elevation model that is particularly suitable for geodetic applications in all parts of the world, including global and regional geoid calculations. The DEMs and associated auxiliary files included in the merged product are: TanDEM-X 90m over all dry land and ice-covered regions, ETOPO2022, GEBCO-2022 and GEBCO-2023 over land and ocean, BedMachineGreenland-v5 over Greenland, BedMachineAntarctica-v3 over Antarctica, GLOBathy (the Global Lakes Bathymetry Dataset) over lakes globally. Masks for ocean, dry land, lakes, islands in the lakes, ponds on the islands, ice-covered land, ice-covered shelves, the area outside Greenland and the ice-covered lake Vostok (Antarctica) were taken into account in the merging. This complete model is anticipated to provide a standardized DEM for various applications in geodesy and geophysics.  Our future plans include high resolution topographic gravity field modelling using this consolidated 30 arc-second digital elevation model and laterally varying global density data.

How to cite: Förste, C., Abrykosov, O., and Ince, E. S.: A consolidated 30 Arc-second Global Digital Elevation Model for Geodesy and Geophysics, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-8340, https://doi.org/10.5194/egusphere-egu24-8340, 2024.

Many geodetic-related observations nowadays require a precise local geoid height that is as accurate as sub-centimeters. Here, we develop a method to combine global Earth Gravitational Model (EGM), Digital Terrain Model (DTM), as well as highly accurate local gravity and Global Navigation Satellite System (GNSS) observations to achieve this goal. We carried out several observation campaigns to obtain high space resolution and high accuracy gravity and GNSS data. Firstly, we analyze the accuracy of the commonly used methods such as those that use EGM only or use EGM and DTM combined. Then we test our method with a synthetic earth that was developed with EGM, DTM, and local high-resolution topography. Our results should that, the high degree EGM-only geoid has a mean error of tens of centimeters; the geoid from combined EGM and DTM can achieve accuracy of several centimeters; and if we want to have a local geoid with deviations less than sub-centimeter, high accurate observations with space resolution as high as 1"x1" are needed.

How to cite: Huang, J., Zheng, G., Yushan, A., and Qiu, B.: Observation requirements for precise determination of local (quasi)geoid, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-14283, https://doi.org/10.5194/egusphere-egu24-14283, 2024.

In the frame of the GeoNetGNSS project, funded by the European Union and National Funds through the Region of Central Macedonia (RCM) in Northern Greece, regional gravimetric and hybrid geoid models have been determined with the main goal being to support a newly established network of Continuously Operating Reference Stations (CORS). The main aim was to assist everyday surveying purposes by delivering accurate orthometric heights based on GNSS/Levelling, i.e., determining 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, employing the Remove-Compute-Restore (RCR) technique and both stochastic and spectral evaluations of Stokes’ integral. Consequently, a hybrid deterministic and stochastic approach was used to model the residuals of the gravimetric geoid solution relative to available GNSS/Levelling geoid heights. The latter refer to 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. Various parametric models ranging from simple north-south bias and tilt to 2^nd and 3^rd order degree polynomial models were evaluated in terms of the fit residual absolute and relative differences. After the deterministic fit, a collocation approach employing exponential and 2^nd order Gauss-Markov covariance functions was used to model the stochastic residuals. Finally, the hybrid deterministic and stochastic corrector surface, provided as grid corrections for the entire area under study, has been determined to accommodate user needs for orthometric height determination. From the results acquired, absolute differences of the order of 1-2 cm and relative ones at the 3-4 ppm have been achieved after validation against independent GNSS/Levelling observations.

How to cite: Natsiopoulos, D. A., Vergos, G., Mamagiannou, E. G., Tzanou, E. A., Triantafyllou, A. I., Tziavos, I. N., Ramnalis, D., and Polychronos, V.: Refinements of regional gravimetric and hybrid geoid models in support of the GeoNetGNSS CORS network in Northern Greece, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-17974, https://doi.org/10.5194/egusphere-egu24-17974, 2024.

Coastal zones exhibit unique altimetry signal characteristics, primarily influenced by the presence of land artifacts. The shape of the altimetry echo serves as a distinctive marker, representing the physical parameters of the surface it originates from. Open ocean reflections for SAR (Synthetic Aperture Radar) mode yield signals with a steep leading edge and a trailing edge modeled by a negative exponential function. In contrast, land areas in coastal zones typically produce specular and quasi-specular waveforms. The presence of specific waveform classes is further influenced by seasonality and changes in land use and patterns such as coastal erosion.

This study aims to classify altimetry waveforms in coastal zones at various global sites and subsequently retrack the identified waveform classes using an optimal retracking strategy. Site selection is based on the availability of in-situ tide gauge data. Waveform classification is achieved using a Long Short-Term Memory (LSTM) auto-encoder, capturing the temporal nature of waveforms and providing an 8-dimensional feature representation. In addition, the LSTM-autoencoder  provides de-noised waveforms, which are used for subsequent retracking processes.

Different waveform shapes necessitate specific retracking strategies. While an Ocean retracker suffices for SAR waveforms over open oceans, it is inadequate for retracking specular, quasi-specular, and multi-peak waveforms. Advanced retracking algorithms such as OCOG, Threshold, ALES, Beta-5, and Beta-9 are employed based on the waveform class.

To validate the proposed strategy, the performance of the altimetry product, sea level anomalies, and retracking outcomes are compared with established coastal altimetry products like XTRACK, in-situ tide gauge data, and popular retracking algorithms like OCOG, Ocean retracker, Threshold, Beta-5 and Beta-9. Sea level anomalies are derived from sensor geophysical data records (SGDR) of altimetry missions and compared with existing coastal altimetry products and in-situ tide gauge records. Evaluation metrics such as Pearson's correlation coefficient and root mean square error assess the agreement in seasonal and yearly trends, as well as the accuracy of measurements.

This comprehensive analysis aims to validate the effectiveness of the proposed coastal waveform post-processing strategy, showcasing its ability to quantify long-term sea level trends and explore regional variations.

How to cite: Kant, S. and Devaraju, B.: Altimetry Waveform Classification and Retracking Strategy for Improved Coastal Altimetry Products, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-770, https://doi.org/10.5194/egusphere-egu24-770, 2024.

It is known that natural hazards such as volcanic eruptions, earthquakes, and tsunamis can trigger acoustic and gravity waves (AGWs) that could reach the ionosphere and generate electron density disturbances known as Travelling Ionospheric Disturbances (TIDs). These disturbances can be investigated in terms of variations in the ionospheric total electron content (TEC) measurements, collected by continuously operating ground-based Global Navigation Satellite Systems (GNSS) receivers. The VARION (Variometric Approach for Real-Time Ionosphere Observation) algorithm is a well-known real-time tool for estimating TEC variations. It is based on single-time differences of geometry-free combinations of GNSS carrier-phase measurements.

Artificial Intelligence (AI), particularly in machine learning, offers computational efficiency and data handling, leading to its exploration in ionospheric studies. In this context, the abundance of data allows the exploration of a VARION-based machine learning classification approach to detect TEC perturbation. For this purpose, we used the VARION-TEC variations from the 2015 Illapel earthquake and tsunami, leveraging the distinct ionospheric response triggered by the event.

We employed machine learning algorithms, specifically Random Forest (RF) and XGBoost (XGB), using the VARION-core observations (i.e., dsTEC/dt) as input features. We formulated a binary classification problem using supervised machine learning algorithms and manually labelled the time frames of TEC perturbations as the target variable. We considered two elevation cut-off time series, namely 15° and 25°, to which we applied the classifier. XGBoost with a 15° elevation cut-off dsTEC/dt time series reached the best performance, achieving an F1 score of 0.77, recall of 0.74, and precision of 0.80 on the test data. More in detail, regarding the testing samples, the model accurately classified 183 out of 247 (74.09%) samples of sTEC variations related to the earthquake and tsunami (True Positives, TP). Moreover, 2975 out of 3021 (98.49%) testing samples were correctly classified as containing no sTEC variations caused by an earthquake (True Negatives, TN). However, 64 out of 247 samples (25.91%) were erroneously classified as not containing sTEC variations related to the event (False Negatives, FN), while 46 out of 3021 (1.51%) were wrongly classified as containing sTEC variations related to the earthquake and tsunami (False Positives, FP).

This model showed a 75-second average deviation in predicting perturbation time frames for testing links, equivalent to 5 steps in the 15-second time series intervals. This highlights the algorithm's potential for early detection of ionospheric perturbations from earthquakes and tsunamis, aiding in early warning purposes.

Finally, the model efficiently detects TIDs within 2-3 minutes, showing an impressive computational efficiency, crucial for effective early warning systems. It relies only on the VARION-generated real-time TEC time series (dsTEC/dt), enabling its application in an operational real-time setting using real-time GNSS data.

In conclusion, this work demonstrates high-probability TEC signature detection by machine learning for earthquakes and tsunamis, which can be used to enhance tsunami early warning systems.

How to cite: Fuso, F., Ravanelli, M., Crocetti, L., and Soja, B.: Using Machine Learning for identifying TEC signatures related to earthquakes and tsunamis: the 2015 Illapel event case study, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-1853, https://doi.org/10.5194/egusphere-egu24-1853, 2024.

    Evaluation of uncertainties of geodetic parameter estimates 
is the problem that is not yet solved in a satisfactory way. 
A direct evaluation of the uncertainties derived from a least 
square solution is labeled "formal" and is usually biased, 
sometimes up to an order of magnitude. Customary, the use of 
formal errors for scientific analysis is discouraged. We claim 
that the root of the problem is neglecting off-diagonal elements 
in the variance-covariance matrix of the noise in the data. 
A careful reconstruction of the full variance-covariance matrix, 
including the off-diagonal terms greatly improves realism of 
uncertainty estimates derived from least squares. We processed 
the dataset of VLBI group delays and built the a priori 
variance-covariance of the atmosphere-driven noise based on 
analysis of the output of NASA high-resolution numerical weather 
models. We found that the uncertainties of parameter estimates 
derived from this least square solution that uses such 
variance-covariance matrices become much closer to realistic 
errors. We consider approaches for for implementation of this 
method in routine data analysis of space geodesy data.

How to cite: Petrov, L. and Hanaba, N.: From formal errors towards realistic uncertainties, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-2619, https://doi.org/10.5194/egusphere-egu24-2619, 2024.

Accurate ionospheric models are essential for single-frequency high-precision Global Navigation Satellite Systems (GNSS) applications. Global ionospheric maps (GIMs), which depicts the global distribution of vertical total electron content (VTEC), are a widely used ionospheric product provided by the International GNSS Service (IGS). To meet the increasing need for real-time applications, the IGS real-time service (RTS) has been established and offers real-time (RT) GIMs that can be used for real or near-real time applications. However, the accuracy of present RT GIMs is still significantly lower compared with the final GIMs. IGS RT GIMs show an RMSE of 3.5-5.5 TECU compared to the IGS final GIMs. In this study, we focus on enhancing the accuracy of RT GIMs through machine learning (ML) approaches, specifically a classical Convolutional Neural Network (CNN) and a Generative Adversarial Network (GAN). The objective is to bridge the gap between the RT GIMs and the final IGS GIMs. This is achieved by using RT GIMs as input and final GIMs as target. The ML approach is applied to the IGS combined RT GIMs and Universitat Politècnica de Catalunya (UPC) RT GIMs. The performance of the improved RT GIMs is evaluated in comparison to the combined IGS final GIM.

We consider over 11'000 pairs of RT GIMs and final GIMs. Over a comprehensive test period spanning 3.5 months, the proposed approach shows promising results with an enhancement of more than 30% in accuracy of RT GIMs. Especially for regions with high VTEC values, which are most critical, the results show a significant improvement. The results demonstrate the model’s great potential in generating more accurate and refined real-time maps.

The integration of ML techniques proves to be a promising avenue for refining and augmenting the precision of real-time ionospheric maps, thereby addressing critical needs in the realm of space weather monitoring and single-frequency applications.

How to cite: Iten, M., Mao, S., and Soja, B.: Enhanced Real-time Global Ionospheric Maps using Machine Learning, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-3117, https://doi.org/10.5194/egusphere-egu24-3117, 2024.

In PPP, the stochastic model of observation determines the availability and reliability of positioning accuracy, and the observations are usually weighted according to the angle of the GNSS observation, and the smaller the angle of the observation, the more the influence of atmospheric noise and multipath on the observation data increases, and the accuracy of the observations decreases. Based on this, we proposed multi-indicator comprehensive assessment based on grey correlation analysis for observation stochastic modeling of PPP. The position dilution of precision (PDOP), carrier-to-noise density ratio (C/N0) and pseudorange multipath indicators are selected to construct a multi-indicator matrix. Firstly, the indicators are normalized, and then the entropy weight of each assessment indicator is calculated to determine the indicator weight. Meanwhile, after selecting the optimal indicator set, the matrix is constructed to find the grey correlation coefficient and finally the grey correlation degree. According to the above method, the comprehensive assessment results of the quality of satellite observation data for each epoch can be obtained, and the PPP weight array can be established. One-week observations from 243 MGEX stations are selected to conduct GPS-only, Galileo-only and BDS-3-only kinematic PPP, the stochastic model using the highest-elevation and the proposed method is applied, respectively. The results show that, compared with the traditional method, the positioning accuracies and convergence time all can be improved using the proposed method. The positioning accuracies of GPS can be improved by about 4.23%, 8.66%, 5.04% and 5.46% in the east(E), north(N), up(U) and three-dimensional(3D) directions, respectively; 15.96%, 14.25%, 14.72% and 15.01% for Galileo; and 13.53%, 8.42%, 11.65% and 11.40% for BDS-3. The average improvements of convergence time in the east, north and up directions are 5.53%, 7.80% and 5.01% for GPS, BDS-3 and Galileo, respectively.

How to cite: Huang, G., Li, M., and Wang, L.: Multi-Indicator Comprehensive Assessment for Observation Stochastic Model of PPP, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-4609, https://doi.org/10.5194/egusphere-egu24-4609, 2024.

The precise point positioning-real-time kinematic (PPP-RTK) method achieves fast convergence in global navigation satellite system (GNSS) positioning and navigation. Correcting slant ionospheric delays is crucial for this purpose. The conventional way of obtaining slant ionospheric corrections at the user end involves generating an ionospheric map using a first-order polynomial function or interpolating using methods such as IDW and Kriging. However, with these approaches is challenging to obtain precise and stable ionospheric corrections especially during ionospheric disturbances, potentially degrading the positioning solution even with augmentation. Fortunately, machine learning has the capability to capture complex and non-linear characteristics of diverse data, offering a potential solution to this issue.

In this study, we aim to improve the accuracy of slant ionospheric delay models using machine learning and evaluate them in PPP-RTK. Initially, we extract highly precise slant ionospheric delays from carrier-phase measurements after ambiguity resolution for two regional GNSS networks in Switzerland and the South of China. Then, we employ the Gaussian Process Regressor to interpolate epoch-specific and satellite-specific slant ionospheric delays, utilizing latitude and longitude as features. Two different approaches are tested: the direct interpolation from reference stations and the indirect interpolation from a gridded map. Our results indicate that the accuracy of interpolated ionospheric delays using machine learning is higher than with conventional methods, including IDW and Kriging. Finally, we evaluate PPP-RTK positioning results with ionospheric corrections from the different interpolation methods, revealing that the machine learning method exhibits superiority in both positioning accuracy and convergence time over conventional methods.

How to cite: Lyu, S., Xiang, Y., Yu, W., and Soja, B.: Machine learning-based regional slant ionospheric delay model and its application for PPP-RTK, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-5743, https://doi.org/10.5194/egusphere-egu24-5743, 2024.

Automatic detection and characterization of spatial and temporal features of surface deformation signals associated with anthropogenic activities is a challenging task, with important implications for the evaluation of multi-hazard related to human activities (e.g. earthquakes, subsidence, sea-level rise and flooding), particularly in coastal areas. In this work, we use synthetic Global Navigation Satellite System (GNSS) displacement time-series and apply Deep Learning algorithms (i.e. Convolutional Neural Network (CNN) and Autoencoder) in extracting the time and space features of ground deformation due to natural and anthropogenic processes. We focus on improving three fundamental aspects such as the spatial coverage, the temporal coverage and the accuracy of measurement that come from GNSS technique. The study area is Northern Italy, and particularly the North Adriatic coasts, where gas and oil production sites as well as gas storage sites are present. If in production sites hydrocarbon is constantly extracted during the year, in storage sites the gas/oil is usually injected from April to October and extracted between November and March. Our goals are to understand the effect of hydrocarbon production and extraction/injection process on surface deformation as precisely measured by the dense network of continuous GNSS stations operating in the study area and the ability of CNN-Autoencoder to characterize ground displacements caused by anthropogenic processes. Aims of this work are to identify temporal and spatial patterns in ground deformation time series caused by oil and gas extraction/or gas storage (i.e. extraction and injection); and estimate reservoir parameters (i.e. volumes, depths and extensions). We realize the training dataset by setting up 202 GNSS stations, randomly locating gas/oil reservoirs, which are described by a simple Mogi model, characterized by different depths and temporal evolution of volume changes. The Mogi model, as an approximate spherical shape of a reservoir, displays the ratio of horizontal displacement to vertical displacement due to volume change (i.e. inflating or deflating) and pressure varying with time. The temporal evolution of the volumes of the Mogi sources is simulated by using different parameters associated with several functions namely seasonal, exponential, multi-linear and bell shape. Weighted Principal Component Analysis (WPCA) is used to deal with missing data, which is a common feature in GNSS time series, under an assumption that the weights of missing data are zero. Furthermore, since the CNN-Autoencoder works by analyzing images, the synthetic GNSS time series are interpolated by leveraging the Kriging Interpolation method, which is a Gaussian Process Regression, to obtain the ground displacement in 2D physical space. After calibrating the CNN-Autoencoder model with the synthetic GNSS time series, the model is applied to real data. The code is written in Python and runs on a High-performance computing (HPC) cluster with Graphic Process Unit (GPU) at National Institute of Geophysics and Volcanology (INGV) in Bologna, Italy. 

How to cite: Vu, D. T., Gualandi, A., Pintori, F., Serpelloni, E., and Pezzo, G.: Deep Learning spatio-temporal analysis of anthropogenic ground deformation recorded by GNSS time series in the North Adriatic coasts of Italy , EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-9203, https://doi.org/10.5194/egusphere-egu24-9203, 2024.

In recent years, geodesy based on spaceborne microwave remote sensing has gained significant advances. However, whether the observations from the Global Navigation Satellite System (GNSS) or Interferometric Synthetic Aperture Radar (InSAR), the results are inevitably influenced by atmospheric tropospheric delay. Although the tropospheric zenith total delay (ZTD) can be estimated through the gridded meteorological data products and empirical models provided by the ERA5 reanalysis product, its accuracy is still insufficient to meet the needs of modern geodesy. To overcome this challenge, we propose leveraging machine learning techniques to learn local spatio-temporal patterns of tropospheric delay for inferring total zenith delay (ZTD) and zenith wet delay (ZWD) at any location within the learning area.

Our findings indicate that artificial neural networks can establish a robust mapping between ZTD estimated by empirical models and GNSS-measured ZTD. Then employing the ensemble learning strategy and the time series dynamics model, the ZTD at any location within the sample area can be inferred. To evaluate our approach, we conducted tests during the active water vapor season in the Tübingen region of Baden-Württemberg, Germany, from June 25 to July 9, 2022. In comparative experiments with the root mean square error (RMSE) of Zenith Total Delay (ZTD) derived from ERA5, our proposed method yielded a significant reduction in RMSE, decreasing it from 16.4292mm to 7.2108mm. This reflects a remarkable accuracy improvement of 56.11%.

The proposed approach holds promise for enhancing the precision of GNSS positioning, InSAR earth observation, and generating more dependable water vapor products.

How to cite: Wang, D., Wang, L., and Kutterer, H.: Machine learning for atmospheric delay correction in geodesy, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-9543, https://doi.org/10.5194/egusphere-egu24-9543, 2024.

Borehole strainmeters are remarkably precise instruments.  They are often installed to record deformation produced by earthquakes, postseismic slip, and slow earthquakes.  Strainmeters can record such tectonic deformation on timescales of minutes to months with a precision of 0.1 to 1 nanostrain; they record sub-Angstrom changes in borehole width.  

However, the instruments’ high precision also extends to non-tectonic signals.  The borehole width often changes by more than 1 Angstrom when it rains, when atmospheric pressure increases, and when snow loads the ground.  Thus if we want to take full advantage of the instruments and investigate tectonic deformation with high precision, we need to understand and remove the deformation produced by non-tectonic signals like water loading.

So in this study, I present several neural network-based models of hydrologic deformation.  Neural networks are ideal for this modelling as they can accommodate the nonlinearity of the system; 1 cm of rain will cause different deformation if it falls on saturated, winter soil than if it falls on dry, summer soil.  Further, neural networks can take advantage of the abundance of local weather data, including at short timescales.  In my initial modelling, I attempt to reproduce and predict strain as a function of current and past precipitation, atmospheric pressure, wind speed, and temperature.  For simplicity and ease of use, all these parameters are taken from the ECMWF reanalysis models.

I design two neural networks to model the observed strain, using physical intuition to limit the number of free parameters and thus improve the training.  The first network is simple; it creates 10 linear combinations of past rainfall, with exclusively positive weights, and then combines those linear combinations to predict the strain.  The second network also creates 10 linear combinations of past rainfall with positive weights.  But it multiplies those linear combinations of rain by nonlinear functions that could represent the state of the Earth and aquifers.  These nonlinear functions include dependencies on past rainfall, atmospheric pressure, wind speed, and temperature.

These networks train quickly, within a few minutes, and they do a reasonable job of producing the first-order features of the strain.  Both models accommodate more than 50% of the hydrologic signal on timescales of days.  Such modelling may or may not be interesting to hydrologists, but for those interested in tectonic deformation, reproducing and removing 50% of the hydrologic signal means removing 50% of the noise.

It is likely that a better developed and regularised model could remove much more of the noise, and we are continuing to add constraints, initial weights, and training schemes to improve the hydrologic modelling.

How to cite: Hawthorne, J.: Neural network-based hydrology corrections for borehole strainmeters, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-10154, https://doi.org/10.5194/egusphere-egu24-10154, 2024.

Displacement time series from Global Navigation Satellite System (GNSS) at daily rates are used commonly to investigate and understand the processes controlling Earth's surface deformation originating from tectonic processes such as postseismic slip, slow slip events and viscoelastic relaxation, but also non-tectonic processes such as reflectometry, atmospheric sensing and remote sensing. For each individual research field, different parts of the total recorded GNSS displacement time series are of intrest. A major difficulty is the modeling and isolation of non-tectonic seasonal signals that are established to be related with non-tidal surface loading.

In the past, many methods were developed with some success based on Kalman filters, matrix factorization and various approaches using curve fitting to separate the tectonic and non-tectonic contributions. However, these methods still have some difficulties in  isolating the seasonal loading signals especially in the presence of interannual variations in the seasonal loading pattern and steps in the time series.

We present here a deep learning model trained on a globally distributed, continuous 8-10 years long dataset of ~8000 stations PPP-GNSS displacement time series from NGL to estimate the seasonal loading signals using a global non-tidal surface loading model developed at ESM-GFZ. We compare our model to other statistical methods for isolation of the seasonal with the established method of subtraction of the non-tidal surface loading signals (hydrological loading, and non-tidal atmospheric and oceanic loading) as our baseline. We also present the evaluation of our model and its capabilities in reducing the seasonal loading signal as well as parts of the high-frequency scattering in the original GNSS time series.

How to cite: Çökerim, K., Bedford, J., and Dobslaw, H.: A Globally Trained Deep Learning Model for Estimation of Seasonal Residual Signals in GNSS displacement time series, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-10290, https://doi.org/10.5194/egusphere-egu24-10290, 2024.

Geological hazards caused by both natural forces and human-induced disturbances, such as land subsidence, earthquakes, tectonic motion, mining activities, coastal erosion, volcanic activities, and permafrost alterations, cause great adverse effects to earth’s surface. The preservation of a comprehensive record detailing past, present, and future surface movements is imperative for effective disaster risk mitigation and property protection. Interferometric Synthetic Aperture Radar (InSAR) is widely recognized as a highly effective and extensively employed geodetic technique for comprehending the spatiotemporal evolution of historical ground surface deformation. However, it only reveals the past deformation evolution process and the deformation update is slowly considering the long revisit cycle of satellites. Deformation evolution in the future is also crucial for preventing and mitigating geological hazards. Unlike traditional mathematical-statistical models and physical models, machine learning methods provide a new perspective and possibility to efficiently and automatically mine the time series information over a large-scale area. In the context of InSAR time series prediction over large areas, the previous researches do not consider the spatiotemporal heterogeneity caused by various factors over a large-scale area and mainly focus on one typical deformation point.

Therefore, in this study, we present a framework designed to predict large-scale spatiotemporal InSAR time series by integrating independent component analysis (ICA) and a Long Short-Term Memory (LSTM) machine learning model. This framework is developed with a specific focus on addressing spatiotemporal heterogeneity within the dataset. The utilization of the ICA method is employed to identify and capture the displacement signals of interest within the InSAR data, enabling the characterization of independent time series signals associated with various natural or anthropogenic processes. Additionally, a K-means clustering approach is incorporated to partition the study area into spatiotemporal homogeneity subregions across a large-scale region, aiming to mitigate potential decreases in model accuracy caused by data heterogeneity. Subsequently, LSTM models are constructed for each cluster, and optimal parameters are determined. The proposed framework is rigorously tested using simulated datasets and validated against two real-world cases—land subsidence in the Willcox Basin and post-seismic deformation following the Sarpol-e Zahab earthquake. Comparative analysis demonstrates that the proposed model surpasses the original LSTM, resulting in a 34% and 17% improvement in average prediction accuracy, respectively. The spatial prediction results in 60 days over the two cases are mapped with high accuracy.

This study introduces an integrated framework that seamlessly integrates InSAR data processing with machine learning techniques such as LSTM to enhance our ability to predict deformation over large-scale geographical areas. The adaptability of the proposed model has made it an alternative to numerical or empirical models, especially when detailed on-site data is scarce or challenging to obtain. While our immediate applications have focused on scenarios on land subsidence and post-seismic deformation, the broader implications of our methodology are evident. We anticipate the proposed framework will be expanded to various application domains, including mining, infrastructure stability, and other situations involving sustained motions. The proposed framework will ultimately contribute to more informed decision-making and risk assessment in complex dynamic systems.

How to cite: Peng, M., Motagh, M., Lu, Z., Xia, Z., Guo, Z., Zhao, C., and Quan, Y.: Improving ground deformation prediction in satellite InSAR using ICA-assisted RNN model , EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-10467, https://doi.org/10.5194/egusphere-egu24-10467, 2024.

Accurate prediction of Earth orientation parameters (EOPs) is critical for astro-geodynamics, high-precision space navigation, and positioning, and deep space exploration. However, the current models' prediction accuracy for EOPs is significantly lower than that of geodetic technical solutions, which can adversely affect certain high-precision real-time users. In this study, we introduce a simultaneous prediction approach for Polar Motion (PM) and Celestial Pole Offsets (CPO) employing deep neural networks, aiming to deliver precise predictions for both parameters.
The methodology comprises three components, with the first being feature interaction and selection. The process of feature selection within the context of deep learning differs from traditional methods for machine learning, and may not be directly applicable to theme since they are designed to automatically learn relevant features. Consequently, we propose in this step a solution based on feature engineering to select the best set of variables that can keep the model as simple as possible but with enough precision and accuracy using recursive feature elimination and the SHAP value algorithm, aiming to investigate the influence of FCN (Free Core Nutation) with its amplitude and phase on the CPO forecasting. This investigation is crucial since FCN is the main source of variance of the CPO series. Considering the role represented by the effective Angular Momentum functions (EAM), and their direct influence on the Earth's rotation, it is logical to assess numerically the impact of EAM on the Polar motion and FCN excitations. SHAP value aids in comprehending how each feature contributes to final predictions, highlighting the significance of each feature relative to others,  and revealing the model's dependency on feature interactions.
During the second phase, we formulate two deep-learning methods for each parameter. The first Neural Network incorporates all features, while the second focuses on the subset of features identified in the initial step. This stage primarily involves exploring feature and hyperparameter tuning to enhance model performance. The SHAP value algorithm is also used in this stage for interpretation. 
In the final phase, we construct a multi-task deep learning model designed to simultaneously predict ( CPO ) and ( PM ).  This model is built using the optimal set of features and hyperparameters identified in the preceding steps. To validate the methodology, we employ the most recent version of the time series from the International Earth Rotation and Reference Systems Service (IERS), namely IERS 20 C04 and EAM provided by the German Research Center for Geosciences (GFZ). We focus on a forecasting horizon of 90 days, the practical forecasting horizon needed in space-geodetic applications.
In the end, we conclude that the developed model is proficient in simultaneously predicting ( CPO ) and ( PM ). The incorporation of ( EAM ), sheds light on its role in CPO excitations and Polar Motion predictions.

How to cite: Guessoum, S., Belda, S., Ferrándiz, J. M., Begga, A., Karbon, M., Schuh, H., Modiri, S., and Heinkelmann, R.:  Feature Selection and Deep Learning for Simultaneous Forecasting of Celestial Pole Offset (CPO) and Polar Motion (PM), EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-10575, https://doi.org/10.5194/egusphere-egu24-10575, 2024.

Global Navigation Satellite Systems (GNSS) are best known for their accurate positioning, navigation and timing capabilities. In total, over 20.000 permanent high-grade GNSS stations are available worldwide, the positions of which are monitored with millimeter accuracy. Thanks to the high accuracy and the fact that these stations are mounted on the ground, subtle movements due to hydrological changes and crustal deformation can be observed. Thus, the GNSS observations contain valuable geophysical information. Although many geodetic applications require these movements to be properly understood and potentially corrected, this is not trivial due to the complexity of the interactions within the Earth’s system. Therefore, there is a severe lack of available models explaining residual GNSS station movements beyond conventionally modeled effects. On the opposite, if these movements are properly understood, GNSS observations might contribute to the correct interpretation of emerging environmental changes.

This study exploits the wealth of satellite-derived Earth observation (EO) data to derive suitable models to explain GNSS station movements. We combine GNSS station coordinate time series and EO variables with the help of machine learning techniques to benefit from various types of information. While the target vector consists of concatenated GNSS station coordinate time series over Europe, EO variables such as precipitation, soil water, snow water equivalent, and land cover data are used as input features. Different machine learning models, including Random Forest, XGBoost, and Multilayer Perceptron, are investigated and compared. Additionally, a sensitivity analysis is performed to determine the individual impact of EO variables to quantify what drives GNSS movements, which in turn, might allow monitoring the corresponding Earth system processes based on GNSS observations.

How to cite: Crocetti, L., Schneider, R., and Soja, B.: Explaining GNSS station movements based on Earth observation data, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-10706, https://doi.org/10.5194/egusphere-egu24-10706, 2024.

Abstract:

Machine Learning (ML) is emerging as a powerful tool for data analysis. Anomaly detection based on classical approaches is sometimes limited in processing speed on big data, especially for massive datasets. Meanwhile, quantum algorithms have been shown to have the potential for optimization, scenario simulation, and artificial intelligence. Thus, this study combines quantum algorithms and ML to improve the binary classification performance of ML models for better sensitivity of surface deformation detection. We experimented with GNSS-InSAR combination data to identify significant deformation regions in Northern Germany. We classify the movement characteristics based on four main features: vertical movement velocities, root mean square errors, standard deviations, and outliers in the GNSS-InSAR time series. Our primary results reveal that the classification accuracy based on Quantum Machine Learning (QML) is outstanding compared to the pure ML technique. Specifically, on the same sample dataset, the classification performance of the neural network based on pure ML is only around 50 to 70%, while that of the QML technique can reach ~90%. The significant deformation regions are concentrated in the river basins of Elbe, Weser, Ems, and Rhine, where the average surface subsidence speed varies around -4.5 mm/yr. Also, we suggest dividing the surface movement features in Northern Germany into five classes to reduce the effect of the data quality variety and algorithm uncertainty. Our findings will advocate the development of quantum computing applications as well as promote the potential of the QML for deformation analyses. 

Keywords:

Quantum Machine Learning, Binary Classification, GNSS-InSAR Data, Deformation Detection.

How to cite: Le, N., Männel, B., Motagh, M., Brack, A., and Schuh, H.: Quantum Machine Learning for Deformation Detection: Application for InSAR Point Clouds, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-11029, https://doi.org/10.5194/egusphere-egu24-11029, 2024.

The reception of non-line-of-sight (NLOS) signals is a prevalent issue for Global Navigation Satellite System (GNSS) applications in urban environments. Such signals can significantly degrade the positioning and navigation accuracy for pedestrians and vehicles. While various methods, such as dual-polarization antennas and 3D building models, have been proposed to identify NLOS signals, they often require additional equipment or impose computational burdens, which limits their practicality. In this study, we introduce a machine learning (ML)-based classifier designed to detect NLOS signals based solely on quality indicators extracted from raw GNSS observations. We examined several input features, including carrier-to-noise density and elevation, and analyzed their relative importance. The effectiveness of our approach was validated using multi-GNSS data collected statically in the city of Hannover. To establish ground truth (i.e., a target) for training and testing the model, we used ray tracing in combination with a 3D building model of Hannover. The developed ML-based classifier achieved an accuracy of approximately 90% for NLOS signal classification. Furthermore, a vehicle-borne data set was used to test the utility of the ML-based signal classifier for kinematic positioning. The performance of the ML-aided positioning solution was compared against a solution without NLOS classification (raw solution) and with the ray-tracing-based classification results (reference solution). It was found that the ML-based solution demonstrated positioning precisions of 0.47 m, 0.55 m and 1.02 in the east, north and up components, respectively. This represents improvements of 64.6%, 33.4% and 36.6% over the raw solution. Additionally, we examined the performance of the ML-based classifier across various urban environments along the vehicle trajectory to gain deeper insights.

How to cite: Pan, Y., Icking, L., Ruwisch, F., Schön, S., and Soja, B.: Non-line-of-sight GNSS Signal Classification for Urban Navigation Using Machine Learning , EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-11427, https://doi.org/10.5194/egusphere-egu24-11427, 2024.

One big challenge in the analysis and interpretation of geodetic data is the separation of the individual signal and noise components contained in the data. Specifically, the global, temporal gravity data obtained by the GRACE and GRACE Follow-On satellite missions contain spatial-temporal gravity signals caused by all kinds of mass variations in the Earth’s system. While only the sum of all signals can be measured, for geophysical interpretation, an extraction of individual signal contributions is necessary.

Therefore, our aim is to develop an algorithm solving the signal separation task in global, temporal gravity data. Since the individual signal components are characterized by specific patterns in space and time, the algorithm to be found needs to be able to extract patterns in the 3-dimensional latitude-longitude-time space.

We propose to exploit the pattern recognition abilities of deep neural networks for solving the signal separation task. Our method uses a multi-channel U-Net architecture which is able to translate the sum of various signals as single-channel input to the individual signal components as multi-channel output. The loss function is a weighted sum of the L2 losses of the individual signals.

We perform a supervised training using synthetic data derived from the updated Earth System Model of ESA. The latter consists of separate datasets for temporal gravity variations caused by mass redistribution processes in the atmosphere, the oceans, the continental hydrosphere, the cryosphere and the solid Earth.

In our study, we use different parts of this dataset to form training and test datasets. In this fully-synthetic framework, the ground truth of the individual signal components is also known in the testing stage, allowing a direct computation of the separation errors of the trained separation model.

In our contribution, we present results on optimizing our algorithm by tuning various hyperparameters of the neural network. Moreover, we demonstrate the impact of the number of superimposed signals and the definition of the loss function on the signal separation performance of our algorithm.

How to cite: Heller-Kaikov, B., Pail, R., and Werner, M.: Signal separation in global, temporal gravity data using a multi-channel U-Net, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-12487, https://doi.org/10.5194/egusphere-egu24-12487, 2024.

High-precision ionospheric prediction is essential for real-time applications of the Global Navigation Satellite System (GNSS), especially for single-frequency receivers. Various machine learning (ML) algorithms have been utilized for ionospheric forecasting and shown great potential. However, previous studies have primarily relied on IGS global ionospheric maps (GIMs) as training data to develop models for global vertical total electron content (VTEC) forecasting. The forecasting accuracy is thereby limited by the input IGS GIMs due to their low spatio-temporal resolution.

Our previous work proposed a neural network-based (NN-based) global ionospheric model. GIMs generated with this approach showcased enhanced accuracy compared with conventional IGS GIMs as we can finely resolve VTEC irregularities. In this study, we benefit from these ML-based GIMs by employing the transfer learning principle to improve the quality of GIM forecasts. The ML-based model for 1-day ahead global VTEC forecasting is first trained based on a series of IGS GIMs from 2004 to 2022. Then, it is fine-tuned using the recent NN-based GIMs from 2020 to 2022. In this context, the model can gain good generalizability from the large dataset of IGS GIMs while having comparable accuracy with NN-based GIMs. Different machine learning approaches, including convolution long short-term memory (ConvLSTM) network and transformer, are implemented and compared. To validate their performance, we perform hindcast studies to compare the 1-day ahead forecasts of our model with satellite altimetry VTEC and conducted single-frequency precise point positioning tests based on the forecast maps.

How to cite: Mao, S., Gou, J., and Soja, B.: An Ionospheric Forecasting Model Based on Transfer Learning Using High-Resolution Global Ionospheric Maps, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-12556, https://doi.org/10.5194/egusphere-egu24-12556, 2024.

Spaceborne GNSS Reflectometry (GNSS-R) is a novel remote sensing technique providing accumulating data volume with global coverage and enhanced temporal resolution. The reflected pre-existing L-Band signal of opportunity transmitted by the Global Navigation Satellite System contains information about the reflection surface properties which can be quantified and converted into data products for further studies. To retrieve such information, Artificial intelligence (AI) models are implemented to estimate geophysical parameters based on the GNSS-R observations. With more and more complex deep learning models being proposed and more and more input features being considered, understanding the decision-making process of the models and the contributions of the input features becomes as important as enhancing the model output accuracy.

This study explores the potential of the Explainable AI (XAI) to decode complex deep learning models for ocean surface wind speed estimation trained by the Cyclone GNSS (CYGNSS) observations. The input feature importance is evaluated by applying the SHAP (SHapley Additive exPlanations) Gradient Explainer to the model on an unseen dataset. By analyzing the SHAP value of each input feature, we find that in addition to the two known parameters that are used in the operational wind speed retrieval algorithm, other scientific and technical ancillary parameters, such as the orientation of the satellite and the signal power information are also useful for the model.

We seek to offer a better understanding of the deep learning models for estimating ocean wind speed using GNSS-R data and explore the potential features for more accurate retrieval. In addition to building an efficient model with effective inputs, XAI also helps us to discover the important factors found by models which can enhance the physical understanding of the GNSS-R mechanism.

How to cite: Xiao, T., Asgarimehr, M., Arnold, C., Zhao, D., Mou, L., and Wickert, J.: Explainable AI for GNSS Reflectometry: Investigating Feature Importance for Ocean Wind Speed Estimation, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-12715, https://doi.org/10.5194/egusphere-egu24-12715, 2024.

Snow is a key variable of the global climate system and the hydrological cycle, as well as one of the most critical sources of freshwater. Therefore, measurements of snow-related parameters such as seasonal snow height (SSH) or snow-water-equivalent (SWE) are of great importance for science, economy and society. Traditionally, these parameters are either measured manually or with automated ground-based sensors, which are accurate, but expensive and suffer from low temporal and spatial resolution.

A new alternative for such systems is the use of GNSS observations, by application of the GNSS interferometric reflectometry (GNSS-IR) method. The technique enables users to infer information about soil moisture, snow depth, or vegetation water content. Signal-to-Noise Ratio (SNR) observations collected by GNSS receivers are sensitive to the interference between the direct signal and the reflected signal (often referred to as “multipath”). The interference pattern changes with the elevation angle of the satellite, the signal wavelength, and the height of the GNSS antenna above the reflecting surface. By comparing this reflector heights estimated for snow surfaces with those from bare soil conditions, snow height can be determined.

The estimation of reflector heights, and respectively SSH, is typically carried out using Lomb-Scargle Periodogram (LSP) spectrum analysis. This study investigates the potential of machine learning methods for this task, using similar input parameters as the standard GNSS-IR retrieval. Results from different supervised algorithms such as Random Forest (RF) or Gradient Boosting (GB) are shown for different GNSS sites and experimental setups. First investigations indicate that snow heights can be successfully obtained with machine learning, with results less noisy than with classical approaches.

How to cite: Aichinger-Rosenberger, M. and Soja, B.: Exploring the performance of machine learning models for the GNSS-IR retrieval of seasonal snow height, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-14724, https://doi.org/10.5194/egusphere-egu24-14724, 2024.

Time series of interferometric SAR (InSAR) images offer the potential to detect and monitor surface displacements with high spatial and temporal resolution, even for small and slow deformation processes. Yet, due to the nature of InSAR, the interferometric signal can contain a multitude of contributions. Different displacement source mechanisms could superpose each other, signals that are residuals of atmospheric and topographic effects could not be completely removed during processing of the time series or non-coherent noise could exist. Therefore, the criteria for the selection of temporally stable pixels are often rather strict, leading to significant reduction of the spatial resolution density.

However, to understand the underlying processes of a deformation field, it is important to extract the displacement signals from the data at the best resolution possible and differentiate signals from different source mechanisms. Furthermore, being able to describe the displacement field as superposition of several simple mechanisms is a possible answer to the general question how the information content from tens of thousands of points each coming with a time series over hundreds of acquisitions can be extracted and comprehended.

We address these issues, by determining the dominant displacement signals of different sources in a subset of reliable pixels of InSAR time series datasets with data driven component analysis methods. Subsequently we use models of these signals to identify their displacement patterns in previously not regarded pixels. We utilize the statistical principal component analysis for removing uncorrelated signal contributions and compare different blind source separation methods, such as independent component analysis and independent vector analysis for differentiating between displacements of different origin.

We apply our method to a dataset of multiple orbits of Sentinel-1 InSAR time series from 2015 to 2022 above the gas storage cavern field Epe in NRW, Germany.  Epe displays a complex surface displacement field, consisting of trends caused by cavern convergence, cyclic gas pressure dependent contributions, as well as ground water dependent seasonal displacements. With our approach, we can successfully distinguish the signals of the different source mechanisms and obtain a dense spatial sampling of these signals. Our results show good agreement with geodetic measurements from GNSS and levelling and show a strong correlation to cavern filling levels and groundwater levels, suggesting causal relations.

How to cite: Seidel, A., Even, M., Westerhaus, M., and Kutterer, H.: Signal decomposition of multi-source displacement fields with component analysis methods, applied to InSAR time series of the Epe gas storage cavern field (Germany), EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-16740, https://doi.org/10.5194/egusphere-egu24-16740, 2024.

In geological characterization, the traditional methods that rely on the covariance matrix for continuous variable estimation often either neglect or oversimplify the challenge posed by subsurface non-stationarity. This study presents an innovative methodology using ancillary data such as geological insights and geophysical exploration to address this challenge directly, with the goal of accurately delineating the spatial distribution of subsurface petrophysical properties, especially, in large geological fields where non-stationarity is prevalent. This methodology is based on the geodesic distance on an embedded manifold and is complemented by the level-set curve as a key tool for relating the observed geological structures to intrinsic geological non-stationarity. During validation, parameters ρ and β were revealed to be the critical parameters that influenced the strength and dependence of the estimated spatial variables on secondary data, respectively. Comparative evaluations showed that our approach performed better than a traditional method (i.e., kriging), particularly, in accurately representing the complex and realistic subsurface structures. The proposed method offers improved accuracy, which is essential for high-stakes applications such as contaminant remediation and underground repository design. This study focused primarily on two-dimensional models. There is a need for three-dimensional advancements and evaluations across diverse geological structures. Overall, this research presents novel strategies for estimating non-stationary geologic media, setting the stage for improved exploration of subsurface characterization in the future.

How to cite: Park, E.: Manifold Embedding Based on Geodesic Distance for Non-stationary Subsurface Characterization Using Secondary Information, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-16940, https://doi.org/10.5194/egusphere-egu24-16940, 2024.

In the analysis of sub-annual climatological or geodetic time series such as tide gauges, precipitable water vapor, or GNSS vertical displacements time series but also temperatures or gases concentrations, seasonal cycles are often found to have a time-varying amplitude and phase.

These time series are usually modelled with a deterministic approach that includes trend, annual, and semi-annual periodic components having constant amplitude and phase-lag. This approach can potentially lead to inadequate interpretations, such as an overestimation of Global Navigation Satellite System (GNSS) station velocity, up to masking important geophysical phenomena that are related to the amplitude variability and are important for deriving trustworthy interpretation for climate change assessment.

We address that challenge by proposing a novel linear additive model called the fractional Sinusoidal Waveform process (fSWp), accounting for possible nonstationary cyclical long memory, a stochastic trend that can evolve over time and an additional serially correlated noise capturing the short-term variability. The model has a state space representation and makes use of the Kalman filter (KF). Suitable enhancements of the basic methodology enable handling data gaps, outliers, and offsets. We demonstrate our method using various climatological and geodetic time series to illustrate its potential to capture the time-varying stochastic seasonal signals.

How to cite: Kermarrec, G., Maddanu, F., Klos, A., and Proietti, T.: The fractional Sinusoidal wavefront Model (fSwp) for time series displaying persistent stationary cycles, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-24, https://doi.org/10.5194/egusphere-egu24-24, 2024.

On some maps of the first military survey of the Habsburg Empire, the upper direction of the sections does not face the cartographic north, but makes an angle of about 15° with it. This may be due to the fact that the sections were subsequently rotated to the magnetic north of the time. Basically, neither their projection nor their projection origin is known yet.

In my research, I am dealing with maps of Inner Austria, the Principality of Transylvania and Galicia (nowadays Poland and Ukraine), and I am trying to determine their projection origin. For this purpose, it is assumed, based on the archival documentation of the survey, that these are Cassini projection maps. My hypothesis is that they are Graz, Cluj Napoca or Alba Julia and Lviv. I also consider the position of Vienna in each case, since it was the main centre of the survey.

The angle of rotation was taken in part from the gufm1 historical magnetic model back to 1590 for the assumed starting points and year of mapping. In addition, as a theoretical case, I calculated the rotation angle of the map sections using coordinate geometry. I then calculated the longitude of the projection starting point for each case using univariate minimization. Since the method is invariant to latitude, it can only be determined from archival data.

Based on these, the starting point for Inner Austria from the rotation of the map was Vienna, which is not excluded by the archival sources, and since the baseline through Graz also started from there, it is partly logical. The map rotation for Galicia and Transylvania also confirmed the starting point of the hypothesis.  Since both Alba Julia and Cluj Napoca lie at about the same longitude, the method cannot make a difference there; and the archival data did not provide enough evidence. In comparison, the magnetic declination rotations yielded differences of about 1°, which may be due to an error in the magnetic model.

On this basis, I have given the assumed projections of the three maps with projection starting points, and developed a method for determining the projection starting points of the other rotated grid maps. The results suggest that there is a very high probability that the section network was rotated in the magnetic north direction, and thus provide a way to refine the magnetic declination data at that time.

With this method I managed to give new indirekt magnetic declinations data from Central-East Europe, which can help to improve the historical magnetic field models. The main reason for this is that we don’t have any measurement from that region.

Furthermore the difference beetwen the angle of the section north and the declination data from gufm1 always 0.8-1°. Maybe there are systematical data error at that region.

Supported by the ÚNKP-23-6 New National Excellence Program of the Ministry for Culture and Innovation from the source of the National Research, Development and Innovation Fund.

How to cite: Koszta, B. and Timár, G.: A possible cartographical data source for historical magnetic field improvement: The direction of the section north of the Habsburg first military survey, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-582, https://doi.org/10.5194/egusphere-egu24-582, 2024.

The alteration of traditional hydrological patterns due to global warming is leading to a modification of the hydrological cycle. This situation draws a complex scenario for the sustainable management of water resources. However, this issue offers a challenge for the development of innovative approaches that allow an in-depth capturing the logical temporal-dependence structure of these modifications to advance sustainable management of water resources, mainly through the reliable predictive models. In this context, Bayesian Causality (BC), addressed through Causal Reasoning (CR) and supported by a Bayesian Networks (BNs), called Bayesian Causal Reasoning (BCR) is a novel hydrological research area that can help identify those temporal interactions efficiently.

This contribution aims to assesses the BCR ability to discover the logical and non-trivial temporal-dependence structure of the hydrological series, as well as its predictability. For this, a BN that conceptually synthesizes the time series is defined, and where the conditional probability is propagated over the time throughout the BN through an innovative Dependence Mitigation Graph. This is done by coupling among an autoregressive parametric approach and causal model. The analytical ability of the BCR highlighted the logical temporal structure, latent in the time series, which defines the general behavior of the runoff. This logical structure allowed to quantify, through a dependence matrix which summarizes the strength of the temporal dependencies, the two temporal fractions that compose the runoff: one due to time (Temporally Conditioned Runoff) and one not (Temporally Non-conditioned Runoff). Based on this temporal conditionality, a predictive model is implemented for each temporal fraction, and its reliability is assessed from a double probabilistic and metrological perspective.

This methodological framework is applied to two Spanish unregulated sub-basins; Voltoya river belongs to Duero River Basin, and Mijares river, in the Jucar River Basin. Both cases with a clearly opposite temporal behavior, Voltoya independent and Mijares dependent, and with increasingly more problems associated with droughts.

The findings of this study may have important implications over the knowledge of temporal behavior of water resources of river basin and their adaptation. In addition, TCR and TNCR predictive models would allow advances in the optimal dimensioning of storage infrastructures (reservoirs), with relevant substantial economic/environmental savings. Also, a more sustainable management of river basins through more reliable control reservoirs’ operation is expected to be achieved. Finally, these results open new possibilities for developing predictive hydrological models within a BCR framework.

How to cite: Zazo, S., Molina, J. L., Patino-Alonso, C., and Espejo, F.: Predictive ability assessment of Bayesian Causal Reasoning (BCR) on runoff temporal series, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-1988, https://doi.org/10.5194/egusphere-egu24-1988, 2024.

Climate-induced forest mortality poses an increasing threat worldwide, which calls for developing robust approaches to generate early warning signals of upcoming forest state change. This research explores the potential of satellite imagery, utilizing advanced spatio-temporal indicators and methodologies, to assess the state of forests preceding mortality events. Traditional approaches, such as techniques based on temporal analyses, are impacted by limitations related to window size selection and detrending methods, potentially leading to false alarms. To tackle these challenges, our study introduces two new approaches, namely the Spatial-Temporal Moran (STM) and Spatial-Temporal Geary (STG) approaches, both focusing on local spatial autocorrelation measures. These approaches can effectively address the shortcomings inherent in traditional methods. The research findings were assessed across three study sites within California national parks, and Kendall's tau was employed to quantify the significance of false and positive alarms. To facilitate the measurement of ecosystem state change, trend estimation, and identification of early warning signals, this study also provides "stew" R package. The implications of this research extend to various groups, such as ecologists, conservation practitioners, and policymakers, providing them with the means to address emerging environmental challenges in global forest ecosystems.

How to cite: Alibakhshi, S.: Spatial-Temporal Analysis of Forest Mortality, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-3857, https://doi.org/10.5194/egusphere-egu24-3857, 2024.

Iram Parvez¹, Massimiliano Cannata², Giorgio Boni¹, Rossella Bovolenta¹ ,Eva Riccomagno³ , Bianca Federici¹

¹ Department of Civil, Chemical and Environmental Engineering (DICCA), Università degli Studi di Genova, Via Montallegro 1, 16145 Genoa, Italy (iram.parvez@edu.unige.it,bianca.federici@unige.it, giorgio.boni@unige.it, rossella.bovolenta@unige.it).

² Institute of Earth Sciences (IST), Department for Environment Constructions and Design (DACD), University of Applied Sciences and Arts of Southern Switzerland (SUPSI), CH-6952 Canobbio, Switzerland(massimiliano.cannata@supsi.ch).

³ Department of Mathematics, Università degli Studi di Genova, Via Dodecaneso 35, 16146 Genova, Italy(riccomag@dima.unige.it).

The deployment of hydrometeorological sensors significantly contributes to generating real-time big data. The quality and reliability of large datasets pose considerable challenges, as flawed analyses and decision-making processes can result. This research aims to address the issue of anomaly detection in real-time data by exploring machine learning models. Time-series data is collected from IstSOS - Sensor Observation Service, an open-source software that stores, collects and disseminates sensor data. The methodology consists of Gated Recurrent Units based on recurrent neural networks, along with corresponding prediction intervals, applied both to individual sensors and collectively across all temperature sensors within the Ticino region of Switzerland. Additionally, non-parametric methods like Bootstrap and Mean absolute deviation are employed instead of standard prediction intervals to tackle the non-normality of the data. The results indicate that Gated Recurrent Units based on recurrent neural networks, coupled with non-parametric forecast intervals, perform well in identifying erroneous data points. The application of the model on multivariate time series-sensor data establishes a pattern or baseline of normal behavior for the area (Ticino). When a new sensor is installed in the same region, the recognized pattern is used as a reference to identify outliers in the data gathered from the new sensor.

How to cite: Parvez, I.: Exploring Machine Learning Models to Detect Outliers in HydroMet Sensors, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-4280, https://doi.org/10.5194/egusphere-egu24-4280, 2024.

For its immunity to post-formation geological modifications, zircon is widely utilized as chronological time capsule and provides critical time series data potential to unravel key events in Earth’s geological history, such as supercontinent cycles. Fourier analysis, which assumes stationary periodicity, has been applied to zircon-derived time series data to find the cyclicity of supercontinents, and wavelet analysis, which assumes non-stationary periodicity, corroborates the results of Fourier Analysis in addition to detecting finer-scale signals. Nonetheless, both methods still prognostically assume periodicity in the zircon-derived time-domain data. To stay away from the periodicity assumption and extract more objective information from zircon data, we opt for a Bayesian approach and treat zircon preservation as a composite stochastic process where the number of preserved zircon grains per magmatic event obeys logarithmic series distribution and the number of magmatic events during a geological time interval obeys Poisson distribution. An analytical solution was found to allow us to efficiently invert for the number and distribution(s) of changepoints hidden in the globally compiled zircon data, as well as for the zircon preservation potential (encoded as a model parameter) between two neighboring changepoints. If the distributions of changepoints temporally overlap with those of known supercontinents, then our results serve as an independent, mathematically robust test of the cyclicity of supercontinents. Moreover, our statistical approach inherently provides a sensitivity parameter the tuning of which allows to probe changepoints at various temporal resolution. The constructed Bayesian framework is thus of significant potential to detect other types of trend swings in Earth’s history, such as shift of geodynamic regimes, moving beyond cyclicity detection which limits the application of conventional Fourier/Wavelet analysis.

How to cite: Qian, H., Tian, M., and Zhang, N.: Unveiling Geological Patterns: Bayesian Exploration of Zircon-Derived Time Series Data, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-5268, https://doi.org/10.5194/egusphere-egu24-5268, 2024.

Semi-enclosed freshwater and brackish ecosystems, characterised by restricted water outflow and prolonged residence times, often accumulate nutrients, influencing their productivity and ecological dynamics. These ecosystems exhibit significant variations in bio-physical-chemical attributes, ecological importance, and susceptibility to human impacts. Untangling the complexities of their interactions remains challenging, necessitating a deeper understanding of effective management strategies adapted to their vulnerabilities. This research focuses on the bio-physical aspects, investigating the differential effects of spring and summer light on phytoplankton communities in semi-enclosed freshwater and brackish aquatic ecosystems.

Through extensive field sampling and comprehensive environmental parameter analysis, we explore how phytoplankton respond to varying light conditions in these distinct environments. Sampling campaigns were conducted at Müggelsee, a freshwater lake on Berlin's eastern edge, and Barther Bodden, a coastal lagoon northeast of Rostock on the German Baltic Sea coast, during the springs and summers of 2022 and 2023, respectively. Our analysis integrates environmental factors such as surface light intensity, diffuse attenuation coefficients, nutrient availability, water column dynamics, meteorological data, Chlorophyll-a concentration, and phytoplankton communities. Sampling encompassed multiple depths at continuous intervals lasting three days.

Preliminary findings underscore significant differences in seasonal light availability, with summer exhibiting extended periods of substantial light penetration. These variations seem to impact phytoplankton abundance and diversity uniquely in each ecosystem. While ongoing analyses are underway, early indications suggest distinct phytoplankton responses in terms of species composition and community structure, influenced by the changing light levels. In 2022 the clear water phase during spring indicated that bloom events have occurred under ice cover much earlier than spring, while in the summer there were weak and short-lived blooms of cyanobacteria. The relationship between nutrient availability and phytoplankton dynamics, however, remains uncertain according to our data.

This ongoing study contributes to understanding the role of light as a primary driver shaping phytoplankton community structures and dynamics in these environments.  Our research findings offer insights for refining predictive models, aiding in ecosystem-specific eutrophication management strategies, and supporting monitoring efforts of Harmful Algal Blooms.

How to cite: Kaharuddin, A. and Kaligatla, R.: Comparative Study of Spring and Summer Light Effects on Phytoplankton Communities in Semi-Enclosed Fresh- and Brackish Aquatic Ecosystems., EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-5733, https://doi.org/10.5194/egusphere-egu24-5733, 2024.

Forecasting the aurora and its location accurately is important to mitigate any potential harm to vital infrastructure like communications and electricity grid networks. Current auroral prediction models rely on our understanding of the interaction between the magnetosphere and the solar wind or geomagnetic indices. Both approaches do well in predicting but have limitations concerning forecasting (geomagnetic indices-based model) or because of the underlying assumptions driving the model (due to a simplification of the complex interaction). By applying machine learning algorithms to this problem, gaps in our understanding can be identified, investigated, and closed. Finding the important time scales for driving empirical models provides the necessary basis for our long-term goal of predicting the aurora using machine learning.

Periodicities of the Earth’s magnetic field have been extensively studied on a global scale or in regional case studies. Using a suite of different time series analysis techniques including frequency analysis and investigation of long-scale changes of the median/ mean, we examine the dominant periodicities of ground magnetic field measurements at selected locations. A selected number of stations from the SuperMAG network (Gjerloev, 2012), which is a global network of magnetometer stations across the world, are the focus of this investigation.

The periodicities retrieved from the different magnetic field components are compared to each other as well as to other locations. In the context of auroral predictions, an analysis of the dominating periodicities in the auroral boundary data derived from the IMAGE satellite (Chisham et al., 2022) provides a counterpart to the magnetic field periodicities.

Ultimately, we can constrain the length of time history sensible for forecasting.

How to cite: Gilmore, K. R., Bentley, S. N., and Smith, A. W.: Magnetospheric time history:  How much do we need for forecasting?, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-6065, https://doi.org/10.5194/egusphere-egu24-6065, 2024.

Dynamical systems can display a range of dynamical regimes (e.g. attraction to, fixed points, limit cycles, intermittency, chaotic behaviour) depending on the values of parameters in the system. In this work we demonstrate how non-parametric entropy estimation codes (in particular NPEET) based on the Kraskov method can be applied to find regime transitions in a 3D chaotic model (the Lorenz 1963 system) when varying the values of the parameters. These infromation-theory-based methods are simpler and cheaper to apply than more traditional metrics from dynamical systems (e.g. computation of Lyapunov exponents). The non-parametric nature of the method allows for handling long time series without a prohibitive computational burden. 

How to cite: Amezcua, J. and Chakraborty, N.: Using information-theory metrics to detect regime changes in dynamical systems, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-6151, https://doi.org/10.5194/egusphere-egu24-6151, 2024.

Evaluation of scaling properties and fractal formalisms is one of the potential approaches for modelling complex series. Understanding the complexity and fractal characterization of drought index time series is essential for better preparedness against drought disasters. This study presents a novel visibility graph-based evaluation of fractal characterization of droughts of three meteorological subdivisions of India. In this method, the horizontal visibility graph (HVG) and Upside-down visibility graph (UDVG) are used for evaluating the network properties for different standardized precipitation index (SPI) series of 3, 6 and 12 month time scales representing short, medium and long term droughts. The relative magnitude of fractal estimates is controlled by the drought characteristics of wet-dry transitions. The estimates of degree distribution clearly deciphered the self-similar properties of droughts of all the subdivisions. For an insightful depiction of drought dynamics, the fractal exponents and spectrum are evaluated by the concurrent application of Sand Box Method (SBM) and Chhabra and Jenson Method (CJM). The analysis was performed for overall series along with the pre- and post-1976-77 Global climate shift scenarios. The complexity is more evident in short term drought series and UDVG formulations implied higher fractal exponents for different moment orders irrespective of drought type and locations considered in this study. Useful insights on the relationship between complex network and fractality are evolved from the study, which may help in improved drought forecasting. The visibility graph based fractality estimation evaluation is efficient in capturing drought and it has vast potential in the drought predictions in a changing environment.

Keywords:  Drought, Fractal, SPI, Visibility Graph

How to cite: Rajesh, S. M., Bahuleyan, M., Nair GR, A., and Sankaran, A.: Fractal complexity evaluation of meteorological droughts over three Indian subdivisions using visibility Graphs, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-9367, https://doi.org/10.5194/egusphere-egu24-9367, 2024.

The Wavelet-Induced Mode Extraction procedure (WIME) [2] was developed drawing inspiration from Empirical Mode Decomposition. The concept involves decomposing the signal into modes, each presenting a characteristic frequency, using continuous wavelet transform. This method has yielded intriguing results in climatology [3,4]. However, the initial algorithm did not account for the potential existence of slight frequency fluctuations within a mode, which could impact the reconstruction of the original signal [4]. The new version (https://atoms.scilab.org/toolboxes/toolbox_WIME/0.1.0) now allows for the evolution of a mode in the space-frequency half-plane, thus considering the frequency evolution of a mode [2]. A natural application of this tool is in the analysis of Milankovitch cycles, where subtle changes have been observed throughout history. The method also refines the study of solar activity, highlighting the role of the "Solar Flip-Flop." Additionally, the examination of temperature time series confirms the existence of cycles around 2.5 years. It is now possible to attempt to correlate solar activity with this observed temperature cycle, as seen in speleothem records [1].

[1] Allan, M., Deliège, A., Verheyden, S., Nicolay S. and Fagel, N. Evidence for solar influence in a Holocene speleothem record, Quaternary Science Reviews, 2018.
[2] Deliège, A. and Nicolay, S., Extracting oscillating components from nonstationary time series: A wavelet-induced method, Physical Review. E, 2017.
[3] Nicolay, S., Mabille, G., Fettweis, X. and Erpicum, M., A statistical validation for the cycles found in air temperature data using a Morlet wavelet-based method, Nonlinear Processes in Geophysics, 2010.
[4] Nicolay, S., Mabille, G., Fettweis, X. and Erpicum, M., 30 and 43 months period cycles found in air temperature time series using the Morlet wavelet, Climate Dynamics, 2009.

How to cite: Faulx, E., Fettweis, X., Mabille, G., and Nicolay, S.: Wavelet-Induced Mode Extraction procedure: Application to climatic data, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-9537, https://doi.org/10.5194/egusphere-egu24-9537, 2024.

A wide range of geoprocesses manifest as observable events in a variety of contexts, including shifts in palaeoclimate regimes, evolutionary milestones, tectonic activities, and more. Many prominent research questions, such as synchronisation analysis or power spectrum estimation of discrete data, pose considerable challenges to linear tools. We present recent advances using a specific similarity measure for discrete data and the method of recurrence plots for different applications in the field of highly discrete event data. We illustrate their potential for palaeoclimate studies, particularly in detecting synchronisation between signals of discrete extreme events and continuous signals, estimating power spectra of spiky signals, and analysing data with irregular sampling.

How to cite: Marwan, N. and Braun, T.: New concepts on quantifying event data, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-10258, https://doi.org/10.5194/egusphere-egu24-10258, 2024.

Nowadays photovoltaic panels are becoming more affordable, efficient, and popular due to their low carbon footprint. PV panels can be installed in many places providing green energy to the local grid reducing energy cost and transmission losses. Since the PV production is highly dependent on the weather conditions, it is extremely important to estimate expected output in advance in order to maintain energy balance in the grid and provide enough time to schedule load distribution. The PV production output can be calculated by various statistical and machine learning prediction methods. In general, the more data available, the more precise predictions can be produced. This poses a problem for recently installed PV panels for which not enough data has been collected or the collected data are incomplete. 

A possible solution to the problem can be the application of an approach called Transfer Learning which has the inherent ability to effectively deal with missing or insufficient amounts of data. Basically, Transfer Learning is a machine learning approach which offers the capability of transferring knowledge acquired from the source domain (in our case a PV panel with a large amount of historical data) to different target domains (PV panels with very little collected historical data) to resolve related problems (provide reliable PV production predictions). 

In our study, we investigate the application, benefits and drawbacks of Transfer Learning for one day ahead PV production prediction. The model used in the study is based on complex neural network architecture, feature engineering and data selection. Moreover, we focus on the exploration of multiple approaches of adjusting weights in the target model retraining process which affect the minimum amount of training data required, final prediction accuracy and model’s overall robustness. Our models use historical meteorological forecasts from Deutscher Wetterdienst (DWD) and photovoltaic measurements from the project PVOutput which collects data from installed solar systems across the globe. Evaluation is performed on more than 100 installed PV panels in Central Europe.

How to cite: Lóderer, M., Sandanus, M., Pavlík, P., and Rozinajová, V.: Application of Transfer Learning techniques in one day ahead PV production prediction, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-10415, https://doi.org/10.5194/egusphere-egu24-10415, 2024.

In each magnetic observatory, the magnetic field is registered in local Cartesian coordinate systems associated with the geographic coordinates of the locations of these observatories. To observe extraterrestrial magnetic field sources, such as the interplanetary magnetic field or magnetic clouds, a method of joint processing of data from magnetic observatories of the international Intermagnet network was implemented. In this method, the constant component is removed from the observation results of individual observatories, their measurement data is converted into the ecliptic coordinate system, and the results obtained from all observatories are averaged after the coordinate transformation.

The first data on joint processing of measurement results from the international network of Intermagnet magnetic observatories in the period before the onset of magnetic storms of various types, during these storms and after their end are presented. There is a significant improvement in the signal-to-noise ratio after combining the measurement results from all observatories, which makes it possible to isolate weaker external magnetic fields. A change in the shape of magnetic field variations is shown, which can provide new knowledge about the mechanism of development of magnetic storms.

How to cite: Zhumabayev, B., Vassilyev, I., Mendakulov, Z., Fedulina, I., and Kapytin, V.: Results of joint processing of magnetic observatory data of international Intermagnet network in a unified coordinate system, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-11897, https://doi.org/10.5194/egusphere-egu24-11897, 2024.

We introduce the CLEAN algorithm to identify narrowband Ultra Low Frequency (ULF) Pc5 plasma waves in Earth’s magnetosphere. The CLEAN method was first used for constructing 2D images in astronomical radio interferometry but has since been applied to a huge range of areas including adaptation for time series analysis. The algorithm performs a nonlinear deconvolution in the frequency domain (equivalent to a least-squares in the time domain) allowing for identification of multiple individual wave spectral peaks within the same power spectral density. The CLEAN method also produces real amplitudes instead of model fits to the peaks and retains phase information. We applied the method to GOES magnetometer data spanning 30 years to study the distribution of narrowband Pc5 ULF waves at geosynchronous orbit. We found close to 30,0000 wave events in each of the vector magnetic field components in field-aligned coordinates. We discuss wave occurrence and amplitudes distributed in local time and frequency. The distribution of the waves under different solar wind conditions are also presented. With some precautions, which are applicable to other event identification methods, the CLEAN technique can be utilized to detect wave events and its harmonics in the magnetosphere and beyond. We also discuss limitations of the method mainly the detection of unrealistic peaks due to aliasing and Gibbs phenomena.

How to cite: Inceoglu, F. and Loto'aniu, P.: Using the CLEAN Algorithm to Determine the Distribution of Ultra Low Frequency Waves at Geostationary Orbit, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-12928, https://doi.org/10.5194/egusphere-egu24-12928, 2024.

Understanding volcanic activity through time series data analysis is crucial for uncovering the fundamental physical mechanisms governing this natural phenomenon.

In this study, we show the application of multifractal and fractal methodologies, along with statistical analysis, to investigate time series associated with volcanic activity. We aim to make use of these approaches to identify significant variations within the physical processes related to changes in volcanic activity. These methodologies offer the potential to identify pertinent changes preceding a high-energy explosion or a significant volcanic eruption.

In particular, we apply it to analyze two study cases. First, the evolution of the multifractal structure of volcanic emissions of low, moderate, and high energy explosions applied to Volcán de Colima (México years 2013-2015). The results contribute to obtaining quite evident signs of the immediacy of possible dangerous emissions of high energy, close to 8.0x10^8 J. Additionally, the evolution of the adapted Gutenberg-Richter seismic law to volcanic energy emissions contributes to confirm the results obtained using multifractal analysis. Secondly, we also studied the time series of the Gutenberg-Richter b-parameter of seismic activities associated with volcanic emissions in Iceland, Hawaii, and the Canary Islands, through the concept of Disparity (degree of irregularity), the fractal Hurst exponent, H, and several multifractal parameters. The results obtained should facilitate a better knowledge of the relationships between the activity of volcanic emissions and the corresponding related seismic activities.  

How to cite: Monterrubio-Velasco, M., Lana, X., Arámbula-Mendoza, R., and Zúñiga, R.: Applying Multifractal Theory and Statistical Techniques for High Energy Volcanic Explosion Detection and Seismic Activity Monitoring in Volcanic Time Series, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-12938, https://doi.org/10.5194/egusphere-egu24-12938, 2024.

Spatially interpolated meteorological data products are widely used in the geosciences as well as disciplines like epidemiology, economics, and others. Recent work has examined methods for quantifying uncertainty in gridded estimates of near-surface air temperature that produce distributions rather than simply point estimates at each location. However, meteorological variables are correlated not only in space but in time, and sampling without accounting for temporal autocorrelation produces unrealistic time series and potentially underestimates cumulative errors. This work first examines how uncertainty in air temperature estimates varies in time, both seasonally and at shorter timescales. It then uses data-driven, spectral, and statistical methods to better characterize uncertainty in time series of estimated air temperature values. Methods for sampling that reproduce spatial and temporal autocorrelation are presented and evaluated. The results of this work are particularly relevant to domains like agricultural and ecology. Physical processes including evapotranspiration and primary production are sensitive to variables like near-surface air temperature, and errors in these important meteorological inputs accumulate in model outputs over time.

How to cite: Doherty, C. and Wang, W.: Characterizing Uncertainty in Spatially Interpolated Time Series of Near-Surface Air Temperature, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-13593, https://doi.org/10.5194/egusphere-egu24-13593, 2024.

Vegetation phenology is the recurring of plant growth, including the cessation and resumption of growth, and plays a significant role in shaping terrestrial water, nutrient, and carbon cycles. Changes in temperature and precipitation have already induced phenological changes around the globe, and these trends are likely to continue or even accelerate. While warming has advanced spring arrival in many places, the effects on autumn phenology are less clear-cut, with evidence for earlier, delayed, or even unchanged end of the growing season (EOS). Meteorological droughts are intensifying in duration and frequency because of climate change. Droughts intricately impact changes in vegetation, contingent upon whether the ecosystem is limited by water or energy. These droughts have the potential to influence EOS changes. Despite this, the influence of drought on EOS remains largely unexplored. This study examined moisture’s role in controlling EOS by understanding the relationship between precipitation anomalies, vegetation’s sensitivity to precipitation (SPPT), and EOS. We also assess regional variations in responses to the impact of SPPT on EOS.

The study utilized multiple vegetation and water satellite products to examine the patterns of SPPT in drought and its impact on EOS across aridity gradients and vegetation types. By collectively evaluating diverse SPPTs from various satellite datasets, this work offers a comprehensive understanding and critical basis for assessing the impact of drought on EOS. We focused on the Northern Hemisphere from 2000 to 2020, employing robust statistical methods. This work found that, in many places, there was a stronger relationship between EOS and drought in areas with higher SPPT. Additionally, a non-linear negative relationship was identified between EOS and SPPT in drier regions, contracting with a non-linear positive relationship observed in wetter regions. These findings were consistent across a range of satellite-derived vegetation products. Our findings provide valuable insights into the effects of SPPT on EOS during drought, enhancing our understanding of vegetation responses to drought and its consequences on EOS and aiding in identifying drought-vulnerable areas.

How to cite: Choi, E. and Gray, J.: Understanding the role of vegetation responses to drought in regulating autumn senescence, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-13879, https://doi.org/10.5194/egusphere-egu24-13879, 2024.

We present a machine-learning-based approach for predicting the geomagnetic main field changes, known as secular variation (SV), in a 5-year range for use for the 14^th generation of International Geomagnetic Reference Field (IGRF-14). The training and test datasets of the machine learning (ML) models are geomagnetic field snapshots derived from magnetic observatory hourly means, and CHAMP and Swarm-A satellite data (MCM Model; Ropp et al., 2020). The geomagnetic field data are not used as-is in the original time series but were differenced twice before training. Because SV is strongly influenced by the geodynamo process occurring in the Earth's outer core, challenges still persist despite efforts to model and forecast the realistic nonlinear behaviors (such as the geomagnetic jerks) of the geodynamo through data assimilation. We compare three physics-uninformed ML models, namely, the Autoregressive (AR) model, Vector Autoregressive (VAR) model, and Recurrent Neural Network (RNN) model, to represent the short-term temporal evolution of the geomagnetic main field on the Earth’s surface. The quality of 5-year predictions is tested by the hindcast results for the learning window from 2004.50 to 2014.25. These tests show that the forecast performance of our ML model is comparable with that of candidate models of IGRF-13 in terms of data misfits after the release epoch (Year 2014.75). It is found that all three ML models give 5-year prediction errors of less than 100nT, among which the RNN model shows a slightly better accuracy. They also suggest that Overfitting to the training data used is an undesirable machine learning behavior that occurs when the RNN model gives accurate reproduction of training data but not for forecasting targets.

How to cite: Sato, S. and Toh, H.: A machine-learning-based approach for predicting the geomagnetic secular variation, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-16981, https://doi.org/10.5194/egusphere-egu24-16981, 2024.

The quality of the seismic signal recorded at permanent and temporary stations is sometimes degraded, either abruptly or over time. The most likely cause is a high level of humidity, leading to corrosion of the connectors but environmental changes can also alter recording conditions in various frequency ranges and not necessarily for all three components in the same way. Assuming that the continuous seismic signal can be described by a normal distribution, we present a new approach to quantify the seismogram quality and to point out any time sample that deviates from this Gaussian assumption. To this end the notion of background Gaussian signal (BGS) to statistically describe a set of samples that follows a normal distribution. The discrete function obtained by sorting the samples in ascending order of amplitudes is compared to a modified probit function to retrieve the elements composing the BGS, and its statistical properties, mostly the Gaussian standard deviation, which can then differ from the classical standard deviation. Hence the ratio of both standard deviations directly quantifies the dominant gaussianity of the continuous signal and any variation reflects a statistical modification of the signal quality. We present examples showing daily variations in this ratio for stations known to have been affected by humidity, resulting in signal degradation. The theory developed can be used to detect subtle variations in the Gaussianity of the signal, but also to point out any samples that don't match the Gaussianity assumption, which can then be used for other seismological purposes, such as coda determination.

How to cite: Beucler, É., Bonnin, M., and Cuvier, A.: Introducing a new statistical theory to quantify the Gaussianity of the continuous seismic signal, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-17344, https://doi.org/10.5194/egusphere-egu24-17344, 2024.

Climate events may induce abnormal ocean wave activities, that can be detected by seismic array on nearby coastlines. We collected long-term continuous array seismic data in the Groningen area and the coastal areas of the North Sea, conducted a comprehensive analysis to extract valuable climate information hidden within the ambient noise. Through long-term spectral analysis, we identified the frequency band ranging from approximately 0.2Hz, which appears to be associated with swell waves within the region, exhibiting a strong correlation with the significant wave height (SWH). Additionally, the wind waves with a frequency of approximately 0.4 Hz and gravity waves with periods exceeding 100 seconds were detected from the seismic ambient noise. We performed a correlation analysis between the ambient noise and various climatic indexes across different frequency bands. The results revealed a significant correlation between the North Atlantic Oscillation (NAO) Index and the ambient noise around 0.17Hz.

Subsequently, we extracted the annual variation curves of SWH frequency from ambient noise at each station around the North Sea and assembled them into a sparse spatial grid time series (SGTS). An empirical orthogonal function (EOF) analysis was conducted, and the Principal Component (PC) time series derived from the EOF analysis were subjected to a correlation analysis with the WAVEWATCH III (WW3) model simulation data, thereby confirming the wave patterns. Moreover, we conducted the spatial distribution study of SGTS. The spatial features revealed that the southern regions of the North Sea exhibit higher wind-wave energy components influenced by the Icelandic Low pressure system and topography, which explains the correlation between ambient noise in the region and the NAO index. Furthermore, spatial features disclosed a correlation between the first EOF mode of the North Sea ocean waves and the third mode of sea surface temperature anomalies. This research shows the potential of utilizing existing off-shore seismic monitoring systems to study global climate variation and physical oceanography.

How to cite: Zhong, Y., Gu, C., Fehler, M., Prieto, G., Wu, P., Yuan, Z., Chen, Z., and Kang, B.: Unveiling Climate-Induced Ocean Wave Activities Using Seismic Array Data in the North Sea Region, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-17566, https://doi.org/10.5194/egusphere-egu24-17566, 2024.

Several machine learning algorithms and analytical techniques do not allow gaps or non-values in input data. Unfortunately, earth observation (EO) datasets, such as satellite images, are gravely affected by cloud contamination and sensor artifacts that create gaps in the time series of collected images. This limits the usage of several powerful techniques for modeling and analysis. To overcome these limitations, several works in literature propose different imputation methods to reconstruct the gappy time series of images, providing complete time-space datasets and enabling their usage as input for many techniques.

However, among the time-series reconstruction methods available in literature, only a few of them are publicly available (open source code), applicable without any external source of data, and suitable for application to petabyte (PB) sized dataset like the full Landsat archive. The few methods that match all these characteristics are usually quite trivial (e.g. linear interpolation) and, as a consequence, they often show poor performance in reconstructing the images. 

For this reason, we propose a new methodology for time series reconstruction designed to match all these requirements. Like some other methods in literature, the new method, named seasonally weighted average generalization (SWAG), works purely on the time dimension, reconstructing the images working on each time series of each pixel separately. In particular, the method uses a weighted average of the samples available in the original time series to reconstruct the missing values. Enforcing the annual seasonality of each band as a prior, for the reconstruction of each missing sample in the time series a higher weight is given to images that are collected exactly on integer multiples of a year. To avoid propagation of land cover changes in future or past images, higher weights are given to more recent images. Finally, to have a method that respects causality, only images from the past of each sample in the time series are used.

To have computational performance suitable for PB sized datasets the method has been implemented in C++ using a sequence of fast convolution methods and Hadamard products and divisions. The method has been applied to a bimonthly aggregated version of the global GLAD Landsat ARD-2 collection from 1997 to 2022, producing a 400 terabyte output dataset. The produced dataset will be used to generate maps for several biophysical parameters, such as Fraction of Absorbed Photosynthetically Active Radiation (FAPAR), normalized difference water index (NDWI) and bare soil fraction (BSF). The code is available as open source, and the result is fully reproducible.

References:

Potapov, Hansen, Kommareddy, Kommareddy, Turubanova, Pickens, ... & Ying  (2020). Landsat analysis ready data for global land cover and land cover change mapping. Remote Sensing, 12(3), 426.

Julien, & Sobrino (2019). Optimizing and comparing gap-filling techniques using simulated NDVI time series from remotely sensed global data. International Journal of Applied Earth Observation and Geoinformation, 76, 93-111.

Radeloff, Roy, Wulder, Anderson, Cook, Crawford, ... & Zhu (2024). Need and vision for global medium-resolution Landsat and Sentinel-2 data products. Remote Sensing of Environment, 300, 113918.

How to cite: Consoli, D., Parente, L., and Witjes, M.: A new methodology for time-series reconstruction of global scale historical Earth observation data, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-18061, https://doi.org/10.5194/egusphere-egu24-18061, 2024.

Climate variability gives rise to many different kinds of extreme impact events, including heat waves, crop failures, or wildfires. The frequency and magnitude of such events are changing under global warming. However, it is less known to what extent such events occur with some regularity, and whether this regularity is also changing as a result of climate change. Here, we present a novel method to systematically study the time-autocorrelation of these extreme impact events, that is, whether they occur with a certain regularity. In studies of climate change impacts, different types of events are often studied in isolation, but in reality they interact. We use ensembles of global biophysical impact simulations from the Inter-Sectoral Impact Model Intercomparison Project (ISIMIP) driven with climate models to assess current conditions and projections. The time series analysis is based on a discrete Fourier transformation that accounts for the stochastic fluctuations from the climate model. Our results show that some climate impacts, such as crop failure, indeed exhibit a dominant frequency of recurrence; and also, that these regularity patterns change over time due to anthropogenic climate forcing.

How to cite: Zantout, K., Frieler, K., and Schewe, J. and the ISIMIP team: The regularity of climate-related extreme events under global warming, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-18197, https://doi.org/10.5194/egusphere-egu24-18197, 2024.

The availability of comprehensive aerial photography is limited to the mid-20th century, posing a challenge for quantitatively analyzing long-term surface changes in proglacial areas. This creates a gap of approximately 100 years, spanning the end of the Little Ice Age (LIA). Employing digital monoplotting and historical terrestrial images, our study reveals quantitative surface changes in a LIA lateral moraine section dating back to the second half of the 19th century, encompassing a total study period of 130 years (1890 to 2020). With the long-term analysis at the steep lateral moraines of Gepatschferner (Kauner Valley, Tyrol, Austria) we aimed to identify changes in vegetation development in context with morphodynamic processes and the changing climate.

In 1953, there was an expansion in the area covered by vegetation, notably encompassing scree communities, alpine grassland, and dwarf shrubs. However, the destabilization of the system after 1980, triggered by rising temperatures and the resulting thawing of permafrost, led to a decline in vegetation cover by 2020. Notably, our observations indicated that, in addition to morphodynamic processes, the overarching trends in temperature and precipitation exerted a substantial influence on vegetation development. Furthermore, areas with robust vegetation cover, once stabilised, were reactivated and subjected to erosion, possibly attributed to rising temperatures post-1980.

This study demonstrates the capability of historical terrestrial images to enhance the reconstruction of vegetation development in context with morphodynamics in high alpine environments within the context of climate change. However, it is important to note that long-term mapping of vegetation development through digital monoplotting has limitations, contingent on the accessibility and quality of historical terrestrial images, as well as the challenges posed by shadows in high alpine regions. Despite these limitations, this long-term approach offers fundamental data on vegetation development for future modelling efforts.

How to cite: Ramskogler, K., Altmann, M., Mikolka-Flöry, S., and Tasser, E.: Long-term vegetation development in context of morphodynamic processes since mid-19th century, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-18210, https://doi.org/10.5194/egusphere-egu24-18210, 2024.

Discrimination of  geomagnetic quasi-periodic signals by using SSA Transform

• Palangio¹, L. Santarelli ¹

¹Istituto Nazionale di Geofisica e Vulcanologia L’Aquila

³Istituto Nazionale di Geofisica e Vulcanologia Roma

Correspondence to:  lucia.santarelli@ingv.it

Abstract

In this paper we present an application of  the SSA Transform to the detection and reconstruction of  very weak geomagnetic signals hidden in noise. In the SSA Transform  multiple subspaces are used for representing and reconstructing   signals and noise.  This analysis allows us to reconstruct, in the time domain, the different harmonic components contained in the original signal by using  ortogonal functions. The objective is to identificate the dominant  subspaces that can be attributed to the  signals and the subspaces that can be attributed to the noise,  assuming that all these  subspaces are orthogonal to each other, which implies that the  signals and noise  are independent of one another. The subspace of the signals is mapped simultaneously on several spaces with a lower dimension, favoring the dimensions that best discriminate the patterns. Each subspace of the signal space is used to encode different subsets of functions having common characteristics, such as  the same periodicities. The subspaces  identification was performed by using singular value decomposition (SVD) techniques,  known as  SVD-based identification methods  classified in a subspace-oriented scheme.The  quasi-periodic variations of geomagnetic field  has been investigated in the range of scale which span from 22 years to 8.9 days such as the  Sun’s polarity reversal cycle (22 years), sun-spot cycle (11 years), equinoctial effect (6 months), synodic rotation of the Sun (27 days) and its harmonics. The strength of these signals vary from fractions of a nT to tens of nT. Phase and frequency variability of these cycles has been evaluated from the range of variations in the geomagnetic field recorded at middle latitude place (covering roughly 4.5 sunspot cycles). Magnetic data recorded at L'Aquila Geomagnetic observatory (geographic coordinates: 42° 23’ N, 13° 19’E, geomagnetic coordinates: 36.3° N,87°.2 E, L-shell=1.6) are used from 1960 to 2009.

How to cite: Paolo Giovanni, P. and Lucia, S.: Discrimination of  geomagnetic quasi-periodic signals by using SSA Transform, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-19601, https://doi.org/10.5194/egusphere-egu24-19601, 2024.

Over the past decades, especially since 2014, large quantities of Earth Observation (EO) data became available in high spatial and temporal resolution, thanks to ever-developing constellations (e.g.: Sentinel, Landsat) and open data policy. However, in the case of optical images, affected by cloud coverage and the spatially changing overlap of relative satellite orbits, creating temporally generalized and dense time series by using only measured data is challenging, especially when studying larger areas.

Several papers investigate the question of spatio-temporal gap filling and show different interpolation methods to calculate missing values corresponding to the measurements. In the past years more products and technologies have been constructed and published in this field, for example Copernicus HR-VPP Seasonal Trajectories (ST) product.  These generalized data structures are essential to the comparative analysis of different time periods or areas and improve the reliability of data analyzing methods such as Fourier transform or correlation. Temporally harmonized input data is also necessary in order to improve the results of Machine Learning classification algorithms such as Random Forest or Convolutional Neural Networks (CNN). These are among the most efficient methods to separate land cover categories like arable lands, forests, grasslands and built-up areas, or crop types within the arable category.

This study analyzes the efficiency of different interpolation methods on Sentinel-2 multispectral time series in the context of land cover classification with Machine Learning. We compare several types of interpolation e.g. linear, cubic and cubic-spline and also examine and optimize more advanced methods like Inverse Distance Weighted (IDW) and Radial Basis Function (RBF). We quantify the accuracy of each method by calculating mean square error between measured and interpolated data points. The role of interpolation of the input dataset in Deep Learning (CNN) is investigated by comparing Overall, Kappa and categorical accuracies of land cover maps created from only measured and interpolated time series. First results show that interpolation has a relevant positive effect on accuracy statistics. This method is also essential in taking a step towards constructing robust pretrained Deep Learning models, transferable between different time intervals and agro-ecological regions.

The research has been implemented with the support provided by the Ministry of Culture and Innovation of Hungary from the National Research, Development and Innovation Fund, financed under the KDP-2021 funding scheme.

Keywords: time series analysis, Machine Learning, interpolation, Sentinel

How to cite: Simon, M., Richter-Cserey, M., Pacskó, V., and Kristóf, D.: Temporal Interpolation of Sentinel-2 Multispectral Time Series in Context of Land Cover Classification with Machine Learning Algorithms, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-22262, https://doi.org/10.5194/egusphere-egu24-22262, 2024.

The variability of the atmospheric drag force on satellites is influenced by several factors, which include neutral density and gas composition, solar activity, and the orientation and shape of the satellite. During periods of geomagnetic activity, changes in these properties contribute to significant variations in the drag force, impacting the satellite trajectory. Therefore, the atmospheric drag force is considered as one of the largest sources of error in the orbit estimation for Low Earth Orbit (LEO) satellites. The methods presently used for satellite orbit determination define a constant term to represent the drag force, which can result in significant errors in long-term propagation and prediction of satellite positions. This work aims to improve SGP4 orbit propagation method by updating the drag term at regular intervals. The estimation of the drag term implements atmospheric drag analysis, which involves calculating the satellite drag coefficients using different Gas-Surface Interaction (GSI) models and neutral density data from Global Ionosphere Thermosphere Model (GITM) to estimate the mean motion derivative. The results demonstrate improved orbit propagation and estimation of orbital decay for the Gravity Recovery and Climate Experiment (GRACE) and Communication/Navigation Outage Forecasting System (C/NOFS) satellites during selected periods containing quiet and storm times.

How to cite: Dey, S., Anderson, P., and Bukowski, A.: Improving Orbit Propagation of LEO Satellites Using Atmospheric Drag Analysis   , EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-827, https://doi.org/10.5194/egusphere-egu24-827, 2024.

Combined precise satellite orbits and clocks stand as core contributions from the International GNSS Service (IGS), integrating the individual inputs of various Analysis Centers (AC). The availability and quality of multi-GNSS products developed by ACs within the IGS multi-GNSS Pilot Project propel IGS towards replacing combined GPS and GLONASS products with homogeneous combined products encompassing all GPS, GLONASS, Galileo, BeiDou, and QZSS systems. A primary challenge faced by the IGS lies in refining the combination algorithm for multi-GNSS orbits and clocks to provide users with the utmost quality products.

This study delves into concepts aimed at enhancing the orbit combination algorithm, with a specific focus on adjusting the weighting scheme and detecting outlier observations. The core of the combination methodology adheres to the concept proposed by GFZ, employing a least-squares framework wherein weights used for combining AC orbits are determined through least-squares variance component estimation (VCE).

Four distinct weighting strategies are introduced and compared in this study. These strategies involve utilizing either the constellation, satellite type, satellite type on the same orbital plane, or each satellite individually to form datasets used in determining weights for each AC. Furthermore, a novel approach is developed to correct the weights for individual ACs based on the results of Satellite Laser Ranging orbit validation. This serves as an additional factor in the combination, mitigating the impact of systematic AC-dependent orbit mismodeling issues. All proposed strategies underwent testing using multi-GNSS orbit solutions over a 10-month period in 2023.

Firstly, the combination results show an agreement between the different AC’s input orbits around 15, 20, 30, 50, and 100 mm for GPS, GLONASS, Galileo, BeiDou, and QZSS, respectively. Regarding the AC weighting strategy, the constellation-specific weighting approach provides the most robust solution and allows for handling differences between AC-specific issues in the orbit modeling of individual constellations. The satellite-specific weighting approach offers better resilience against the adverse effects caused by the inhomogeneous quality of satellite blocks/types/generations within a constellation, especially for BeiDou. However, the satellite-specific weighting encounters problems related to the appearance of invalid negative variances/weights for individual satellites as the output of VCE, mainly for BDS-3 and QZSS. The negative variance component can be an important indication of defects in our variance component model. Grouping satellites of similar characteristics in a satellite-type-specific weighting approach increases redundancy and reduces the issue but not entirely. Ultimately, we demonstrate potential solutions to address this issue. This involves simplifying the iterated VCE or resorting to the legacy inverse mean square differences between the mean orbit and the AC’s orbits as weights, particularly in cases where the classic VCE proves ineffective.

How to cite: Zajdel, R., Mansur, G., Brack, A., Sakic, P., and Männel, B.: Optimizing Multi-GNSS Orbit Combination: A Comprehensive Study on Weighting Strategies and Outlier Detection ;, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-876, https://doi.org/10.5194/egusphere-egu24-876, 2024.

Orbital elements define the shape, size, and orientation of a satellite’s orbit, as well as the position of the orbiting satellite along the ellipse at a specific time. Currently, precise orbit determination relies solely on satellite observations. However, future plans involve equipping Genesis and Galileo satellites with Very Long Baseline Interferometry (VLBI) transmitters. This would enable to observe satellites with VLBI radio telescopes and allow to determine orbital elements from VLBI observations to satellites.

This study investigates the potential of VLBI observations to satellites to contribute to the determination of orbital elements. In a first step, schedules, including satellite and quasar observations, are created using VieSched++.  The Vienna VLBI and Satellite Software (VieVS) is used to simulate and analyze these schedules.  To introduce the orbital elements in the Least Squares Adjustment, the partial derivatives of the position vector with respect to the orbital elements are needed. There are different approaches available for computing these partials, including numerical, analytical, or using partials obtained from the ORBGEN module in the Bernese GNSS software.  Next, the partials of the position vector are utilized to determine the partial derivative of the time delay tau with respect to the orbital elements.

This enables the estimation of orbital elements from simulated VLBI observations to satellites. The estimated parameters' quality is evaluated based on the mean formal errors and repeatabilities. Furthermore, the correlations between all orbital elements are examined.

How to cite: Wolf, H., Böhm, J., and Hugentobler, U.: Potential of VLBI observations to satellites to estimate orbital elements , EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-2806, https://doi.org/10.5194/egusphere-egu24-2806, 2024.

GNSS processing for POD suffers from systematic errors when the location of the instantaneous phase center is not known
with a few millimeter accuracy. The traditional approach to model the GNSS phase center origin and variations is to
determine antenna phase maps iteratively from the residuals. A more direct approach consists in modeling the antenna
phase map through an expansion in well-chosen Zernike polynomials, in order to reduce potential correlations with dynamic
modeling errors. This strategy has been applied to derive the GNSS antenna phase maps of several altimetry missions such
as Sentinel-3A, Jason-3, Sentinel-6 MF and SWOT. The derived phase corrections were tested on CNES POE-G GNSS-only
reduced-dynamic orbit solutions to assess their impact and validate their benefits owing to independent SLR observations. 

How to cite: Baños Garcia, A.: In-flight GNSS phase map calibration modelling with Zernike polynomials, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-3521, https://doi.org/10.5194/egusphere-egu24-3521, 2024.

Combined satellite-only global gravity field models represent a combined solution of gravity field observations from multiple geodetic measurement principles and satellite missions. The advantage of such a combination is that it compensates for the weaknesses of individual observing techniques. However, when combining solutions estimated by different institutions, inconsistencies may arise due to the different algorithms and models used in the actually available software, leading to a deterioration in performance. To mitigate such performance degradation, it is advantageous to perform all evaluations with a uniform software package. Since our in-house Gravity Recovery Object Oriented Programming System (GROOPS) software tool has become a widely accepted tool in the scientific community, we have now also incorporated the Satellite Laser Ranging (SLR) functionality to ensure the continued development of the software. On this basis, the opportunity arises to uniformly determine all the contributions to the combined gravity field using a single software package. This contribution is intended as a preliminary study for the next Gravity Observation Combination (GOCO) model. In this regard, we present low-degree solutions based on SLR observations using GROOPS and compare them with findings from other research groups (e.g., Cheng et al. 2013, Krauss et al. 2019) as well as solutions based on the satellite mission GRACE and GRACE-FO.

How to cite: Suesser- Rechberger, B., Mayer-Guerr, T., Krauss, S., Dumitraschkewitz, P., Oehlinger, F., and Tieber-Hubmann, C.: Contribution of SLR to satellite-only global gravity field model, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-5366, https://doi.org/10.5194/egusphere-egu24-5366, 2024.

Since 2023, three different solutions for the latest (2020) realization of the International Terrestrial Reference System (ITRS) are publicly available, namely the ITRF2020, the JTRF2020 and the DTRF2020. All solutions are based on the same input data but were derived using different combination approaches and data correction strategies. Since the ITRS realizations are used as a priori reference frames for precise orbit determination (POD) of Earth orbiting satellites, it is important to investigate the impact of the different frames on the POD results.

In this study, we briefly introduce the different features of the ITRS realizations and elaborate how the data correction models (e.g., periodic variations vs. non-tidal loading corrections) of the different xTRF2020 solutions can be optimally applied for the POD of selected satellites tracked by Satellite Laser Ranging (SLR) stations. We conclude the study with results obtained for various orbital parameters, such as the scaling factor of the non-gravitational (non-conservative) accelerations as well as the estimated empirical accelerations. Finally, we summarize the optimal settings of each ITRS realization for the satellite PODs discussed in this paper (i.e., LAGEOS-1, LARES-2, Jason-1/2/3).

How to cite: Bloßfeld, M., Zeitlhöfler, J., Rudenko, S., and Seitz, M.: Application of ITRS 2020 realizations for the SLR-based POD of selected geodetic and Earth-observing satellites, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-5385, https://doi.org/10.5194/egusphere-egu24-5385, 2024.

Laser ranging to spherical satellites is a major source for the determination of geophysical and geometric parameters like the scale of the reference system and the lowest degree (1-2) gravity field coefficients, i.e. geocenter motion, dynamic oblateness and the orientation of the rotation axis of the Earth. The International Laser Ranging Service (ILRS) is collecting Satellite Laser Ranging (SLR) observations of a global station network, providing the range data as normal points to its analysis centers, which perform precise orbit determination (POD) and network solutions based on 7 day orbital arcs. Currently, efforts are undertaken to extend the classical ILRS processing of the LAGEOS and ETALON satellites by LARES 2, as well as lower-flying satellites, i.e. LARES, Stella and Starlette, necessitating an adaption of the SLR-POD model and parametrization due to the increased sensitivity to orbit perturbations at low orbit altitudes.

We present the status of the SLR-POD at AIUB, where in support of the ILRS analysis center at BKG the incorporation of the low-flying SLR satellites into the 7 day POD and network solution of LAGEOS/ETALON/LARES-2 is beeing tested, making use of long-arc stacking techniques of daily arcs to continuous 7 day arcs. All orbit and geophysical parametes are estimated in one common estimation process to avoid implicit regularization by apriori information. Special attention is paid to the co-estimation of the low-degree gravity field coefficients and the correlations with the empirical dynamic parameters deployed in the classical LAGEOS/ETALON POD model.

How to cite: Meyer, U., Geisser, L., König, D., Dach, R., Thaller, D., and Jäggi, A.: Orbit parameterization aspects in global solutions of spherical Laser Ranging Satellites, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-5427, https://doi.org/10.5194/egusphere-egu24-5427, 2024.

Satellite Laser Ranging (SLR) observations are provided by a global station network of the International Laser Ranging Service (ILRS). Since almost all SLR stations are unique in terms of utilized equipment, e.g., laser system, photo-detector or timing devices, their measurement performances may slightly differ. Furthermore, the tracked satellites have various properties, e.g., material composition (number and type of retro-reflectors or mantel material), diameter, area-to-mass ratio, altitude or inclination, which have an impact on the measurement precision and the requirements on the background force modeling. A reliable estimation of geodetic parameters solely based on SLR can only be performed by combining SLR observations to several spherical satellites provided by the entire ILRS network. To take the quality of each individual SLR measurement into account, several stochastic models, e.g., static or time-variable station- and/or satellitespecific weights, are introduced and their impact on the parameter estimation is studied.

How to cite: Geisser, L., Meyer, U., Arnold, D., and Jäggi, A.: Stochastic Modeling of SLR Observations and its Impact on the Parameter Estimation, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-5649, https://doi.org/10.5194/egusphere-egu24-5649, 2024.

The GENESIS mission plays a pivotal role in the FutureNAV program envisioned by the European Space Agency. This groundbreaking venture aims to co-locate four space geodetic techniques on a single platform in space. One of the primary mission objectives is accurately determining geodetic parameters, including geocenter motion, low-degree gravity field, Earth rotation parameters, and the positions of ground stations in tracking networks. Although preliminary satellite inclination and altitude were provided, there is untapped potential for studying ways to enhance the efficiency of incorporating GENESIS into geodetic products.

This research focuses on the preliminary optimization of GENESIS orbital parameters – semi-major axis, inclination, and eccentricity- to assess the benefits arising from diverse observation geometries on geodetic products. The analysis is based on simulations of different variants of GENESIS orbital parameters tracked by a network of 20 satellite laser ranging (SLR) stations. We provide GENESIS-only solutions as well as the combined solution with a selected subset of geodetic satellites that are used today or in the future for the realization of the terrestrial reference frames: LAGEOS-1, LAGEOS-2, LARES-1, and LARES-2. GENESIS will be equipped with two GNSS receivers contributing to high-accuracy orbit determination, serving as a priori parameters for SLR-based solutions. Therefore, we check the GENESIS sensitivity to global geodetic parameters, assuming that the precise orbits are not derived from SLR but can be well-defined from other techniques.

We study the impact of different GENESIS orbits on the gravity potential parameters, especially the zonal terms, Earth rotation parameters, and geocenter coordinates. Our findings underscore that, through meticulous processing, GENESIS has the potential to significantly contribute to achieving the goals of the Global Geodetic Observing System (GGOS), particularly in terms of refining the Z component of the geocenter coordinates.

How to cite: Kur, T. and Sośnica, K.: Sensitivity of different variants of GENESIS orbit to global geodetic parameters, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-6359, https://doi.org/10.5194/egusphere-egu24-6359, 2024.

All BeiDou global navigation satellite system (BDS-3) satellites are equipped with Ka-band inter-satellite link (ISL) payloads to achieve the inter-satellite ranging and communication. With the rapid development of low earth orbit (LEO) satellites, the LEO onboard BDS-3 observations also become available. The LEO onboard and ISL data can be an effective supplement for precise orbit determination (POD) of the BDS-3 satellite. In this research, we processed the integrated POD of BDS-3 and LEO satellites with the real ground station, LEO onboard GNSS, and ISL observations. To analyze the contribution of different data to BDS-3 POD accuracy, four POD schemes are present: ground stations only, ground stations + 1 LEO, ground stations + ISL, and ground stations + 1 LEO + ISL. The ground tracking data are from about 40 globally distributed ground stations and 10 stations in Asia-Pacific region, respectively. The LEO onboard GNSS observations are from a dual-constellation GNSS receiver of the LUTAN-01A satellite, which is a Chinese LEO synthetic-aperture-radar (SAR) satellite for geological observation. The Ka-band observations from more than 400 ISL established between BDS-3 satellites are also used in the integrated POD. The obtained orbits are evaluated by orbit overlaps comparison, the comparison with IGS analysis center precise orbits, and SLR (satellite laser ranging) validation. Compared to the POD using the observation of only 10 ground stations, the addition of 1 LEO onboard GNSS or ISL observations can improve the orbit accuracy of BDS-3 by more than 60%. Furthermore, adding both LEO onboard GNSS and ISL observations simultaneously can lead to further improvements in BDS-3 orbit accuracy.

How to cite: Chen, H., Geng, T., Xie, X., Li, Q., Su, X., and Zhao, Q.: Enhanced orbit determination for BDS-3 satellites with LEO onboard GNSS and inter-satellite link data, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-7776, https://doi.org/10.5194/egusphere-egu24-7776, 2024.

For radar altimetry missions such as Sentinel-6, a precise orbit is mandatory for deriving reliable sea surface heights. In addition to accurate tracking measurements, precise orbit determination relies on high-fidelity non-gravitational force models. At 1300km the solar radiation pressure (SRP), which varies mainly with the satellite’s orientation towards the Sun, is the dominating non-gravitational force. Additionally, the acceleration due to the Earth radiation pressure (ERP) acts on the satellite and decreases with increasing satellite altitude. As the radiation of Sun and Earth is partly absorbed at the satellite’s surface, the satellite experiences an additional force due to the thermal reradiation of heat (thermal reradiation pressure, TRP). Aerodynamic forces are in constrast negligible at around 1300km altitude.

In previous investigations, we extended the conventional radiation pressure force models with a focus on a GRACE-like satellite. Our SRP and ERP model extensions can be easily applied to other satellites with available geometry and thermo-optical material properties. However, transferring the heat-conductive TRP model to other satellites is more challenging, as assumptions on the materials’ thermal diffusivity and thickness as well as inner heat sources need to be made to adequately model the satellite’s surface temperature.

In this study, we attempt to develop a TRP force model for Sentinel-6. We depart from GRACE settings and refine our model stepwise. Boundary conditions are updated and the material properties are replaced with available information or assumptions. Then, a stepwise tuning is necessary to match the modelled surface temperatures with thermistor measurements. We choose one beta cycle during the year 2023 for our experiments. Preliminary investigations reveal that the tuning of the satellite’s thermal properties varies strongly with the beta angle.

How to cite: Vielberg, K., Kusche, J., and Peter, H.: Tuning thermal reradiation pressure accelerations for Sentinel-6, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-7841, https://doi.org/10.5194/egusphere-egu24-7841, 2024.

High-quality GPS observations from low Earth orbiting (LEO) satellites can be used to derive thermosphere densities along the satellite orbit. Such GPS-derived densities are currently computed operationally for all three Swarm satellites, in the framework of the Swarm Data, Innovation, and Science Cluster. Considering the increasing number of LEO satellites equipped with GPS receivers, this so-called GPS-based accelerometry approach offers great potential for improving thermosphere models and for studying the influence of solar and geomagnetic activity on the thermosphere.

To better quantify the accuracy that can be obtained with this approach, we assess the performance using the GRACE mission as a test case. For this mission high quality accelerometer data are available, which we can use to validate our GPS-based results. In addition, the GRACE mission has experienced a large variation in density signals, which allows us to assess the performance under a large range of conditions.

We present our GPS-based accelerometry processing strategy, which is based on a Kalman filter approach. The radiation pressure accelerations are accurately modelled and empirical accelerations capture the remaining aerodynamic signal. The empirical accelerations are modeled as Gauss-Markov processes defined by a steady-state variance, process noise and correlation time, which require careful tuning. This applies in particular to the setting of the process noise in the along-track direction, due to the large variations in the encountered aerodynamic signal. Best performance is obtained when the process noise setting is adapted to these variations. Using these adaptive filter settings, results are shown for periods with low, moderate, and high density. In a next step, we will implement the improved filter settings into our regular Swarm GPS-derived density processing chain.

How to cite: van den IJssel, J., Siemes, C., and Visser, P.: Assessment of GPS-based accelerometry performance with adaptive filter settings, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-8395, https://doi.org/10.5194/egusphere-egu24-8395, 2024.

The Copernicus Precise Orbit Determination (CPOD) Service delivers, as part of the Ground Segment of the Copernicus Sentinel-1, -2, -3, and -6 missions, orbital products and auxiliary data files for their use in the corresponding Payload Data Ground Segment (PDGS) processing chains at ESA and EUMETSAT, and to external users through the newly available Copernicus Data Space Ecosystem (https://dataspace.copernicus.eu/).

The CPOD Service is based on FocusPOD, a suite of tools for POD and geodesy powered by GMV MAORI, a new GMV in-house Flight Dynamics & Geodesy library, written from scratch in modern C++ and python. The CPOD Service makes use of GNSS measurements to generate the orbital products, and of Satellite Laser Ranging (SLR) measurements for validation purposes. Recently, DORIS-processing capabilities have been added to FocusPOD to generate orbit solutions based on this geodetic technique, which is available on-board Sentinel-3 and -6 missions.

The purpose of this work is to present the DORIS processing capabilities recently developed, including DORIS RINEX data parsing, observation preprocessing steps, and precise orbit determination results. The highlight will be the achievable accuracy based on DORIS and an analysis of the obtained residuals depending on the chosen parametrisation, including validation against GNSS-based solutions and SLR.

How to cite: Fernández, M., Fernández, C., Peter, H., Féménias, P., and Nogueira Loddo, C.: Copernicus POD Service – POD RESULTS BASED ON DORIS, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-8672, https://doi.org/10.5194/egusphere-egu24-8672, 2024.

The Copernicus Precise Orbit Determination (CPOD) Service delivers, as part of the Ground Segment of the Copernicus Sentinel-1, -2, -3, and -6 missions, orbital products and auxiliary data files for their use in the corresponding Payload Data Ground Segment (PDGS) processing chains at ESA and EUMETSAT, and to external users through the newly available Copernicus Data Space Ecosystem (https://dataspace.copernicus.eu/).

For the last few years, a progressive degradation of the accuracy of some of the CPOD orbital products has been observed, caused by the increasing solar activity. Solar activity follows an 11-year cycle, and since the minimum in 2020, overall solar activity has been higher and geomagnetic storms have been happening more often. This has two impacts on POD: a more “turbulent” atmosphere which brings higher frequency density changes, making the modelling of the satellite´s drag more challenging, and an increase of ionospheric scintillation, particularly over the polar regions, that causes an increase of the GNSS carrier phase noise.

This study aims at characterising better the impact of the solar activity on the different POD products, with a focus on the degradation of orbit determination and predictions required by the Sentinel-1 mission. Overall tendencies since the solar minimum in 2020 are analysed, including a detailed look on strong geomagnetic storms. Mitigation strategies to overcome this situation are evaluated, namely adapting the POD processing dynamic parametrisation, and updating the solar activity proxies (particularly the geomagnetic indexes) more frequently.

How to cite: Lara Espinosa, S., Fernández, C., Fernández, M., Peter, H., and Féménias, P.: Copernicus POD Service – Impact of High Solar activity on POD, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-8756, https://doi.org/10.5194/egusphere-egu24-8756, 2024.

Among the core products of the International GNSS Service (IGS) are precise satellite orbits and clocks, which are generated by the Analysis Center Coordinator (ACC) as a combination of the solutions provided by different Analysis Centers (AC). A strategic goal of the IGS is to facilitate multi-GNSS solutions, implying that the currently operational system-wise GPS and GLONASS combinations should be replaced by a consistent set of multi-GNSS products, eventually containing at least GPS, GLONASS, Galileo, BeiDou, and QZSS.

Over the past years, the Satellite Precise Orbit and Clock Combination (SPOCC) software tool has been developed at GFZ. It provides a fully consistent multi-GNSS orbit and clock combination that covers all available and possible future constellations and is based on a well-defined unified least-squares framework. The resulting combined orbit and clock products are a weighted average of the individual AC solutions with weights determined through least-squares variance component estimation (VCE). A main objective is to support multi-GNSS precise point positioning (PPP) users.

We will introduce the combination workflow, which essentially consists of alignments harmonizing the AC products followed by the VCE and the weighted averaging, and is complemented by quality checks such as outlier detection. For the orbit combination, the alignment consists of Helmert transformations applied to the AC orbits, which is iterated with the VCE-based weighted averaging until convergence. The clock alignments consist of a radial correction from the orbit differences between the AC solutions, a removal of the impact of different reference clocks in the AC solutions, as well as an adjustment of all non-GPS satellite clocks for different inter-system bias (ISB) references at the ACs. The combination can be configured for different weighting schemes, including AC specific weights, AC+constellation specific weights, up to satellite type or even satellite specific weights, and the Helmert transformations can be based on different sets of satellite orbits.

The SPOCC software has been extensively tested with the operational IGS products, the IGS Multi-GNSS Experiment (MGEX) products, and the IGS repro3 products. Performance evaluations by means of a comparison of the combination with the input products and the official IGS combination, through a satellite laser ranging (SLR) validation, and with PPP results will be used to show that the software achieves reliable results that are suitable for the users’ high precision GNSS applications.

SPOCC is implemented in Python and will be provided as open source software.

How to cite: Brack, A., Mansur, G., Sakic, P., Zajdel, R., and Männel, B.: SPOCC - a GFZ Software Tool for a Multi-GNSS Orbit and Clock Combination, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-10249, https://doi.org/10.5194/egusphere-egu24-10249, 2024.

Progress in precise satellite orbit determination (POD) and navigation depends on the future ranging and time transfer capabilities. This leads to the need for high-precision links as well as high-precision clocks. However, not only a higher accuracy is required, but also the use of combination of complementary observation techniques to reduce systematic errors within an observation network. In a simulation study, we show our first concept of a GEodesy and Time Reference In Space (GETRIS). The initial GETRIS concept is based on the idea to have the reference in space build on geosynchronous orbit (GSO) satellites, but using Medium Earth Orbit (MEO) satellites is also possible. The goal is to achieve orbit accuracies of the GETRIS satellites at the same level as for ground stations – a few millimeters. Using high-precision optical links, the GETRIS shall establish connections to satellites in the near Earth environment and in deep space. When creating our GETRIS concept, we focus on three key pillars of a simulation study: Instrumentation, geometry and modelling. In terms of instrumentation, we performed scenarios using the synergy between L-band observations as well as high-precision dual one-way Optical Inter-Satellite Links (OISL) and ground-space based dual one-way links, called Optical Two-Way Links (OTWL), in different combinations. The geometry changes depending on the used observations network and the satellite constellation. Thereby, we analyze scenarios using a MEO-only and MEO+GSO constellations. To finally achieve mm-level orbit accuracies, an advanced modelling of non-gravitational forces is essential. A GETRIS can not only help with the connection of near Earth and deep space satellites, but also support the Global Geodetic Observing System (GGOS) and satellite missions such as GENESIS, which aim to realize a precise terrestrial reference frame with 1 mm accuracy and a stability of 0.1 mm/year.

How to cite: Marz, S., Schlicht, A., and Hugentobler, U.: Towards a GEodesy and Time Reference In Space (GETRIS): A simulation study, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-10344, https://doi.org/10.5194/egusphere-egu24-10344, 2024.

The ESA GENESIS mission, which obtained green light at ESA's Council Meeting at Ministerial Level in November 2022 and which is expected to be launched in 2027, aims to significantly enhance the accuracy and stability of the Terrestrial Reference Frame (TRF). This shall be achieved by equipping one satellite at approximately 6000 km altitude with well-calibrated instruments for all four space-geodetic techniques contributing to TRF realizations, i.e., Global Navigation Satellite Systems (GNSS), Satellite Laser Ranging (SLR), Very Long Baseline Interferometry (VLBI) and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS), and by exploiting the such realized very precise space collocations.

The GENESIS satellite is foreseen to carry a zenith- and nadir-pointing GNSS antenna to track (at least) GPS and Galileo signals. Because of its very high altitude, GENESIS will cover much larger nadir angles as seen from the GNSS transmitting antennas, compared to receivers at ground or in low Earth orbit. This will partly result in GNSS observations with lower signal-to-noise ratios. Furthermore, to date, only little reliable information is available on the GNSS transmit antenna gain and carrier phase patterns at very large nadir angles. These problems lead to questions with respect to the best possible exploitation of GNSS data by GENESIS, e.g., whether phase pattern calibrations will need to be performed by means of tracked GNSS data (which would weaken the GNSS contribution to GENESIS).

The aim of this study is to assess the impact of GNSS transmit antenna phase pattern errors on the GNSS-based POD of GENESIS, as well as global GNSS network solutions for GNSS orbits and clock corrections, Earth rotation and geocenter parameters and station coordinates based on GNSS observations from GENESIS and terrestrial stations. To accomplish this, we employ simulated GNSS pseudo-range and carrier phase data for GENESIS and ground stations, which have been generated based on detailed link-budget computations and a comprehensive set of transmit antenna gain patterns. The data are used for closed-loop simulation investigations, which allow to compare the reconstructed orbit and geodetic parameter solutions to the simulation truth and offer a quantification of the impact of transmit antenna phase pattern uncertainties on the estimated parameters.

How to cite: Arnold, D., Miller, A., Kobel, C., Montenbruck, O., Steigenberger, P., and Jäggi, A.: GNSS-based orbit and geodetic parameter estimation by means of simulated GENESIS data, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-12683, https://doi.org/10.5194/egusphere-egu24-12683, 2024.

How to cite: Salas, M., Fernández, J., and van den IJssel, J.: Precise Relative Navigation in Medium Earth Orbits with Global Navigation Satellite Systems and Intersatellite Links for Black Hole Imaging, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-13048, https://doi.org/10.5194/egusphere-egu24-13048, 2024.

Improving the concepts of Global Navigation Satellite Systems (GNSS) has become a vital task for subsequent GNSS applications like the determination of the Terrestrial Reference Frame (TRF). A promising goal is the reduction of uncertainties in non-conservative force modeling such as Solar Radiation Pressure (SRP) modelling in Precise Orbit Determination (POD) and the effect on the estimated orbits and geocenter coordinates. In previous simulation studies, accelerometers on next-generation GNSS satellites have proven to be a promising opportunity. In this way, the periodic signals in the estimated geocenter coordinates induced by SRP mismodeling can be eliminated regardless of the angle of the Sun to the satellite and its orbital plane. At the same time, the satellite clock can be effectively decoupled from the satellite position estimates. In this study, we focus on the impact of highly accurate clocks and the synchronization of clocks between satellites, which would make it possible to estimate common clock parameters for the synchronized satellites. In doing so, we start with Galileo-type POD using prior simulated observations with the assumption of perfectly known clocks. Then, we simulate various scenarios assuming different clock models and compare the results with the perfect case scenario. This procedure will explore the potential of various ground reference and satellite clock accuracies. Additionally, we use inter-satellite links to synchronize the satellite clocks over one and over multiple orbital planes. Finally, we strive to assess the potential of improved clock modeling on the TRF, focusing on the estimation of geocenter coordinates.

How to cite: Schreiner, P., Glaser, S., König, R., Neumayer, K. H., Raut, S., and Schuh, H.: On the potential of highly accurate clocks and inter-satellite clock synchronization for GNSS satellite precise orbit and geocenter determination, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-16139, https://doi.org/10.5194/egusphere-egu24-16139, 2024.

Routine and occasional/emergency orbital maneuvers are essential for many satellites to maintain their optimal trajectory and to achieve a wide range of operational objectives in a continuous way. However, incorrectly modelled highly dynamic changes of the orbit during maneuvers can significantly reduce the accuracy of precise orbit determination (POD) to an extent that is unacceptable for scientific requirements.

The aim of this study is to investigate strategies for maneuver handling of Low Earth Orbiting (LEO) satellites based on observations from on-board GNSS receivers complemented by a priori knowledge of thrust intensity and maneuver epochs that are provided by telemetry measurements. Assuming that the initial information is subject to instrumental biases, corrections for the maneuver accelerations are estimated together with nominal deterministic and pseudo-stochastic orbit parameters such as instantaneous velocity changes and piecewise constant accelerations.

Several estimation strategies are tested using recent developments in the Bernese GNSS software, which is continuously maintained and further developed at the Astronomical Institute of the University of Bern (AIUB). In particular, the test cases cover single long/short maneuvers as well as two consecutive maneuvers within one orbital arc. Depending on the length of the maneuver and the number of available observations, different polynomial functions (up to degree 2) are used to model the thrust acceleration. Finally, the quality of the solution is evaluated internally by comparing it to the days without maneuvers and by checking the consistency between the reduced dynamic and kinematic orbit. External validation is also performed with respect to the official independent products.

How to cite: Kalarus, M., Arnold, D., Padovan, S., Dach, R., and Jäggi, A.: Precise orbit determination for the maneuvering satellites, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-16732, https://doi.org/10.5194/egusphere-egu24-16732, 2024.

The Galileo for Science Project (G4S_2.0) is funded by the Italian Space Agency and has several goals in the field of Fundamental Physics to be achieved by exploiting the satellites of the Galileo-FOC Constellation. In this regard, a key point is to obtain a suitable satellite orbit solution by performing an accurate Precise Orbit Determination (POD). To this purpose modeling in a reliable way the complex effects of the Non-Conservative Forces, i.e. of Non-Gravitational Perturbations (NGPs), is essential. The activities undertaken in the construction of a Box-Wing model and of a Finite Element Model of the satellite will be presented with the preliminary results obtained by including these models into the POD of the Galileo satellites. In particular, using the orbital element residuals obtained from a POD we can test our new models and the improvements in POD quality.

How to cite: Lefevre, C., Visco, M., Lucchesi, D., Sapio, F., Peron, R., Cinelli, M., Di Marco, A., Fiorenza, E., Loffredo, P., Lucente, M., Magnafico, C., Santoli, F., and Vespe, F.: The Galileo for Science project: Non-Conservative Forces modeling for the Galileo FOC satellites, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-16819, https://doi.org/10.5194/egusphere-egu24-16819, 2024.

Since the launch of Seasat (1978), the first satellite to study ocean topography, our knowledge of the rise of 
mean sea level has evolved. Since then, 18 additional satellites were launched, with more and more satellite 
missions (up to 10 satellites are now simultaneously flying) dedicated to the measurement of the global and 
regional sea-surface height, carrying on board state of the art precision orbit determination tracking techniques 
and instruments. 

Jason-3 (2016) and Sentinel-6 MF (2020) are part and parcel of these ocean topography missions. The two 
reference satellites were operated in tandem (with Sentinel-6 MF flying 30 seconds behind its predecessor) 
between mid-December 2020 to April 2022 for calibration purposes. The main difference between these two 
satellites has to do with their respective platform design. Indeed, Sentinel-6 MF solar panels are fixed on the 
satellite and has an almost fixed attitude, unlike Jason-3 which has some yaw steering periods. 

In this study, we focus on the solar radiation pressure modeling errors of both Sentinel-6 MF and Jason-3 
during their tandem phase (4.5 beta cycles). The idea is to analyze the estimated empirical accelerations of 
these two satellites as a function of their beta angle. The Solar Radiation Pressure (SRP) depends only on two 
parameters: the orbital angle with respect to the sub-solar point and the beta angle. We will then propose 
updates of the SRP models. The effect of the terrestrial radiative perturbations will also be assessed.

How to cite: Saquet, E., Cherrier, M., Couhert, A., and Mercier, F.: Assessment of Jason-3 and Sentinel-6 MF radiation pressure model, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-16831, https://doi.org/10.5194/egusphere-egu24-16831, 2024.

Within the IGS, it was agreed that Precise Point Positioning (PPP) based on satellite orbit and clock corrections of the IGS analysis centers allow a direct access to the IGS realization of the International Terrestrial Reference Frame (ITRF). This convention is considered convenient for all PPP users and should not be changed in future.

On the other hand, the groups determining the GNSS satellite orbits do prefer an origin of the frame that is related to the Earth instantaneous center of mass since this is the reference of the gravitational orbit force model. With this background, some discussions take place to change the convention related to the origin of the terrestrial frame because it is convenient for the orbit determination. This convention is, however, in contradiction to the expected needs of the PPP users that do prefer a stable coordinate origin in time.

We will introduce a strategy to serve both needs by applying the center of mass corrections for the orbit determination only.

How to cite: Dach, R., Arnold, D., Brockmann, E., Kalarus, M., Prange, L., Schaer, S., Stebler, P., and Jäggi, A.: Review the IGS Strategy for Precise Point Positioning Applications, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-16959, https://doi.org/10.5194/egusphere-egu24-16959, 2024.

The Galileo for Science Project (G4S_2.0) is funded by the Italian Space Agency and has
several goals in the field of Fundamental Physics to be achieved by exploiting the satellites
of the Galileo-FOC Constellation and the accuracy of their onboard atomic clocks. In
particular, the clock-bias, estimated in the data reduction of the tracking observations
allows to place constraints on the possible presence of Dark Matter in our galaxy in the
form of Domain Walls (DW) eventually produced in the very early Universe by ultralight
scalar field(s). The impact of the DW on an atomic clock would provide a delta-like
transient shift on the pseudo-derivative of the clock-bias. Such signal depends both on the
nature of the clock and the characteristics of the ultralight scalar comprising the DW.
Ongoing work on the clock-bias will be introduced as regards to data pre-processing and
simulations on false alarm and detection efficiency.

How to cite: Di Marco, A., Sapio, F., Visco, M., Lucchesi, D., Cinelli, M., Fiorenza, E., Lefevre, C., Loffredo, P., Lucente, M., Magnafico, C., Peron, R., Santoli, F., and Vespe, F.: The Galileo for Science project: Constraints on Dark Matter with the Galileo-FOC Constellation, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-18289, https://doi.org/10.5194/egusphere-egu24-18289, 2024.

SWOT (Surface Water and Ocean Topography) is a recently launched international satellite mission developed in close collaboration between CNES and NASA space agencies aimed to reach a new level of accuracy in observing global water systems of the Earth. In order to meet the high accuracy requirements of the mission most precise determined orbits are crucial. Therefore we generate orbits using dynamic Precise Orbit Determination (POD) with multiple techniques, i.e. DORIS, GPS and SLR with the aim of generating a highly precise orbit with minimal residual error. For this purpose, single technique orbits are generated based on DORIS and GPS only, using SLR for validation only. For quality analysis we evaluate the estimated parameters of the dynamic POD and perform orbit comparisons to external orbit solutions. Subsequently, to reduce technique-specific effects of the dynamic modeling, we generate a combined orbit solution based on DORIS and GPS, and estimate the reference points of the observation techniques on the satellite to examine the calibration by the manufacturer. Based on the generated orbit solutions altimetry evaluation such as cross-over point analysis is made and discussed.

How to cite: Reinhold, A., Schreiner, P., and Schöne, T.: On multi technique precise orbit determination for SWOT with respect to altimetry applications., EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-18467, https://doi.org/10.5194/egusphere-egu24-18467, 2024.

Tidal variability originating from the orbital dynamics of the Sun and the Moon can be observed in virtually all subsystems of the Earth. The evoked tidal phenomena in the atmosphere, the solid Earth, and the world oceans cause a large-scale redistribution of masses, primarily on daily and sub-daily time scales. The implied tidal variability impacts geodetic measurements. For example, the induced mass transport induces temporal changes in the Earth's gravity field which impact the orbits of artificial satellites. However, observations of a single satellite are generally insufficient to precisely estimate tidal signatures, resulting in a decreased accuracy of the Precise Orbit Determination (POD) of near-Earth satellites. Therefore, a priori prediction of tidal signals, especially ocean tidal signatures, by tidal atlases is necessary to exploit the full potential of geodetic data sets.

The most accurate ocean tide atlases are produced by incorporating satellite altimetry observations into the modeling process. However, limitations arising from the ambient signal-to-noise level have hindered their ability to accurately estimate small signals associated with minor tidal constituents. For those minor constituents, data-unconstrained ocean tide models can yield valuable constraints. For processing satellite altimetry data, initial experiments have been undertaken to integrate empirical and numerical models, aiming to deliver comprehensive tidal corrections (Hart-Davis et al., 2021, doi: 10.3390/rs13163310). It has been proposed that experimentation is necessary across all geodetic applications to determine the preferred model for specific tidal constituents and the optimal approach for merging models. This also includes the possibility of including minor ocean tides only implicitly, by deriving their admittance function from suitable neighboring tidal constituents.

How to cite: Klemann, V., Sulzbach, R., Kehm, A., Blossfeld, M., Hart-Davis, M., Dobslaw, H., and Mayer-Guerr, T.: Treatment of Modern Global Ocean and Atmospheric Tide Atlases in Precise Orbit Determination, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-19842, https://doi.org/10.5194/egusphere-egu24-19842, 2024.

The density of the upper atmosphere can be determined by orbit and accelerometer data from low Earth orbit satellites. Especially the accelerometers of geodetic satellites, measuring the non-gravitational accelerations acting on them are a very viable observation.

The density estimation is mainly based on three separate disciplines, which are: (1) Precise radiative non-gravitational force modelling, (3) Modelling of the interaction between the rarefied atmospheric gases and the satellite, i.e. modelling of drag coefficients, and (3) the calibration of the accelerometer data by dynamic Precise Orbit Determination (POD). This contribution focuses mainly on the last point. Nevertheless, we also validate the modelled radiative accelerations and use them as reference for the calibration results.

The accelerometers of all geodetic satellites are affected by a drifting bias and scale factors unequal to one. Therefore a calibration of the data is indispensable. Usually time dependent bias and scale factors are estimated. For standard POD or Gravity Field Recovery (GFR) these parameters are estimated together with empiric and other model parameters. In both cases, the estimated accelerometer calibration parameters are not of major interest, but improve the orbit fit or gravitational field coefficients. The used parametrizations and weighting strategies of the observation data, do not give realistic or physical accelerometer calibration results because parameters are not sensitive and effects are absorbed or smeared into other parameters and models. This is unsatisfying, especially for the anticipated use for the density determination.

In this contribution we use dynamic POD and investigate different parametrization strategies tailored for a physical accelerometer calibration. We investigated the effect of constraining the accelerometer calibration parameters in that way, that a continuous calibration over all arcs is achieved, where normally each arc is treated locally separated from all other arcs. The scale factor is concurrently estimated, but over a longer batch of arcs. We varied the length between one day and years. Furthermore, different calibration equations, different observation data and combinations (kinematic positions, science orbit data, inter-satellite ranging), weighting strategies, initial parameters and pre-processing of the accelerometer data is investigated. The validation of the results is not easy, because usual metrics like post-fit residuals do not reflect the quality of the accelerometer calibration. We introduce a validation approach using the modelled non-gravitational forces and also show the influence of the different calibration options on the resulting density or drag acceleration.

All results and data for the whole GRACE and GRACE-FO missions are available on our data server (link in presentation/ uploaded material). 

How to cite: Wöske, F., Rievers, B., and Huckfeldt, M.: Tailored accelerometer calibration by POD for thermospheric density computation with GRACE and GRACE-FO, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-20733, https://doi.org/10.5194/egusphere-egu24-20733, 2024.

The International Terrestrial Reference System is realised in the form of multi-year reference frames such as the International Terrestrial Reference Frame (ITRF) or in the form of epoch reference frames relying on short observation time spans up to several weeks. The realisation is based on the combination of space-geodetic techniques, namely the global navigation satellite systems (GNSS), satellite laser ranging (SLR), very long baseline interferometry (VLBI) and Doppler orbitography and radiopositioning integrated by satellite (DORIS). In some ITRF and epoch reference frame solutions, SLR and VLBI are responsible for realising the datum parameters origin (only by SLR) and the scale, while the orientation of the network with respect to the Earth’s body is maintained by a mathematical constraint. The integration of the techniques is achieved by introduction of local ties (LTs) at co-located sites, i.e., by ground-based measurements of difference vectors between the technique-specific reference points. High accuracy of current LTs between techniques and the establishment of new co-location sites are necessary to provide (and further improve) a reliable realisation of the geodetic datum. Co-location sites with the SLR technique are of particular significance as this is the only technique that enables the realisation of a terrestrial reference frame origin with a high level of accuracy. As previous studies demonstrate, the performance of the observational networks has a significant impact on the accuracy and stability of the corresponding datum realisation, especially for epoch reference frames.

This study aims to examine how improving the performance of the existing network of co-located SLR stations could affect the quality of determined datum parameters. The considered simulation scenarios study the performance of SLR stations co-located with the VLBI technique and improve the performance of those that do not meet the standards set by the International Laser Ranging Service (ILRS). Moreover, it is examined how significant the improvement of the datum parameters is in the case of extending the SLR network with stations located nearby existing VLBI telescopes (due to a ‘better’ datum transfer via a higher number of local ties).

How to cite: Najder, J., Kehm, A., Bloßfeld, M., Sośnica, K., and Glomsda, M.: Improved geodetic datum realization based on simulation studies for co-located SLR-VLBI stations, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-897, https://doi.org/10.5194/egusphere-egu24-897, 2024.

The growing demand for Earth science applications poses challenges in improving geodetic reference frames. Systematic errors currently restrict the accuracy of these frames because the classical geometric ties between multiple geodetic techniques fall short of sufficiency. Our objective is to identify and analyze the impact of variable GNSS receiver hardware delays (incl. antenna-hardware delays) on carrier-phase time transfer with an accuracy of picoseconds/millimeters. We propose using a ground-based GNSS pseudolite system synchronized to an optical timing system (clock tie) developed at the Geodetic Observatory Wettzell to calibrate the variable hardware delays and facilitate a closure in time between multiple geodetic techniques.

This study analyzes the requirements for developing a GNSS pseudolite and its transmission chain. We reformulate the classic iono-free Precise Point Positioning (PPP) mathematical theory to incorporate pseudolite data, separating the known receiver clock error from unknown transceiver hardware delays. The analysis suggests a preference for highly directive and mechanically stable Right Hand Circularly Polarized (RHCP) log periodic or helix transmission antennae. Calibration for Phase Center Offset (PCO), Phase Center Variations (PCVs) and careful installation to minimize multipath are crucial. This results in a carrier-phase observation model with three unknowns: transceiver hardware delays (our focus), frequency-dependent ambiguity terms, and low tropospheric delay influence.

Utilizing a USRP-based transmission procedure, we successfully tracked an E1B Galileo signal replica with an in-house developed GNSS software-defined receiver (SDR). The transmission was implemented using two approaches: over-the-air and loopback. The over-the-air transmission was carefully planned using a link budget calculation to ensure that it did not exceed the allowed free-air transmission constraints. Empirical validation ensured a carrier-to-noise ratio (C/N0) below 30dB/Hz near critical public areas. In the loopback approach, the transmitted GNSS signal was fed into the local SDR within the pseudolite, sharing the same Analog-Digital-Converter (ADC)/ Digital-Analog-Converter (DAC)ADC/DAC, clock and local oscillators. In a future stage, this signal is supposed to be compared to a reference signal derived from the optical timing system. 

In our analysis, we also assessed the stability of the USRP frequency synthesizer, known as Phase Lock Loop (PLL), in the context of high-precision applications, such as real-time kinematic (RTK) positioning. We found that tuning the synthesizer in integer-n mode is crucial in maintaining a stable carrier frequency and achieving a 100% real-time kinematic positioning fixing rate. 

How to cite: Lăpădat, A. M., Kodet, J., and Pany, T.: Towards calibration of GNSS receiver hardware delays for improving geodetic reference systems through clock ties. A requirements analysis for developing a GNSS pseudolite transmission chain, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-1600, https://doi.org/10.5194/egusphere-egu24-1600, 2024.

Mission Genesis of the European Space Agency (ESA) has been approved for launch in 2027. Genesis will be the first satellite in orbit to have a dedicated Very Long Baseline Interferometry (VLBI) transmitter on board, next to Global Navigation Satellite System (GNSS) and Doppler Orbitography and Radiopositioning Integrated on Satellite (DORIS) receivers as well as a Satellite Laser Ranging (SLR) reflector; consequently, Genesis will realize a space tie combining all geometric space geodetic techniques. If perfectly calibrated, the space tie will enhance and improve local ties measured on the ground. The following scenario is possible: If the orbit of Genesis is determined from the satellite techniques alone, the station coordinates of the VLBI radio telescopes in the "satellite frame" can be derived by VLBI observations to Genesis, thereby assessing the tie with the "VLBI frame", realized with decades of VLBI observations to quasars.

We present our plans to devise observing strategies for VLBI to reach accuracies as defined in the Genesis white paper. We start with our findings for VLBI transmitters on Galileo satellites, before we show the simulation results for the VLBI transmitter on Genesis. We illustrate the advantages of the Genesis satellite at 6000 km altitude compared to Galileo satellites in terms of sky coverage and accuracy of station coordinates, but also in terms of orbit estimation. Furthermore, we provide an outlook on geodetic parameters, which could not be determined with VLBI so far but will be possible with Genesis.

How to cite: Böhm, J., Wolf, H., and Kern, L.: Benefits for the terrestrial reference frame with VLBI observations to Genesis, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-3821, https://doi.org/10.5194/egusphere-egu24-3821, 2024.

The Satellite Laser Ranging (SLR) technique is used to independently validate the microwave-based satellite orbit products. In the so-called SLR validation, the orbit quality is assessed based on the analysis of the SLR residuals, which are the discrepancies between the direct SLR range measurements and the station-satellite vector calculated based on the SLR station positions and the evaluated orbits in Earth-fixed reference frame. Therefore the results of SLR validation are strongly related to the SLR station coordinates. In 2022, the new realization of the International Terrestrial Reference Frame – ITRF2020 – has been released, which considers a few innovations, mainly, an extended model of post-seismic deformations, and the seasonal station coordinate variations in form of annual and semi-annual terms.  In this study, we investigate the impact of recent advancements in ITRF into the SLR-based orbit validation of LEO and GNSS satellites.      

We perform the SLR validation of LEO orbit (Swarm-ABC, Sentinel-3A/B, Jason-3) products provided by European Space Agency (ESA) Copernicus Service and Technical University of Graz for one year. Also, we validate Galileo and BeiDou-3 orbit products delivered by ESA and Center for Orbit Determination in Europe in 2023. 

We incorporate the latest ITRF2020 realization into the SLR validation processing, contrasting the outcomes with solutions that involve the previous ITRF2014 release to illustrate the impact of TRF aging on validation results. Additionally, we examine the influence of including seasonal station motions on SLR validation outcomes. Furthermore, a comparison is made between SLR validation results when utilizing the most recent alternative TRF realizations, namely DTRF2020 and JTRF2020. We discuss the dependency of residuals on different measurement conditions, such as elevation angle and azimuth angle, and their time variability.

How to cite: Strugarek, D. and Zajdel, R.: Impact of terrestrial reference frame on the SLR validation results of GNSS and LEO orbits, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-4333, https://doi.org/10.5194/egusphere-egu24-4333, 2024.

The latest realizations of the ITRS, specifically the ITRF2020, the JTRF2020 and the DTRF2020, have been computed using input data series provided by the IAG technique services IVS, ILRS, IGS and IDS. They cover the entire observation period of the individual techniques until the end of 2020. Since 1996, recalculations of the ITRF have been performed approximately every 3 to 6 years. The main reason for recalculation is to ensure a high accuracy of the ITRF for current applications. In particular, seismic events that occure after an ITRF release as well as the general increase of the ITRF extrapolation error with time are key factors that cause the increase of the ITRF uncertainty.

To enhance the frequency of ITRS realizations and consequently improve the accuracy of the ITRF, the ITRS Product Center plans to calculate annual updates of the ITRF2020 starting in 2024. The IAG technique services will provide three additional years of analyzed observations (2021-2023) collected after the end of the ITRF2020 observation period in February 2024. As an ITRS Combination Center, at DGFI-TUM, we will analyze the data series w.r.t. discontinuities, post-seismic deformations and their consistency with the input data series provided for the ITRS 2020 realizations. Model changes performed in between by the individual technique services, e.g. new PCO (phase center offsets) for GNSS satellites, updated mean long-term range biases for SLR satellites or gravitational deformation models for some more VLBI antennas, are expected to have an impact on the relevant ITRF parameters (station coordinates, EOP and datum parameters). Its order of magnitude and the effect of possible inconsistencies on the DTRF solution need to be investigated. We will present the first results of our analyses and draw preliminary conclusions regarding the accuracy of a possible DTRF2020 extension.

How to cite: Seitz, M., Bloßfeld, M., Glomsda, M., Angermann, D., Rudenko, S., and Zeitlhöfler, J.: First results of the analysis of the input data series provided by the IAG technique services for the extension of xTRF2020, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-5732, https://doi.org/10.5194/egusphere-egu24-5732, 2024.

LAser RElativity Satellite 2 (LARES-2) successfully joined the constellation of geodetic satellites tracked by Satellite Laser Ranging (SLR) stations on July 13, 2022. LARES-2 has a spherical shape and a very favorable area-to-mass ratio that minimizes the non-gravitational orbit perturbations. Due to very small retroreflectors, the spread of center-of-mass corrections for different detectors installed at SLR sites is much smaller than for LAGEOS satellites. LARES-2 orbits at a similar height as LAGEOS-1, however, with a complementary inclination angle of 70° forming a butterfly configuration together with LAGEOS-1.

Although the primary objective of LARES-2 is verification of the Lense-Thirring effect emerging from general relativity, the satellite also has a substantial impact on the geodetic parameters derived from SLR observations. We process 18 months of LARES-2 data and compare the LAGEOS-1/2 solutions with the combined LAGEOS-1/2+LARES-2 solutions. We show the impact of LARES-2 on the (1) SLR station coordinates, (2) pole coordinates, (3) length-of-day excess, (4) low-degree gravity field parameters focusing on C₂₀ and C₃₀ coefficients, (5) scale of the reference frame, (6) geocenter motion. We show that LARES-2 can especially improve the Z component of the geocenter coordinates and de-correlate C₂₀ from the length-of-day parameter. The secular drifts of the ascending nodes for LARES-1 and LAGEOS-1 caused by C₂₀ are the same in terms of absolute values but with opposite signs. This allows us to successfully separate the measurements of length-of-day excess (or the UT rate) from the C₂₀-induced changes. We also analyze the empirical accelerations acting on LARES-2 which result from unmodeled non-gravitational orbit perturbations, such as thermal effects, and compare them to those observed for LAGEOS satellites. The observation geometry of LARES-2 is especially beneficial for stations located at high and medium latitudes, which allows it to improve the estimation of station coordinates provided by LAGEOS-1/2. Therefore, LARES-2 substantially contributes not only to general relativity and fundamental physics but also to space geodesy improving the future realizations of the international terrestrial reference frames.

How to cite: Sośnica, K., Gałdyn, F., Najder, J., Zajdel, R., and Strugarek, D.: Contribution of LARES-2 to the realization of reference frames, deriving Earth rotation and gravity field parameters, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-6189, https://doi.org/10.5194/egusphere-egu24-6189, 2024.

Global Navigation Satellite Systems (GNSS) are based on measuring the time that elapses between the signal’s transmission at the satellite and its reception on the ground. Therefore, clock information is required on both sides. While the GNSS satellites are equipped with atomic clocks, ground stations usually use the time information from the internal oscillator of their GNSS receiver, which has a much lower time-keeping performance compared to the satellite clocks. Nevertheless, some continuously operated tracking stations obtain their time information from an external atomic clock, as it is the case with many stations of the International GNSS Service (IGS).

To compensate for synchronization errors, current GNSS analysis models generally introduce clock biases for satellites and receivers into the observation equations. The often-made assumption of a pure white noise behavior for the estimated clocks may lead to high correlations with other geodetic parameters, such as the radial orbit error for the satellite clock, or the station height coordinate and tropospheric delay parameters for the station clock. A general solution to this problem is to reduce the amount of unknown clock parameters by modeling them in the adjustment process. In order to be modeled adequately, the corresponding clock must have a high degree of stability, which is particularly crucial for the ground stations.

In this contribution, we investigate the clock stability of globally distributed IGS tracking stations. Those IGS stations, that are steered by an external Hydrogen-Maser (H-Maser) clock, are considered in a global network analysis over a period of several weeks. The generated clock products are used to compare the frequency stabilities within the station network, as well as with the mean behavior of GPS and Galileo satellite blocks. After some further research on stations with significantly higher deviations, the final result of this contribution will be a set of reliable ground stations, that will serve as a basis for future clock modeling approaches at GFZ.

How to cite: Widczisk, J. S., Männel, B., and Wickert, J.: Investigations into GNSS clock biases in a global network of IGS H-Maser stations, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-6472, https://doi.org/10.5194/egusphere-egu24-6472, 2024.

In recent years, new determinations of the ITRF based on full-blown reanalyses of frame inputs from the four space-geodetic techniques have been produced at intervals of 3-6 years. Between frame determinations, ITRF users must rely on predictions of station positions of the reference stations included in the frame whose accuracy rapidly degrades over time, thus causing errors in the products derived from such predictions.    
JTRF2020 is the most recent TRF solution computed at JPL by assimilating the frame input data submitted by  IGS, IVS, ILRS, and IDS for ITRF2020. Determined with a square-root information filter and Dyer-McReynolds smoother algorithm, JPL frame products lend themselves to being updated rather easily as long as frame inputs from the four technique centers consistent with the frame-defining data set are readily available. 
In this presentation, we will discuss and test SREF (Square-root Reference frame Estimation Filter) updating capabilities in relation to JTRF2020. We will upload state estimate and its covariance computed at the last step of JTRF2020, and update them by assimilating at daily intervals the extended frame inputs made available by IGS (Repro3 extension), IVS (BKG operational combined series with loading effects restored using loading information from the NASA GSFC solution), ILRS (v170 and v171), and IDS (wd20) from 2021 through the end of 2022.   
Discussions will focus on the peculiarities of the extended frame inputs in relation to the data submitted for the ITRF2020 computation, and in particular on the data pre-processing and transformations we’ve applied to the extended frame inputs in order to ensure consistency with JTRF2020. We’ll also assess the quality of the JTRF2020 updates in terms of frame-defining parameters.     

How to cite: Abbondanza, C., Chin, T. M., Gross, R. S., and Heflin, M. B.: Updating JTRF2020, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-6698, https://doi.org/10.5194/egusphere-egu24-6698, 2024.

Having a Very Long Baseline Interferometry (VLBI) transmitter (VT) onboard Galileo satellite allows us to determine the misorientation between GNSS and VLBI frames. To exploit the maximum performance, we study the operational strategies for VLBI ground segment. We simulate VLBI observations of a VT onboard a Galileo satellite to evaluate the rotation transformation between the VLBI and GNSS frames. The contribution of a VT as space tie is assessed by the evaluation of the formal precision of the orientation parameters between the VLBI and GNSS frames using different ground stations/baselines, aiming to find the optimal observation geometry for the best precision on the rotation transformation.

How to cite: Sert, H., Hugentobler, U., Karatekin, O., and Dehant, V.: Effect of network geometry on determination of VLBI-GNSS frame orientation using a VLBI transmitter onboard Galileo satellites, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-8143, https://doi.org/10.5194/egusphere-egu24-8143, 2024.

The multipath phenomenon is one of the factors affecting the accuracy of GNSS positioning. It results from reflections of the satellite signal from objects in the vicinity of the GNSS antenna. There are groups of techniques that allow minimizing the impact of this error on positioning results. These include: antenna placement, the use of the appropriate type of antenna, the use of a professional receiver as well as proper post-processing of observations. However, it is impossible to completely eliminate the influence of multipath on the measurement results. In the case of carrier phase differential positioning, this error has two main effects. First of all, the multipath increases the initial search space for correct ambiguities. Consequently, the accuracy of the vector solution between the reference station and the rover receiver is affected. The authors of this article examined how the characteristics of the multipath error changed at the stations of the Polish network of ASG-EUPOS reference stations in 2010-2021. Two computational strategies were adopted to determine the multipath: Code Minus Carrier linear combination (CMC) and pseudorange multipath observable (MP). Based on the research, it was found how the multipath values changed depending on the change of the receiver and the terrain around the reference stations. It was determined which stations had high multipath values in 2010 and what changes occurred over the 11 years. Based on the carried out analyses, it was also recommended to perform periodic tests that would allow it to detect incorrect configuration or incorrect operation of receivers.

How to cite: Tomaszewski, D., Pelc-Mieczkowska, R., and Rapiński, J.: Changes in the multipath value at ASG-EUPOS GNSS reference network stations in 2010-2021, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-8188, https://doi.org/10.5194/egusphere-egu24-8188, 2024.

Highly accurate Terrestrial Reference Frames (TRF) – based on the combination of the four space-geodetic techniques Satellite Laser Ranging (SLR), Very Long Baseline Interferometry (VLBI), Global Navigation Satellite Systems (GNSS) and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) – are the fundamental backbone for a broad range of applications like land surveying, the geodetic monitoring of geophysical processes within the Earth system or navigation on and near the Earth’s surface. Recent efforts at the Geodetic Observatory Wettzell (GOW), Germany, aim at a transition from the purely geometric link between space-geodetic techniques via local ties as the current standard to an innovative quasi-error-free combination based on a common clock (CC) and a common target (CT).

Once the CC/CT-based infrastructure at GOW is fully developed and operational, it will be possible to uncover systematics between the space-geodetic techniques as well as individual instruments. However, to guarantee the long-term accuracy and stability of the TRF, it is indispensable to know and, if possible, to eliminate the systematics over the entire observation period of the techniques. A prerequisite for this is to compile an inventory of the existing discrepancies between the techniques and their possible causes.

The DFG research unit ‘Clock Metrology: Time as a New Variable in Geodesy’ features a joint project by DGFI-TUM and Uni Bonn with focus on developing a new CC-/CT-based approach to combine the space-geodetic techniques. As a basis, we develop an approach to analyse and cross-compare station position time series from different instruments/techniques observed over several decades. Based on the example of GOW co-locating all four space-geodetic techniques, we investigate absolute station position time series consistently aligned to the datum of the DTRF2020, DGFI-TUM’s most-recent realisation of the International Terrestrial Reference System (ITRS), as well as differential time series eliminating datum-realisation-related variations in the time series of one technique. Finally, we prepare a pool of metadata (log files, data time series from meteorological sensors and weather models, estimated clock and tropospheric parameters, etc.) and include these data in the analysis to identify causes of systematics. 

From the analyses, discontinuities, time-variable drifts and the spectra of intra- and inter-technique position difference time series between individual instruments at GOW can be identified and interpreted. The result of the work is an inventory which lists both, known and previously unmodelled systematics, and, as far as possible, their causes, thus providing the basis for the consistent combination of techniques in a common space-time.

How to cite: Kehm, A., Seitz, M., and Glaser, S.: Analysis of long time series of space-geodetic techniques at co-location sites to identify technique- and instrument-specific systematics, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-8612, https://doi.org/10.5194/egusphere-egu24-8612, 2024.

Geodesy provides the highest precision and accuracy International Terrestrial Reference Frame, International Celestial Reference Frame and Earth Orientation Parameters. However, in our processing chain, we take mathematical shortcuts, drop higher order polynomials, assume linearity where it is no longer valid, omit correlations and colored noise, and use outdated models. If intra- or inter-technique combinations are done, they happen at different stages, and different methods are employed. The datums applied to the reference frames are inherited over decades, accumulating all uncertainties of their predecessors. Dependencies between the reference frames and the EOP are largely ignored. Finally we inflate our errors by a predefined factor, to somehow account for all of that.
This is just a short list of the inconsistencies within our main products. Even for a specialist it will be almost impossible to list them all, for a mere end-user its an insurmountable task. In this work we will investigate these central products of geodesy, focusing mainly on the errors, their derivation, and significance from a user perspective. We look exemplarily at various official IVS and IAG products, and their reported errors. We investigate how transparent their nature and derivation is for the final user, if the parameters in question follow our physical understanding of the matter, and what insight we might gain from them.

How to cite: Karbon, M., Belda, S., Acuze, E., Moreira, M., Escapa, A., and Ferrándiz, J. M.: A critical look at the reported errors of geodetic products, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-8737, https://doi.org/10.5194/egusphere-egu24-8737, 2024.

The techniques of space geodesy, comprising the four techniques, Global Navigation Satellite Systems (GNSS), Very Long Baseline Interferometry (VLBI), Satellite Laser Ranging (SLR) and Doppler Orbitography and Ranging Integrated by Satellite (DORIS) are currently reaching a measurement resolution in the range of 1 part per billion for the terrestrial reference frame. However, a small set of discrepancies remain evident within each of the techniques as well as in the combination of different techniques. Systematic measurement errors are causing this and problems in the local ties between the reference points of the various measurement systems and biases in the atmospheric refraction correction have long been suspected as the main contributors. 

However, it turns out that errors in the internal delay compensation of the measurement systems are also a significant contributor. They are extremely hard to detect, since they are small and come with different characteristics. It is understood that the experienced delay variation is related to a complex pattern of ambient temperature variation inside of the electronic devices. These changes relate to the micro-climate of the electronic signal path and can both be slow and highly variable. With the advent of high bandwidth mode-locked lasers and active delay compensation in the optical domain, it is now possible to utilize coherent time as an independent probe for instrumental signal delays. 

The research unit FOR5456 of the German National Science Foundation (DFG) has been formed in 2022 in order to apply and investigate active delay compensation to the techniques of space geodesy. This talk introduces the application of coherent time in space geodesy and its potential to act as a novel tie in fundamental stations.

How to cite: Schreiber, K. U.: Clock Ties: A novel approach for the reduction of systematic errors, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-9298, https://doi.org/10.5194/egusphere-egu24-9298, 2024.

How to cite: Kierulf, H. P.: Glacial induced variations in the uplift – a challenge for the reference frame , EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-9527, https://doi.org/10.5194/egusphere-egu24-9527, 2024.