G – Geodesy

G1.1 – Recent Developments in Geodetic Theory

EGU21-312 | vPICO presentations | G1.1

Tensor Invariants for Gravitational Curvatures

Xiao-Le Deng, Wen-Bin Shen, Meng Yang, and Jiangjun Ran

The tensor invariants (or invariants of tensors) for gravity gradient tensors (GGT, the second-order derivatives of the gravitational potential (GP)) have the advantage of not changing with the rotation of the corresponding coordinate system, which were widely applied in the study of gravity field (e.g., recovery of global gravity field, geophysical exploration, and gravity matching for navigation and positioning). With the advent of gravitational curvatures (GC, the third-order derivatives of the GP), the new definition of tensor invariants for gravitational curvatures can be proposed. In this contribution, the general expressions for the principal and main invariants of gravitational curvatures (PIGC and MIGC denoted as I and J systems) are presented. Taking the tesseroid, rectangular prism, sphere, and spherical shell as examples, the detailed expressions for the PIGC and MIGC are derived for these elemental mass bodies. Simulated numerical experiments based on these new expressions are performed compared to other gravity field parameters (e.g., GP, gravity vector (GV), GGT, GC, and tensor invariants for the GGT). Numerical results show that the PIGC and MIGC can provide additional information for the GC. Furthermore, the potential applications for the PIGC and MIGC are discussed both in spatial and spectral domains for the gravity field.

How to cite: Deng, X.-L., Shen, W.-B., Yang, M., and Ran, J.: Tensor Invariants for Gravitational Curvatures, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-312,, 2021.

The problem of determining the height anomaly in a local area of the radius ψ0 using gravity disturbances and gravity anomalies is discussed. The influence of the far zone, as usually, is approximately taken into account using the global gravity field model and the truncation coefficients Qn0) introduced by M.S. Molodensky [1]. The modification Qn00) by O.M. Ostach [2] of these coefficients is described. They provide - in contrast to the original coefficients - the continuity of the used integral transform kernel Ker0 (ψ) in the whole its definition domain. As a consequence, the modified coefficients decrease faster compared to the original ones with an increase of the degree n (frequency). It reduces the error of the far zone influence. Coefficients are interpreted as Fourier coefficients of the outer part of the kernel when it is decomposed into the orthogonal system of nonnormalized Legendre polynomials. The relationship between Qn0) and Qn00) is indicated. In the frequency domain, the expression for the truncated kernel ΔKer0 (ψ) of the integral transform used (Stokes or Hotine-Koch) differs from the corresponding full kernel by a multiplier, which is proposed to be called the frequency characteristic of the kernel truncation operator onto the inner zone of radius ψ0.

In local modeling, when describing the details of the "useful signal", it is advisable to use approximation by means of spherical radial basis functions (SRBF) instead of traditional integration due to their good spatial localization [3, 4]. The procedure of constructing scaling functions and corresponding wavelets is briefly described. New scaling functions, based on the above-mentioned concept of frequency characteristic of the kernel truncation operator onto the inner zone of the radius ψo, are proposed. To prove the effectiveness of these scaling functions, numerical experiments were conducted. Both gravity anomalies Δg and disturbances δg were used as input data. The results of the calculations showed a high accuracy of recovering height anomalies from gravity anomalies. Besides, introduction of frequency characteristic of kernel truncation of corresponding integral transform onto the inner zone allows to cut off implicit influence of far zone. Known scaling functions that do not use this frequency characteristic lead, as experiments have shown, to biased results.


How to cite: Sugaipova, L. and Neyman, Y.: On frequency response of Stokes and Hotine-Koch integral transforms in calculation of height anomaly in the local area by means of SRBF, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-500,, 2021.

EGU21-2614 | vPICO presentations | G1.1

Stable finite element method for solving the oblique derivative boundary value problems in geodesy

Marek Macák, Zuzana Minarechová, Róbert Čunderlík, and Karol Mikula

We presents local gravity field modelling in a spatial domain using the finite element method (FEM). FEM as a numerical method is applied for solving the geodetic boundary value problem with oblique derivative boundary conditions (BC). We derive a novel FEM numerical scheme which is the second order accurate and more stable than the previous one published in [1]. A main difference is in applying the oblique derivative BC. While in the previous FEM approach it is considered as an average value on the bottom side of finite elements, the novel FEM approach is based on the oblique derivative BC considered in relevant computational nodes. Such an approach should reduce a loss of accuracy due to averaging. Numerical experiments present (i) a reconstruction of EGM2008 as a harmonic function over the extremely complicated Earth’s topography in the Himalayas and Tibetan Plateau, and (ii) local gravity field modelling in Slovakia with the high-resolution 100 x 100 m while using terrestrial gravimetric data.

[1] Macák, Z. Minarechová, R. Čunderlík, K. Mikula, The finite element method as a tool to solve the oblique derivative boundary value problem in geodesy. Tatra Mountains Mathematical Publications. Vol. 75, no. 1, 63-80, (2020)

How to cite: Macák, M., Minarechová, Z., Čunderlík, R., and Mikula, K.: Stable finite element method for solving the oblique derivative boundary value problems in geodesy, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-2614,, 2021.

EGU21-11729 | vPICO presentations | G1.1 | Highlight

Laplacian structure mirroring surface topography in determining the gravity potential by successive approximations

Petr Holota and Otakar Nesvadba

Similarly as in other branches of engineering and mathematical physics, a transformation of coordinates is applied in treating the geodetic boundary value problem. It offers a possibility to use an alternative between the boundary complexity and the complexity of the coefficients of the partial differential equation governing the solution. In our case the Laplace operator has a relatively simple structure in terms of spherical or ellipsoidal coordinates which are frequently used in geodesy. However, the physical surface of the Earth and thus also the solution domain substantially differ from a sphere or an oblate ellipsoid of revolution, even if optimally fitted. The situation becomes more convenient in a system of general curvilinear coordinates such that the physical surface of the Earth is imbedded in the family of coordinate surfaces. Applying tensor calculus the Laplace operator is expressed in the new coordinates. However, its structure is more complicated in this case and in a sense it represents the topography of the physical surface of the Earth. The Green’s function method together with the method of successive approximations is used for the solution of the geodetic boundary value problem expressed in terms of the new coordinates. The structure of iteration steps is analyzed and if useful and possible, it is modified by means of integration by parts. Subsequently, the iteration steps and their convergence are discussed and interpreted, numerically as well as in terms of functional analysis.

How to cite: Holota, P. and Nesvadba, O.: Laplacian structure mirroring surface topography in determining the gravity potential by successive approximations, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-11729,, 2021.

EGU21-128 | vPICO presentations | G1.1 | Highlight

Validations of Three Global Gravity Field Models Using the QDaedalus System Observed Astrogeodetic Vertical Deflections in the Munich Region, Germany

Muge Albayrak, Christian Hirt, Sébastien Guillaume, Ck Shum, Michael Bevis, Emel Zeray Öztürk, and Ibrahim Öztug Bildirici

The total station-based QDaedalus system, developed in 2014 by ETH Zurich in Switzerland, incorporates a charge-coupled device (CCD) camera in support of daytime geodetic and nighttime astrogeodetic observations. The successful realization of astrogeodetic observations has resulted in astrogeodetic vertical deflection (VD) data collection in Germany, Italy, Hungary, Australia, and Turkey. Astrogeodetic observations carried out in Munich, Germany were used to determine the precision and accuracy of the newly installed QDaedalus system, which was found to be ~0.2 arcseconds for both the North-South (N-S) and East-West (E-W) VD components. In this study, 10 benchmark observations in the Munich region were also used to assess the quality of three global gravity field models—Global Gravitation Model Plus (GGMplus), Earth Residual Terrain Modelled 2160 (ERTM2160) and Earth Gravitational Model 2008 (EGM2008)—through comparison with the QDaedalus observations. The results of these comparisons between the predicted and observed VD data are: (i) The GGMplus predicted VD values were found to be closer to the observed VDs, with the differences for both the N-S and E-W VD components being ~0.2″, and reaching a maximum of 0.3″ and 0.4″ for the N-S and E-W components, respectively; (ii) The ERTM2160 predicted values were also found to be closer to the observed VDs, with differences of 0.4″ or less for the N-S component, with the exception of one benchmark (BM 8), and 0.2″ or less for the E-W component, with the exception of one benchmark (BM 9); and, (iii) When the predicted VDs computed using EGM2008 were analysed, we found that they were less accurate than the predicted GGMplus and ERTM2160 values. Therefore, the maximum differences between the observed and EGM2008 predicted VD data were for 0.9″ N-S and 1.8″ for E-W. Finally, we conclude with a comparison of the results of this Munich Region study with the results of a prior QDaedalus study, which was conducted in Istanbul (Albayrak et al. 2020), to assess the accuracy of the EGM2008 and GGMplus models.


Albayrak, M., Hirt, C., Guillaume, S., Halicioglu, K., Özlüdemir, M.T., Shum, C.K., 2020. Quality assessment of global gravity field models in coastal zones: a case study using astrogeodetic vertical deflections in Istanbul, Turkey, Studia Geophysica et Geodaetica, 64(3), 306–329. doi: 10.1007/s11200-019-0591-2

How to cite: Albayrak, M., Hirt, C., Guillaume, S., Shum, C., Bevis, M., Zeray Öztürk, E., and Bildirici, I. Ö.: Validations of Three Global Gravity Field Models Using the QDaedalus System Observed Astrogeodetic Vertical Deflections in the Munich Region, Germany, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-128,, 2021.

EGU21-1112 | vPICO presentations | G1.1 | Highlight

Validation of calibrated GOCE gravity gradients GRD_SPW_2 by least-squares spectral weighting   

Martin Pitoňák, Michal Šprlák, Vegard Ophaug, Ove Omang, and Pavel Novák

The Gravity field and steady-state Ocean Circulation Explorer (GOCE) was the first mission which carried a novel instrument, gradiometer, which allowed to measure the second-order directional derivatives of the gravitational potential or gravitational gradients with uniform quality and a near-global coverage. More than three years of the outstanding measurements resulted in two levels of data products (Level 1b and Level 2), six releases of global gravitational models (GGMs), and several grids of gravitational gradients (see, e.g., ESA-funded GOCE+ GeoExplore project or Space-wise GOCE products). The grids of gravitational gradients represent a step between gravitational gradients measured directly along the GOCE orbit and data directly from GGMs. One could use grids of gravitational gradients for geodetic as well as for geophysical applications. In this contribution, we are going to validate the official Level 2 product GRD_SPW_2 by terrestrial gravity disturbances and GNSS/levelling over two test areas located in Europe, namely in Norway and former Czechoslovakia (now Czechia and Slovakia). GRD_SPW_2 product contains all six gravity gradients at satellite altitude from the space-wise approach computed only from GOCE data for the available time span (r-2, r-4, and r-5) and provided on a 0.2 degree grid. A mathematical model based on a least-squares spectral weighting will be developed and the corresponding spectral weights will be presented for the validation of gravitational gradients grids. This model allows us to continue downward gravitational gradients grids to an irregular topographic surface (not to a mean sphere) and transform them into gravity disturbances and/or geoidal heights in one step. Before we compared results obtained by spectral downward continuation, we had to remove the high-frequency part of the gravitational signal from terrestrial data because in gravitational gradients measured at GOCE satellite altitude is attenuated. To do so we employ EGM2008 up to d/o 2160 and the residual terrain model correction (RTC) has been a) interpolated from ERTM2160 gravity model, b) synthesised from dV_ELL_Earth2014_5480_plusGRS80, c) calculated from a residual topographic model by forward modelling in the space domain.  

How to cite: Pitoňák, M., Šprlák, M., Ophaug, V., Omang, O., and Novák, P.: Validation of calibrated GOCE gravity gradients GRD_SPW_2 by least-squares spectral weighting   , EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1112,, 2021.

EGU21-11022 | vPICO presentations | G1.1 | Highlight

Sampling theorem of satellite gravimetry from the perspective of the Bender configuration

Anshul Yadav, Balaji Devaraju, Matthias Weigelt, and Nico Sneeuw

EGU21-12598 | vPICO presentations | G1.1

Towards tide gauges selection for model-based hydrodynamic leveling connections; with application to assess the potential impact on the quality of the European Vertical Reference Frame

Yosra Afrasteh, Cornelis Slobbe, Martin Verlaan, Martina Sacher, Roland Klees, Henrique Guarneri, Lennart Keyzer, Julie Pietrzak, Mirjam Snellen, and Firmijn Zijl

Model-based hydrodynamic leveling allows transferring heights between tide gauges by means of model-derived mean water level (MWL) differences between them. In this study, we aim to exploit the technique to improve the quality of the European Vertical Reference Frame (EVRF). In doing so, the candidate tide gauges must fulfill two criteria. First, they must be connected to the Unified European Leveling Network (UELN). Second, the hydrodynamic model to be used should be capable of resolving the local MWL at the tide gauge locations. The latter can be very challenging as some tide gauges are located in areas with complicated hydrodynamic processes. To identify which tide gauges have the largest impact on the quality of the EVRF, we conducted geodetic network analyzes. Here we used all tide gauges within 10 km of UELN height markers. Moreover, we assumed to have access to a hydrodynamic model covering all European seas, or alternatively regional models for separate basins, providing the MWLs with uniform precision. Our results indicate a reduction of the mean propagated standard deviation of the adjusted heights between 20% to 40% compared to the UELN-only solution. The magnitude of the improvement depends on the setup of the experiment and the selected noise level for model-derived MWL differences. Detailed analysis shows that we already obtain a significant improvement (>20%) by adding only a limited number of hydrodynamic leveling connections. Moreover, we found that the tide gauges located in the countries with the most UELN height markers are most profitable in terms of improvement. The impact hardly depends on the tide gauges' geographic location, which shows the method's freedom and flexibility in selecting the tide gauges.

How to cite: Afrasteh, Y., Slobbe, C., Verlaan, M., Sacher, M., Klees, R., Guarneri, H., Keyzer, L., Pietrzak, J., Snellen, M., and Zijl, F.: Towards tide gauges selection for model-based hydrodynamic leveling connections; with application to assess the potential impact on the quality of the European Vertical Reference Frame, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-12598,, 2021.

EGU21-1598 | vPICO presentations | G1.1

Selection of an optimal algorithm for outlier detection in GNSS time series

Nhung Le Thi, Benjamin Männel, Mihaela Jarema, Gopi Krishna Seemala, Kosuke Heki, and Harald Schuh

In data mining, outliers can lead to misleading interpretations of statistical results, particularly in deformation monitoring based on fluctuations and disturbances simulated by numerical models for the analysis of deformations. Therefore, outlier filtering cannot be ignored in data standardization. However, it is not likely that a filtering algorithm is efficient for every data pattern. We investigate five outlier filtering algorithms using MATLAB® (Release 2020a): moving average, moving median, quartiles, Grubbs, and generalized extreme Studentized deviation (GESD) to select the optimal algorithms applied for GNSS time series data. This study is conducted on two types of data used for ionosphere disturbance analysis in the region of the Ring of Fire and crustal deformation monitoring in Germany, one showing seasonal time series patterns and the other presenting the trend models. We apply the simple random sampling method that ensures the principles of unbiased surveying techniques. The optimal algorithm selection is based on the sensitivity of outlier detection and the capability of the central tendency measures. The algorithm robustness is also tested by altering random outliers but maintaining the standard distribution of each dataset. Our results show that the moving median algorithm is most sensitive for outlier detection because it is robust statistics and is not affected by anomalies; followed in turn by quartiles, GESD, and Grubbs. The outlier filtering capability of the moving average algorithm is least efficient, with a percentage of outlier detection below 20% compared to the moving median (corresponding 95% probability). In deformation analysis, disturbances on numerical models are often the basis for motion assessment, while these anomalies are smoothed by moving median filtering. Hence, the quartiles algorithm can be considered in this case. Overall, the moving median is best suited to filter outliers for seasonal and trend time series data; in particular, for deformation analysis, the optimal solution is applying the quartiles or extending the threshold factor and the sliding window of the moving median.

Keywords: Outlier filtering, Time series, Deformation analysis, Moving median, Quartiles, MATLAB.

How to cite: Le Thi, N., Männel, B., Jarema, M., Krishna Seemala, G., Heki, K., and Schuh, H.: Selection of an optimal algorithm for outlier detection in GNSS time series, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1598,, 2021.

Best integer equivariant (BIE) estimators provide minimum mean squared error (MMSE) solutions to the problem of GNSS carrier-phase ambiguity resolution for a wide range of distributions. The associated BIE estimators are universally optimal in the sense that they have an accuracy which is never poorer than that of any integer estimator and any linear unbiased estimator. Their accuracy is therefore always better or the same as that of Integer Least-Squares (ILS) estimators and Best Linear Unbiased Estimators (BLUEs).

Current theory is based on using BIE for the multivariate normal distribution. In this contribution this will be generalized to the contaminated normal distribution and the multivariate t-distribution, both of which have heavier tails than the normal. Their computational formulae are presented and discussed in relation to that of the normal distribution. In addition a GNSS real-data based analysis is carried out to demonstrate the universal MMSE properties of the BIE estimators for GNSS-baselines and associated parameters.


Keywords: Integer equivariant (IE) estimation · Best integer equivariant (BIE) · Integer Least-Squares (ILS) . Best linear unbiased estimation (BLUE) · Multivariate contaminated normal · Multivariate t-distribution . Global Navigation Satellite Systems (GNSSs)

How to cite: Teunissen, P.: Theory of best integer equivariant estimation for contaminated normal and multivariate t-distribution with applications, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-2027,, 2021.

EGU21-3116 | vPICO presentations | G1.1

Improving the sensitivity levels generated from hypothesis testing by combining VLBI with GNSS data

Pakize Küreç Nehbit, Susanne Glaser, Kyriakos Balidakis, Pierre Sakic, Robert Heinkelmann, Harald Schuh, and Haluk Konak

The individual space geodetic techniques have different advantages and disadvantages. For instance, the global observing network of Very Long Baseline Interferometry (VLBI) consists of much fewer stations with a poorer distribution than the one of Global Navigation Satellite Systems (GNSS). In a combination thereof, this fact can be compensated, mainly to the benefit of the former.

The sensitivity level provides information on the detection capacity of observing stations based on undetectable gross errors in a geodetic network solution. Furthermore, sensitivity can be understood as the minimum value of the undetectable gross errors by hypothesis testing. The location of the station in the network and the total weight of its observations contribute to the sensitivity levels thereof. Also, the total observation number of a radio source and the quality of the observations are critical for the sensitivity levels of the radio sources. Besides these criteria, a radio source having a larger structure index has a larger sensitivity level. In this study, it is investigated whether the sensitivity levels of VLBI stations in the CONT14 campaign improve by combination with GNSS. The combination was done at the normal equation level using 153 GNSS stations in total, 17 VLBI radio telescopes, and local ties at 5 co-located stations which are ONSA-ONSALA60, NYA1-NYALES20, ZECK-ZELENCHK, MATE-MATERA, and HOB2-HOBART26 during the CONT14 campaign spanning 15 days. To evaluate the observations of GNSS and VLBI, the software of EPOS8 and VieVS@GFZ (G2018.7, GFZ, Potsdam, Germany) were used respectively. In the VLBI-only solution, FORTLEZA shows the poorest sensitivity level compared to the other VLBI radio telescopes. As a result of the combination with GNSS, it can be seen that the sensitivity levels of FORTLEZA improved by about 60% in all sessions of CONT14. It can be concluded that VLBI stations, which are poorly controlled by the other radio telescopes in the network, can be supported by the other space geodetic techniques to improve the overall quality of the solution.

How to cite: Küreç Nehbit, P., Glaser, S., Balidakis, K., Sakic, P., Heinkelmann, R., Schuh, H., and Konak, H.: Improving the sensitivity levels generated from hypothesis testing by combining VLBI with GNSS data, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3116,, 2021.

EGU21-1765 | vPICO presentations | G1.1

Lp LOSC-Support Vector Machines for Regression Estimation and their Application to Geomatics

Jeff Chak Fu Wong and Tsz Fung Yu

The classification of vertical displacements and the estimation of a local geometric geoid model and coordinate transformation were recently solved by the L2 support vector machine and support vector regression. The Lp quasi-norm SVM and SVR (0<p<1) is a non-convex and non-Lipschitz optimization problem that has been successfully formulated as an optimization model with a linear objective function and smooth constraints (LOSC) that can be solved by any black-box computing software, e.g., MATLAB, R and Python. The aim of this talk is to show that interior-point based algorithms, when applied correctly, can be effective for handling different LOSC-SVM and LOSC-SVR based models with different p values, in order to obtain better sparsity regularization and feature selection. As a comparative study, some artificial and real-life geoscience datasets are used to test the effectiveness of our proposed methods. Most importantly, the methods presented here can be used in geodetic classroom teaching to benefit our undergraduate students and further bridge the gap between the applications of geomatics and machine learning.

How to cite: Wong, J. C. F. and Yu, T. F.: Lp LOSC-Support Vector Machines for Regression Estimation and their Application to Geomatics, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1765,, 2021.

EGU21-8511 | vPICO presentations | G1.1

Impact of Earth's curvature on coastal sea level altimetry with ground-based GNSS Reflectometry

Vitor Hugo Almeida Junior, Marcelo Tomio Matsuoka, and Felipe Geremia-Nievinski

Global mean sea level is rising at an increasing rate. It is expected to cause more frequent extreme events on coastal sites. The main sea level monitoring systems are conventional tide gauges and satellite altimeters. However, tide gauges are few and satellite altimeters do not work well near the coasts. Ground-based GNSS Reflectometry (GNSS-R) is a promising alternative for coastal sea level measurements. GNSS-R works as a bistatic radar, based on the use of radio waves continuously emitted by GNSS satellites, such as GPS and Galileo, that are reflected on the Earth’s surface. The delay between reflected and direct signals, known as interferometric delay, can be used to retrieve geophysical parameters, such as sea level. One advantage of ground-based GNSS-R is the slant sensing direction, which implies the reflection points can occur at long distances from the receiving antenna. The higher is the receiving antenna and the lower is the satellite elevation angle, the longer will be the distance to the reflection point. The geometrical modeling of interferometric delay, in general, adopts a planar and horizontal model to represent the reflector surface. This assumption may be not valid for far away reflection points due to Earth’s curvature. It must be emphasized that ground-based GNSS-R sensors can be located at high altitudes, such in lighthouses and cliffs, and GNSS satellites are often tracked near grazing incidence and even at negative elevation angles. Eventually, Earth’s curvature would have a significant impact on altimetry retrievals. The osculating spherical model is more adequate to represent the Earth’s surface since its mathematical complexity is in between a plane and an ellipsoid. The present work aims to quantify the effect of Earth’s curvature on ground-based GNSS-R altimetry. Firstly, we modeled the interferometric delay for each plane and sphere and we calculated the differences across the two surface models, for varying satellite elevation and antenna altitude. Then, we developed an altimetry correction in terms of half of the rate of change of the delay correction with respect to the sine of elevation. We simulated observation scenarios with satellite elevation angles from zenith down to the minimum observable elevation on the spherical horizon (negative) and antenna altitudes from 10 m to 500 m. We noted that due to Earth’s curvature, the reflection point is displaced, brought closer in the x-axis and bent downward in the y-axis. The displacement of the reflection point increases the interferometric delay. Near the planar horizon, at zero elevation, the difference increases quickly and so does the altimetry correction. Finally, considering a 1-cm altimetry precision threshold to sea-level measurements, we observed that the altimetry correction for Earth’s curvature is needed at 10°, 20°, and 30° satellite elevation, for an antenna altitude of 60 m, 120 m, and 160 m, respectively.

How to cite: Almeida Junior, V. H., Matsuoka, M. T., and Geremia-Nievinski, F.: Impact of Earth's curvature on coastal sea level altimetry with ground-based GNSS Reflectometry, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8511,, 2021.

EGU21-9504 | vPICO presentations | G1.1

mSTAR: Multicriteria Spatio Temporal Altimetry Retracking

Lutz Oettershagen, Bernd Uebbing, Jonas Charfreitag, Petra Mutzel, and Jürgen Kusche

Observing coastal sea-level change from satellite altimetry is challenging due to land influence on the estimated sea surface height (SSH), significant wave height (SWH), and backscatter. In recent years specialized algorithms have been developed which allow retrieving meaningful estimates up to the coast. Among these, the Spatio Temporal Altimetry Retracker (STAR) has introduced a novel approach by partitioning the total return signal into individual sub-signals which are then processed leading to a point-cloud of potential estimates for each of the three parameters which tend to cluster around the true values, e.g., the real sea surface. The original STAR algorithm interprets each point-cloud as a weighted directed acyclic graph (DAG). The spatio-temporal ordering of the potential estimates induces a layering, and each layer is fully connected to the next. The weights of the edges are based on a chosen distance measure between the connected vertices. The STAR algorithm selects the final estimates by searching the shortest path through the DAG using forward traversal in topological order. This approach includes the inherent assumption that neighboring SSHs etc. should be similar. However, a drawback of the original STAR approach is that each of the point clouds for the three parameters can only be treated individually since the applied standard shortest path approach can not handle multiple edge weights. Therefore, the output of the STAR algorithm for each parameter does not necessarily correspond to the same sub-signal. To overcome this limitation, we propose to employ a multicriteria approach to find a final estimate that takes the weighting of two or three point-clouds into account resulting in the multicriteria Spatio Temporal Altimetry Retracking (mSTAR) framework. An essential difference between the single and the multicriteria shortest path problems is that there is no single optimal solution in the latter. We call a path Pareto-optimal if there is no other path that is strictly shorter for all criteria. Unfortunately, the number of Pareto-optimal paths can be exponential in the input size, even if the considered graph is a DAG. A simple and common approach to tackle this complexity issue is to use the weighted sum scalarization method, in which the objective functions are weighted and combined to a single objective function, such that a single criteria shortest path algorithm can find a Pareto-optimal path. Varying the weighting, a set of Pareto-optimal solutions can be obtained. However, it is in general not possible to find all Pareto-optimal paths this way. In order to find all Pareto-optimal paths, label-correcting or label-setting algorithms can be used. The mSTAR framework supports both scalarization and labeling techniques as well as exact and approximate algorithms for computing Pareto-optimal paths. This way mSTAR is able to find multicriteria consistent estimates of SSH, SWH, and backscatter.

How to cite: Oettershagen, L., Uebbing, B., Charfreitag, J., Mutzel, P., and Kusche, J.: mSTAR: Multicriteria Spatio Temporal Altimetry Retracking, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9504,, 2021.

EGU21-8401 | vPICO presentations | G1.1 | Highlight

Modelling moving force of tectonic plates with the use of length of day variation

Csilla Fodor and Péter Varga

The nature, the age and probably first of all the magnitude of driving forces of plate motion since long are a subject of scientific debates and it cannot be regarded as clarified even today.

The physical basis of recent plate tectonics is characterized by interaction between plates by viscous coupling to a convecting mantle.  Authors are going to demonstrate that changes in the Earth's axial rotation can affect the movement of tectonic plates, and the phenomenon of tidal friction is able to shift the lithospheric plates.

The tidal friction regulates the length of day (LOD)and consequently also the rotational energy of the Earth. It can be investigated with the use of total tidal energy, which can be determined as a sum of three energies (energy of axial rotation of the Earth, Moon’s orbital energy around the common centre of mass and the mutual potential energy). It was found that during the last 3 Ga the Earth lost 33% of its rotational energy. The LOD 0.5Ga BP (before present) was ~21 h. This means that the rotational energy loss rate was 4.1 times higher during the Pz (Phanerozoic, from 560 Ma BP to our age) than earlier in the Arch (Archean, 4 to 2.5 Ga BP) and Ptz (Proterozoic 2.5 to0.56 Ga BP). The low-velocity zone (LVZ) at 100-200 km depth interval, close to the boundary between the lithosphere and the asthenosphere characterized by a negative anomaly of shear wave velocities. Consequently, the LVZ can result in a decoupling effect. Tidal friction brakes the lithosphere and the part of the Earth below the asthenosphere with different forces. By model calculation, we show that this force difference is sufficient to move the tectonic plates along the Earth’s surface.  

Reference: Varga P., Fodor Cs., 2021. About the energy and age of the plate tectonics, Terra Nova. (in print)

How to cite: Fodor, C. and Varga, P.: Modelling moving force of tectonic plates with the use of length of day variation, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8401,, 2021.

EGU21-3636 | vPICO presentations | G1.1

Load-Tide Sensitivity to 3-D Earth Structure

Hilary R Martens, Christian Boehm, Martin van Driel, and Amir Khan

Earth deformation caused by the tidal redistribution of ocean mass is governed by the material properties of Earth's interior. Surface displacements induced by ocean tidal loading can exceed several centimeters over periods of hours. The rich spectrum of elastic and gravitational responses of the solid Earth produced by the load tides are predominantly sensitive to crust and upper-mantle structure, and inverting load-tide observations for Earth structure can complement independent constraints inferred from seismic tomography and Earth's body tides. 

Global Navigation Satellite Systems (GNSS) record the load-tide displacements with sub-millimeter precision and at high temporal resolution on the order of minutes. Recent studies have demonstrated agreement between predicted and GNSS-observed oceanic load tides in several regions worldwide to a similar level of accuracy. However, residuals between load-tide observations and predictions, which have been limited to spherically symmetric models for Earth structure, exhibit spatially coherent patterns that cannot be fully explained by random measurement or tide-model error and therefore present key opportunities to refine our understanding of Earth's 3-D structure at depths important to mantle convection and plate tectonics. 

Here, we present a novel numerical approach based on a preconditioned conjugate-gradient solver and the spectral-element method to investigate the sensitivities of Earth's load tides to 3-D variations in elastic Earth structure, including ellipticity, topography, and lateral contrasts in elasticity, density and crustal thickness. We leverage and extend the Salvus high-performance library to include gravitational physics and to solve quasi-static problems. High-order shape transformations and adaptive mesh refinement allow us to capture the spatial heterogeneity of the ocean tides with kilometer resolution as well as the large scale of exterior domain, which is needed to model the gravitational potential at reasonable computational cost. We perform a series of benchmark tests to verify the 3-D numerical-modeling approach against established quasi-analytical methods for modeling load-induced Earth deformation (LoadDef software). We then compute the sensitivities of load-induced surface displacements to 3-D Earth structure in two ways: (1) direct comparison of predicted surface displacements computed using 1-D and 3-D Earth models, and (2) direct computation of derivatives of surface displacements with respect to density and elasticity structure using the adjoint method.

Additional high-impact applications of the surface-load modeling capabilities include: quantifying seasonal fluctuations in mountain snowpack, tracking the depletion of groundwater reservoirs during periods of drought, improving constraints on ocean-tide models and refining the load-tide corrections employed in GNSS signal processing.

How to cite: Martens, H. R., Boehm, C., van Driel, M., and Khan, A.: Load-Tide Sensitivity to 3-D Earth Structure, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3636,, 2021.

G1.2 – Mathematical methods for the analysis of potential field data and geodetic time series

EGU21-267 | vPICO presentations | G1.2

10 years of matching pursuits for inverse problems: what’s been done and what’s to come

Naomi Schneider and Volker Michel

In the light of significant challenges like the climate change, the visualization of the gravitational potential remains a priority in geodesy. A decade ago, the Geomathematics Group Siegen proposed alternative representations for such problems.

The respective methods are based on matching pursuits: hence, they build a representation in a so-called best basis. However, they include additional aspects which occur, for instance, when the downward continuation of the gravitational potential is approximated.

In this talk, we summarize the different developmental stages from 2011 up to now which started with a basic implementation and then included aspects of orthogonality, weakness and dictionary learning, respectively. Further, we give an outlook on our next steps with these methods. For the current status-quo, we show numerical results with respect to the downward continuation of the gravitational potential.

How to cite: Schneider, N. and Michel, V.: 10 years of matching pursuits for inverse problems: what’s been done and what’s to come, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-267,, 2021.

Conventionally, exploration in geology involves distinct research groups, each looking at a different observable and performing separate inversions for subsurface structure. In this work we discuss the advantages and performance of a combined inversion coupling gravity-anomaly, acoustic-wavefield and surface velocities as observables in one single framework. The gravity potential, which varies across the Earth, is sensitive to density anomalies at depth and can be obtained by solving a Poisson type equation. Its inversion is ill-posed since its solutions are non-unique in the depth and the density of the inverted anomaly. We also consider the surface displacement caused by a compressible wave as a consequence of an earthquake at depth. This inversion results in a wavespeed reconstruction but lacks interpretability, i.e. whether the anomaly is thermal or chemical in origin. The surface velocity, caused by the motion of highly viscous rocks in the subsurface, is the third observable. It can be modelled by the (nonlinear) Stokes equations, which account for the density and viscosity of a subsurface anomaly.

All three equations and their adjoints are implemented in one single Python framework using the finite element library FeNICS. To investigate the shape of the cost function, a grid search in the parameter space for three geological settings is presented. Additionally, the performance of gradient-based inversions for each observable separately or in combination, respectively, is presented. We further investigate the performance of a shape-optimizing inversion method, assuming the material parameters are known, while the shape is unknown.

How to cite: Simons, F. J. and Reuber, G. S.: Investigation of a Coupled Deterministic Inversion for the Interior of the Earth by using Gravity-Anomaly, Acoustic-Wavefield and Geodetic Velocity measurements, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-6648,, 2021.

EGU21-8291 | vPICO presentations | G1.2

Harmonica and Boule: Modern Python tools for geophysical gravimetry

Leonardo Uieda, Santiago R. Soler, Agustina Pesce, Lorenzo Perozzi, and Mark A. Wieczorek

Gravimetry is a routine part of the geophysicists toolset, historically used in geophysics following the geodetic definitions of gravity anomalies and their related “reductions”. Several authors have shown that the geodetic concept of a gravity anomaly does not align with goals of gravimetry in geophysics (the investigation of anomalous density distributions). Much of this confusion likely stems from the lack of widely available tools for performing the corrections needed to arrive at a geophysically meaningful gravity disturbance. For example, free-air corrections are completely unnecessary since analytical expressions for theoretical gravity at any point have existed for over a decade. Since this is not easily done in a spreadsheet or short script, modern tools for processing and modelling gravity data for geophysics are needed. These tools must be trustworthy (i.e., extensively tested) and designed with software development and geophysical best practices in mind.

We present the Python libraries Harmonica and Boule, which are part of the Fatiando a Terra project ( Both tools are open-source under the permissive BSD license and are developed in the open by a community of geoscientists and programmers.

Harmonica provides tools for processing, forward modelling, and inversion of gravity and magnetic data. The first release of Harmonica was focused on implementing methods for processing and interpolation with the equivalent source technique, as well as forward modelling with right-rectangular prisms, point sources, and tesseroids. Current work is directed towards implementing a processing pipeline for gravity data, including topographic corrections in Cartesian and spherical coordinates, atmospheric corrections, and more. The software is still in early stages of development and design and would benefit greatly from community involvement and feedback.

Boule implements reference ellipsoids (including oblate ellipsoids, spheres, and soon triaxial ellipsoids), conversions between ellipsoidal and geocentric spherical coordinates, and normal gravity calculations using analytical solutions for gravity fields at any point outside of the ellipsoid. It includes ellipsoids for the Earth as well as other planetary bodies in the solar system, like Mars, the Moon, Venus, and Mercury. This enables the calculation of gravity disturbances for Earth and planetary data without the need for free-air corrections. Boule was created out of the shared needs of Harmonica, SHTools (, and pygeoid ( and is developed with input from developers of these projects.

We welcome participation from the wider geophysical community, irrespective of programming skill level and experience, and are actively searching for interested developers and users to get involved in shaping the future of these projects.

How to cite: Uieda, L., Soler, S. R., Pesce, A., Perozzi, L., and Wieczorek, M. A.: Harmonica and Boule: Modern Python tools for geophysical gravimetry, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8291,, 2021.

EGU21-12570 | vPICO presentations | G1.2

Seafloor topography variations mapped by regional gravity tensor analysis 

Lucia Seoane, Guillaume Ramillien, José Darrozes, Frédéric Frappart, Didier Rouxel, Thierry Schmitt, and Corinne Salaun

The AGOSTA project initially proposed by our team and lately funded by CNES TOSCA consists of developing efficient approaches to restore seafloor shape (or bathymetry), as well as lithospheric parameters such as the crust and elastic thicknesses, by combining different types of observations including gravity gradient data. As it is based on the second derivatives of the potential versus the space coordinates, gravity gradiometry provides more information inside the Earth system at short wavelengths. The GOCE mission has measured the gravity gradient components of the static field globally and give the possibility to detect more details on the structure of the lithosphere at spatial resolutions less than 200 km. We propose to analyze these satellite-measured gravity tensor components to map the undersea relief more precisely than using geoid or vertical gravity previously considered for this purpose. Inversion of vertical gravity gradient data derived from the radar altimetry technique also offers the possibility to reach greater resolutions (at least 50 km) than the GOCE mission one. The seafloor topography estimates are tested in areas well-covered by independent data for validation, such as around the Great Meteor guyot [29°57′10.6″N, 28°35′31.3″W] and New England seamount chain [37°24′N 60°00′W, 120° 10' 30.4" W] in the Atlantic Ocean as well as the Acapulco seamount [13° 36' 15.4" N, 120° 10' 30.4" W] in the Central Pacific.

How to cite: Seoane, L., Ramillien, G., Darrozes, J., Frappart, F., Rouxel, D., Schmitt, T., and Salaun, C.: Seafloor topography variations mapped by regional gravity tensor analysis , EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-12570,, 2021.

EGU21-1886 | vPICO presentations | G1.2

Determining the height of Mount Everest using the shallow layer method

Youchao Xie, Wenbin Shen, Jiancheng Han, and Xiaole Deng

We proposed an alternative method to determine the height of Mount Everest (HME) based on the shallow layer method (SLM), which was put forward by Shen (2006). We use the precise external global Earth gravity field model (i.e., EGM2008 and EIGEN-6C4 models) as input information, and the digital topographic model (i.e., DTM2006.0) and crust models (i.e., CRUST2.0 and CRUST1.0 models) to construct the shallow layer model. There are four combined strategies:(1) EGM2008 and CRUST1.0 models, (2) EGM2008 and CRUST2.0 models, (3) EIGEN-6C4 and CRUST1.0 models, and (4) EIGEN-6C4 and CRUST2.0 models, respectively. We calculate the HME by two approaches: first approach, the HME is directly calculated by combining the geoid undulation (N) and geodetic height (h); second approach, we calculate the HME by the segment summation approach (SSA) using the gravity field inside the shallow layer determined by the SLM. Numerical results show that for four combined strategies, the differences between our results and the authoritatively released value 8848.86 m by the Chinese and Nepalese governments on December 8, 2020 are 0.448 m, -0.009 m, -0.295 m, and -0.741 m using first approach and 0.539 m, 0.083 m, -0.214 m, and -0.647 m using second approach. The combined calculation of the HME by the terrain model and gravity field model is more accurate than that by the gravity field model alone. This study is supported by the National Natural Science Foundations of China (NSFC) under Grants 42030105, 41721003, 41804012, 41631072, 41874023, Space Station Project (2020)228.

How to cite: Xie, Y., Shen, W., Han, J., and Deng, X.: Determining the height of Mount Everest using the shallow layer method, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1886,, 2021.

EGU21-10940 | vPICO presentations | G1.2

A Bayesian framework for simultaneous determination of susceptibility and magnetic thickness from magnetic data

Jörg Ebbing, Wolfgang Szwillus, and Yixiati Dilixiati

The thickness of the magnetized layer in the crust (or lithosphere) holds valuable information about the thermal state and composition of the lithosphere. Commonly, maps of magnetic thickness are estimated by spectral methods that are applied to individual data windows of the measured magnetic field strength. In each window, the measured power spectrum is fit by a theoretical function which depends on the average magnetic thickness in the window and a ‘fractal’ parameter describing the spatial roughness of the magnetic sources. The limitations of the spectral approach have long been recognized and magnetic thickness inversions are routinely calibrated using heat flow measurements, based on the assumption that magnetic thickness corresponds to Curie depth. However, magnetic spectral thickness determinations remain highly uncertain, underestimate uncertainties, do not properly integrate heat flow measurements into the inversion and fail to address the inherent trade-off between lateral thickness and susceptibility variations.

We present a linearized Bayesian inversion that works in space domain and addresses many issues of previous depth determination approaches. The ‘fractal’ description used in the spectral approaches translates into a Matérn covariance function in space domain. We use a Matérn covariance function to describe both the spatial behaviour of susceptibility and magnetic thickness. In a first step, the parameters governing the spatial behaviour are estimated from magnetic data and heat flow data using a Bayesian formulation and the Monte-Carlo-Markov-Chain (MCMC) technique. The second step uses the ensemble of parameter solution from MCMC to generate an ensemble of susceptibility and thickness distributions, which are the main output of our approach.

The newly developed framework is applied to synthetic data at satellite height (300 km) covering an area of 6000 x 6000 km. These tests provide insight into the sensitivity of satellite magnetic data to susceptibility and thickness. Furthermore, they highlight that magnetic inversion benefits greatly from a tight integration of heat flow measurements into the inversion process.

How to cite: Ebbing, J., Szwillus, W., and Dilixiati, Y.: A Bayesian framework for simultaneous determination of susceptibility and magnetic thickness from magnetic data, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-10940,, 2021.

EGU21-1082 | vPICO presentations | G1.2

Isolating internal secular variation in Geomagnetic Virtual Observatory time series using Principle Component Analysis

William Brown, Ciarán Beggan, Magnus Hammer, Chris Finlay, and Grace Cox

Geomagnetic Virtual Observatories (GVOs) are a method for processing magnetic satellite data in order to simulate the observed behaviour of the geomagnetic field at a fixed location. As low-Earth orbit satellites move at around 8 km/s and have an infrequent re-visit time to the same location, a trade-off must be made between spatial and temporal coverage, typically averaging over half the local time orbit precession period, within a radius of influence of 700 km. The annual differences (secular variation, SV) of residuals between GVO time series data and an internal field model at a single GVO location will be strongly correlated with its neighbours due to the influence of large-scale external field sources and the effect of local time precession of the satellite orbit. Using Principal Component Analysis we identify and remove signals related to these noise sources to better resolve internal field variations on sub-annual timescales.

We apply our methodology to global grids of monthly GVOs for the Ørsted, CHAMP, CryoSat-2 and Swarm missions, covering the past two decades. We identify common principle components representing orbit precession rate dependent local time biases, and major external field sources, for all satellites. We find that the analysis is enhanced by focussing on regions of geomagnetic latitude where different external field sources dominate, identifying distinct influences in polar, auroral and low-to-mid latitude regions. Annual differences are traditionally used to calculate SV so as to remove annual and semi-annual external field signals, but these signals can be re-introduced if our corrected SV is re-integrated. We find that by representing secular variation with monthly first differences, rather than annual differences, we can identify and remove annual and semi-annual external field variations from the SV, which then improves the use of re-integrated main field GVO time series. By better accounting for contaminating signals from correlated external fields and aliasing, we are able to produce a global grid of GVO time series which better represents internal secular variation at monthly time resolution.

How to cite: Brown, W., Beggan, C., Hammer, M., Finlay, C., and Cox, G.: Isolating internal secular variation in Geomagnetic Virtual Observatory time series using Principle Component Analysis, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1082,, 2021.

EGU21-3359 | vPICO presentations | G1.2

Nonuniqueness and Uniqueness for Inverse Magnetization Problems

Christian Gerhards, Alexander Kegeles, and Peter Menzel

Nonuniqueness is a well-known issue with inverse problems involving geophysical potential fields (typically gravitational or magnetic fields). If no additional assumptions are made on the underlying source, only certain harmonic contributions can be reconstructed uniquely from knowledge of the potential. Such harmonic contributions have no intuitive geophysical interpretation. However, in various applications some specific properties are of particular interest: e.g., the direction of the magnetization in paleomagnetic studies or the lithospheric susceptibility in geomagnetism. In this presentation, we give a brief overview on the characterization of nonuniqueness and on a priori assumptions on the underlying magnetization that might lead to uniqueness or at least partial uniqueness.

How to cite: Gerhards, C., Kegeles, A., and Menzel, P.: Nonuniqueness and Uniqueness for Inverse Magnetization Problems, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3359,, 2021.

EGU21-15142 | vPICO presentations | G1.2

Seismic imaging combining active and passive sources using distributed acoustic sensing

Florian Faucher, Otmar Scherzer, and Maarten V. de Hoop

DAS finds growing interest in seismic exploration by offering a dense and low-cost coverage of the area investigated. Nonetheless, contrary to the usual geophones that measure the displacement, DAS provides information on the strain. In this work, we perform quantitative imaging of elastic media designing a new misfit functional that is adapted to these data-sets. This misfit criterion is based on the reciprocity-gap, hence defining the full reciprocity-gap waveform inversion. The main feature of our misfit is that it does not require the knowledge of the exciting source positions, and it allows us to combine data from active and passive (of unknown location) sources. In particular, the data from passive sources contain the low-frequency information needed to build initial models, while the exploration data contain the higher frequencies. We consequently follow a multi-resolution framework that we illustrate with two-dimensional elastic experiments.

How to cite: Faucher, F., Scherzer, O., and de Hoop, M. V.: Seismic imaging combining active and passive sources using distributed acoustic sensing, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-15142,, 2021.

EGU21-8876 | vPICO presentations | G1.2

A novel data-driven method to estimate GIA signal from Earth observation data

Bramha Dutt Vishwakarma, Yann Ziegler, Sam Royston, and Jonathan L. Bamber

Geophysical inversions are usually solved with the help of a-priori constraints and several assumptions that simplify the physics of the problem. This is true for all the inversion approaches that estimate GIA signal from contemporary datasets such as GNSS vertical land motion (VLM) time-series and GRACE geopotential time-series. One of the assumptions in these GIA inversions is that the change in VLM due to GIA can be written in terms of surface mass change and average mantle density. Furthermore, the surface density change is obtained from GRACE data using the relations derived in Wahr et al., 1998, which actually is only applicable for surface processes (such as hydrology) and not for sub-surface processes such as GIA. This leaves us with a tricky signal-separation problem. Although many studies try to overcome this by constraining the inversion with the help of constrains from a priori GIA models, the output is not free from influence of GIA models that are known to have huge uncertainties. In this presentation, we discuss this problem in detail, then provide a novel mathematical framework that solves for GIA without any a priori GIA model. We validate our method in a synthetic environment first and then estimate a completely data-driven GIA field from contemporary Earth-observation data.

How to cite: Vishwakarma, B. D., Ziegler, Y., Royston, S., and Bamber, J. L.: A novel data-driven method to estimate GIA signal from Earth observation data, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8876,, 2021.

EGU21-1999 | vPICO presentations | G1.2

How small can ground movements be to be detectable with GNSS?

Roland Hohensinn, Pia Ruttner, Benedikt Soja, and Markus Rothacher

High-precision GNSS (Global Navigation Satellite System) positioning can reach an accuracy at the millimeter level, and by collecting these data over years, very small ground movements can be resolved. These data can be used to study geodynamics, like continental drifts, tidal- and non-tidal loading effects, or earthquakes, for example. Here we focus on the sensitivity of GNSS for resolving these different types of movements. We derive minimal detectable displacements for linear drift rates, annual- and semiannual periodic motions, and offsets – these are main parameters of the so-called standard linear trajectory model for GNSS station motions. For our analysis, our data comes from several hundreds of permanent GNSS stations across Europe– the GNSS stations’ coordinates are obtained at a daily sampling rate, with almost 25 years of data available for some stations. Based on cleaned residual GNSS time series we calibrate a “power-law plus white noise” stochastic model for each station. Together with the functional trajectory model we compute the formal errors of the movement parameters based on a least-squares adjustment. Based on these errors we then introduce the statistics to derive minimum detectable displacements for the movement parameters.

Our analysis shows that the minimum detectable trends can be as low as few tenth of millimeters per year. The minimum detectable amplitudes at the annual and semiannual periods are at the millimeter level or lower, and the detectable offset is few millimeters on average, too. As expected, the minimum detectable displacements depend strongly on the length of the datasets and on the noise characteristics. Another important parameter is the number of discontinuities and offsets for each station – it impacts the minimum detectable trend. We conclude that such an analysis can be very useful for sensitivity studies in climate change monitoring. Furthermore, the methodology cannot only be applied in the field of GNSS time series analysis, but also to any other time series data in geosciences.

How to cite: Hohensinn, R., Ruttner, P., Soja, B., and Rothacher, M.: How small can ground movements be to be detectable with GNSS?, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1999,, 2021.

EGU21-7421 | vPICO presentations | G1.2

The quality of velocities from GNSS campaign measurements when gaps in data exist

Yener Turen, Dogan Ugur Sanli, and Tuna Erol

In this study, we investigate the effect of gaps in data on the accuracy of deformation rates produced from GNSS campaign measurements. Our motivation in investigating gaps in data is that campaign GNSS time series might not be collected regularly due to various constraints in real life conditions. We used the baseline components produced from continuous GPS time series of JPL, NASA from a global network of the IGS to generate data gaps. The solutions of the IGS continuous GNSS time series were decimated to the solutions of the campaign data sampled one measurement per each month or three measurements per year. Furthermore, the effect of antenna set-up errors, which show Gaussian distribution, in campaign measurements was taken into account following the suggestions from the literature. The number of gaps in campaign GNSS time series was incremented plus one for each different trial until only one month is left within the specific year. Eventually, we tested whether the velocities obtained from GNSS campaign series containing data gaps differ significantly from the velocities derived from continuous data which is taken as to be the “truth”. The initial efforts using the samples from a restricted amount of data reveal that the deformation rate produced from the east component is more sensitive to the gaps in data than that of the components north and vertical.

Keywords: GPS time series; GPS campaigns; Velocity estimation; Gaps in data; Deformation.

How to cite: Turen, Y., Sanli, D. U., and Erol, T.: The quality of velocities from GNSS campaign measurements when gaps in data exist, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-7421,, 2021.

The frequency-dependent autocovariance (FDA) function is defined in this paper as the autocovariance function of a wideband oscillation filtered by the Fourier transform bandpass filter (FTBPF). It was shown that the FDA estimation is a useful algorithm to detect mean amplitudes of oscillations in a very noisy time series. In this paper the least-squares polynomial harmonic model was used to remove the trend, low frequency as well as the annual and semi-annual oscillations from the IERS eopc04R_IAU2000_daily length of day (LOD) time series to compute their residuals. Next, the mean amplitudes of the signal as a function of frequency were determined from the difference between the FDA of LOD residuals and FDA of power-law noise model similar to the noise present in LOD residuals.  Several power-law noise model data were generated with a similar spectral index and variance as the noise in LOD data to estimate the mean amplitude spectrum in the seasonal and shorter period frequency band.  It was shown that the mean amplitudes of the oscillations in LOD residuals are very small compared to the noise standard deviation and do not depend on the filter bandwidth of the FTBPF. These small amplitudes explain why LOD prediction errors increase rapidly with the prediction length.

How to cite: Kosek, W.: Mean amplitudes of the signal in the seasonal and shorter period length of day time series computed by the frequency-dependent autocovariance, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9080,, 2021.

G1.3 – High-precision GNSS: methods, open problems and Geoscience applications

EGU21-504 | vPICO presentations | G1.3 | G Division Outstanding ECS Award Lecture 2021

Benchmarking GPS stations: an improved way to identify the GPS sensitivity

Anna Klos, Jürgen Kusche, Artur Lenczuk, Grzegorz Leszczuk, and Janusz Bogusz

Global Positioning System (GPS) stations are affected by a plethora of real and system-related signals and errors that occur at various temporal and spatial resolutions. Geophysical changes related to mass redistribution within the Earth system, common mode components, instability of GPS monuments or thermal expansion of ground, all contribute to the GPS-derived displacement time series. Different spatial resolutions that real and system-related errors occur within are covered thanks to the global networks of GPS stations, characterized presently by an unprecedented spatial density. Various temporal resolutions are covered by displacement time series which span even 25 years now, as estimated for the very first stations established. However, since the GPS sensitivity remains unrecognized, retrieving one signal from this wide range of processes may be very uncertain. Up to now, a comparison between GPS-observed displacement time series and displacements predicted by a set of models, as e.g. environmental loading models, was used to demonstrate the accuracy of the model to predict the observed phenomena. Such a comparison is, however, dependent on the accuracy of models and also on the sensitivity of individual GPS stations. We present a new way to identify the GPS sensitivity, which is based on benchmarking of individual GPS stations using statistical clustering approaches. We focus on regional sets of GPS stations located in Europe, where technique-related signals cover real geophysical changes for many GPS permanent stations and those located in South America and Asia, where hydrological and atmospheric loadings dominate other effects. We prove that combining GPS stations into smaller sets improves our understanding of real and system-related signals and errors.

How to cite: Klos, A., Kusche, J., Lenczuk, A., Leszczuk, G., and Bogusz, J.: Benchmarking GPS stations: an improved way to identify the GPS sensitivity, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-504,, 2021.

EGU21-7825 | vPICO presentations | G1.3

Comparison and generalization of GNSS satellite attitude models

Sebastian Strasser, Simon Banville, Andreas Kvas, Sylvain Loyer, and Torsten Mayer-Gürr

Global navigation satellite system (GNSS) constellations such as GPS, GLONASS, Galileo, and BeiDou and the Japanese regional system QZSS apply various satellite attitude modes during eclipse season, which is the period when the Sun is close to the orbital plane of the satellite. Due to different satellite manufacturers and technological advances over time, these modes can vary between constellations but also between different satellite types within a constellation. For some constellations, namely Galileo and QZSS, the satellite attitude law has been officially published by the satellite operator. For most other GNSS satellite types, researchers have developed attitude models, for example using reverse kinematic precise point positioning, that approximate the actual attitude behaviour.

Outside of eclipse seasons, GNSS satellites generally apply either a nominal yaw-steering or an orbit normal attitude law. While both modes point the antennas towards Earth, the former yaws the satellite around the antenna axis to point the solar panels towards the Sun, while the latter always keeps a fixed yaw angle. When a satellite applying a yaw-steering law is in eclipse season and close to the orbit noon or midnight point, it may have to yaw faster than physically possible to keep the nominal attitude. The various attitude modes used by the satellites aim to prevent this scenario by applying a modified attitude law during this period, for example by yawing at a constant rate around orbit noon/midnight or by switching to orbit normal mode.

Comparisons of attitude files generated by analysis centers of the International GNSS Service (IGS) within the scope of its 3rd reprocessing campaign show significant differences in some cases. This contribution compares all available attitude models with the aim of finding similarities that allow for generalization, which in turn simplifies the implementation of the various attitude modes into GNSS software packages. The developed functions have been implemented into the open-source software GROOPS (, which makes them publicly available and documented.

How to cite: Strasser, S., Banville, S., Kvas, A., Loyer, S., and Mayer-Gürr, T.: Comparison and generalization of GNSS satellite attitude models, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-7825,, 2021.

EGU21-6287 | vPICO presentations | G1.3

Extension of the repro3 ANTEX file with BeiDou and QZSS satellite antenna pattern

Arturo Villiger, Rolf Dach, Lars Prange, and Adrian Jäggi

During the preparations for the International GNSS Service (IGS) contribution to the next reference frame, called repro3, the disclosed pre-launch chamber calibrated Galileo satellite antenna pattern were analyzed. Those tests revealed a discrepancy between the GPS and GLONASS z-component of the phase center offsets (PCO), aligned to the IGS14 scale, and the calibrated Galileo z-PCOs. In order to make the PCOs compatible to the repro3 it was decided to rely on the calibrated Galileo pattern and adjust the GPS and GLONASS PCOs accordingly. Combined with multi-GNSS receiver calibrations for all systems the repro3 might contribute to the scale determination for the next reference frame.

As the repro3 is based on GPS, GLONASS, and Galileo only those three systems have been analyzed leading to the repro3 ANTEX file, containing all used antenna pattern, which is aligned to the Galileo induced scale. In order to extend the repro3 ANTEX file with satellite calibrations for BeiDou and QZSS a dedicated reprocessing based on CODEs MGEX solution is made to assess the available PCOs for those satellites and tests their consistency with the repro3 scale. The results should allow to extend the repro3 ANTEX with the BDS and QZSS pattern for experimental purposes.

How to cite: Villiger, A., Dach, R., Prange, L., and Jäggi, A.: Extension of the repro3 ANTEX file with BeiDou and QZSS satellite antenna pattern, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-6287,, 2021.

EGU21-8507 | vPICO presentations | G1.3

Impact of Multi-GNSS Antenna-Receiver Calibrations in the Coordinate Domain

Johannes Kröger, Tobias Kersten, Yannick Breva, and Steffen Schön

In order to obtain highly precise positions with Global Navigation Satellite Systems (GNSS), it is mandatory to take all error sources adequately into account. This includes phase center corrections (PCC), composed of a phase center offset (PCO) and corresponding azimuthal and elevation-dependent phase center variations (PCV). These corrections have to be applied to the observations since the pattern of the GNSS receiver antennas deviate from an ideal omnidirectional radiation pattern.
The Institut für Erdmessung (IfE) is one of the IGS accepted institutions for absolute antenna calibration. Recently, the operationally calibration procedure has been further developed to a post processing approach. Thus, PCC can also be estimated for all frequencies (including e.g. GPS L2C, L5) and systems like Galileo and Beidou. Additionally, the newly developed approach allows to assess the impact of using different receivers with different settings on an individual calibration. 
Previous studies already have shown, that the geodetic receivers used during the absolute calibration of antennas have an impact on the estimated PCC. However, currently this impact is only analysed at the level of the respective patterns and not in the coordinate domain. Moreover, the results are always only valid for the respective antenna-receiver combination. Therefore, more samples of different combinations are required.
In this contribution, we study calibration results of several antenna-receiver combinations using a zero baseline configuration during the calibration process in order to assess the receiver’s impact due to different signal tracking modes. The resulting PCC are analysed on the pattern level regarding (i) the repeatability of individual calibrations and (ii) differences between different antenna-receiver combinations. Finally, the impact of the different PCC are validated in the coordinate domain by a well controlled short baseline and common clock set-up. Here, again a zero baseline configuration with the identical receivers used during the calibration process is performed. Consequently, the impact of the respective antenna-receiver combination with individually estimated PCC on the positioning is analysed.

How to cite: Kröger, J., Kersten, T., Breva, Y., and Schön, S.: Impact of Multi-GNSS Antenna-Receiver Calibrations in the Coordinate Domain, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8507,, 2021.

EGU21-8306 | vPICO presentations | G1.3

An efficient solution for fast generation of multi-GNSS real-time products

Hongjie Zheng, Hanyu Chang, Yongqiang Yuan, Qingyun Wang, Yuhao Li, and Xingxing Li

Global navigation satellite systems (GNSS) have been playing an indispensable role in providing positioning, navigation and timing (PNT) services to global users. Over the past few years, GNSS have been rapidly developed with abundant networks, modern constellations, and multi-frequency observations. To take full advantages of multi-constellation and multi-frequency GNSS, several new mathematic models have been developed such as multi-frequency ambiguity resolution (AR) and the uncombined data processing with raw observations. In addition, new GNSS products including the uncalibrated phase delay (UPD), the observable signal bias (OSB), and the integer recovery clock (IRC) have been generated and provided by analysis centers to support advanced GNSS applications.

       However, the increasing number of GNSS observations raises a great challenge to the fast generation of multi-constellation and multi-frequency products. In this study, we proposed an efficient solution to realize the fast updating of multi-GNSS real-time products by making full use of the advanced computing techniques. Firstly, instead of the traditional vector operations, the “level-3 operations” (matrix by matrix) of Basic Liner Algebra Subprograms (BLAS) is used as much as possible in the Least Square (LSQ) processing, which can improve the efficiency due to the central processing unit (CPU) optimization and faster memory data transmission. Furthermore, most steps of multi-GNSS data processing are transformed from serial mode to parallel mode to take advantage of the multi-core CPU architecture and graphics processing unit (GPU) computing resources. Moreover, we choose the OpenBLAS library for matrix computation as it has good performances in parallel environment.

       The proposed method is then validated on a 3.30 GHz AMD CPU with 6 cores. The result demonstrates that the proposed method can substantially improve the processing efficiency for multi-GNSS product generation. For the precise orbit determination (POD) solution with 150 ground stations and 128 satellites (GPS/BDS/Galileo/GLONASS/QZSS) in ionosphere-free (IF) mode, the processing time can be shortened from 50 to 10 minutes, which can guarantee the hourly updating of multi-GNSS ultra-rapid orbit products. The processing time of uncombined POD can also be reduced by about 80%. Meanwhile, the multi-GNSS real-time clock products can be easily generated in 5 seconds or even higher sampling rate. In addition, the processing efficiency of UPD and OSB products can also be increased by 4-6 times.

How to cite: Zheng, H., Chang, H., Yuan, Y., Wang, Q., Li, Y., and Li, X.: An efficient solution for fast generation of multi-GNSS real-time products, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8306,, 2021.

EGU21-7160 | vPICO presentations | G1.3

Multi-GNSS real-time orbit and clock quality changes over time 

Kamil Kazmierski, Radoslaw Zajdel, and Krzysztof Sośnica

Navigation systems have substantially evolved in the last decade. The multi-GNSS constellation including GPS, GLONASS, Galileo, and BeiDou consists of more than a hundred active satellites. To fully exploit their potential, users should be able to take advantage of those systems not only in postprocessing mode employing final solutions but also in real-time. It is also important to make satellite signals highly useful in a real-time regime not only in standard positioning mode but also with the precise positioning technique. That is why real-time products are highly desirable. One of the IGS Analysis Centers that support multi-GNSS real-time solution is CNES which provides not only orbits and clocks but also code and phase biases and VTEC global maps. Over the last few years, real-time products have been changing similarly to navigation systems, which come along with observation availability and calculation strategy changes.

We utilize the signal-in-space ranging error (SISRE) as the main orbit and clock quality indicator. Additionally, SLR observations are used as an independent source of information about orbit quality. Three years of data, between 2017 and 2020, are used to check the progress in the quality of the delivered products to the users through the internet streams provided by CNES.

The progress in the product quality in the test period is obvious and it depends on the satellite system, block or satellite type, time, and the height of the Sun above the orbital plane. The most accurate orbits are available for GPS, however, the very stable atomic clocks of Galileo compensate for systematic errors in Galileo orbits. Consequently, the SISRE for Galileo is lower than that for GPS, equaling 1.6 and 2.3 cm for Galileo and GPS, respectively. The SISRE value for GLONASS, despite the good quality of the orbits, is disturbed by the lower quality of the onboard clocks and is equal to 4-6 cm. The same quality level is for BeiDou-2 MEO and IGSO satellites. Products for BeiDou-2 GEO satellites are less accurate and with poor availability due to a large number of satellite maneuvers, thus they are not very useful for real-time positioning.

For positioning purposes, the presented results may be interesting especially in the context of the proper observation weighting in the multi-GNSS combinations. It is worth mentioning that the quality of the real-time products is not constant and neglecting this fact may bring undesirable positioning errors, especially for long processing campaigns.

How to cite: Kazmierski, K., Zajdel, R., and Sośnica, K.: Multi-GNSS real-time orbit and clock quality changes over time , EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-7160,, 2021.

EGU21-14343 | vPICO presentations | G1.3

Assessment of geodetic products from Multi-GNSS analyses at the Onsala site

Periklis-Konstantinos Diamantidis, Grzegorz Kłopotek, Rüdiger Haas, and Jan Johansson

The dawn of Beidou and Galileo as operational Global Navigation Satellite Systems (GNSS) alongside Global Positioning System (GPS) and GLONASS as well as new features that are now present in all GNSS, such as a triple-frequency setup, create new possibilities concerning improved estimation and assessment of various geodetic products. In particular, the multi-GNSS analysis gives an access to a better sky coverage allowing for improved estimation of zenith wet delays (ZWD) and tropospheric gradients (GRD), and can be used to determine integer phase ambiguities. The Multi-GNSS Experiment (MGEX), as realised by the International GNSS Service (IGS), provides orbit, clock and observation data for all operational GNSS. To take advantage of the new capabilities that these constellations bring, space-geodetic software packages have been retrofitted with Multi-GNSS-compliant modules. Based on this, two software packages, namely GipsyX and c5++, are utilised by way of the static Precise Point Positioning (PPP) approach using six months of data, and an assessment of the derived geodetic products is carried out for several GNSS receivers located at the Onsala core site. More specifically, we perform both single-constellation and multi-GNSS data analysis using Kalman filter and least-squares methods and assess the quality of the derived station positions, ZWD and GRD. A combined solution using all GNSS constellations is carried out and the improvement with respect to station position repeatabilities is assessed for each station. Results from the two software packages are compared with respect to each other and the discrepancies are discussed. Inter-system biases, which homogenise the different time scale that each GNSS operates in, and are necessary for the multi-GNSS combination, are estimated and presented. Finally, the applied inter-system weighting and its impact on the derived geodetic products are discussed.

How to cite: Diamantidis, P.-K., Kłopotek, G., Haas, R., and Johansson, J.: Assessment of geodetic products from Multi-GNSS analyses at the Onsala site, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-14343,, 2021.

EGU21-2531 | vPICO presentations | G1.3

Combining multi-GNSS phase bias products for improved undifferenced ambiguity resolution

Jianghui Geng, Yuanxin Pan, Songfeng Yang, and Pan Li

The rapid development of multi-GNSS constellations, e.g., Galileo and BeiDou, is catalyzing innovations in high-precision applications. Precise point positioning ambiguity resolution (PPP-AR) has been essential to achieving the highest positioning precision using multi-GNSS data in wide areas. In recent years, several International GNSS Service analysis centers (IGS ACs such as CNES, CODE, WHU) have been providing phase bias products to enable PPP-AR, but whether these AC-specific multi-GNSS (e.g., GPS/Galileo/BeiDou-2/3) products are compatible with each other and whether they can be reconciled for an IGS combination product are pending. In this study, we combined phase bias products from four organizations for GPS/Galileo/BeiDou-2/3 in 2020. All phase bias products are first converted to observable-specific representation and then reconciled with satellite clocks before the combination; their capability of recovering integer undifferenced ambiguities has been always kept after properly addressing inter-system biases and satellite attitude discrepancies. It is found that the RMS of clock alignment residuals are around 6.8, 7.1, 14.9 and 14.6 ps for GPS, Galileo BeiDou-2 and BeiDou-3, respectively. BeiDou products perform worse due largely to sparse tracking networks and deficient orbit models. In a kinematic PPP experiment with 151 global MGEX (Multi-GNSS Experiment) stations, the combined phase bias products provide better or at least equivalent positioning results as opposed to AC specific products. Compared with ambiguity-float solutions, ambiguity-fixed PPP solutions can improve the positioning precision by 29-50% in the east component. With combined phase bias products, the positioning precision of GPS/Galileo/BDS-2/3 PPP-AR solutions can achieve 0.62, 0.64 and 1.90 cm in the east, north and up components, respectively, in contrast to 0.87, 0.88 and 2.60 cm for GPS only PPP-AR solutions.

How to cite: Geng, J., Pan, Y., Yang, S., and Li, P.: Combining multi-GNSS phase bias products for improved undifferenced ambiguity resolution, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-2531,, 2021.

EGU21-9039 | vPICO presentations | G1.3

Multi-frequency and multi-GNSS PPP-RTK for vehicle navigation in urban environments

Bo Wang, Xin Li, Jiaxin Huang, Guolong Feng, Hongbo Lv, Xinjuan Han, Yaxin Zhong, and Xingxing Li

PPP-RTK which combines the advantages of real-time kinematic (RTK) and precise point positioning (PPP), is able to provide centimeter-level positioning accuracy with rapid integer ambiguity resolution. In recent years, with the development of BDS and Galileo as well as the modernization of GPS and GLONASS, more than 130 GNSS satellites are available and new-generation GNSS satellites are capable of transmitting signals at three or more frequencies. Multi-GNSS and multi-frequency observations bring more possibilities for enhancing the performance of PPP-RTK. In this contribution, we develop a multi-frequency and multi-GNSS PPP-RTK model aiming to achieve rapid centimeter-level positioning for vehicle navigation in urban environments. The precise undifferenced atmospheric corrections are derived from multi-frequency and multi-GNSS observations of regional networks. Then the corrections are distributed to users to achieve PPP rapid ambiguity resolution. Vehicle experiments in different scenarios such as suburbs, overpasses, tunnels are conducted to validate the proposed method. Our results indicate that the multi-frequency and multi-GNSS PPP-RTK can achieve 2~3 cm positioning accuracy in the horizontal direction, 5~6 cm positioning accuracy in the vertical direction with the time to first fix of 5~7 s. In the urban environments where signals are interrupted frequently, a fast ambiguity recovery can be achieved within 5 s. Moreover, the PPP-RTK performance is significantly improved with multi-GNSS and multi-frequency observations. Compared to GPS-only solution, the positioning accuracy can be improved by 75%, and the fixing percentage can be up to 90% with this new method.

How to cite: Wang, B., Li, X., Huang, J., Feng, G., Lv, H., Han, X., Zhong, Y., and Li, X.: Multi-frequency and multi-GNSS PPP-RTK for vehicle navigation in urban environments, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9039,, 2021.

EGU21-5556 | vPICO presentations | G1.3

Multi-GNSS Single-Difference Baseline Processing at NGS with newly developed M-PAGES software

Bryan Stressler, Andria Bilich, Clement Ogaja, and Jacob Heck

The U.S. National Geodetic Survey (NGS) has historically processed dual-frequency GPS observations in a double-differenced mode using the legacy software called the Program for the Adjustment of GPS Ephemerides (PAGES). As part of NGS’ modernization efforts, a new software suite named M-PAGES (i.e., Multi-GNSS PAGES) is being developed to replace PAGES. M-PAGES consists of a suite of C++ and Python libraries, programs, and scripts built to process observations from all GNSS constellations. The M-PAGES team has developed a single-difference baseline processing strategy that is suitable for multi-GNSS. This approach avoids the difficulty of forming double-differences across systems or frequencies, which may inhibit integer ambiguity resolution. The M-PAGES suite is expected to deploy to NGS’ Online Positioning User Service (OPUS) later this year. Here, we present the processing strategy being implemented along with a performance evaluation from sample baseline solutions obtained from data collected within the NOAA CORS Network.

How to cite: Stressler, B., Bilich, A., Ogaja, C., and Heck, J.: Multi-GNSS Single-Difference Baseline Processing at NGS with newly developed M-PAGES software, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-5556,, 2021.

The contribution will present a general solution for the estimation of rank deficient integer parameters. A procedure will be presented that allows the computation of integer estimable function for any integer rank deficient least squares problem. The procedure is then applied to GNSS estimation problems. In the framework of undifferenced and uncombined GNSS models, the specific solution to some rank deficient integer least squares model will be presented, namely: the choice of pivot ambiguities in a network of receivers, GLONASS positioning, codeless positioning in the presence of ionospheric delay, satellite specific pseudorange biases estimation in the presence of ionospheric delay. It will been shown how the developed theory generalize previous results and ad hoc solutions present in the literature. Numerical results from real GNSS data will be presented too.

How to cite: Tagliaferro, G.: A General Solution to the Rank Deficient Integer Least Squares and its Application to GNSS Positioning, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-4213,, 2021.

EGU21-9976 | vPICO presentations | G1.3

The Effect of the State-of-the-Art Mapping Functions on Precise Point Positioning

Faruk Can Durmus and Bahattin Erdogan

Global Navigation Satellite Systems (GNSS) are effectively used for different applications of Geomatic Engineering. There are lots of model error sources that affect the performance of the point positioning. Especially for the Precise Point Positioning (PPP) technique, which depends on the absolute point positioning, these errors should be modelled since PPP technique utilizes un-differenced and ionosphere-free combinations. Studies about PPP technique show that the effect of tropospheric delay caused by water vapor and dry air in the troposphere, which affects GNSS signals, is an important parameter should be modelled. Total zenith delay consists of both hydrostatic and wet delay. Hydrostatic delay can be accurately estimated by using atmospheric surface pressure and height with empirical models. Although there are many empirical models currently used for the determination of the zenith wet delay, the accuracies of these models are inadequate due to the temporal and spatial variation of atmospheric water vapor. Moreover, the tropospheric delay occurs along the path of GNSS signals and the Mapping Functions (MFs) are used to convert the tropospheric signal delay along the zenith direction to the slant direction. In this study, it is aimed to measure the effect of the globally produced MFs as Niell Mapping Function (NMF), Vienna Mapping Function 1 (VMF1), Global Mapping Function (GMF) and Global Pressure Temperature model 2 (GPT2) for GNSS positioning accuracy. Only GPS satellite system has been taken into account. For the analysis it has planned to process approximately 294 permanent stations from Crustal Dynamics Data Information System (CDDIS) archive with Jet Propulsion Laboratory’s GipsyX v1.2 software. In order to reveal the effect of different season the GPS observations in January, April, July and October, 2018 have been obtained. The solutions were derived for different session durations as 2, 4, 6, 8, 12 and 24 hours for each global MFs and root mean square values have been estimated for each session durations.

Keywords: State-of-the-Art Mapping Function, Troposphere, Precise Point Positioning, Accuracy, GipsyX

How to cite: Durmus, F. C. and Erdogan, B.: The Effect of the State-of-the-Art Mapping Functions on Precise Point Positioning, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9976,, 2021.

EGU21-14144 | vPICO presentations | G1.3

Static and Pseudo-Kinematic PPP-AR Performance in Antarctic Region

Serdar Erol, Bilal Mutlu, Bihter Erol, and Muhammed Raşit Çevikalp

Because of the inclined-orbit of GNSS constellations that are not cover the Polar Regions, the polar gaps occur between certain latitudes and therefore in these regions the satellite observations are limited around the zenith direction. In addition, from summer to winter season, the daylight and weather conditions vary tremendously in the Polar Regions. In the context of this study, the PPP accuracy performance was tested as a function of winter and summer seasons, GPS-only and GPS&GLONASS constellations, PPP-AR and PPP-Float solution strategies, static and kinematic processing modes, varying occupation times (1h, 2h, 4h, 8h, 12h and daily), and increasing latitudes towards the South Pole at the OHI3, ROTH, MCM4, and AMU2 GNSS stations in the Antarctica continent. Besides, the effect of the ambiguity solution strategies and the used constellations in the process on PPP convergence time was also examined. In the assessment results of the study, it was revealed that the PPP-AR strategy, additional GLONASS system to GPS constellation, and increased occupation times improved the static and kinematic positioning accuracy. Besides, although similar accuracies were obtained in both seasons, the position accuracy was slightly better in winter. Regarding the investigation on convergence time, the PPP-AR solution using the GPS&GLONASS constellations improved the convergence time by 66% comparing to the GPS-only PPP-Float solution. Finally, according to the assessment of the PPP-AR accuracy performance depending on the increasing latitude towards the South Pole, it has been observed that the 2D position accuracy remained stable for three stations except for AMU2. Besides, the vertical position accuracy decreased as it approaches the South Pole and the GLONASS system contributed to the improvement of the accuracy.

How to cite: Erol, S., Mutlu, B., Erol, B., and Çevikalp, M. R.: Static and Pseudo-Kinematic PPP-AR Performance in Antarctic Region, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-14144,, 2021.

EGU21-8172 | vPICO presentations | G1.3

Climatic Effects on GPS PPP Accuracy

Aziz Saraçoğlu and Doğan Uğur Şanlı

Recently researchers revealed that meteorological seasons have an effect on the accuracy of GPS. This modified the conventional prediction formulation in which the accuracy was dependent on observing session duration. However, the available accuracy model is from a major climate zone classification. In this study, we evaluate climatic effects on PPP accuracy from a different climate classification: the widely used Köppen Geiger climate zones. GPS data are obtained from SOPAC (Scripps Orbit and Permanent Array Centre) archives. Synthetic GPS campaigns are generated from the permanent stations of the IGS (International GNSS Service). The data are processed using the PPP module of the NASA/JPL's GipsyX software. The RMS values obtained from the processing solutions are used to determine the effect of climate on PPP accuracy. Eventually, we compare the two climate classifications and present our initial impressions from a core network across the new climate zones.

Keywords: GPS, GNSS, accuracy, PPP, climatic effects

How to cite: Saraçoğlu, A. and Şanlı, D. U.: Climatic Effects on GPS PPP Accuracy, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8172,, 2021.

EGU21-334 | vPICO presentations | G1.3

The quality analysis of GNSS observations tracked by Android smart devices and positioning performance assessment

Jacek Paziewski, Marco Fortunato, Augusto Mazzoni, Robert Odolinski, Guangcai Li, Mathilde Debelle, René Warnant, and Xiaopeng Gong

This study assesses the quality of multi-constellation GNSS observations of selected Android smartphones namely Huawei P30, Huawei P20 and Huawei P Smart as well as Xiaomi Mi 8 and Xiaomi Mi 9. We investigate the properties of phase ambiguities to anticipate the feasibility of precise positioning with integer ambiguity fixing. The results reveal a significant drop of smartphone carrier-to-noise density ratio (C/N0) with respect to geodetic receivers and discernible differences among constellations and frequency bands. We show that the higher the elevation of the satellite, the larger discrepancy in C/N0 between the geodetic receivers and smartphones. We depict that an elevation dependence of the signal strength is not always the case for the smartphones. We discover that smartphone code pseudoranges are noisier by about one order of magnitude as compared to the geodetic receivers, and that the code signals on L5 and E5a outperform these on L1 and E1, respectively. It was shown that smartphone phase observations are contaminated by the effects that can destroy the integer property and time-constancy of the ambiguities. The long term drifts were detected for GPS L5, Galileo E1, E5a and BDS B1 phase observations of Huawei P30. To isolate the observational noise from low frequency effects we take advantage of time differencing using the variometric approach. These investigations highlight competitive phase noise characteristics for the Xiaomi Mi 8 when compared to the geodetic receivers. We also reveal poor phase signal quality for the Huawei P30 smartphones related to the unexpected long-term drifts of the phase signals. The observation quality assessment is supported with the evaluation of a positioning performance. We proved that it is feasible to obtain a precise solution in a smartphone to smartphone relative positioning mode with fixed ambiguities. Such results move us towards a collaborative precise positioning with smartphones.

How to cite: Paziewski, J., Fortunato, M., Mazzoni, A., Odolinski, R., Li, G., Debelle, M., Warnant, R., and Gong, X.: The quality analysis of GNSS observations tracked by Android smart devices and positioning performance assessment, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-334,, 2021.

EGU21-3345 | vPICO presentations | G1.3

Potential and limitations of processing smartphone GNSS raw observation data in PPP

Marcus Franz Glaner, Klaus Gutlederer, and Robert Weber

Since the release of Android 7.0 in 2016, raw GNSS measurements tracked by smartphones operating with Android can be accessed. Before this date, solely the position solution of the smartphone's internal "black box" algorithm could be further processed in various applications. Now the smartphone's GNSS observations can be used directly to estimate the user position with specialized self-developed algorithms and correction data. Since smartphones are equipped with simple, cost-effective GNSS chips and antennas, they provide challenging, low-quality GNSS measurements. Furthermore, most smartphones on the market offer GNSS measurements on just one frequency. 

Precise Point Positioning (PPP) is one of the most promising processing techniques for Global Navigation Satellite System (GNSS) data. PPP is characterized by the use of precise satellite products (orbits, clocks, and biases) and the application of sophisticated algorithms to estimate the user's position. In contrast to relative positioning methods, PPP does not rely on nearby reference stations or a regional reference network. Furthermore, the concept of PPP is very flexible, which is another advantage considering the challenging nature of (single frequency) GNSS measurements from smartphones.

In this contribution, we present PPP results applying the uncombined model on raw GNSS observations from various smartphone devices. In contrast to the typical use of the ionosphere-free linear combination for PPP, this flexible PPP model applies the raw GNSS observation equations, is suitable for any number of frequencies, and allows the utilization of ionosphere models as an ionospheric constraint. We explore the potential and limitations of using raw GNSS observations from smartphones for PPP to reach a position accuracy at the decimeter level. Therefore, we test different correction data types and algorithms and examine diverse ways to handle the tropospheric and ionospheric delay. The PPP calculations are performed with our self-developed in-house software raPPPid.

How to cite: Glaner, M. F., Gutlederer, K., and Weber, R.: Potential and limitations of processing smartphone GNSS raw observation data in PPP, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3345,, 2021.

EGU21-12648 | vPICO presentations | G1.3

Displacement monitoring using multi-technique antenna calibrations in processing GNSS data from multi-frequency low-cost receivers

Andrea Gatti, Giulio Tagliaferro, and Eugenio Realini

EGU21-5700 | vPICO presentations | G1.3

Absolute phase center calibration of low-cost GNSS patch antennas – Is it worth the effort?

Gregor Moeller, Felix Piringer, María Pérez Ortega, Robert Presl, and Markus Rothacher

GNSS antennas are a key factor in precise GNSS positioning. With the increasing availability of low-cost dual-frequency GNSS receivers also the demands on low-cost GNSS antennas increases. Unfortunately, the electronic center of most GNSS antennas is not located in the mechanical Antenna Reference Point (ARP). As a consequence, Phase Center Corrections (PCC) have to be introduced to correct for frequency-dependent signal delays within the antenna system. The PCCs are typically in the range of several millimeters to centimeters. Thus, uncorrected phase center variations can be a significant error source in precise positioning.

For the purpose of antenna calibration, the Institute of Geodesy and Photogrammetry at ETH Zürich acquired a six-axis industrial robot of type KUKA AGILUS KR 6 R900 sixx. In an initial study, the absolute accuracy of the robot has been determined to be better than 1.5 mm (standard deviation). By introducing a set of extended Denavit-Hartenberg parameters, the absolute position accuracy of the robot is further increased to 0.3 mm over the entire workspace and 0.1 mm for a predefined sequence of robot poses, respectively. Therefore, the robot operates well below the phase noise of the GNSS measurements (typically around 1 mm) and is therefore seen as suitable for the calibration of GNSS antennas with sub-millimeter accuracy.

Besides the numerous benefits of absolute field calibration with an industrial robot, several challenges remain if it comes to low-cost GNSS antennas. The main challenges are that for each antenna a specific mounting system has to be built and that low-cost antennas are in general less shielded against multipath (compared to geodetic antennas). Besides, only little information exists about the stability of the electronic reference point and how much the electronic properties change when the antenna is mounted on different platforms (cars, drones, cubesats, etc).

To address the critical issues in low-cost GNSS antenna calibration and study the impact of the PCCs on the positioning solution, a calibration campaign has been initiated at ETH Zürich in autumn 2020. In this campaign, a set of low-cost multi-GNSS dual-frequency patch and loop antennas - suited for centimeter-positioning - has been calibrated and tested. Therefore, in the vicinity of the GNSS reference station (ETH2) the robot has been installed and a sequence of randomized robot poses has been executed in which the ARP of each antenna was defined as rotation point. The GNSS signals recorded during this sequence were processed together with the robot attitude information using the time-differencing approach defined by D. Willi (2019) using a spherical harmonics parameterization.

The PCCs obtained from the calibration campaign were stored in ANTEX files for a subsequent validation. In this presentation, we will highlight the developed calibration procedures for low-cost GNSS antennas, summarize the main results of the calibration and validation campaign, and will give the framework in which a calibration of low-cost GNSS antennas is considered beneficial.

Willi D., GNSS receiver synchronization and antenna calibration, PhD Thesis, ETH Zürich, 2019,

How to cite: Moeller, G., Piringer, F., Pérez Ortega, M., Presl, R., and Rothacher, M.: Absolute phase center calibration of low-cost GNSS patch antennas – Is it worth the effort?, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-5700,, 2021.

EGU21-12709 | vPICO presentations | G1.3

Performance Assessment of GNSS-R Polarimetric Observations for Sea Level Monitoring

Mahmoud Rajabi, Mstafa Hoseini, Hossein Nahavandchi, Maximilian Semmling, Markus Ramatschi, Mehdi Goli, Rüdiger Haas, and Jens Wickert

Determination and monitoring of the mean sea level especially in the coastal areas are essential, environmentally, and as a vertical datum. Ground-based Global Navigation Satellite System Reflectometry (GNSS-R) is an innovative way which is becoming a reliable alternative for coastal sea-level altimetry. Comparing to traditional tide gauges, GNSS-R can offer different parameters of sea surface, one of which is the sea level. The measurements derived from this technique can cover wider areas of the sea surface in contrast to point-wise observations of a tide gauge.  

We use long-term ground-based GNSS-R observations to estimate sea level. The dataset includes one-year data from January to December 2016. The data was collected by a coastal GNSS-R experiment at the Onsala space observatory in Sweden. The experiment utilizes three antennas with different polarization designs and orientations. The setup has one up-looking, and two sea-looking antennas at about 3 meters above the sea surface level. The up-looking antenna is Right-Handed Circular Polarization (RHCP). The sea-looking antennas with RHCP and Left-Handed Circular Polarization (LHCP) are used for capturing sea reflected Global Positioning System (GPS) signals. A dedicated reflectometry receiver (GORS type) provides In-phase and Quadrature (I/Q) correlation sums for each antenna based on the captured interferometric signal. The generated time series of I/Q samples from different satellites are analyzed using the Least Squares Harmonic Estimation (LSHE) method. This method is a multivariate analysis tool which can flexibly retrieve the frequencies of a time series regardless of possible gaps or unevenly spaced sampling. The interferometric frequency, which is related to the reflection geometry and sea level, is obtained by LSHE with a temporal resolution of 15 minutes. The sea level is calculated based on this frequency in six modes from the three antennas in GPS L1 and L2 signals.

Our investigation shows that the sea-looking antennas perform better compared to the up-looking antenna. The highest accuracy is achieved using the sea-looking LHCP antenna and GPS L1 signal. The annual Root Mean Square Error (RMSE) of 15-min GNSS-R water level time series compared to tide gauge observations is 3.7 (L1) and 5.2 (L2) cm for sea-looking LHCP, 5.8 (L1) and 9.1 (L2) cm for sea-looking RHCP, 6.2 (L1) and 8.5 (L2) cm for up-looking RHCP. It is worth noting that the GPS IIR block satellites show lower accuracy due to the lack of L2C code. Therefore, the L2 observations from this block are eliminated.

How to cite: Rajabi, M., Hoseini, M., Nahavandchi, H., Semmling, M., Ramatschi, M., Goli, M., Haas, R., and Wickert, J.: Performance Assessment of GNSS-R Polarimetric Observations for Sea Level Monitoring, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-12709,, 2021.

EGU21-12499 | vPICO presentations | G1.3

Can GNSS-R help us to monitor the effects of inverse barometer in coastal areas ?

Théo Gravalon, Lucia Seoane, José Darrozes, and Guillaume Ramillien

The GNSS Reflectometry is an innovative technique, largely developed in the last years, to monitor local sea level heights. The agreement between sea level measurements derived from SNR-based GNSS-R and tide gauges observations have demonstrated the performance of this approach. In the presented study, we are interested in a subtidal scale phenomenon, the Local Inverse Barometer effect (LIB) which consists in the response of the sea surface to atmospheric pressure changes. The LIB is, in fact, not well modelled in coastal regions where GNSS-R provide continuous observations. The sea level anomaly obtained as the difference between GNSS-R sea level measurements and a tide model, T_TIDE developed by Rich Pawlowicz, is analyzed in order to detect the local inverse barometer effect. For this purpose, we have used 1-year of GNSS data of two antennas of the existing national network, Port-Tudy (Groix island, France) and Lyttelton (eastern coast of the South Island, New-Zealand), where the LIB effect is expected to be significant due to their location outside the equatorial band.

On the whole time series, a trend between the sea level anomaly and the LIB effect can be observed at mid to low frequencies (lower than 0.5 cycle per day). Moreover, high barometric variations caused by the passage of strong depressions lead to good correlations (> 0.7) between these two parameters.

Our results suggest that the GNSS reflectometry allows the observation of subtidal scale phenomena such as the impact of atmospherical variations in complex coastal environments.

How to cite: Gravalon, T., Seoane, L., Darrozes, J., and Ramillien, G.: Can GNSS-R help us to monitor the effects of inverse barometer in coastal areas ?, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-12499,, 2021.

EGU21-4707 | vPICO presentations | G1.3

GNSS Interferometric Reflectometry for Station Location Suitability Analysis

Jeffrey Verbeurgt, Ellen Van De Vijver, Cornelis Stal, and Alain De Wulf

National geodetic reference systems can be continuously monitored using applications of Global Navigation Satellite Systems (GNSS). Within these reference systems, Continuously Operating GNSS Reference Stations (CORSs) are often employed to provide 24/7 satellite tracking data. Understanding the influence of the surroundings of a CORS on the recorded satellite tracking data is indispensable for quality analysis of both acquired data and station location suitability. One of the main sources of inaccurate tracking data is the result of the combined reception of direct as well as indirect, environment-reflected satellite signals by the CORS, in which the latter can be considered interference compromising the signal’s accuracy. The magnitude of this interference is usually evaluated by the Signal-to-Noise Ratio (SNR), a parameter stored by default in the RINEX interchange format for raw GNSS data. The technique of GNSS Interferometric Reflectometry (GNSS-IR) exploits the availability of the SNR data and has been frequently used for applications such as soil moisture monitoring, detection of vegetation water content, measuring snowfall or determining water levels. In this research, we propose to employ GNSS-IR to investigate the effect of the surrounding on a CORS in order to evaluate station location suitability. More specifically, this will be done by using the signal to estimate the Reflector Height (RH), which depends on the reflector roughness (i.e. the roughness of the surface surrounding the CORS). The quality of this estimation will be validated by comparing with the actual measurement of the RH of the CORS on site.

In our approach, a statistically sound method is developed quantifying the stability of the RH determination. The proposed methodology consists of using Lomb-Scargle periodograms to select the dominant oscillation frequency of each satellite track SNR data, followed by an analysis and filtering of the peak amplitudes. This leads to the analysis product: number of significant peak amplitudes for an individual CORS over (sub-)daily timeframes. With historical data covering long time periods, statistical analysis of the (sub-)daily timeseries allows for reviewing the station location suitability. In Belgium, CORS are located on two typical positions: in Flanders, the 32 antennas are mainly installed on rooftops of buildings; in Wallonia, the 23 antennas are installed on a concrete pole next to highways. There is no evidence of one choice of station position being more suitable than the other. However, cars are known to be an important factor in signal reflections. In our analysis of station suitability,  the effect of cars passing by on the highway near a Walloon CORS, but also movements on, e.g., parking lots next to buildings with a rooftop CORS, will be investigated. With the developed methodology, guidelines for station location selection could be further developed, together with a system to continuously monitor CORS position suitability using GNSS-IR, triggering a warning when significant changes in the environment changes the local reflectometry fingerprint.

How to cite: Verbeurgt, J., Van De Vijver, E., Stal, C., and De Wulf, A.: GNSS Interferometric Reflectometry for Station Location Suitability Analysis, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-4707,, 2021.

EGU21-15151 | vPICO presentations | G1.3

An innovative methodology for locating ionosphere layer height: case study on 2011 Tohoku-Oki earthquake and tsunami

Michela Ravanelli and Giovanni Occhipinti

One of the main issues in GNSS ionosphere seismology is to localize the exact height of the single thin layer (Hion) with which the ionosphere is approximated. Hion is generally assumed to be the altitude of the maximum ionospheric ionization (hmF2), i.e., in the ionospheric F-layer. In this sense, Hion is often  be presumed from physical principles or ionospheric models. The determination of  Hion is, therefore, fundamental since it affects the coordinates of the ionospheric pierce point (IPP) and subsequentely of the sub-ionospheric pierce point (SIP).

In this work, we present a new developed methodology to determine the exact localization of Hion. We tested this approach on the TIDs (Travelling ionospheric disturbances) connected with the 2011 Tohoku-Oki earthquake and tsunami [1]. In detail, we computed the slant Total Electron Content (sTEC) variations at different Hion (in the range from 100 to 600 km) with the VARION (Variometric Approach for Real-Time Ionosphere Observation) algorithm [2,3], then we interpolated the different pattern in sTEC values related to different waves detected in the ionosphere (AGWepi, IGWtsuna and AWRayleigh) finding the mean velocity value of these waves. Subsequentely, the minimized difference between the estimated propagation velocity and the values from physical models fix us the correct Hion.

Our results show a Hion of 370 km, while ionopshere model IRI 2006 located the maximum of ionospheric ionization at an height of 270 km. This difference is important to understand how a different Hion can impact on the location of the sTEC perturbation, affecting the shape and the extent of the source from TEC observations.







[2] Giorgio Savastano, Attila Komjathy, Olga Verkhoglyadova, Augusto Mazzoni, Mattia Crespi, Yong Wei, and Anthony J Mannucci, “Real-time detection of tsunami ionospheric disturbances with a stand-alone gnss receiver: A preliminary feasibility demonstration, ”Scientific reports, vol. 7, pp. 46607, 2017.

[3] Giorgio Savastano, Attila Komjathy, Esayas Shume, Panagiotis Vergados, Michela Ravanelli, Olga Verkhoglyadova, Xing Meng, and Mattia Crespi, “Advantages of geostationary satellites for ionospheric anomaly studies: Ionospheric plasma depletion following a rocket launch,”Remote Sensing, vol. 11, no. 14, pp. 1734, 2019

How to cite: Ravanelli, M. and Occhipinti, G.: An innovative methodology for locating ionosphere layer height: case study on 2011 Tohoku-Oki earthquake and tsunami, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-15151,, 2021.

EGU21-824 | vPICO presentations | G1.3

Higher-Order Ionospheric Corrections derived from realistic electron density fields

Florian Zus and Jens Wickert

We developed a rapid and precise algorithm to compute Higher-Order Ionospheric Corrections (HOIC) utilizing realistic electron density fields. The electron density field is derived from the International Reference Ionosphere (IRI) and the required magnetic field is the International Geomagnetic Reference Field (IGRF). Direct application of such HOICs is regarded impractical due to the large data volume to be handled. Therefore, we developed a parameterized version; for any location near the Earth's surface (grid with a resolution of 2.5° times 5°) a set of HOICs are computed (various elevation and azimuth angles) and the coefficients of a polynomial expansion (Zernike polynomials) are stored in a look-up-table. These look-up-tables cover the time period 1990-2019 and are available via FTP ( We call this parameterized version GFZ-HOIC. A scalable version utilizing GNSS Total Electron Content (TEC) maps is under construction. A version available for real time applications is foreseen. With such accurate and easy-to-use HOICs available we performed extensive impact studies. For example, we examine how HOIC leak into estimated station coordinates, clocks, zenith delays and tropospheric gradients in Precise Point Positioning (PPP). The study includes a few hundred globally distributed stations and covers the time period 1990-2019. The PPP simulation shows the known significant systematic impact of HOICs on the estimated station y-coordinates and the estimated north-gradient components. In addition, the PPP simulation reveals the significant systematic impact of HOICs on the estimated zenith delays. This impact is not caused by higher-order terms in the formula for the refractive index of the ionosphere. This impact is caused by the ray-path bending effects. These ray-path bending effects are automatically taken into account thanks to the ray-tracing algorithm that is used in the derivation of the HOICs. In conclusion, GFZ-HOICs are both highly accurate and easy-to-use so that we can recommend them for practical applications.

How to cite: Zus, F. and Wickert, J.: Higher-Order Ionospheric Corrections derived from realistic electron density fields , EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-824,, 2021.

EGU21-7201 | vPICO presentations | G1.3

Statistical investigations of polar patch occurrence during high solar activity

Rafal Sieradzki and Jacek Paziewski

The circumpolar ionosphere is recognised as one of the most disturbed region of the ionized part of the atmosphere. The reasons for that are mainly dynamic conditions in the coupled system of the magnetosphere and the ionosphere as well as feeding of the polar plasma from the mid-latitude reservoir. One of the consequences of these phenomenon is the occurrence of large-scale ionospheric structures called polar patches. These are commonly defined as the enhancement of the F-region plasma characterized with a foreground-to-background density ratio larger than 2 and a size up to several hundred kilometres.

In this work we present GNSS-based characteristics of a patch occurrence in the northern hemisphere. The study covers a period of January–May 2014 corresponding to the maximum of the solar activity. The detection of structures was performed with a relative STEC value that is defined as a difference between epoch-wise L4 data and 4th order polynomial corresponding to background variations of the ionosphere. In order to ensure a continuous monitoring of the ionosphere over the north pole, we used data from ~45 permanent stations. The results prove that ground-based GNSS data can be successfully used in the climatological investigations of polar patches. We found a strong seasonal effect in the occurrence of these structures with the maximum at the turn of February and March and the minimum in May. Such outcomes correspond to variations of a TEC gradient between subauroral and polar regions. This parameter seems to be also responsible for a subdaily pattern of patches observed for particular months. The comparison of GNSS-based results with in-situ SWARM data revealed some differences, which are probably related to different characteristics of the ionosphere provided by both techniques. Furthermore, the study confirms that most of the patches are observed for the negative values of IMF Bz,  whereas IMF By component has no significant impact on the number of analysed structures. 

How to cite: Sieradzki, R. and Paziewski, J.: Statistical investigations of polar patch occurrence during high solar activity, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-7201,, 2021.

EGU21-4702 | vPICO presentations | G1.3

Heteroskedasticity between GNSS time-series repeatabilities and noise magnitudes

Huseyin Duman and Doğan Uğur Şanlı

In the analysis of GNSS time series, when the sampling frequency and time-series lengths are almost identical, it is possible to highlight a linear relationship between the series repeatabilities (i.e. WRMS) and noise magnitudes. In the literature, linear equations as a function of WRMSs allowed many researchers to estimate the noise magnitudes. However, this was built upon homoskedasticity. We experienced the higher WRMSs, the more erroneous analysis results using the noise magnitudes from the linear equations stated. We hence studied whether or not homoscedasticity clearly describes the modeling errors. To test that, we used the published results of GPS baseline components from the previous work in the literature and realized here that each component forms part of the totality. We introduced all baseline component results as a whole into statistical analysis to check heteroskedasticity. We established null and alternative hypotheses on the residuals which are homoscedastic (H0) or heteroskedastic (HA). We adopted both the Breusch-Pagan test and the Goldfeld-Quandt test to prove heteroskedasticity and obtained p-values for both methods. The p-value, which is the probability measure, equals to almost zero for both test methods, that is, we fail to accept the null hypothesis. Consequently, we can confidently state that the relationship between the WRMSs and the noise magnitudes is heteroskedastic.

Keywords: Noise magnitudes, repeatabilities, heteroskedasticity, time-series analysis

How to cite: Duman, H. and Şanlı, D. U.: Heteroskedasticity between GNSS time-series repeatabilities and noise magnitudes, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-4702,, 2021.

EGU21-8811 | vPICO presentations | G1.3

Noise correction and integration of HR-GNSS and seismological data for small earthquakes

Iwona Kudłacik and Jan Kapłon

High-rate GNSS (HR-GNSS) observations are used for high-precision applications, where the point position changes in short intervals are required, such as earthquake analysis or structural health monitoring. We aim to apply the HR-GNSS observations into mining tremors monitoring, where the dynamic displacement amplitudes reach maximally dozens of millimetres. The study contains the analysis of several mining tremors of magnitudes 3-4 in Poland, recorded within the EPOS-PL project.

The HR-GNSS position is obtained with over 1 Hz frequency in kinematic mode with relative or absolute approaches. For short periods (up to several minutes), the positioning accuracy is very high, but the displacement time series suffer from low-frequency fluctuations. Therefore, it is not possible to apply them directly in the analysis of seismic phenomena, thus it is necessary to filter out low- and high-frequency noise.

In this study, we discussed some methods that are useful to reduce the noise in HR-GNSS displacement time series to obtain precise and physically correct results with reference to seismological observations, which for dynamic position changes are an order of magnitude more accurate. We presented the band-pass filtering application with automatic filtration limits based on occupied bandwidth detection and the discrete wavelet transform application with multiresolution analysis. The correction of noise increases the correlation coefficient by over 40%, reaching values over 0.8. Moreover, we tested the application of the basic Kalman filter to the integration of sensors: HR-GNSS and an accelerometer to visualize the most actual displacements of the station during a small earthquake - a mining tremor. The usefulness of this algorithm for the assumed purpose was confirmed. This algorithm allows to reduce the noise from HR-GNSS results, and on the other hand, to minimize the potential seismograph drift and its errors caused by the limited dynamic range of the seismograph. An unquestionable advantage is the possibility of obtaining a time series of displacements with a high frequency (equal to the frequency of seismograph observations, e.g. 250 Hz) showing the full range of station motion: dynamic and static displacements caused by an earthquake.

How to cite: Kudłacik, I. and Kapłon, J.: Noise correction and integration of HR-GNSS and seismological data for small earthquakes, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8811,, 2021.

EGU21-842 | vPICO presentations | G1.3

GNSS network of Uzbekistan: achievements, prospects and challenges

Dilbarkhon Fazilova, Hasan Magdiev, and Lola Sichugova

In 2005, a governmental program for the creation of a geodetic network (SGN) based on GNSS measurements started in the Republic of Uzbekistan. Its main goal is to provide a modern, reliable and accurate geocentric coordinate system for land management, construction, environmental protection and the creation of a spatial database for various sectors of the economy. The SGN established in the country based on the availability of infrastructure and geographical needs and therefore, it does not cover the entire country. SGN consists three levels: reference geodetic points (RGP), high precision satellite geodetic network (SGN-0) points and first class satellite geodetic network (SGN-1) points. Since 2018, a network of 50 Continuously Operating Reference Stations (CORS) has also been developing. The installation of more than 200 GNSS stations in the period from 2005 to 2020 allows the country's scientific community to solve a number of practical geodetic problems. Among them implementation global ITRS system into local area for transition to new national geocentric coordinate system, quasi-geoid determination based on high degree Global Geopotential Models (such as EGM2008, EIGEN-6C4, GECO) and local geodynamic research for stress field modeling.

How to cite: Fazilova, D., Magdiev, H., and Sichugova, L.: GNSS network of Uzbekistan: achievements, prospects and challenges, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-842,, 2021.

EGU21-12489 | vPICO presentations | G1.3

The first result of geodetic implications on intra-graben subsidence along the eastern part of the Gediz graben

Yavuz Gül, Hüseyin Duman, Kemal Özgür Hastaoğlu, Fatih Poyraz, İbrahim Tiryakioğlu, Hediye Erdoğan, Alperen Doğan, and Süleyman Güler

The Western Anatolian extensional tectonic regime results in developing a set of approximately E-W trending Horst-Graben morphology. The Gediz graben accommodating many fertile lands is one of the significant tectonic structures associated with that regime. Intensive grape cultivation requiring irrigation has been conducted in these lands for many years, which causes a permanent decrease in the water budget as a consequence of increasing farming activities. Hence, we have aimed to clarify better spatial subsidence of the eastern part of the Gediz graben and performed at first InSAR data to obtain land-surface deformations. Towards the middle of graben, the line-of-sight deformation rates of InSAR from LiCSAR products reach gradually up to nearly 10 cm/yr. To confirm these rates, we monumented four continuous GNSS stations.  One of which was located out of the graben while the rest were at the graben in June 2020. Analysis of such a short time-series does not make sense; however, the vertical displacements for the closest stations to the center of the graben reach up to about 8 cm. while out of the graben station seems to be stable visually. It is worth stating that the givens are biased due most likely to the periodic signals. Consequently, the gradually increasing subsidence rates towards the graben center showed that have not been driven only by tectonic settlements but could also be driven by other phenomena. These results are the first results of the ongoing project no 119Y180 supported by TUBITAK.

Keywords: Land subsidence, GPS, InSAR, Gediz Graben

How to cite: Gül, Y., Duman, H., Hastaoğlu, K. Ö., Poyraz, F., Tiryakioğlu, İ., Erdoğan, H., Doğan, A., and Güler, S.: The first result of geodetic implications on intra-graben subsidence along the eastern part of the Gediz graben, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-12489,, 2021.

G1.4 – Data science and machine learning in geodesy

EGU21-4665 | vPICO presentations | G1.4

Deep Learning for the derivation of GNSS Reflectometry global ocean wind speed

Milad Asgarimehr, Caroline Arnold, Felix Stiehler, Tobias Weigel, Chris Ruf, and Jens Wickert

The Global Navigation Satellite System Reflectometry (GNSS-R) is a novel remote sensing technique exploiting GNSS signals after reflection off the Earth's surface. The capability of spaceborne GNSS-R to monitor ocean state and the surface wind is recently well demonstrated, which offers an unprecedented sampling rate and much robustness during rainfall. The Cyclone GNSS (CyGNSS) is the first spaceborne mission fully dedicated to GNSS-R, launched in December 2016.

Thanks to the low development costs of the GNSS-R satellite missions as well as the capability of tracking multiple reflected signals from numerous GNSS transmitters, the GNSS-R datasets are much bigger compared to those from conventional remote sensing techniques. The CyGNSS provides a high number of unique samples in the order of a few millions monthly.  Deep learning can therefore be implemented in GNSS-R even more efficiently than other remote sensing domains. With the upcoming GNSS-R CubeSats, the data volume is expected to increase in the near future and GNSS-R “Big data” can be a future challenge. Deep learning methods are additionally able to correct the potential effects, both technical and geophysical, dictated by data empirically when the mechanisms are not well described by the theoretical knowledge. This poses the question if GNSS-R should embrace deep learning and can benefit from this modern data scientific method like other Earth Observation domains.

The receivers onboard CyGNSS cross-correlate the reflected signals received at a nadir antenna to a locally generated replica. The cross-correlation power at a range of the signal delay and Doppler frequency shift is the observational output of the receivers being called delay-Doppler Maps (DDMs). The mapped power is inversely proportional to the ocean roughness and consequently surface winds.

Few recent studies innovatively show some merits of machine learning techniques for the derivations of ocean winds from the DDMs. However, the capability of machine learning techniques, especially deep learning for an operational data derivation needs to be better characterized. Normally, the operational retrieval algorithms are developed based on an existing dataset and are supposed to operate on the upcoming measurements. Therefore, machine learning-based models are supposed to generalize well on the unseen data in future periods. Herein, we aim at the characterization of deep learning capabilities for these GNSS-R operational purposes.

In this interdisciplinary study, we present a deep learning algorithm processing the CyGNSS measurements to derive wind speed data. The model is supposed to meet an acceptable level of generalization on the upcoming unseen data, and alternatively can be used as an operational processing algorithm. We propose a deep model based on convolutional and fully connected layers processing the DDMs besides ancillary input features. The model leads to the so-far best quality of global wind speed estimates using GNSS-R measurements with a general root mean square error of 1.3 m/s over unseen data in a time span different from that of the training data.

How to cite: Asgarimehr, M., Arnold, C., Stiehler, F., Weigel, T., Ruf, C., and Wickert, J.: Deep Learning for the derivation of GNSS Reflectometry global ocean wind speed, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-4665,, 2021.

EGU21-10267 | vPICO presentations | G1.4

Recurrent Neural Networks for Ionospheric Time Delays Prediction Using Global Navigation Satellite System Observables

Maria Kaselimi, Nikolaos Doulamis, and Demitris Delikaraoglou

Total Electron Content (TEC) is the integral of the location-dependent electron density along the signal path and is a crucial parameter that is often used to describe ionospheric variability, as it is strongly affected by solar activity. TEC is highly depended on local time, latitude, longitude, season, solar and geomagnetic conditions. The propagation of the signals from GNSS (Global Navigation Satellite System) throughout the ionosphere is strongly influenced by short- and long-term changes and ionospheric regular or irregular variations. 
Long short-term memory network (LSTM) is a specific recurrent neural network architecture and is capable of learning time dependence in sequential problems and can successfully model ionosphere variability. As LSTM networks “memorize” long term correlations in a sequence, they can model complex sequences with various features, where solar radio flux at 10.7 cm and magnetic activity indices are taken into consideration to provide more accurate results. 
Here, we propose a deep learning architecture to create regional TEC models around a station. The proposed model allows different solar and geomagnetic parameters to be inserted into the model as features. Our model has been evaluated under different solar and geomagnetic conditions. Also, the proposed model is tested for different time periods and seasonal variations and for varying geographic latitudes. 

How to cite: Kaselimi, M., Doulamis, N., and Delikaraoglou, D.: Recurrent Neural Networks for Ionospheric Time Delays Prediction Using Global Navigation Satellite System Observables, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-10267,, 2021.

EGU21-545 | vPICO presentations | G1.4

A new spatio-temporal graph neural network method for the analysis of GNSS geodetic data

Mostafa Kiani Shahvandi and Benedikt Soja

Graph neural networks are a newly established category of machine learning algorithms dealing with relational data. They can be used for the analysis of both spatial and/or temporal data. They are capable of modeling how time series of nodes, which are located at different spatial positions, change by the exchange of information between nodes and their neighbors. As a result, time series can be predicted to future epochs.

GNSS networks consist of stations at different locations, each producing time series of geodetic parameters, such as changes in their positions. In order to successfully apply graph neural networks to predict time series from GNSS networks, the physical properties of GNSS time series should be taken into account. Thus, we suggest a new graph neural network algorithm that has both a physical and a mathematical basis. The physical part is based on the fundamental concept of information exchange between nodes and their neighbors. Here, the temporal correlation between the changes of time series of the nodes and their neighbors is considered, which is computed by geophysical loading and/or climatic data. The mathematical part comes from the time series prediction by mathematical models, after the removal of trends and periodic effects using the singular spectrum analysis algorithm. In addition, it plays a role in the computation of the impact of neighboring nodes, based on the spatial correlation computed according to the pair-wise node-neighbor distance. The final prediction is the simple weighted summation of the predicted values of the time series of the node and those of its neighbors, in which weights are the multiplication of the spatial and temporal correlations.

In order to show the efficiency of the proposed algorithm, we considered a global network of more than 18000 GNSS stations and defined the neighbors of each node as stations that are located within the range of 10 km. We performed several different analyses, including the comparison between different machine learning algorithms and statistical methods for the time series prediction part, the impact of the type of data used for the computation of temporal correlation (climatic and/or geophysical loading), and comparison with other state-of-the-art graph neural network algorithms. We demonstrate the superiority of our method to the current graph neural network algorithms when applied to time series of geodetic networks. In addition, we show that the best machine learning algorithm to use within our graph neural network architecture is the multilayer perceptron, which shows an average of 0.34 mm in prediction accuracy. Furthermore, we find that the statistical methods have lower accuracies than machine learning ones, as much as 44 percent.

How to cite: Kiani Shahvandi, M. and Soja, B.: A new spatio-temporal graph neural network method for the analysis of GNSS geodetic data, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-545,, 2021.

EGU21-2308 | vPICO presentations | G1.4

Ultra-short-term prediction of LOD using LSTM neural networks

Junyang Gou, Mostafa Kiani Shahvandi, Roland Hohensinn, and Benedikt Soja

The Earth Orientation Parameters (EOP) are fundamentals of geodesy, connecting the terrestrial and celestial reference frames. The typical way to generate EOP of highest accuracy is combining different space geodetic techniques. Due to the time demand for processing data and combining different techniques, the combined EOP products often have latencies from several days to several weeks. However, real-time EOP are needed for multiple geodetic and geophysical applications, including precise navigation and operation of satellites. Predictions of EOP in ultra-short time can overcome the problem of latency of EOP products to a certain extent.

In 2010, the Earth Orientation Parameters Prediction Comparison Campaign (EOP PCC) collected predictions from 20 methods, which were mainly based on statistical approaches, and provided a combined solution. In recent years, more hybrid and machine learning methods have been introduced for EOP prediction.

The rapid expansion of computing power and data volume in recent years has made the application of deep learning in geodesy increasingly promising. In particular, the Long Short-Term Memory (LSTM) network, one of the most popular variations of Recurrent Neural Network (RNN), is promising for geodetic time series prediction. Thanks to the special structure of its cells, LSTM network can capture the non-linear structure between different time epochs in the time series. Therefore, it is suitable for EOP prediction problems.

In this study, we investigate the potential of using LSTM for the prediction of Length of Day (LOD). The LOD data from a combination of space geodetic techniques are first preprocessed in order to obtain residuals. For this step, we experiment with the application of Savitzky-Golay filters, Singular Spectrum Analysis and the Gauss Markov model. We then employ LSTM networks of different architectures and its variations such as bidirectional LSTM networks to predict the LOD residuals in ultra-short time. Furthermore, we study the impact of Atmospheric Angular Momentum (AAM) and its forecast data on the predictions. The performance of this method is compared with other results of EOP PCC in a hindcast experiment under the same conditions. In addition, we assess the performance of LOD predictions using longer time series than for the EOP PCC to consider improvements of EOP products over the last decade.

How to cite: Gou, J., Kiani Shahvandi, M., Hohensinn, R., and Soja, B.: Ultra-short-term prediction of LOD using LSTM neural networks, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-2308,, 2021.

EGU21-7178 | vPICO presentations | G1.4

Application of Machine Learning for Evaluation of GNSS Processing Protocols

Severin Rhyner, Denis Jordan, Dante Salvini, and Rolf Dach

The Center for Orbit Determination in Europe (CODE) hosts one of the global analysis centers of the International GNSS Service (IGS). Each day, the data of about 250 GNSS stations are processed in a highly automated manner. The processing protocols contain many quality parameters related to station coordinates, satellite orbits, and satellite/receiver clock corrections.

In the context of a reprocessing campaign, 25 years of GNSS measurements are analysed within a short timeframe and therefore a huge number of processing protocols are generated. A manual inspection of all these protocols is highly time consuming. Machine learning (ML) represents a promising approach to provide a data driven and objective evaluation of these protocols. The main objective of a ML framework is to analyse a big number of independent quality parameters in order to automatically detect individual days with problems in the data analysis. Furthermore, we expect that ML could contribute to the detection of unexpected systematics in the solutions and has the potential to improve the GNSS analysis strategy.

As a first step, we have focused on one aspect of the processing protocols, namely the orbit misclosures (discontinuities at the end of the orbital arcs) at midnight. It is known that the orbit modelling of GNSS satellites is more difficult during eclipse seasons. In order to assess the capabilities of different machine learning algorithms for our purpose, we have evaluated the magnitude of the orbit misclosures and have tried to recover the information on whether the satellite was passing the earth shadow or not. State-of-the-art ML algorithms (Random Forest and Decision Tree) showed promising results of up to 80% success rate.

How to cite: Rhyner, S., Jordan, D., Salvini, D., and Dach, R.: Application of Machine Learning for Evaluation of GNSS Processing Protocols, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-7178,, 2021.

EGU21-13011 | vPICO presentations | G1.4

Galileo data integrity and consistency in the IGS consolidated navigation product

Octavian Andrei

EGU21-3569 | vPICO presentations | G1.4

Deep Learning for Autonomous Extraction of Millimeter-scale Deformation in InSAR Time Series

Bertrand Rouet-Leduc, Romain Jolivet, Manon Dalaison, Paul Johnson, and Claudia Hulbert

Systematically characterizing slip behaviours on active faults is key to unraveling the physics of tectonic faulting and the interplay between slow and fast earthquakes. Interferometric Synthetic Aperture Radar (InSAR), by enabling measurement of ground deformation at a global scale every few days, may hold the key to those interactions. 
However, atmospheric propagation delays often exceed ground deformation of interest despite state-of-the art processing, and thus InSAR analysis requires expert interpretation and a priori knowledge of fault systems, precluding global investigations of deformation dynamics. 
We show that a deep auto-encoder architecture tailored to untangle ground deformation from noise in InSAR time series autonomously extracts deformation signals, without prior knowledge of a fault's location or slip behaviour.
Applied to InSAR data over the North Anatolian Fault, our method reaches  2 mm detection, revealing a slow earthquake twice as extensive as previously recognized.
We further explore the generalization of our approach to inflation/deflation-induced deformation, applying the same methodology to the geothermal field of Coso, California. 

How to cite: Rouet-Leduc, B., Jolivet, R., Dalaison, M., Johnson, P., and Hulbert, C.: Deep Learning for Autonomous Extraction of Millimeter-scale Deformation in InSAR Time Series, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3569,, 2021.

EGU21-766 | vPICO presentations | G1.4

A Novel Multitask CNN for Automatically Extracting Shoreline Variations of Lakes in Qinghai-Tibet Plateau from 1970 to 2020

Chen Xingyu, Ran Jiangjun, Xin Linyang, and Yan Zhengwen

Variations of lake areas and shorelines can effectively reflect hydrological and climatic changes. This research focuses on the automatic and simultaneous extraction of lake areas and shorelines from optical remote sensing images and SAR images, and then analyze the area changes of lakes in Tibet Plateau, in order to provide some insights for Plateau wetland environment changes. In our research, we design a novel end-to-end lightweight multitask CNN and a modified deep CNN to automatically extract those. The experimental results over the testing image patches achieve the Accuracy of 0.9962, Precision of 0.9912, Recall of 0.9982, F1-score of 0.9941, and mIoU of 0.9879, which align with or even are better than those of mainstream semantic segmentation models (UNet, DeepLabV3+, etc.). Especially, the in-situ shoreline of the Selinco Lake located in the Central and Southern Tibetan Plateau is also collected by GPS measurements to evaluate the results of the proposed method further and the validation indicates a high accuracy in our results (DRMSE: 30.84 m, DMAE: 22.49 m, DSTD: 21.11 m), with only about one-pixel deviation for Landsat-8 images. On the basis of the preceding verification results, the sequential variations of Tibetan Plateau lakes are captured and reveal Tibetan Plateau lakes generally show an increasing trend. Such as the Selinco Lake which has an expansion trend from 1660 Square kilometers to 2410 Square kilometers, grown by 45% over half a century. It is expected that these conclusions will provide some valuable information on the variations of the Tibetan Plateau wetland environment.