G – Geodesy

G1.1 – Mathematical methods for the analysis of potential field data and geodetic time series

EGU22-400 | Presentations | G1.1

Investigation of earthquake precursors using magnetometric stations in Japan

Hamideh Taherinia and Shahrokh Pourbeyranvand

Earthquakes are one of the most devastating natural disasters, and their impact on human society, in terms of casualties and economic damage, has been significant throughout history. Earthquake prediction can aid in preparing for this major event, and its purpose is to identify earthquake-prone areas and reduce their financial and human losses. Any parameter that changes before the earthquake in a way that one can predict the earthquake with a careful study of its variations is called a precursor. Recently, more attention has been paid to geophysical, geomagnetic, geoelectrical, and electromagnetic precursors. In the present study, the geomagnetic data of three stations, obtained through INTERMAGNET, with a distance of less than 500 km to the 5 Sep. Japan earthquake are investigated. Then the method of characteristic curves is used to remove the effect of diurnal variation of the geomagnetic field. After that, by examining the anomalies which are more distinct after implementation of the method, the cases are matched with the seismic activities of the region. By separating the noise from the desired signal, a pure anomaly can be observed. Among the various magnetic components, the horizontal components are more suitable than the others for the proposed process because of more variations in the geomagnetic field in the vertical direction due to the presence of the geomagnetic gradient. In the present study, one year of magnetic data, including three stations and for X, Y, and Z components, and seismic data for Japan are used to implement this method. The method is based on plotting different magnetic field components in specific time intervals in the same 24 hours frame. This will lead to a plot which shows the geomagnetic nature of each component of the geomagnetic field for each station After averaging the values for every point at the horizontal axis of the plot, which is a unit of time depending on the sampling (hourly mean, minute mean, etc.) a curve will be obtained which is called the characteristic curve. Then we reduce the characteristic curve values from geomagnetic data to reveal the anomalies, free of diurnal variation noise so that the possible anomalies related to earthquakes will be shown more distinctly. After drawing the components of the magnetic field and removing the daily changes from each of the components, we can observe the anomalies related to the earthquakes to justify the observed anomalies better and considering the standard deviation for each component, pre-seismic anomalies have a more significant distinction than the original data for being studied as a seismic precursor. After all, further investigation revealed the presence of a magnetic storm during the time period under investigation. This led to uncertainty in the feasibility of using the geomagnetic data in the present study as a precursor. However, several other pieces of evidence confirm the existence of precursory geomagnetic phenomena before earthquakes. Thus based on the current data and results, it is not possible to conclude the applicability of precursory geomagnetic studies and further data and studies are required.

How to cite: Taherinia, H. and Pourbeyranvand, S.: Investigation of earthquake precursors using magnetometric stations in Japan, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-400, https://doi.org/10.5194/egusphere-egu22-400, 2022.

EGU22-1545 | Presentations | G1.1

A first attempt at a continental scale geothermal heat flow model for Africa

Magued Al-Aghbary, Mohamed Sobh, and Christian Gerhards

Reliable and direct geothermal heat flow (GHF) measurements in Africa are sparse. It is a challenging task to create a map that reflects the GHF and covers the African continent in in its entirety.

We approached this task by training a random forest regression algorithm. After carefully tuning the algorithm's hyperparameters, the trained model relates the GHF to various geophysical and geological covariates that are considered to be statistically significant for the GHF. The covariates are mainly global datasets and models like Moho depth, Curie depth, gravity anomalies. To improve the predictions, we included some regional datasets. The quality and reliability of the datasets are assessed before the algorithm is trained.

The model's performance is validated against Australia, which has a large database of GHF measurements. The predicted GHF map of Africa shows acceptable performance indicators and is consistent with existing recognized GHF maps of Africa.

How to cite: Al-Aghbary, M., Sobh, M., and Gerhards, C.: A first attempt at a continental scale geothermal heat flow model for Africa, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-1545, https://doi.org/10.5194/egusphere-egu22-1545, 2022.

EGU22-2447 | Presentations | G1.1

Regional modeling of water storage variations in a Kalman filter framework

Viviana Wöhnke, Annette Eicker, Laura Jensen, and Matthias Weigelt

Water mass changes at and below the surface of the Earth cause changes in the Earth’s gravity field which can be observed by at least three geodetic observation techniques: ground-based point measurements using terrestrial gravimeters, space-borne gravimetric satellite missions (GRACE and GRACE-FO) and geometrical deformations of the Earth’s crust observed by GNSS. Combining these techniques promises the opportunity to compute the most accurate (regional) water mass change time series with the highest possible spatial and temporal resolution, which is the goal of a joint project with the interdisciplinary DFG Collaborative Research Centre (SFB 1464) "TerraQ – Relativistic and Quantum-based Geodesy".

A method well suited for data combination of time-variable quantities is the Kalman filter algorithm, which sequentially updates water storage changes by combining a prediction step with observations from the next time step. As opposed to the standard way of describing gravity field variations by global spherical harmonics, we will introduce space-localizing radial basis functions as a more suitable parameterization of high-resolution regional water storage change. A closed-loop simulation environment has been set up to allow the testing of the setup and the tuning of the algorithm. In a first step only simulated GRACE data together with realistic correlated observation errors will be used in the Kalman filter to sequentially update the parameters of a regional gravity field model. However, the implementation was designed to flexibly include further observation techniques (GNSS, terrestrial gravimetry) at a later stage. This presentation will outline the Kalman filter framework, introduce the regional parameterization approach, and address challenges related to, e.g., ill-conditioned matrices and the proper choice of the radial basis function parameterization.

How to cite: Wöhnke, V., Eicker, A., Jensen, L., and Weigelt, M.: Regional modeling of water storage variations in a Kalman filter framework, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-2447, https://doi.org/10.5194/egusphere-egu22-2447, 2022.

EGU22-2963 | Presentations | G1.1

Experimenting with automatized numerical methods

Naomi Schneider and Volker Michel

The approximation of the gravitational potential is still of interest in geodesy as it is utilized, e.g., for the mass transport of the Earth. The Inverse Problem Matching Pursuits (IPMPs) were proposed as alternative solvers for these kind of problems. They were successfully tested on diverse applications, including the downward continuation of the gravitational potential.

It is well-known that, for such linear inverse problems on the sphere, there exist a variety of global as well as local basis systems, e.g. spherical harmonics, Slepian functions as well as radial basis functions and wavelets. Each type has its specific pros and cons. Nonetheless, approximations are often represented in only one of them. On the contrary, the IPMPs enable an approximation as a mixture of diverse trial functions. They are chosen iteratively from an intentionally overcomplete dictionary such that the Tikhonov functional is reduced. However, an a-priori defined, finite dictionary has its own drawbacks, in particular with respect to efficiency.

Thus, we developed a learning add-on which uses an infinite dictionary instead while simultaneously reducing the computational cost. The add-on is implemented as constrained non-linear optimization problems with respect to the characteristic parameters of the different basis systems. In this talk, we give details on the matching pursuits and, in particular, the learning add-on and show recent numerical results with respect to the downward continuation of the gravitational potential.

How to cite: Schneider, N. and Michel, V.: Experimenting with automatized numerical methods, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-2963, https://doi.org/10.5194/egusphere-egu22-2963, 2022.

EGU22-10879 | Presentations | G1.1

Efficient Parameter Estimation of Sampled Random Fields Using the Debiased Spatial Whittle Likelihood

Frederik J Simons, Arthur P. Guillaumin, Adam M. Sykulski, and Sofia C. Olhede

We establish a theoretical framework, an algorithmic basis, and a computational workflow for the statistical analysis of multi-variate multi-dimensional random fields - sampled (possibly irregularly, with missing data) and finite (possibly bounded irregularly). Our research is practically motivated by geodetic and scientific problems of topography and gravity analysis in geophysics and planetary physics, but our solutions fulfill the more general need for sophisticated methods of inference that can be applied to massive remote-sensing data sets, and as such, our mathematical, statistical, and computational solutions transcend any particular application. The generic problem that we are addressing is: two (or more) spatial fields are observed, e.g., by passive or active sensing, and we desire a parsimonious statistical description of them, individually and in their relation to one another. We consider the fields to be realizations of a random process, parameterized as a Matern covariance structure, a very flexible description that includes, as special cases, many of the known models in popular use (e.g. exponential, autoregressive, von Karman, Gaussian, Whittle, ...) Our fundamental question is how to find estimates of the parameters of a Matern process, and the distribution of those estimates for uncertainty quantification. Our answer is, fundamentally: via maximum-likelihood estimation.  We now provide a computationally and statistically efficient method for estimating the parameters of a stochastic covariance model observed on a regular spatial grid in any number of dimensions. Our proposed method, which we call the Debiased Spatial Whittle likelihood, makes important corrections to the well-known Whittle likelihood to account for large sources of bias caused by boundary effects and aliasing. We generalise the approach to flexibly allow for significant volumes of missing data including those with lower-dimensional substructure, and for irregular sampling boundaries. We build a theoretical framework under relatively weak assumptions which ensures consistency and asymptotic normality in numerous practical settings including missing data and non-Gaussian processes. We also extend our consistency results to multivariate processes. We provide detailed implementation guidelines which ensure the estimation procedure can still be conducted in O(n log n) operations, where n is the number of points of the encapsulating rectangular grid, thus keeping the computational scalability of Fourier and Whittle-based methods for large data sets. We validate our procedure over a range of simulated and real world settings, and compare with state-of-the-art alternatives, demonstrating the enduring practical appeal of Fourier-based methods, provided they are corrected and augmented by the procedures that we developed.

How to cite: Simons, F. J., Guillaumin, A. P., Sykulski, A. M., and Olhede, S. C.: Efficient Parameter Estimation of Sampled Random Fields Using the Debiased Spatial Whittle Likelihood, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-10879, https://doi.org/10.5194/egusphere-egu22-10879, 2022.

EGU22-3240 | Presentations | G1.1

Oceanic load tides in the western United States

Hilary Martens, Mark Simons, Luis Rivera, Martin van Driel, and Christian Boehm

The solid Earth’s deformation response to surface loading by ocean tides depends on the material properties of Earth’s interior. Comparisons of observed and predicted oceanic load tides can therefore shed new light on the structure of the crust and mantle. Recent advances in satellite geodesy, including altimetry and Global Navigation Satellite Systems (GNSS), have improved the accuracy and spatial resolution of ocean-tide models as well as the ability to measure precisely three-dimensional surface displacements caused by ocean tidal loading. Here, we investigate oceanic load tides in the western United States using measurements of surface displacement made by a dense array of GNSS stations in the Network of the Americas (NOTA). Dominant tidal harmonics from three frequency bands are considered (M2, O1, Mf). We compare the empirical load-tide estimates with predictions of surface displacements made by the LoadDef software package (Martens et al., 2019), with the goal of refining models for Earth’s (an)elastic and density structure through the crust and upper mantle of the western US.

How to cite: Martens, H., Simons, M., Rivera, L., van Driel, M., and Boehm, C.: Oceanic load tides in the western United States, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-3240, https://doi.org/10.5194/egusphere-egu22-3240, 2022.

EGU22-1590 | Presentations | G1.1

The Effects of Seasonal Variation on GPS Height Component

Nihal Tekin Ünlütürk and Uğur Doğan

In this study, the effects of seasonal variation on the vertical position accuracy of GPS calculated by time series analysis of continuous GPS stations were investigated. Weather changes, water vapor in the atmosphere affect the position accuracy of GPS and cause fluctuations in GPS height values. It is also known that the height component has more air passage changes. Since it is easier to interpret the effects of the height component due to its topographic features and seasonal changes are more effective than the rest of the country, four continuous GPS stations, covering the 2014-2019 date range, from the Turkish National Permanent GNSS Network (TUSAGA-Aktif) were used in the East of Turkey were chosen. The daily coordinates of the stations were obtained as a result of GAMIT/GLOBK software solution. By applying time series analysis to the daily coordinate values of the stations, statistically significant trend, periodic and stochastic components of the stations were determined. As a result of the analysis, the vertical annual velocities of the stations and the standard deviations of the velocities were determined.

For the stations determined according to the ellipsoid heights, the velocity and standard deviation values of the height component were calculated for each month, season and year. As the ellipsoid height increases, the velocity and its standard deviation values decrease. While the minimum velocity values are observed for the station with the lowest ellipsoidal height in winter, for the station with the highest ellipsoidal height in autumn, the minimum their standard deviation values are determined in winter for the station with the lowest ellipsoidal height, and in summer for the station with the highest ellipsoidal height. According to the results obtained, the coordinate displacements caused by seasonal variation may be important and their effects should be considered especially in high precision geodetic surveys.

In addition, the velocity values of the stations were calculated for different years, and a decrease was observed in the height component depending on the observation duration. As the observation duration for the height component increases, both the velocity values and their standard deviation values decrease. In order to avoid velocity estimation error completely, the data length should be more than 4.5 years.

Keywords: GPS height compenent, GPS time series, Seasonal effect, Velocity estimation

How to cite: Tekin Ünlütürk, N. and Doğan, U.: The Effects of Seasonal Variation on GPS Height Component, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-1590, https://doi.org/10.5194/egusphere-egu22-1590, 2022.

EGU22-3605 | Presentations | G1.1

Impact of Offsets on Assessing the Low-Frequency Stochastic Properties of Geodetic Time Series

Kevin Gobron, Paul Rebischung, Olivier de Viron, Alain Demoulin, and Michel Van Camp

Understanding and modelling the properties of the stochastic variability -- often referred to as noise -- in geodetic time series is crucial to obtain realistic uncertainties for deterministic parameters, e.g., long-term velocities, and helpful in characterizing non-modelled processes. With the ever-increasing span of geodetic time series, it is expected that additional observations would help better understanding the low-frequency properties of the stochastic variability. In the meantime, recent studies evidenced that the choice of the functional model for the time series may bias the assessment of these low-frequency stochastic properties. In particular, the presence of frequent offsets, or step discontinuities, in position time series tends to systematically flatten the periodogram of position residuals at low frequencies and prevents the detection of possible random-walk-type variability.


In this study, we investigate the ability of frequently-used statistical tools, namely the Lomb-Scargle periodogram and Maximum Likelihood Estimation (MLE) method, to correctly retrieve low-frequency stochastic properties of geodetic time series in the presence of frequent offsets. By evaluating the biases of each method for several functional models, we demonstrate that neither of these tools is reliable for low-frequency investigation. By assessing alternative approaches, we show that using  Least-Squares Harmonic Estimation and Restricted Maximum Likelihood Estimation (RMLE) solves part of the problems reported by previous works. However, we evidence that, even when using those optimal methods, the presence of frequent offsets inevitably blurs the estimated low-frequency properties of geodetic time series by increasing low-frequency stochastic parameter uncertainties more than that of other stochastic parameters.

How to cite: Gobron, K., Rebischung, P., de Viron, O., Demoulin, A., and Van Camp, M.: Impact of Offsets on Assessing the Low-Frequency Stochastic Properties of Geodetic Time Series, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-3605, https://doi.org/10.5194/egusphere-egu22-3605, 2022.

EGU22-3766 | Presentations | G1.1

Application of the Generalized Method of Wavelet Moments to the analysis of daily position GNSS time series.

gael kermarrec, davide cucci, jean-philippe montillet, and stephane guerrier

The modelling of the stochastic noise properties of GNSS daily coordinate time series allows to associate realistic uncertainties with the estimated geophysical parameters (e.g. tectonic rate, seasonal signal). Up to now, geodetic software based on Maximum Likelihood Estimation (MLE) jointly inverse a functional (i.e. geophysical parameters) and stochastic noise models. This method suffers from a computational time exponentially increasing  with the length of the GNSS time series, which becomes an issue when considering that the first permanent stations were installed in the late 80’s – early 90’s having recorded more than 25 years of geodetic data. Combining this issue with the tremendous number of permanent stations blanketing the world (i.e. more than 20,000 stations), the processing time in the analysis of large GNSS network is a key parameter. 

Here, we propose an alternative to the MLE called the Generalized Method of Wavelet Moments (GMWM). This method is based on the wavelet variance, i.e. a decomposition of the time series using the Haar wavelet. We show the first results and compare them with the MLE in terms of computational efficiency and absolute error on the estimated parameters. The versatility of this new method is its flexibility of choosing various stochastic noise models (e.g., Matérn, power law, flicker, white noise, random walk), and its robustness against outliers. Additional developments to account for deterministic components such as seasonal signal, offsets or post-seismic relaxation is easy. We explain the principle beyond the method and apply it to both simulated and real GNSS coordinate time series. Our first results are compared with the estimation using  the Hector software.

How to cite: kermarrec, G., cucci, D., montillet, J., and guerrier, S.: Application of the Generalized Method of Wavelet Moments to the analysis of daily position GNSS time series., EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-3766, https://doi.org/10.5194/egusphere-egu22-3766, 2022.

Considering that the precise orbit and clock products provided by international GNSS service (IGS) were of a magnitude different from those required by the global geodetic observing system (GGOS) in accuracy of 1 mm, the Lomb-Scargle periodogram was used to analyze the systematic deviation and the periodical deviation between the precise products of GNSS analysis centers (ACs) and the IGS final precision products. On this basis, a deviation correction model was established based on the least square method for the correction of precision parameters. The deviation correction results show that the standard deviation of the precise clock decreases by 15.4% on average, the standard deviation of the radial orbit decreases by 33.3% on average, and the standard deviation of the ensemble effects of radial orbit and clock decreases by 24.0% on average. The signal-in-space user ranging error (SISURE) also significantly decreases from the level of centimeters to millimeters. The positioning verification results of the 15 stations show that the consistency between the positioning results of the precision products using single AC and the positioning results of IGS final precision products is also improved after deviation correction, and the average improvement ratio of three ACs is 14.3%. It is proved that the deviation correction model can effectively improve the consistency between the precision products of ACs and the final products of IGS.

How to cite: Hou, Y., Chen, J., and Zhang, Y.: Characteristics analysis and correction of GPS precise products in analysis centers based on Lomb-Scargle periodogram, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-6864, https://doi.org/10.5194/egusphere-egu22-6864, 2022.

EGU22-8369 | Presentations | G1.1

Accuracy of velocities from annually repeated GPS campaigns

D. Ugur Sanli, Ece Uysal, Deniz Oz Demir, and Huseyin Duman

The determination of GPS velocity accuracy and velocity uncertainty has been one of the topics of interest to researchers in recent years. Velocity and velocity uncertainty from continuous GPS data have been studied as deeply as possible, but velocity and velocity uncertainty from campaign measurements are still the subject of ongoing research. Recent studies have shown that the positioning accuracy of GPS PPP is latitude-dependent. At the same time, the velocity and velocity uncertainty produced by the PPP should also be treated in the same way. In this sense, it is necessary to make a global assessment. NASA JPL offers researchers a rich global database constituting GNSS time series analysis results across the globe. In this study, an experiment is conducted to determine the velocity quality of GPS campaign measurements from around 30 globally distributed stations of the IGS network. This time, our motivation is to determine the accuracy and uncertainty of GPS campaign rates from at least 4 years of data, which are performed annually on the same date. As in our previous study, we decimated coordinate components from the NASA JPL time series to generate GPS campaigns. In other words, we use 24-hour data for annual campaign measurements and repeat campaigns on three consecutive days each year. The deformation rates from NASA JPL were considered real and the accuracy of the deformation rates produced by our experiments was evaluated. Preliminary findings suggest that velocity deviations from the truth may be more severe, at 4 mm/year horizontally and 10 mm/year vertically. In the presentation, we discuss the ground truths that lead to this bias and the global distribution of velocity accuracy and velocity uncertainty.

How to cite: Sanli, D. U., Uysal, E., Oz Demir, D., and Duman, H.: Accuracy of velocities from annually repeated GPS campaigns, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-8369, https://doi.org/10.5194/egusphere-egu22-8369, 2022.

G1.2 – High-precision GNSS: methods, open problems and Geoscience applications

EGU22-12264 | Presentations | G1.2 | Highlight

On the Impact of GNSS Multipath Correction Maps on Slant Wet Delays for Tracking Severe Weather Events

Norman Teferle, Addisu Hunegnaw, Hüseyin Duman, Hakki Baltaci, Yohannes Getachew Ejigu, and Jan Dousa

Climate change has led to an increase in the frequency and severity of weather events with intense precipitation and subsequently a greater susceptibility to flash flooding of cities worldwide. As a result, accurate fore- and now-casting of imminent extreme precipitation has become critical for the warning and mitigation of these hydro-meteorological hazards. Networks of ground-based Global Navigation Satellite System (GNSS) stations enable the measurement of integrated water vapour along slant pathways, providing three-dimensional (3D) water vapour distributions at low cost and in real-time. This makes these data a valuable complementary source of information for tracking storm events and predicting their paths. However, it is well established that multipath effects at GNSS stations do impact incoming signals, especially at low elevations. While the GNSS products for meteorology to date consist predominantly of estimates of zenith total delay and horizontal gradients, these products are not optimal for constraining the 3D distribution of water vapour above a station. The direct use of slant delays counteracts this lack of azimuthal information but is more susceptible to multipath errors at low elevations. This study investigates the impact of multipath-corrected slant wet delay (SWD) estimates on tracking extreme weather events using the convective storm event over Bulgaria, Greece and Turkey on July 27, 2017, which resulted in flash floods and significant property damage. First, we recovered the one-way SWD by adding GNSS post-fit phase residuals, representing the non-isotropic component of the SWD, i.e., the higher-order inhomogeneity. As the MP errors in the GNSS phase observables can significantly affect the SWD from individual satellites, we employed an averaging strategy for stacking the post-fit phase residuals obtained from our Precise Point Positioning (PPP) processing strategy to generate station-specific MP correction maps. The spatial stacking was carried out in congruent cells with an optimal resolution in elevation and azimuth at the local horizon but with decreasing azimuth resolution as the elevation angle increases. This permits an approximately equal number of observations allocated to each cell. Using these MP correction maps in a final step, the one-way SWD were improved to employ them for the analysis of the weather event. We found that the non-isotropic component of the one-way SWD contributes up to 11% of the SWD estimates. Moreover, we validated the SWD between ground-based water-vapour radiometry and GNSS-derived SWD for different elevation angles. Furthermore, the spatio-temporal fluctuations in the SWD as measured by GNSS closely mirrored the moisture field from the ERA5 re-analysis associated with this weather event. By employing an adequate windowing system for generating these MP correction maps in combination with high-precision real-time GNSS analysis, it is possible to provide improved SWD estimates for the tracking of severe weather events.

How to cite: Teferle, N., Hunegnaw, A., Duman, H., Baltaci, H., Ejigu, Y. G., and Dousa, J.: On the Impact of GNSS Multipath Correction Maps on Slant Wet Delays for Tracking Severe Weather Events, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-12264, https://doi.org/10.5194/egusphere-egu22-12264, 2022.

EGU22-4504 | Presentations | G1.2

Orbit, clock and attitude analysis of QZS-1R

Peter Steigenberger, André Hauschild, and OIiver Montenbruck
More than ten years after the launch of the first satellite of the Japanese Quasi-Zenith Satellite System (QZSS), a replenishment satellite for this spacecraft was launched into inclined geo-synchronous orbit (IGSO) in October 2021. Triple-frequency signal transmission of QZS-1R started on November 14, 2021. In the same month, Cabinet Office, Government of Japan published satellite metadata of QZS-1R including mass, center of mass coordinates, laser retro-reflector offsets, satellite antenna phase center offsets and variations, transmit power, attitude law, as well as spacecraft dimensions and optical properties.
Precise orbit and clock parameters of QZS-1R are estimated with the NAPEOS software. The performance of a box-wing model derived from the satellite metadata is evaluated by day boundary discontinuities, orbit overlaps as well as Satellite Laser Ranging residuals. The analysis of the QZS-1R clock parameters estimated together with the orbits is complemented by a one-way carrier phase clock analysis of selected GNSS receivers connected to highly stable clocks in order to study also the short-term clock behavior.
Like previous QZSS IGSO satellites, QZS-1R transmits the L1 Sub-meter Level Augmentation Service (SLAS) via a dedicated antenna separated about 1.2 m from the main navigation antenna. Therefore, simultaneous observations of, e.g., the L1C/A and the L1 SLAS signals allow to determine the QZS-1R attitude. Attitude estimates from a regional network of eight stations are presented and compared to the nominal attitude of the spacecraft.

How to cite: Steigenberger, P., Hauschild, A., and Montenbruck, O.: Orbit, clock and attitude analysis of QZS-1R, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-4504, https://doi.org/10.5194/egusphere-egu22-4504, 2022.

EGU22-11628 | Presentations | G1.2

Combined orbit and clock zero-difference solution at CODE: ambiguity resolution strategy

Emilio José Calero Rodríguez, Arturo Villiger, Stefan Schaer, Rolf Dach, and Adrian Jäggi

The use of zero-difference processing schemes becomes more and more popular within the GNSS (Global Navigation Satellite Systems) community. This change from double- to zero-difference approaches increases the demand of PPP-AR (Ambiguity Resolution for Precise Point Positioning) enabling products. Those products can be created in two ways, either estimate the geometrical part (orbits) based on a double-difference global network solution with a separate zero-difference solution for the clocks and phase biases, or in a combined zero-difference solution. The latter one allows a more flexible approach; however, the challenge lies in the handling of the increased number of parameters and ambiguity resolution.

The estimation of combined orbit and clock zero-difference enabling products needs a thought-out design of the processing strategy, where the elimination and back-substitution steps are vital to deal with the large number of parameters. Nonetheless, the amount of ambiguity parameters dramatically grows with an increasing size of the network, posing some computational limitations, since they should not be eliminated for a successful ambiguity resolution. Such a restriction originates from fixing float orbits: their accuracy does not allow to estimate reliable ambiguity parameters. To cope with that, we propose a new algorithm capable to decouple them from the orbits, allowing to fix between-satellite ambiguities in a later station-wise parallelisation.

On the poster, we describe selected details on the ambiguity resolution strategy that we have developed. The obtained results are characterized and compared to other solutions using classical ambiguity resolution schemes.

How to cite: Calero Rodríguez, E. J., Villiger, A., Schaer, S., Dach, R., and Jäggi, A.: Combined orbit and clock zero-difference solution at CODE: ambiguity resolution strategy, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-11628, https://doi.org/10.5194/egusphere-egu22-11628, 2022.

EGU22-2477 | Presentations | G1.2

Contribution of the Galileo system to space geodesy and fundamental physics

Krzysztof Sośnica, Radosław Zajdel, Grzegorz Bury, Kamil Kazmierski, Tomasz Hadaś, Marcin Mikoś, Maciej Lackowski, and Dariusz Strugarek

Although the full operational capability of the Galileo system has not been officially announced as yet, the European GNSS, Galileo, has already remarkably contributed to geodesy, positioning, navigation, timing, and fundamental physics. Galileo metadata with the details on the satellite construction and surface properties allow for the development of the high-accuracy satellite macro-models and precise orbit determination. Two integrated onboard observation techniques – satellite laser ranging (SLR) and microwave GNSS – allow for the integration of space geodetic techniques and co-location in space. Calibrated satellite and receiver antenna offsets allow for scale realization and scale transfer for the reference frames.

GNSS orbits of superior quality constitute the basis for other geodetic products, such as Earth rotation parameters, station coordinates, geocenter motion, international terrestrial reference frames, tropospheric and ionospheric delays. Moreover, the high-quality orbits and clocks installed on a pair of Galileo satellites launched onto eccentric orbits allow for studying effects emerging from general relativity, both related to the time redshift, as well as to orbital Schwarzschild, Lense-Thirring, and de Sitter effects constituting the essential issues of fundamental physics. Finally, high-quality and frequently-updated broadcast orbits together with very stable clocks onboard Galileo assure the superior accuracy of the real-time positioning when compared to other GNSS.

We discuss the advantages and limitations of the Galileo system in terms of its applicability to geodesy, concentrating on daily and sub-daily Earth rotation parameters – polar motion and length-of-day variability, station coordinates, and geocenter motion. We address the system-specific errors discovered in GPS, GLONASS, and Galileo time series due to different satellite revolution periods, aliasing effects, tidal constituents, and orbit modeling issues. Some orbit modeling issues related, e.g., to thermal effects, remain unresolved, however, their impact may be mitigated by estimating empirical parameters and the combination of laser and microwave observations. The co-location in space onboard Galileo paves new opportunities for the realization of the reference frames tied in space, onboard GNSS satellites. We provide results on the recent developments of precise orbit determination and co-location in space based on integrated SLR and GNSS observations. Eventually, we discuss the latest applications of high-accurate orbits of Galileo satellites in near-circular and eccentric orbits toward the verification of the effects emerging from general relativity.

How to cite: Sośnica, K., Zajdel, R., Bury, G., Kazmierski, K., Hadaś, T., Mikoś, M., Lackowski, M., and Strugarek, D.: Contribution of the Galileo system to space geodesy and fundamental physics, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-2477, https://doi.org/10.5194/egusphere-egu22-2477, 2022.

EGU22-12557 | Presentations | G1.2

Estimable phase and code biases in the frame of global multi-GNSS processing

Sebastian Strasser, Torsten Mayer-Gürr, Barbara Süsser-Rechberger, and Patrick Dumitraschkewitz

Signal biases are hardware delays that occur during the transmission and reception of GNSS signals. On the satellite side, there is a delay between the generation of a signal and its transmission at the antenna. The same is the case on the receiver side, where a delay occurs between signal reception at the antenna and the actual measurement of a specific signal in the receiver. As the name suggests, code biases refer to the delays affecting code observations. Similarly, phase observations are affected by phase biases. In general, signal biases differ per constellation, satellite, frequency, signal attribute, as well as receiver hardware and settings.

The main issue with signal biases is that they are usually not known. Therefore, they have to be estimated during GNSS processing. However, the relative nature of GNSS observations prevents the estimation of absolute signal biases. This results in several rank deficiencies in the normal equation system when signal biases are estimated together with other geodetic parameters in a global multi-GNSS processing.

We present a general approach based on eigenvalue analysis to solve these rank deficiencies. Therefore, the co-estimation of pseudo-absolute transmitter and receiver signal biases in our multi-GNSS processing becomes possible. This approach also enables ambiguity resolution of GLONASS phase obervations.

How to cite: Strasser, S., Mayer-Gürr, T., Süsser-Rechberger, B., and Dumitraschkewitz, P.: Estimable phase and code biases in the frame of global multi-GNSS processing, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-12557, https://doi.org/10.5194/egusphere-egu22-12557, 2022.

EGU22-2566 | Presentations | G1.2

Empirical stochastic modeling of observation noise in global GNSS network processing

Patrick Dumitraschkewitz, Torsten Mayer-Gürr, and Sebastian Strasser

Global navigation satellite systems (GNSS) are integral to a wide array of scientific and commercial applications. Precise orbit determination of satellites in low Earth orbit relies on high-quality GNSS products. Examples of such satellites are those of the Copernicus Earth observation program of the European Union or the satellite gravimetry missions GRACE/GRACE-FO and GOCE. Numerous ground-based applications also require these products, for example: estimation of terrestrial water storage variations, earthquake monitoring, GNSS reflectometry, tropospheric and ionospheric research, surveying, or civil engineering. Furthermore, GNSS-derived station coordinates play an important role in the determination of the International Terrestrial Reference Frame. The analysis centres of the International GNSS Service (IGS) generate such products by processing observations from a global network of ground stations to one or more GNSS constellations.

So far, this kind of processing only incorporates elevation-dependent a priori modelling of observation variances and disregards temporal correlations. Meanwhile, numerous studies have shown the positive impact the incorporation of sophisticated stochastic modelling has on GNSS processing and resulting products. However, there have not been any large-scale investigations regarding the impact of stochastic modelling of observation noise on global GNSS processing.

In this contribution, we discuss a post-fit residuals approach for deriving temporal correlations in global multi-GNSS processing and their limitations. We used several years of observations and a selected IGS network of ground stations. Based on this data we analysed the post-fit residuals and the derived temporal correlations per station with respect to their seasonal effects, specific used receivers, antennas, and different transmitter signal types.

How to cite: Dumitraschkewitz, P., Mayer-Gürr, T., and Strasser, S.: Empirical stochastic modeling of observation noise in global GNSS network processing, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-2566, https://doi.org/10.5194/egusphere-egu22-2566, 2022.

EGU22-1146 | Presentations | G1.2

Impact of Different Phase Center Correction Values on Geodetic Parameters: A Standardized Simulation Approach

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

For highly precise and accurate positioning and navigation solutions with GNSS, it is mandatory to take all error sources – including phase center corrections (PCC) – adequately into account. These corrections are provided by different calibration facilities and are published in the official IGS antenna exchange format (ANTEX) file for several geodetic antennas.

Currently, the IGS antenna working group (AWG) is discussing which metrics should be used as a basis for accepting new calibration facilities as an official IGS calibration facility. To this end, requirements have to be set for comparing different sets of PCC for the same type of antenna.

Mostly, characteristic values of difference patterns (dPCC) are analysed, e.g. maximum deviations, RMS of dPCC, or percentage of dPCC values that are smaller than 1 mm. For users and station providers, however, it is most interesting to investigate the impact of dPCC on geodetic parameters, e.g. topocentric coordinate deviations and troposphere estimates. Since the impact is not only depending on the antenna in use and the station’s location but also on the applied processing strategies, a standardized comparison strategy is needed.

In this contribution, we present the impact of different PCC values on geodetic parameters using a standardized simulation approach. We show results for several globally distributed stations using different processing strategies and their respective impact on the geodetic parameters. This includes the application of different elevation cut-off angles, observation weightings w.r.t satellite coverages and elevation angles as well as use of different frequencies and linear combinations. The obtained results are analysed in detail, repeated behaviours are grouped and compared to widely used characteristic values of dPCC. Thus, an overall conclusion of the similarity of different PCC models can not only be drawn on the pattern level, but also their impact on geodetic parameters can be assessed.

How to cite: Kröger, J., Kersten, T., Breva, Y., Brekenkamp, M., and Schön, S.: Impact of Different Phase Center Correction Values on Geodetic Parameters: A Standardized Simulation Approach, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-1146, https://doi.org/10.5194/egusphere-egu22-1146, 2022.

EGU22-11421 | Presentations | G1.2

Rapid characterization of tsunami sources with GNSS-TEC ionospheric monitoring 

Lucie Rolland, Edhah Munaibari, Florian Zedek, Sladen Anthony, T. Dylan Mikesell, Coïsson Pierdavide, and Delouis Bertrand

Large earthquakes strongly shake the upper atmosphere, leaving distinctive signatures in total electron content (TEC) measured using GNSS trans-ionospheric monitoring. The ionosphere is particularly sensitive to brutal uplift motions of the ground or sea surface, triggering upward propagating mechanical waves. In specific conditions that we will detail in this presentation, GNSS-TEC measurements contain critical information on the immediate consequences of an earthquake. If accurate and provided rapidly, independent knowledge of the sea surface deformation extent and distribution could feed tsunami early warning systems.

Radio waves emitted by GNSS satellites integrate the ionospheric electron density wavefield along their propagation path. At ground level, GNSS receivers can only sense the TEC, which contains the contribution of the ionospheric wavefronts. These wavefronts are destructively or constructively integrated, depending on the involved geometry of observation. In some conditions, even a close station will not sense the TEC perturbation, while a station located 200 km away will sense large TEC fluctuations. This complex behavior mainly depends on the line-of-sight 3D geometry crossing the electron density perturbation. To study how this geometry can affect the estimation of the generating motion, we first build TEC sensitivity maps and highlight more blind or sensitive zones at the Earth’s surface. We apply the procedure to past tsunamigenic earthquakes at mid and low latitudes. Those are the 2010 Mw 7.6 Mentawaii earthquake (Indonesia), the 2016 Mw 7.8 Kaikoura earthquake (New Zealand), and the 2010 Mw 8.8 Maule earthquake (Chile). The TEC sensitivity maps allow us to investigate how the reciprocal locations of the available GNSS stations and satellites can affect the localization of the origin of the ionospheric disturbances. In a second step, we build localization maps with a full waveform method (IonoSeis software) and, where possible, with a time delay fitting method. We compare the resulting maps with the Earth’s surface deformation distribution estimated by more conventional seismo-geodetic methods. We finally show how the extension and densification of GNSS networks with multi-GNSS low-cost receivers and enhanced ionosphere monitoring could help mitigate tsunamis better.

How to cite: Rolland, L., Munaibari, E., Zedek, F., Anthony, S., Mikesell, T. D., Pierdavide, C., and Bertrand, D.: Rapid characterization of tsunami sources with GNSS-TEC ionospheric monitoring , EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-11421, https://doi.org/10.5194/egusphere-egu22-11421, 2022.

EGU22-7150 | Presentations | G1.2

On the implications of ionospheric disturbances for GNSS precise positioning: a case study of Greenland

Jacek Paziewski, Yaqi Jin, Wojciech J. Miloch, Rafal Sieradzki, Wojciech Jarmolowski, Manuel Hernandez-Pajares, Pawel Wielgosz, Jens Berdermann, Mainul Hoque, Per Høeg, Alberto Garcıa-Rigo, Haixia Lyu, Beata Milanowska, Lasse B. N. Clausen, Enric Monte-Moreno, and Raul Orús-Pérez

Ionospheric irregularities impair GNSS signals and, in turn, affect the performance of GNSS positioning. Such effects are especially evident for the high latitudes, which are currently gaining the attention of research and industry branches. These activities should be supported with reliable positioning and navigation services. Such needs motivate us to assess, for the first time, the impact of ionospheric irregularities on GNSS positioning performance in Greenland. We fill the gap and evaluate the performance of positioning methods that were not investigated comprehensively until now but meet the demands of a wide range of users. In this regard, we address the needs of mass-market users that most frequently employ single-frequency receivers and expect a meter to submeter-level accuracy in an absolute mode; and the users who require the highest precision solution based on geodetic-grade dual-frequency receivers. We take advantage of the datasets collected at the GNET permanent network in Greenland during three ionospheric storms, namely the St. Patrick storm of March 17, 2015, June 22, 2015, and August 25–­26, 2018. We discover a significant impact of the ionospheric disturbances on the ambiguity resolution performance and the accuracy of the float solution in RTK positioning. Next, assessing the single-frequency ionospheric-free PPP, we demonstrate that the model is generally unaffected by the ionospheric disturbances. Hence, the model is predestined for the application by the users of single-frequency receivers in the areas of frequent ionospheric disturbances. Finally, based on the observation analyses, we revealed that phase signals on the L2 frequency band are more prone to the cycle slips induced by ionospheric irregularities than those transmitted on the first one.

How to cite: Paziewski, J., Jin, Y., Miloch, W. J., Sieradzki, R., Jarmolowski, W., Hernandez-Pajares, M., Wielgosz, P., Berdermann, J., Hoque, M., Høeg, P., Garcıa-Rigo, A., Lyu, H., Milanowska, B., Clausen, L. B. N., Monte-Moreno, E., and Orús-Pérez, R.: On the implications of ionospheric disturbances for GNSS precise positioning: a case study of Greenland, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-7150, https://doi.org/10.5194/egusphere-egu22-7150, 2022.

EGU22-5780 | Presentations | G1.2

Total Electron Content Monitoring Complemented with Crowdsourced GNSS Observations

Grzegorz Kłopotek, Benedikt Soja, Mudathir Awadaljeed, Laura Crocetti, Markus Rothacher, Linda See, Rudi Weinacker, Tobias Sturn, Ian McCallum, and Vicente Navarro

    Global Navigation Satellite System (GNSS) is a well-recognized observation technique in studies on the ionosphere due to its sensitivity to the total electron content (TEC). The era of modern smartphones, running on Android version 7.0 and higher, facilitates the acquisition of raw dual-frequency GNSS measurements, paving the way for the GNSS community data to be potentially exploited in geoscience applications. One can assume that the continuous progress in this domain may result in future in a performance of those smart devices reaching the level of GNSS receivers (and antennas) used for atmospheric monitoring. The prospective utilization of a very large number of GNSS-capable smartphones, as a dynamic crowdsourcing receiver network, could form thus an attractive source of complementary GNSS data, allowing to significantly increase the spatial resolution of observations available for the analysis and cover areas of the globe where GNSS receivers are not yet present. The enormous volume of prospective GNSS community data brings, however, major challenges related to data acquisition, its storage, and subsequent processing for deriving various parameters of interest, also in near-real time. The same applies to the analysis of such huge and heterogeneous data sets, requiring a dedicated approach in order to exploit the data in a thorough manner and fully benefit from such a concept.
Application of Machine Learning Technology for GNSS IoT data fusion (CAMALIOT) is an ongoing ESA NAVISP project with activities covering acquisition of GNSS observations from modern smartphones and development of the dedicated infrastructure regarding GNSS processing and machine learning at scale. An Android application, developed within that project, is utilized to retrieve code and phase observations from the modern generation of smartphones. The acquired user-specific data is available to the user in the form of RINEX3-compliant files and can be uploaded by the user to the central server for subsequent processing.
This contribution highlights the CAMALIOT project in relation to the ionosphere and provides information on the developed Android application, data ingestion and processing, complemented with methodology and initial results related to the TEC retrieval based on smartphone data collected in the vicinity of geodetic GNSS receivers, with the latter used for deriving reference time series. Concerning the smartphone data, the amount and quality of observations are much lower compared to the high-grade GNSS equipment and a dedicated pre-processing stage is needed in order to discard bad observations in a proper manner. An apparent correlation between the data quality, utilized frequency bands and satellite constellation involved is visible too. This area of GNSS still suffers from the limitations related mainly to the components comprising the smartphone, resulting in the lower quality of the acquired GNSS observations, compared to those obtained with the use of high-grade GNSS receivers and antennas. This translates to a greater susceptibility to multipath as well as a much more frequent occurrence of observation gaps and cycle slips, affecting the data availability and continuity of the carrier-phase measurements.

How to cite: Kłopotek, G., Soja, B., Awadaljeed, M., Crocetti, L., Rothacher, M., See, L., Weinacker, R., Sturn, T., McCallum, I., and Navarro, V.: Total Electron Content Monitoring Complemented with Crowdsourced GNSS Observations, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-5780, https://doi.org/10.5194/egusphere-egu22-5780, 2022.

The polar ionosphere is characterized by massive structures, known as patches, resulting from intake of mid-latitude plasma or, to a lesser extent, from particle precipitation. The occurrence of patches is an object of multi-instrumental investigations performed with various space- and ground-based techniques, involving among others the measurements of Global Navigation Satellite Systems. With regard to the latter approach, the patch definition has to be reformulated to the electron density accumulated along a signal path. This step requires an additional validation of the relation between an elevation angle of GNSS measurements and an integrated enhancement of plasma.

The work compares polar patch signatures observed in GNSS time series during a maximum solar activity. The assessment of integrated patch enhancement was realized with relative STEC values that are computed for several GNSS stations located in the northern polar cap. Investigating the results at different elevation angles, one can observe a lack of typical geometrical dependency of relative STEC. We believe this effect is related to an approximately spherical shape of patches. Such a conclusion seems to be confirmed by a similar enhancement observed for measurements with different orientations. According to the obtained results, we find this is justified to use STEC as an indicator of patch enhancement for GNSS data.    

How to cite: Sieradzki, R.: A study on the relation between an elevation angle of GNSS measurements and an integrated plasma enhancement of polar patches., EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-3870, https://doi.org/10.5194/egusphere-egu22-3870, 2022.

EGU22-5477 | Presentations | G1.2

Evaluation of NTCM-G ionospheric delay correction model for single-frequency SPP users.

Beata Milanowska, Paweł Wielgosz, Mainul Hoque, Dariusz Tomaszewski, Wojciech Jarmołowski, Anna Krypiak-Gregorczyk, Karolina Krzykowska-Piotrowska, and Jacek Rapiński

The adverse effects of ionospheric delays limit the positioning accuracy of single-frequency GNSS users. To mitigate these effects, GNSS system providers make several ionospheric delays models available for their global users. For example, the GPS has offered the Klobuchar model from the beginning. More recently, Galileo users can use the NeQuick G model. In the meantime, several independent models available for real-time navigation have emerged. Recent examples are the NTCM (Neustrelitz Total Electron Content Model) correction model provided by the German Aerospace Center (DLR) and real-time global ionosphere maps (RT-GIMs) provided by the National Centre for Space Studies (CNES).

In this contribution, we evaluate the performance of several global ionospheric delay correction models in SPP mode. We used single-frequency pseudorange data from 12 GNSS stations distributed globally, covering different latitudes for the evaluation. The test data includes GNSS observations from DOY 93/2020 to DOY 80/2021, covering almost one full year of increasing solar activity. We validated the performance of the NTCM-G model driven by the Galileo Az parameters against the Klobuchar, NeQuick 2, NeQuick G, and CNES RT GIMs models. Finally, we compared the results to reference solutions obtained with CODE GIM and also using the ionosphere-free linear combination. We showed that NTCM-G corrections presented accuracy comparable with the NeQuick G model and better than the Klobuchar one.

How to cite: Milanowska, B., Wielgosz, P., Hoque, M., Tomaszewski, D., Jarmołowski, W., Krypiak-Gregorczyk, A., Krzykowska-Piotrowska, K., and Rapiński, J.: Evaluation of NTCM-G ionospheric delay correction model for single-frequency SPP users., EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-5477, https://doi.org/10.5194/egusphere-egu22-5477, 2022.

EGU22-12698 | Presentations | G1.2

Calibrating tropospheric errors on ground-based GNSS reflectometry: calculation of bending and delay effects

Peng Feng, Rüdiger Haas, Gunnar Elgered, and Joakim Strandberg

During the last decade, GNSS interferometric reflectometry (GNSS-IR) has shown great potential for sea level monitoring. In combination with geodetic positioning, GNSS-IR provides a possibility to directly link the sea level measurements to the global terrestrial reference frame. However, many error sources can still be better modeled, and the accuracy of GNSS-IR sea level measurements can be improved. Specifically, we revise the tropospheric error model in ground-based GNSS-IR for sea level applications. Unlike GNSS positioning applications, in GNSS-IR the bending effect is as important as the delay effect. Also, usually very low elevation angle observations are used in GNSS-IR, which makes the atmospheric impact even more important. For the bending effect, we propose a new calculation which takes into account the water vapour content and utilizes the widely used mapping function approach to account for the elevation dependence. For the GNSS-IR atmospheric delay, we revise the geometry of the GNSS signal path for the case of coastal GNSS-IR where the antenna is within < 100 m from the sea surface. The atmospheric delay for the reflected signal is separately evaluated at the surface specular reflection point. The delay from the satellite to the reflection point and the direct signal can both be derived from the zenith delay and mapping function, at their respective local coordinates. The delay from the reflection point to the antenna is obtained assuming an average layer refractivity. We validated our model with ray-tracing radiosonde data. At 2° elevation angle, the new method can correct > 98 % of the atmospheric bending effect, compared to about 88 % with the previously adopted approach. With fewer approximations than the previous approach (directly using the mapping function), the new delay error model is also more accurate but with less absolute improvement of about 3 % compared to the previously existing model.

How to cite: Feng, P., Haas, R., Elgered, G., and Strandberg, J.: Calibrating tropospheric errors on ground-based GNSS reflectometry: calculation of bending and delay effects, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-12698, https://doi.org/10.5194/egusphere-egu22-12698, 2022.

EGU22-1304 | Presentations | G1.2

Investigation of the effect of tropospheric mapping functions for different station heights and latitudes on PPP

Faruk Can Durmus, Ali Hasan Dogan, and Bahattin Erdogan

Global Navigation Satellite Systems (GNSS) are used for different geodetic applications such as monitoring deformations and determining plate velocities. Precise positions of stations are needed for such studies. GNSS error sources should be modelled or eliminated to achieve precise coordinates. Some error sources (e.g., receiver and satellite clock errors) can be eliminated by differencing techniques in relative point positioning. However, in precise point positioning (PPP) these errors should be modelled since the technique uses un-differenced and ionosphere-free combinations. Tropospheric signal delay, one of the atmospheric error sources of GNSS, does not depend on the signal frequency; hence, it should be modelled. This delay is modelled in zenith direction, although it occurs along the signal path. This relation is provided with tropospheric mapping functions (MFs). In this study, the effects of MFs for different station heights and latitudes have been investigated. The datasets of 294 continuously operating reference stations were processed with Jet Propulsion Laboratory’s GipsyX v1.2 software. Moreover, the datasets were subdivided into non-overlapping periods between 2 and 24 h to examine the effects of MFs on different session durations.


Keywords: GPS, PPP, Troposphere, Mapping Functions, GipsyX v1.2

How to cite: Durmus, F. C., Dogan, A. H., and Erdogan, B.: Investigation of the effect of tropospheric mapping functions for different station heights and latitudes on PPP, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-1304, https://doi.org/10.5194/egusphere-egu22-1304, 2022.

EGU22-245 | Presentations | G1.2

Effects of different tropospheric mapping functions on GPS positioning

Gizem Sezer and Bahattin Erdogan

Global Navigation Satellite Systems (GNSS) can be operated 24 hours in all weather conditions; thus, it is widely preferred in many geodetic studies. With GNSS, position information can be obtained with high accuracy. However, in order to achieve precise position, GNSS error sources such as atmospheric effects should be eliminated. Since ionospheric delay depends on the frequency of the transmitted signal, it can be eliminated with dual-frequency receivers. But, the tropospheric delay does not depend on the signal frequency. Therefore, it can not be eliminated by signal combinations. The effect of tropospheric delay depends on various factors such as station’s altitude, signal direction, cut off angle, atmospheric pressure, temperature and relative humidity. Although tropospheric delays occur along the signal path, these delays are estimated in zenith direction. Tropospheric mapping functions (MFs) are used to project slant to zenith delay. In this study, the effects of most preferred MFs in the literature, which are Global Mapping Function (GMF), Niell Mapping Function (NMF) and Vienna Mapping Function 1 (VMF1), on position accuracy was investigated. For this aim, three networks with different baseline lengths, (1) less than 100 km, (2) between 100 km and 500 km and (3) more than 500 km, were designed including 10 stations. In addition, to examine the seasonal effect of the MFs, four month dataset (January – April – July – October) were selected. These dataset were processed with the Bernese software implementing relative point positioning method by fixing 3 stations. Moreover, the dataset were subdivided into different session durations (2-3-4-6-8-12 and 24 hours) and the effect of session duration on position accuracy was analysed. According to the initial results, it can be concluded that the position accuracy on short session duration depends on the baseline length and more accurate results were obtained in the shortest network. In addition, more accurate results were obtained by VMF1 for the up component; however, for the horizontal components, there were no significant differences between the MFs.


Keywords: GPS, Accuracy, Troposphere, Mapping Functions, Bernese

How to cite: Sezer, G. and Erdogan, B.: Effects of different tropospheric mapping functions on GPS positioning, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-245, https://doi.org/10.5194/egusphere-egu22-245, 2022.

EGU22-7899 | Presentations | G1.2

Validation of low-cost receiver derived tropospheric products against ERA5 reanalysis

Katarzyna Stępniak and Jacek Paziewski

The aim of the study is to investigate the quality of the tropospheric estimates obtained with the use of the latest dual-frequency low-cost GNSS receivers. We aim to verify if the low-cost receivers may provide information on the parameters that describe the state of the troposphere with accuracy and reliability close to that of high-grade receivers. In this way, we address a scientific question on the potential usability of such receivers for climate applications. We investigate selected GNSS tropospheric estimates such as zenith tropospheric delays (ZTDs) and horizontal gradients. ZTD accuracy is validated in comparison to ERA5, which is the fifth generation reanalysis for the global climate and weather produced by European Centre for Medium-Range Weather Forecasts (ECMWF).

The experiment is based on GNSS data collected during two measurement campaigns. The 1st campaign was carried out over three days in the winter 2020; the 2nd one was held over three days in the summer 2021. Three collocated stations equipped with u-blox ZED F9P receivers and one station with a high-grade Trimble Alloy receiver were used. Receivers were connected to two different types of GNSS antennas: a surveying-grade Leica AR10 and a patch ANN-MB antenna. Collected GNSS data were processed using Bernese GNSS Software v.5.2 in Precise Point Positioning (PPP) mode based on dual-frequency ionosphere-free model.

The presented results confirm that the tropospheric solutions based on low-cost receivers data can achieve high accuracy. Low-cost equipment provides tropospheric parameters with precision and reliability only slightly lower than that of high-grade one. We also show that an application of a surveying-grade antenna to a low-cost receiver may noticeably enhance the accuracy of the tropospheric estimates derived with such receivers. Finally, validation against the ERA5 climate reanalysis confirms that both sets can provide high-quality, accurate tropospheric estimates, which can be further used in climate applications.

How to cite: Stępniak, K. and Paziewski, J.: Validation of low-cost receiver derived tropospheric products against ERA5 reanalysis, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-7899, https://doi.org/10.5194/egusphere-egu22-7899, 2022.

EGU22-8242 | Presentations | G1.2

Tropospheric Parameter Estimation with Dual-Frequency GNSS Smartphones

Raphael Stauffer, Roland Hohensinn, Iván Darío Herrera Pinzón, Gregor Möller, and Markus Rothacher

With the introduction of the operating system Android 7 Nougat in the year 2016, it became possible to access the GNSS code and carrier phase observations on Android smartphones. These observations can now be processed with state-of-the-art GNSS processing software, which allows an in-depth evaluation of the smartphone`s GNSS performance. The availability of the carrier phase observations is an important step towards sub-decimeter-level positioning. Since a few years, there are also smartphones on the market that are equipped with dual-frequency GNSS chipsets.

In this presentation, the capability of dual-frequency GNSS smartphones for the estimation of tropospheric delays is investigated. Static measurements over several weeks are performed using a Google Pixel 4 XL smartphone. The measurements are processed using relative positioning methods in a real-time mode, where a Continuously Operating Reference Station (CORS) acts as a base. The estimated differential tropospheric parameters – derived for short and medium baseline lengths – are then added to the absolute values computed at the reference station by Precise Point Positioning (PPP). Using this method, we demonstrate that the tropospheric zenith total delays can be successfully determined from smartphone observations. When comparing the estimated tropospheric delays with those determined at a nearby geodetic receiver, differences in the range of a few millimeters to centimeters are visible. In view of these accuracies, the suggested method shows the potential to resolve small-scale tropospheric structures and thus, can be an interesting data source for numerical weather prediction models or related GNSS crowdsourcing projects.

How to cite: Stauffer, R., Hohensinn, R., Herrera Pinzón, I. D., Möller, G., and Rothacher, M.: Tropospheric Parameter Estimation with Dual-Frequency GNSS Smartphones, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-8242, https://doi.org/10.5194/egusphere-egu22-8242, 2022.

EGU22-11197 | Presentations | G1.2

Evaluation of positioning accuracy with the use of sports watches equipped with GNSS modules

Kamil Kazmierski, Marcin Mikos, and Natalia Wachulec

It is difficult to imagine today's world without Global Navigation Satellite Systems (GNSS). The dynamic development of GNSS has contributed to the fact that current users are able to use four global systems that use more than 120 satellites. This progress was related not only to the space segment but also to the user segment. Modern technology and miniaturization have resulted in the users' disposal of different types of GNSS receivers, including geodetic receivers, gaining popularity low-cost receivers, or other devices using the GNSS signal, such as smartphones, sports trackers, or sports watches.

Modern sports watches are equipped with many sensors, among which GNSS chipsets play an important role. Those GNSS chipsets make it possible to determine the distance traveled and other related parameters that are important from the point of view of athletes. The most modern constructions can track several constellations at the same time. However, it is difficult to find reliable information to determine the actual quality of positioning by these low-cost GNSS receivers. Most of the works use comparative methods of watches and visual analysis of the route covered. Due to the above-mentioned gap in this area, the positioning quality of leading manufacturers of sports watches was assessed in this study.

Ten sports watches from Garmin, Polar, and Suunto were assessed in the study regarding the geodetic grade GNSS Trimble receiver. The watches were evaluated in three experiments: field positioning experiment, distance accuracy experiment conducted on the athletics track, and the accuracy of the altitude determination conducted on the 37 m high tower. The tests were performed for all the GNSS system options available in watches. The best positioning quality was obtained for the Polar M430 watch that uses only GPS for which almost all recorded epochs obtain positioning accuracy better than 5 m. When measuring distance, most watches had a result that was less than 1% from the theoretical value. Garmin Vivoactive 4s achieved the best results in height determination. For 11 different measured levels, located about 3 m apart, it obtained an average difference equal to 0.48 m. The results show also that the use of the additional GNSS system degrades the obtained results in some cases.

How to cite: Kazmierski, K., Mikos, M., and Wachulec, N.: Evaluation of positioning accuracy with the use of sports watches equipped with GNSS modules, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-11197, https://doi.org/10.5194/egusphere-egu22-11197, 2022.

EGU22-9079 | Presentations | G1.2

Low-cost and smartphone GNSS sensors: current capabilities and perspectives for seismic and tropospheric monitoring applications

Roland Hohensinn, Raphael Stauffer, Iván Darío Herrera Pinzón, Gregor Möller, Matthias Aichinger-Rosenberger, Yara Rossi, Yuanxin Pan, Grzegorz Kłopotek, Benedikt Soja, and Markus Rothacher

In recent years, dual-frequency GNSS chipsets became available on the mass market. The ongoing developments in sensor and processing technologies steadily improve the positioning performance so that nowadays sub-decimeter accuracies can be achieved with such devices, even in real-time. Thus these sensors become a powerful, inexpensive choice for equipping or densifying existing GNSS monitoring networks. Station densification can be of significant added value for earthquake early warning systems, assimilation of GNSS water vapor estimates into numerical weather prediction models and the detection of severe weather events. Even if somewhat noisier, smartphone data can be used for GNSS-based remote sensing purposes as well.

This contribution is twofold, and focusses on both, the current capabilities and the perspectives of these GNSS low-cost technologies for such remote sensing applications. In the first part we highlight the accuracy of PPP-enabled seismic and tropospheric monitoring using low-cost loggers and stations developed in-house. We show that differential smartphone GNSS observations on short- and medium-length baselines can be used to sense the state of the regional troposphere. In the second part, we present first results on the performance of the u-blox D9S application board, which enables highest precision by PPP-RTK with ambiguity resolution, and the feasibility of high-precision positioning is assessed for long baselines involving smartphone data as well. Finally, we briefly discuss the potential of data-driven methods for mitigating multipath, which is still one of the main error sources when using equipment of low quality. Concerning the GNSS processing, we rely on further-developed versions of open-source and commercial GNSS software packages. Regarding sensor technology, u-blox chips -- which are currently deployed in our self-sufficient GNSS stations -- are used together with different low-cost and medium-grade GNSS antennas (both, patch and recent helical-type low-cost antennas).

We conclude that low-cost GNSS sensor technology is on the way to satisfy the same demands in accuracy as geodetic-grade equipment -- centimeter-level accuracy can be obtained, even in real-time. New possibilities for station densifications arise by employing low-cost, autonomous stations or by crowdsourcing of GNSS data with smartphones. These observations can aid in resolving small-scale structures in the atmosphere, or for a quick detection and localization of geohazards.

How to cite: Hohensinn, R., Stauffer, R., Herrera Pinzón, I. D., Möller, G., Aichinger-Rosenberger, M., Rossi, Y., Pan, Y., Kłopotek, G., Soja, B., and Rothacher, M.: Low-cost and smartphone GNSS sensors: current capabilities and perspectives for seismic and tropospheric monitoring applications, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-9079, https://doi.org/10.5194/egusphere-egu22-9079, 2022.

EGU22-2512 | Presentations | G1.2

Cost-effective GNSS sensors applied for crustal deformation purposes: insights from an experiment in NE-Italy

Lavinia Tunini, David Zuliani, and Andrea Magrin

The global data coverage of the Global Navigation Satellite Systems (GNSS) provides a fundamental and unique dataset for a wide range of applications, such as crustal deformation, topographic measurements, or near surface processes studies. However, a strong limitation is represented by the high costs of the GNSS receivers and the supporting software, which make them available only by the scientific communities capable of affording them. The GNSS technology has been continuously and rapidly growing and, in recent years, new cost-efficient (low-cost) instruments have entered the mass market, gaining the attention of the scientific community for potentially being high-performing alternative solutions. In this study, we matched in parallel a dual-frequency cost-effective receiver (u-blox ZED F9P) and two high-cost receivers, all connected to the same geodetic-class antenna. We tested the system by processing the data together with the observations coming from a network of GNSS permanent stations operating in North-East Italy. We compare the time-series obtained using cost-effective geodetic equipment with those obtained using geodetic-class instruments. We show that mm-order precision can be achieved by cost-effective GNSS receivers, while the results in terms of time series are largely comparable to those obtained using high-price geodetic receivers.

How to cite: Tunini, L., Zuliani, D., and Magrin, A.: Cost-effective GNSS sensors applied for crustal deformation purposes: insights from an experiment in NE-Italy, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-2512, https://doi.org/10.5194/egusphere-egu22-2512, 2022.

EGU22-13439 | Presentations | G1.2

The VARION approach to volcanoes: case study on 2021 Etna eruptions

Michela Ravanelli, Federico Ferrara, Federica Fuso, Andrea Cannata, Mattia Crespi, and Giovanni Occhipinti

The 2022 Tonga event highlight the necessity to have more and more knowledge about the activity
of volcanoes. To this point, it is well known that volcanoes explosion can trigger ionospheric
perturbation detectable through the Global Navigation Satellite System (GNSS) signal [1].

The VARION (Variometric Approach for Real-Time Ionosphere Observation) algorithm has been
successfully applied to detection of ionospheric perturbations in several real-time scenarios [2, 3].
VARION, thus, estimates sTEC (slant total electron content) variations starting from the single time
differences of geometry-free combinations of GNSS carrier-phase measurements.

The aim of this work is to analyse some Etna explosions occurred in 2021 with the VARION algorithm
in order to better study the coupling between volcanoes and ionosphere. This study can pave the
way to a real-time ionospheric monitoring of Etna volcano.

[1] Manta, Fabio, et al. "Correlation between GNSS‐TEC and eruption magnitude supports the use
of ionospheric sensing to complement volcanic hazard assessment." Journal of Geophysical
Research: Solid Earth 126.2 (2021): e2020JB020726.

[2] Ravanelli, Michela, et al. "GNSS total variometric approach: first demonstration of a tool for
real-time tsunami genesis estimation." Scientific Reports 11.1 (2021): 1-12.

[3] Savastano, Giorgio, et al. "Advantages of geostationary satellites for ionospheric anomaly
studies: Ionospheric plasma depletion following a rocket launch." Remote Sensing 11.14 (2019):

How to cite: Ravanelli, M., Ferrara, F., Fuso, F., Cannata, A., Crespi, M., and Occhipinti, G.: The VARION approach to volcanoes: case study on 2021 Etna eruptions, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-13439, https://doi.org/10.5194/egusphere-egu22-13439, 2022.

EGU22-13326 | Presentations | G1.2

A Web Based Open Source Deformation Analysis Platform for identifying Crustal Movements

Mehmet Bak and Rahmi Nurhan Celik

Deformation measurements and deformation analysis are important fields of study in geodesy. Investigating the results obtained from the deformation analysis is very important for human safety. By monitoring the movements of the earth's crust or engineering structures, many measures can be taken to protect human life against potential disasters. For this reason, geodetic measurement techniques have been used since the beginning of the 20th century. Important studies have been carried out, especially with the development of GNSS measurement techniques for monitoring displacement movements and deformations. Both academic and commercial software are available for deformation analysis for the determination of earth crust movements. However, the increasing interest in studying crustal movements has revealed new demands. Today, developing technology has allowed the development of new platforms for deformation analysis.

In this study, an open source web-based deformation analysis platform named Web-NDefA (Web-'N'etwork 'Def'ormation 'A'nalysis), which was developed for 3D static deformation analysis using geodetic methods, is introduced. In addition, the analysis of a data group obtained from Continuously Operating Reference Stations in the Marmara Region with this platform is also explained. After the processing of the base vectors obtained from univariant GNSS networks with the LGO (Leica Geo Office) software, Web-NDefA is used to load the ASCII file of the base solutions to the platform, to adjust the measurements according to the free adjustment method, to obtain the confidence criteria and to analyse the networks compared according to the static deformation model and S-Transformation method. It is a static deformation analysis platform that performs 3-Dimensional statistical analysis that provides visualization, computation of coordinate differences, and drawing velocity vectors. This platform is written with client-side programming languages. HTML (HyperText Markup Language), CSS (Cascading Style Sheets), JavaScript applications were made.

As a result, in this study, information about the design of the have developed open source web platform is given and GNSS data obtained from certain days in 2016, 2019 and 2020 in the Marmara Region are analysed. In this way, a new vision is put forward to the applications used in GNSS-based static deformation analysis and experts who are interested in monitoring and analysing deformations can access such platforms more easily.

How to cite: Bak, M. and Celik, R. N.: A Web Based Open Source Deformation Analysis Platform for identifying Crustal Movements, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-13326, https://doi.org/10.5194/egusphere-egu22-13326, 2022.

Ambiguity fixing on the geometry free combination presents some desirable characteristics. In particular, it does not require precise ephemeris, modelling of station displacement motion or tropospheric modelling or estimation. For such reasons, it can be particularly interesting in the case where such data and models are not available or if simpler processing is wanted. Such fixing procedure has been studied in the past for dual-frequency and triple frequency cases. Unfortunately, especially in the two frequency case, this procedure is not practical due to the long observation period needed to reliable fix a correct integer set. In this contribution, we review the fixing performances of the “geometry free” model using an undifferenced uncombined approach. Furthermore, we present the case to four and five frequency cases using Galileo and Beidou observations showing that reliable fixing in a reduced time span is possible. All analyses presented are performed using real GNSS data from the IGS permanent network. Finally, some possible applications are presented with a focus on ionospheric studies.

How to cite: Tagliaferro, G.: Ambiguity fixing on geometry free like model using modernized GNSS signals, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-4881, https://doi.org/10.5194/egusphere-egu22-4881, 2022.

EGU22-2327 | Presentations | G1.2

Inconsistency in Precise Point Positioning products from GPS, GLONASS and Galileo 

Radosław Zajdel, Kamil Kazmierski, and Krzysztof Sośnica

Global Navigation Satellite Systems (GNSSs) are widely used for Earth system monitoring, e.g., solid earth and atmosphere. However, the time series of station coordinates and zenith tropospheric delay derived using GNSS are inherently affected by several technique-specific errors that influence the interpretation of geophysical processes and phenomena. GPS plays a crucial role and is most often used in interdisciplinary studies. However, the multiplicity of navigation systems, including fully operational GLONASS and Galileo, allowed us to assess system-specific high-frequency signals and inconsistencies arising from using different constellations.

This work shows that using different GNSS constellations leads to the appearance of various artificial signals with amplitudes up to several millimeters in the series of station coordinates. The presence of the GNSS system-specific artifacts and inter-system disagreements are demonstrated using the 2-year long series of station coordinates and zenith total delay parameters for 15 stations using Precise Point Positioning algorithms. Finally, we assessed the benefit of using GPS, GLONASS, and Galileo jointly.

We identified the origin of the spurious signals in orbital errors. The most dominant orbital artifacts for Galileo appear with periods of 14.08 h, 17.09 h, 34.20 h, 2.49 d, ~3.4 d. The corresponding signals for GLONASS appear with periods of 5.63 h, 7.36 h, 10.64 h, 21.26 h, 3.99 d, and ~8 d. Moreover, when estimating discrete 24-hour solutions from high-rate GNSS data, high-frequency signatures are under-sampled, resulting in long-term aliased periodic signals. The GPS orbital signals arise at the periods corresponding to the harmonics of the K1 tide, which leads to the inconsistency of the GPS-based products with ocean tidal loading models reaching on average 12 mm for the K2 tidal term in the Up component. The magnitude of the orbital signals varies between different site locations and depends on the GNSS observation geometry and dominant direction of satellites' flybys. For example, because of the high inclination of the GLONASS orbital planes, the stations located in absolute low latitudes observe mostly North-South satellite flybys; thus, the estimated East component of the coordinates is exposed to the orbital artifacts.

Galileo is less vulnerable to the orbital signals than GPS or GLONASS. The difference is visible mainly for the East coordinate component. The Galileo-based daily estimates are up to 55% and 36% better than those delivered from GLONASS and GPS. Finally, using a combination of GPS and Galileo increases the precision of estimates by 10% compared with the best-case Galileo-only solution and remarkably reduces the system-specific errors in station coordinate time series.

How to cite: Zajdel, R., Kazmierski, K., and Sośnica, K.: Inconsistency in Precise Point Positioning products from GPS, GLONASS and Galileo , EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-2327, https://doi.org/10.5194/egusphere-egu22-2327, 2022.

EGU22-7489 | Presentations | G1.2

Analysis of different weighting functions of observations for GPS and Galileo PPP

Damian Kiliszek, Andrzej Araszkiewicz, and Krzysztof Kroszczyński

At present, significant development of the positioning methods using the Global Navigation Satellite System (GNSS) can be seen. One of the most developed methods is the absolute Precise Point Positioning (PPP) method. This can be particularly seen using multi-GNSS measurements. The development of multi-GNSS increases the number of satellites observed and increases the accuracy of the products, but also creates new requirements for observation modeling. Obtaining the correct values, ​​of the estimated parameters, requires the appropriate determination of the deterministic model as well as the stochastic model. Currently, the deterministic model is well known. In contrast, the stochastic model is not fully known and still requires a number of studies. Stochastic modeling is based on determining the covariance matrix and which can be modeled using a weighting function that takes into account the elevation angle of the observed satellite. ​

In our analysis, we focus on studies on the weighting functions of GNSS observations for the PPP method. Analysis was performed on the Multi-GNSS Pilot Project (MGEX) stations which were characterized by global distribution and various equipment in 2021. Studies were conducted for the GPS‑only, Galileo-only, and GPS+Galileo constellations, with particular emphasis on the Galileo observations, which has achieved significant progress in recent years. Eight different observation weighting models have been selected for analysis: one of them assumes that all observations have the same precision, without dependence on the elevation angle; for the other used functions, the observation precision value depends on the elevation angle. Parameters such as accuracy, convergence time, zenith path delay (ZPD), and inter-system bias (ISB) are analyzed.

Based on the tests performed, we show that, depending on the solutions adopted (i.e. GPS-only, Galileo-only, GPS+Galileo), the best results were obtained for different weighting functions. We have shown that using different weighting functions have no impact on the horizontal component but a visible impact on the vertical component,  the tropospheric delay, and the convergence time. Also, we choose the best functions for GPS-only and Galileo-only and used them for the GPS+Galileo solution. For this new approach obtained a shorter convergence time and higher accuracy of the ZPD. More information and results will be presented at the conference.

How to cite: Kiliszek, D., Araszkiewicz, A., and Kroszczyński, K.: Analysis of different weighting functions of observations for GPS and Galileo PPP, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-7489, https://doi.org/10.5194/egusphere-egu22-7489, 2022.

EGU22-12926 | Presentations | G1.2

Considering Satellite Attitude Quaternions in BeiDou Precise Point Positioning Performance

Robert Galatiya Suya, Yung-Tsang Chen, Chiew-Foong Kwong, and Penghe Zhang

The use of theoretical modeling algorithms to compute the satellite altitude causes some errors which are eventually absorbed by the satellite clocks. This adversely reduces the fixed positioning performance in global navigation satellite system (GNSS) precise point positioning (PPP). Currently, different International GNSS service (IGS) analysis centers (ACs) provide satellite altitude quaternions which are an auxiliary dataset necessary in PPP fixed solutions. Hence, this study aims at a comprehensive evaluation of the effect of accounting for the BeiDou satellite attitude quaternions in PPP. The quaternions provided by different ACs are applied to BeiDou PPP using different weighting schemes suitable for handling satellites in three distinct orbits. The obtained numerical results indicate that considering the quaternions in BeiDou PPP reduces the observation residuals, improves the ambiguity fixing, and enhances positioning performance.

How to cite: Suya, R. G., Chen, Y.-T., Kwong, C.-F., and Zhang, P.: Considering Satellite Attitude Quaternions in BeiDou Precise Point Positioning Performance, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-12926, https://doi.org/10.5194/egusphere-egu22-12926, 2022.

EGU22-7927 | Presentations | G1.2

First experience with GNSS data quality monitoring in the distributed EPOS e-infrastructure

Fikri Bamahry, Juliette Legrand, Carine Bruyninx, and Andras Fabian

The European Plate Observing System (EPOS) is a very large and complex European e-infrastructure that provides pre-operational access to a first set of datasets and services for Solid Earth research. The EPOS-GNSS Data Gateway provides, through an Application Program Interface (API) and a web portal, access to GNSS (Global Navigation Satellite Systems) RINEX data from a distributed infrastructure of data nodes. Currently, ten EPOS-GNSS nodes have been installed, and three of them are still in the pre-operational phase. To monitor the long-term data quality of EPOS-GNSS stations at the nodes level, ROB is developing a new service. The first step of this service is a web portal (www.gnssquality-epos.oma.be) that provides access to data quality metrics of the RINEX data available from the different EPOS-GNSS nodes.

The web portal presents plots of the long-term tracking performance of more than 1000 EPOS-GNSS stations. The plots focus on several data quality metrics such as the number of observed versus expected observations, the number of missing epochs, the number of observed satellites, the number of cycle slips, and multipath values on code observations. These metrics have been computed at the node level using GLASS and Anubis Software (https://gnutsoftware.com/software/anubis). The metrics provide helpful information for node managers or station users to assess the EPOS-GNSS station’s performance and detect potential degradation of the RINEX data quality. The outlook of this work is to investigate the possible usage of data quality metrics to detect data unsuitable for high-precision GNSS analysis for geophysical or meteorological applications. Here, we will present the newly developed web portal, the considered data quality metrics, and some preliminary results of this ongoing work.

How to cite: Bamahry, F., Legrand, J., Bruyninx, C., and Fabian, A.: First experience with GNSS data quality monitoring in the distributed EPOS e-infrastructure, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-7927, https://doi.org/10.5194/egusphere-egu22-7927, 2022.

EGU22-8890 | Presentations | G1.2

Accuracy of GNSS positioning: GPS+GLONASS case

Deniz Cetin, D.Ugur Sanli, and Sermet Ogutcu

For a long time, the main factor affecting the accuracy of GPS PPP has been the observing session duration. Researchers have recently shown that the accuracy of PPP also varies with latitude. The reason for the latitudinal variation is the inability to determine the tropospheric zenith delay with a globally homogeneous precision and its impact on the position determination results. A formula has been developed to give the accuracy of the PPP position in a local geocentric system based on observation session duration and latitude. Currently, the interest of researchers is to determine the accuracy of Multi-GNSS solutions. In this context, the MGEX experiment of the IGS provides a rich data source to researchers. In this study, 15 globally distributed GNSS stations were selected from the MGEX network, GPS+GLONASS data was evaluated with CSRSPPP software, and the accuracy of the GNSS positioning was investigated. Continuous GNSS observations and 8-hour campaign measurements are evaluated comparatively. The results of the study showed that 60% of the RMS values obtained from the 24-hour data became smaller, indicating that it was equal between the horizontal and vertical coordinate components. The improvement in campaign solutions is better and around 80% overall. The share of this between horizontal position and vertical position is around 73% and 87%, respectively. The average improvement in the RMS of the coordinate components is around 0.5 mm for the campaign solutions, but the improvement can reach up to 2 mm at some stations. Our motivation was to determine whether this improvement was reflected in the accuracy modeling. Initial findings show that the results are in agreement with the latest accuracy modeling, and it turns out that the positioning accuracy of GNSS PPP also depends on the latitude of the GNSS site as well as the observation session, as in the GPS PPP.

How to cite: Cetin, D., Sanli, D. U., and Ogutcu, S.: Accuracy of GNSS positioning: GPS+GLONASS case, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-8890, https://doi.org/10.5194/egusphere-egu22-8890, 2022.

G1.3 – Data science and machine learning in geodesy

As a specific family of machine learning algorithms, deep learning (DL), successfully applied to several application areas is a relatively new and novel methodology receiving much attention. The DL has been widely applied to a series of problems including email filtering, image and speech recognition, and language processing, but is only beginning to impact on geoscience problems. On the other hand, the standard least-squares (SLS) theory of linear models has been widely used in many earth science areas. This theory connects the explanatory variables to the predicted ones, called observations, through a linear(ized) model in which the unknowns of this relation are estimated using the least squares method. The design matrix, containing the explanatory variables of a set of objects, is usually linearly related to the predicted variables. There are however applications that the predicted variables are unknown (nonlinear) functions of explanatory variables, and hence such a design matrix is not known a-priori. We present a methodology that formulates the deep learning problem in the least squares framework of the linear models. As a supervised method, a network is trained to construct an appropriate design matrix, an essential element of the linear model. The entries of this design matrix, as nonlinear functions of the explanatory variables, are trained in an iterative manner using the descent optimization methods. Such a design matrix allows to employ the existing knowledge on the least squares theory to the DL applications. A few examples are presented to demonstrate the theory.

How to cite: Amiri-Simkooei, A.: Least-squares-based formulation of deep learning: Theory and applications to geoscience data analytics, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-7272, https://doi.org/10.5194/egusphere-egu22-7272, 2022.

EGU22-4039 | Presentations | G1.3

Apply noise filters for better forecast performance in Machine Learning

Nhung Le, Benjamin Männel, Randa Natras, Pierre Sakic, Zhiguo Deng, and Harald Schuh ‬‬‬‬‬‬‬‬‬‬‬‬‬


In Machine Learning (ML), one of the crucial tasks is understanding data characteristics to be able to extract exactly relevant information, while noise contained in data can cause misleading estimations and decrease the generalizability of ML-based prediction models. So far, only few previous studies have applied noise filtering techniques when building forecast models. Hence, their efficiency on ML-based forecasts has not yet been comprehensively demonstrated. Therefore, we aim to determine optimal noise filters to enhance the forecast performance of Total Electron Contents (TEC), crustal motion, and Earth’s polar motion. We investigate six noise filtering algorithms (Moving Mean, Moving Median, Lowess, Loess, and Savitzky Golay) on forecast models to select the best-suited filters. Five ML algorithms are applied to train forecast models, that are Support Vector Machine (SVM), Regression Trees, Linear Regression (LR), Ensembles of Trees, and Gaussian Process Regression (GPR). The findings show that the Savitzky Golay algorithm is the most effective on the ML-based forecast models, followed by Loess and Gaussian filters, while Moving Mean is the least sensitive. Noise filters are more sensitive for forecast models based on SVM and LR than Ensembles of Trees and GPR. Applying the Savitzky Golay filter for SVM and LR optimal models can enhance the prediction accuracy up to 14.0 %, 16.1 % and 89.5 % corresponding to forecasting TEC, crustal motion, and Earth's polar motion, respectively; while that for Ensembles and GPR are only from approximate 3.0 to 27.0 %. Overall, using noise filters is one of the practical solutions to improve prediction performance. They can also be used to smoothen time series with variable characteristics and to generalize high-rate data.


Machine Learning, Noise filters, Savitzky Golay filter, TEC forecast, Crustal motion, Earth’s polar motion.

How to cite: Le, N., Männel, B., Natras, R., Sakic, P., Deng, Z., and Schuh ‬‬‬‬‬‬‬‬‬‬‬‬‬, H.: Apply noise filters for better forecast performance in Machine Learning, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-4039, https://doi.org/10.5194/egusphere-egu22-4039, 2022.

EGU22-1101 | Presentations | G1.3

Differential Learning: A method for polar motion time series prediction

Mostafa Kiani Shahvandi, Matthias Schartner, and Benedikt Soja

Nowadays, many applications such as Global Navigation Satellite Systems (GNSS) or spacecraft tracking require a rapid determination, or even predictions, of the Earth Orientation Parameters (EOP). However, due to the measurement techniques utilized to estimate EOP, the latency can be considerably longer than required, which especially hinders real-time applications, resulting in a need for accurate EOP prediction methods.

With the resurgence of machine learning in the last decade, time series prediction is increasingly studied in this context. We propose a learning algorithm for the prediction of polar motion components (xp, yp). The algorithm is based on the concept of Ordinary Differential Equation (ODE) fitting. Within this investigation, a general formula for ODE fitting based on multivariate time series is proposed, with special focus on second order ODEs. The mathematical relations are derived and presented in both linear and non-linear forms, particularly with LSTM and Elman neural networks. In addition, a sensitivity analysis framework is proposed for the linear case, which is used for the determination of the importance of features. 

We compared the prediction performance of our method with those from three different studies. First, the conditions of the first Earth Orientation Prediction Comparison Campaign (EOPPCC) are followed. In this case, the ultra-short term predictions (up to 10 days) can be improved on average by 62.5% and 45.6% for xp and yp, respectively,  compared to the best performing EOPPCC method. Second, the prediction performance in long-term prediction (up to one year) is compared against Multichannel Singular Spectrum Analysis (MSSA). In this case, the prediction performance is improved on average for xp and yp by 40.9% and 66.4%, respectively. Finally, comparisons against Copula-based methods for long-term prediction are conducted (average improvement 32.3% for xp and 57.8% for yp).

The advantages of this method include (1) exploitation of physical information via Effective Angular Momentum (EAM) functions and by using the concept of ODE fitting, which often corresponds to the laws governing physical phenomena; (2) presence of sensitivity analysis frameworks; and (3) high predictive performance.

How to cite: Kiani Shahvandi, M., Schartner, M., and Soja, B.: Differential Learning: A method for polar motion time series prediction, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-1101, https://doi.org/10.5194/egusphere-egu22-1101, 2022.

EGU22-5003 | Presentations | G1.3

Deep learning for extreme wind speed prediction with CyGNSSnet

Caroline Arnold, Daixin Zhao, Tianqi Xiao, Lichao Mou, and Milad Asgarimehr

The CyGNSS (Cyclone Global Navigation Satellite System) satellite system measures GNSS signals reflected off the Earth’s surface. A global ocean wind speed dataset is derived, which fills a gap in Earth observation data and can improve cyclone forecasting. We proposed CyGNSSnet(1), a deep learning model for predicting wind speed from CyGNSS observables, and found an improved performance of 29% compared to the current operational model. However, the prediction of extreme winds remained challenging: For wind speeds exceeding 12 m/s, the operational model outperformed CyGNSSnet.

Here, we explore methods to improve the performance of CyGNSSnet at high wind speeds. We introduce a hierarchical model that combines specialized CyGNSSnet instances trained in different wind speed regimes with a classifier to select an instance. In addition, we explore strategies to improve the wind speed predictions by emphasizing extreme values in training, and we discuss the potentials and shortcomings of the approaches.

  • (1) Asgarimehr, M., Arnold, C., Weigel, T., Ruf, C. & Wickert, J. GNSS reflectometry global ocean wind speed using deep learning: Development and assessment of CyGNSSnet. Remote Sensing of Environment 269, 112801 (2022).

How to cite: Arnold, C., Zhao, D., Xiao, T., Mou, L., and Asgarimehr, M.: Deep learning for extreme wind speed prediction with CyGNSSnet, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-5003, https://doi.org/10.5194/egusphere-egu22-5003, 2022.

EGU22-1503 | Presentations | G1.3

Machine learning based multipath mitigation for high-precision GNSS data processing

Yuanxin Pan, Gregor Möller, Roland Hohensinn, and Benedikt Soja

Multipath is the main unmodeled error source hindering high-precision GNSS (Global Navigation Satellite System) data processing. Classical multipath mitigation methods, such as sidereal filtering (SF) and multipath hemispherical map (MHM), have certain disadvantages: they are either too complicated for implementation or not effective enough for multipath mitigation. In this study, we demonstrate that machine learning (ML) based models, such as random forest, can overcome these drawbacks by spatial interpolation over sky map and thus mitigate multipath effectively. 30 days of 1 Hz geodetic grade GPS data as well as 6 days of low-cost data are used to train and test the ML models. Based on a series of test cases, the best number of days for model training and the validity period for the models are discussed in this contribution. For quantification, the multipath reduction rate and kinematic positioning precision are computed using different ML models and compared to those derived from SF and MHM. The statistical results show that the XGBoost ML model can achieve higher multipath reduction rates compared to SF and MHM, especially for pseudorange measurements, which is important for low-cost devices. It reduces the multipath by 48% and 55% for pseudorange and carrier phase measurements, respectively, and outperforms SF (40% and 52%) and MHM (37% and 49%). The positioning precision when using different multipath models is similar, with differences of less than 1 mm. We conclude that the ML based multipath mitigation method is effective and easy-to-use, which can be applied under real-time scenarios.

How to cite: Pan, Y., Möller, G., Hohensinn, R., and Soja, B.: Machine learning based multipath mitigation for high-precision GNSS data processing, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-1503, https://doi.org/10.5194/egusphere-egu22-1503, 2022.

EGU22-1834 | Presentations | G1.3

Improving the Accuracy of GNSS Orbit Predictions using Machine Learning Approaches

Junyang Gou, Christine Rösch, Endrit Shehaj, Kangkang Chen, Mostafa Kiani Shahvandi, Benedikt Soja, and Markus Rothacher

Precise orbit determination is vital for the increasingly vast number of space objects around the Earth. Moreover, accurate orbit prediction of GNSS satellites is essential for many real-time geodetic applications, including real-time navigation. The typical way to obtain accurate orbit predictions is using physics-based orbit propagators. However, the prediction errors accumulate with time because of insufficient modeling of the changing perturbing forces. Motivated by the rapid expansion of computing power and the considerable data volume of satellite orbits available in recent years, we can apply machine learning (ML) and deep learning (DL) algorithms to assess if they can be used to further reduce orbit errors.

In this study, we focus on the orbit prediction of GNSS constellations. We investigate the potential of using different ML and DL algorithms for improving the accuracy of the ultra-rapid products from IGS. As ground truth we consider the IGS final products, and the differences between the ultra-rapid and final products are computed and serve as targets for the ML/DL methods. In this context, we combine the advantages of physics-based and data-driven ML/DL methods. Since the major errors of GNSS orbits are expected to be caused by the deficiency of solar radiation pressure models, we consider different related parameters as additional features to implicitly model the solar impact, such as the C0,0 terms of global ionosphere maps. In order to accurately model the effect of solar radiation pressure on the radial, along-track and cross-track components of the satellite orbit system, the geometric relation between the Sun, the satellite and the Earth are also considered. Furthermore, the performances of different ML/DL algorithms are compared and discussed. Due to the temporal characteristics of the problem, certain sequential modeling algorithms, such as Long Short-Term Memory and Gated Recurrent Unit, show superiority. Our approach shows promising results with average improvements of over 40% in 3D RMS within the 24-hours prediction interval of the ultra-rapid products.

How to cite: Gou, J., Rösch, C., Shehaj, E., Chen, K., Kiani Shahvandi, M., Soja, B., and Rothacher, M.: Improving the Accuracy of GNSS Orbit Predictions using Machine Learning Approaches, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-1834, https://doi.org/10.5194/egusphere-egu22-1834, 2022.

EGU22-12032 | Presentations | G1.3

Towards the characterization of Slow Slip deformation by means of deep learning

Giuseppe Costantino, Sophie Giffard-Roisin, Mauro Dalla Mura, David Marsan, Mathilde Radiguet, and Anne Socquet

Detecting small Slow Slip Events (SSEs) is still an open challenge. The difficulty in revealing low magnitude events is related to their detection in the geodetic data, which must be improved either by employing more powerful equipment or by developing novel methods for the systematic discovery of small events, which can be crucial for the precise characterization of the slip spectrum. The improvement of the ability to detect small SSEs and the associated seismic response can play a decisive role in the understanding of the mechanics of active faults, remarkably subduction in which tremors cannot serve as a proxy for the slow slip or Episodic Tremor and Slip (ETS) is not regularly observed, making it necessary to provide new observations and methods to perceive potential bursts of slow slip.

Here we explore three Deep Learning–based strategies applied to GNSS data to characterize earthquakes and SSEs. Unlike seismic data, geodetic observations are crucial for dealing with SSEs, since they contain the required spatiotemporal information. Yet, since the low number of available labelled events (earthquakes or SSEs) producing significant displacement at GNSS station does not allow to adequately train Deep Learning models, we adopt synthetic geodetic data (Okada, 1985), obtained by generating events with uniformly distributed parameters. Thus, the model will not be biased towards the most numerous parameters, with a possibly stronger predictive power. The approach inspired by (van den Ende, Ampuero, 2020) was used for the characterization (i.e., estimation of epicentral location and magnitude), which associates geodetic time series with the location information of the GNSS stations. Yet, rearranging the geodetic displacement from GNSS time series into images can let Convolutional Neural Networks (CNN) to better account for the data spatial consistency, leading to more precise results. Furthermore, Transformers have also been tested with image time series of ground deformation. To assess the reliability of the tested methods, a magnitude threshold on the synthetic test set has been estimated, which depends on the depth and the hypocenter location of the event, showing a trade-off between the Signal-to-Noise (SNR) ratio and the relative position of the test events with respect to the GNSS network, revealing physical consistence. The results are also spatially consistent, as the location and magnitude errors tend to increase as the actual epicenters move offshore, with the location error showing a strong inverse proportionality on the magnitude. The employment of time series of deformation with Transformer networks lead to the best results and may allow us to better handle the noise complexity and to account for a spatio–temporal analysis of the ground deformation linked to SSE triggering. Nevertheless, the image–based model outperforms the other two on real data, showing evidence that the synthetic data does still not overlap with the real one, opening towards several perspectives. A more complex synthetic noise can be produced by allowing for synthetic data gaps and outliers (e.g., common modes), or machine learning–based denoising strategies can be envisioned to pre–process the data to improve the SNR ratio.

How to cite: Costantino, G., Giffard-Roisin, S., Dalla Mura, M., Marsan, D., Radiguet, M., and Socquet, A.: Towards the characterization of Slow Slip deformation by means of deep learning, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-12032, https://doi.org/10.5194/egusphere-egu22-12032, 2022.

EGU22-9105 | Presentations | G1.3

Modeling of Residual GNSS Station Motions through Meteorological Data in a Machine Learning Approach

Pia Ruttner, Roland Hohensinn, Stefano D'Aronco, Jan Dirk Wegner, and Benedikt Soja

Global Navigation Satellite System (GNSS) long-term residual height time series exhibit signals related to environmental influences. These can partly b explained through environmental surface loads, which are described with physical models. In this work, a model is computed to connect the GNSS residuals with raw meteorological parameters. A Temporal Convolutional Network (TCN) is trained on 206 GNSS stations in central Europe, and applied to 68 test stations in the same area. The resulting Root Mean Square (RMS) error reduction is on average 0.8% lower for the TCN modeled time series, compared to using physical models for the reduction. In a further experiment, the TCN is trained on the GNSS time series after reducing those by the surface loading models. The aim is a further increase of RMS reduction, which is achieved with 2.7% on average, resulting in an overall mean reduction of 28.6%. The results suggest that with meteorological features as input data, TCN modeled reductions are able to compete with reductions derived from physical models. Trained on the residuals reduced by environmental loading models, the TCN is able to slightly increase the overall reduction of variations in the GNSS station position time series.

How to cite: Ruttner, P., Hohensinn, R., D'Aronco, S., Wegner, J. D., and Soja, B.: Modeling of Residual GNSS Station Motions through Meteorological Data in a Machine Learning Approach, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-9105, https://doi.org/10.5194/egusphere-egu22-9105, 2022.

EGU22-405 | Presentations | G1.3

Ship-based GNSS ionospheric observations for the detection of tsunamis with deep learning

Yuke Xie, James Foster, Michela Ravanelli, and Mattia Crespi

Tsunami detection and forecasting require observations from open-ocean sensors. It is well known that tsunamis can generate internal gravity waves that propagate through the ionosphere from the earthquake center along with the tsunami wave. These disturbances can be detected by Global Navigation Satellite Systems (GNSS) receivers. The VARION (Variometric Approach for Real-Time Ionosphere Observation) algorithm has been successfully applied to detecting traveling ionospheric perturbations (TIDs) in several real-time scenarios, and it has also been successfully demonstrated that this algorithm is suitable for moving systems such as ship-based GNSS receivers. We present analyses of GNSS data collected from ships and examine the potential of a ship-based GNSS network for the ionospheric detection of tsunamis. 

In this project, we focused on the detection of tsunami signals from the TIDs using deep learning methods. Benefiting from the large amount of data from widely distributed GNSS permanent stations, we developed a prototype convolutional neural network for tsunami detection, achieving highly accurate prediction scores on the validation and test data. We used the observations coming from our 10-ship pilot network real-time GNSS system from the Pacific ocean to detect the TIDs related to the 2015 Illapel, Chile earthquake and tsunami. Using our algorithm in a post-processing mode we found that our ships successfully detected the ionospheric tsunami signal even though there was no detectable sea-surface height perturbation for the ship. Comparing the performance using our deep learning method with other anomaly detection approaches in a real-time scenario, we found that our approach works very efficiently with the pre-trained model. The results of our study, although preliminary, are very encouraging and we conclude that ships can be cost-effective real-time tsunami early-warning sensors. Given that there are thousands of existing ships in the Pacific Ocean, this is a promising opportunity to improve hazard mitigation.

How to cite: Xie, Y., Foster, J., Ravanelli, M., and Crespi, M.: Ship-based GNSS ionospheric observations for the detection of tsunamis with deep learning, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-405, https://doi.org/10.5194/egusphere-egu22-405, 2022.

EGU22-5408 | Presentations | G1.3

Machine Learning Approach for Forecasting Space Weather Effects in the Ionosphere with Uncertainty Quantification

Randa Natras, Benedikt Soja, Michael Schmidt, Marie Dominique, and Ayşe Türkmen

Space weather can cause strong sudden disturbances in the Earth’s ionosphere that can degrade the performance and reliability of Global Navigation Satellite System (GNSS) operations. To minimize such degradations, ionospheric effects need to be precisely and timely corrected by providing information of the spatially and temporally variable Total Electron Content (TEC). To obtain such corrections and early warning information of space weather events, we need to model the nonlinear space weather processes focusing on their impact on the ionosphere. Machine Learning (ML) models can learn nonlinear relationships from data to solve complex phenomena such as space weather. To interpret ML model results, it is crucial to know their quality and reliability. Quantifying the uncertainty of the ML results is an important step toward developing a “trustworthy” model, providing reliable results, and improving the model explainability.

This study presents a novel ML model to forecast the vertical TEC (VTEC) utilizing state-of-the-art supervised learning techniques and robustly assessing the uncertainty of the achieved results. The data are systematically analyzed, selected and pre-processed for optimal model learning, especially during space weather events. Results from our previous study (Natras and Schmidt, 2021) were improved in terms of data, ensemble modelling, and uncertainty quantification. The input data are expanded with additional parameters of the solar wind and the interplanetary magnetic field from OmniWeb and spectral irradiance measurements from the solar instrument LYRA onboard the spacecraft PROBA2 (Dominique et al., 2013). Also, new input features have been derived, such as daily differences, time derivatives, moving averages, etc. We applied ensemble modeling to combine diverse ML models based on different learning algorithms with different training data sets. The ensemble model enhances the performance of base learners and quantifies the uncertainty of results. This approach shows potential for forecasting VTEC in different ionospheric regions during quiet and storm periods, while providing the uncertainties of the forecasting results.

Keywords: Machine Learning, Space Weather, Ionosphere, Vertical Total Electron Content (VTEC), Forecasting, Uncertainty Quantification



Dominique, M., Hochedez, JF., Schmutz, W. et al. (2013): The LYRA Instrument Onboard PROBA2: Description and In-Flight Performance. Sol Phys 286, 21-42 https://doi.org/10.1007/s11207-013-0252-5

Natras, R., Schmidt, M. (2021): Ionospheric VTEC Forecasting using Machine Learning, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8907, https://doi.org/10.5194/egusphere-egu21-8907


How to cite: Natras, R., Soja, B., Schmidt, M., Dominique, M., and Türkmen, A.: Machine Learning Approach for Forecasting Space Weather Effects in the Ionosphere with Uncertainty Quantification, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-5408, https://doi.org/10.5194/egusphere-egu22-5408, 2022.

EGU22-7331 | Presentations | G1.3

Spatio-temporal Graph Neural Networks for Ionospheric TEC Prediction Using Global Navigation Satellite System Observables

Maria Kaselimi, Vassilis Gikas, Nikolaos Doulamis, Anastasios Doulamis, and Demitris Delikaraoglou

Precise modeling of the ionospheric Total Electron Content (TEC) is critical for reliable and accurate GNSS applications. 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 (temporal variability), latitude, longitude (spatial variability), solar and geomagnetic conditions. The propagation of the signals from GNSS (Global Navigation Satellite System) satellites throughout the ionosphere is strongly influenced by temporal changes and ionospheric regular or irregular variations. Here, we propose a deep learning architecture for the prediction of the vertical total electron content (VTEC) of the ionosphere based on GNSS data. 

The data used in many deep learning tasks until recently where mostly represented in the Euclidean space. However, geodesy studies data that have an underlying structure that is non-Euclidean space. Geospatial data are large and complex, as in the case of GNSS networks data, and their non- Euclidean nature has imposed significant challenges on the existing machine learning algorithms. The task of VTEC prediction is challenging mainly due to the complex spatiotemporal dependencies and an inherent difficulty in temporal forecasting. Spatial-temporal graph neural networks (STGNNs) aim to learn hidden patterns from spatial-temporal graphs. The key idea of STGNNs is to consider spatial and temporal dependency at the same time. Spatial Dependency: Assuming a network of permanent stations of International GNSS Service (IGS), each station represents a node of the graph, and their Euclidean distance is used to formulate the set of edges of the graph. Thus, we achieve exchange between nodes and their neighbors. Temporal dependency: The graph operates in a dynamic environment. Thus, we leverage the recurrent neural networks (RNNs) to model the temporal dependency. As a result, time series of VTEC data can be predicted to future epochs. Solar and geomagnetic indices are formulated as node attributes and are also present temporal variability.

Topics to be discussed in the study include the design of the graph neural network structure, the training methods exploiting steepest descent algorithms, data analysis, as well as preliminary testing results of the VTEC predictions as compared, with state-of-the-art graph architectures.

How to cite: Kaselimi, M., Gikas, V., Doulamis, N., Doulamis, A., and Delikaraoglou, D.: Spatio-temporal Graph Neural Networks for Ionospheric TEC Prediction Using Global Navigation Satellite System Observables, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-7331, https://doi.org/10.5194/egusphere-egu22-7331, 2022.

EGU22-2702 | Presentations | G1.3

Development of a global model for zenith wet delays based on the random forest approach

Qinzheng Li, Johannes Böhm, Linguo Yuan, and Robert Weber

Tropospheric delays have been a major error source for space geodetic techniques and the performance of their modeling is significantly limited due to the high spatiotemporal variability of the moisture in the lower atmosphere. In this study, tropospheric zenith wet delay (ZWD) modeling was realized based on the machine learning (random forest approach, RF) and using 10 years (2010-2019) of radiosonde measurements at 586 globally distributed stations. Subsequently, the ZWD modeling accuracy was validated based on the sounding profiles across the globe for the year 2020. We find that ZWD modeling accuracy is significantly improved by taking account meteorological parameters in the functional formulation, especially for surface water vapor pressure. When surface meteorological data are available, the RF-based ZWD models with meteorological parameterization can achieve an overall accuracy of 2.9 cm and the bias close to zero across the globe, which clearly outperforms current empirical models, such as the GPT3, or other models based on surface meteorological measurements. From the analyses of spatial characteristics of the ZWD accuracy, it can be concluded that the RF-based ZWD models especially mitigate the systematic biases in the regions with monsoon climate and tropical rainforest climate types. 

How to cite: Li, Q., Böhm, J., Yuan, L., and Weber, R.: Development of a global model for zenith wet delays based on the random forest approach, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-2702, https://doi.org/10.5194/egusphere-egu22-2702, 2022.

EGU22-4531 | Presentations | G1.3

Machine learning and meteorological data for spatio-temporal prediction of tropospheric parameters

Laura Crocetti, Benedikt Soja, Grzegorz Kłopotek, Mudathir Awadaljeed, Markus Rothacher, Linda See, Rudi Weinacker, Tobias Sturn, Ian McCallum, and Vicente Navarro

Radio signals transmitted by Global Navigation Satellite System (GNSS) satellites propagate through the atmosphere before being received on Earth. Thereby, the signal is delayed and tropospheric parameters can be estimated. The good global coverage of GNSS receivers, combined with the high temporal resolution and the high accuracy, make GNSS a suitable tool for studies on the atmosphere.

Atmospheric delays are differentiated into a zenith hydrostatic (ZHD) and a non-hydrostatic, or zenith wet delay (ZWD). The hydrostatic part has a larger contribution (causing a delay of roughly 2.4 meters in the zenith direction) but can be modeled with sufficient accuracy using analytical methods. The ZWD has a smaller contribution (causing a delay between 0 to 40 centimeters) and depends mainly on the water vapour content in the atmosphere. However, due to the variable nature of water vapour, the ZWD is difficult to model and is therefore typically estimated. Its quantification is essential since it drives weather systems and climate change to a great extent. For many applications, such as weather forecasting or positioning using low-cost GNSS receivers such as smartphones, global real-time monitoring or even predictions of ZWD would be required and be beneficial.

In the last decade, machine learning (ML) algorithms have gained a lot of interest and are successfully utilized in many different fields. Thereby, ML algorithms have proven to be able to efficiently process and combine large amounts of data and solve problems of various kinds.

This motivated us to investigate the feasibility of ML algorithms for the prediction of tropospheric parameters, in particular ZWD, with the help of meteorological data such as the water vapour content. The work aims to develop a global model capable of predicting ZWD in space and time. Therefore, different ML algorithms are used to train a model based on meteorological features. The performance of the utilized algorithms is evaluated based on commonly used performance metrics, such as Root Mean Squared Error (RMSE) and R².

Preliminary investigations are carried out utilizing 3000 GNSS stations distributed over Europe. The performance of various ML methods, such as Linear Regression methods, Random Forest, (Extreme) Gradient Boosting, and Multilayer Perceptron is compared. Furthermore, different feature combinations, as well as training sample sizes are investigated. It is revealed that linear methods are not able to properly reflect the observations. Instead, our Random Forest approach provides, so far, the highest model accuracy with an RMSE of 1.7 centimeters and an R² value of 0.88.

How to cite: Crocetti, L., Soja, B., Kłopotek, G., Awadaljeed, M., Rothacher, M., See, L., Weinacker, R., Sturn, T., McCallum, I., and Navarro, V.: Machine learning and meteorological data for spatio-temporal prediction of tropospheric parameters, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-4531, https://doi.org/10.5194/egusphere-egu22-4531, 2022.

G1.5 – Recent Developments in Geodetic Theory

EGU22-2429 | Presentations | G1.5

Global gravity field modelling by the finite element method involving mapped infinite elements.

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

We present a numerical approach for solving the oblique derivative boundary value problem (BVP) based on the finite element method (FEM) with mapped infinite elements. To that goal, we formulate the BVP consisting of the Laplace equation in 3D semi-infinite domain outside the Earth which is bounded by the approximation of the Earth's surface where the oblique derivative boundary condition is given. At infinity, regularity of the disturbing potential is prescribed. As the numerical method, we have implemented the FEM with mapped infinite elements, where the computational domain is divided into
two centrical parts, one meshed with finite elements and one with infinite ones. In numerical experiments, we firstly test a convergence of the proposed numerical scheme and then we deal with global gravity field modelling using EGM2008 data. To perform such numerical experiments, we create a special discretization of the Earth's surface to fulfil the conditions that arise from correct geometrical properties of finite elements. Then a reconstruction of EGM2008 aims to indicate efficiency of the presented numerical approach.

How to cite: Macák, M., Minarechová, Z., Čunderlík, R., Mikula, K., and Tomek, L.: Global gravity field modelling by the finite element method involving mapped infinite elements., EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-2429, https://doi.org/10.5194/egusphere-egu22-2429, 2022.

Spherical harmonic transforms aiming at degrees as high as a few tens of thousands are vital in geodesy to improve our knowledge of the Earth's gravity field.  A prominent example is spectral gravity forward modelling of topographic masses, which is able to approximate fine gravity field structures up to the sub-km-level and beyond (degree ~20,000 and higher).  Driven by these applications, we have developed CHarm, a C library to perform spherical harmonic transforms.  CHarm is centered around (but not limited to) high-degree expansions, say, well beyond degree 2700.  Its goal is to be numerically stable on the one hand, while achieving reasonable computational efficiency with minimized memory requirements on the other hand.  Supported are surface spherical harmonic analysis and solid (3D) synthesis, both with point and area-mean data values.  Standard quadratures due to Gauss--Legendre and Driscoll--Healy are implemented for exact harmonic analysis of point data values.  The library can be compiled in double precision or, in case higher numerical accuracy is sought, in quadruple precision.  For efficient FFT transforms along the latitude parallels, the state-of-the-art FFTW library is employed to boost the performance.  Unique to CHarm is a routine integrating solid spherical harmonic expansions on band-limited undulated surfaces.  It can deliver, for instance, area-mean potential values on planetary surfaces.  Available are also routines to compute Fourier coefficients of Legendre functions and integrals of a product of two spherical harmonics or of two Legendre functions over a restricted domain.  To utilize the power of multicore processors, CHarm can be compiled with enabled parallelization on shared-memory architectures (OpenMP).  A significant effort is put into the documentation of the library (HTML, PDF) to allow its easy use.

In this contribution, we discuss the motivation behind the development of CHarm, explain its main functionalities and demonstrate some usage case studies.  Within a high-degree closed-loop synthetic environment, we assess the numerical accuracy, the computational speed and the memory management of the library.  A discussion on the future work closes the contribution.  CHarm is available at https://edisk.cvt.stuba.sk/~xbuchab/charm/doc/index.html.

How to cite: Bucha, B.: CHarm: C library to work with spherical harmonics up to almost arbitrarily high degrees, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-11206, https://doi.org/10.5194/egusphere-egu22-11206, 2022.

EGU22-1880 | Presentations | G1.5

Modelling the local gravity field by rectangular harmonics with numerical validations

Georgios Panou and Romylos Korakitis

For the representation of the Earth’s global gravity field, Spherical Harmonics (SH) are widely used in geodetic community. On the other hand, for the representation of a local or regional gravity field, Spherical Cap Harmonics (SCH) and Rectangular Harmonics (RH) are alternative techniques with important advantages over SH. Although SCH are extensively presented in literature, RH are found in very few applications, especially of the gravity field. This work derives different functional forms of the disturbing potential, outside of the Earth’s masses, using RH. Also, the necessary transformation from geocentric into local rectangular coordinates is presented. The Rectangular Harmonic Coefficients (RHC) of the different mathematical models of the disturbing potential can be estimated through a least squares’ adjustment process. In order to select the best mathematical model, numerical experiments, based on data generated from a geopotential model, are conducted and the results are validated. Then, for the best model of the disturbing potential, its functionals (gravity anomaly and disturbance, height anomaly, geoid undulation and deflection of vertical) are given in terms of RHC. We conclude that RH representations are both suitable and convenient for the modelling of the local or regional gravity field.

How to cite: Panou, G. and Korakitis, R.: Modelling the local gravity field by rectangular harmonics with numerical validations, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-1880, https://doi.org/10.5194/egusphere-egu22-1880, 2022.

Gravity forward modelling is one of the fundamental topics in geodesy and geophysics. A spherical shell is a commonly used reference model among the mass bodies for the spatial domain of gravity forward modelling. The reason is that it has simple analytical expressions for gravitational effects (e.g. gravitational potential (GP), gravity vector (GV), gravity gradient tensor (GGT), and gravitational or gravity curvatures (GC)). The finer grid size will need more computation time when adopting the numerical strategy of a spherical shell discretized using tesseroids. This contribution presents the simpler analytical expressions for the GV and GGT of a homogeneous zonal band. The new analytical formula of the GC of a homogeneous zonal band is derived. The computation time and relative errors of the GP, GV, GGT, and GC between a spherical zonal band and a spherical shell discretized using tesseroids are quantitatively investigated with different grid sizes. Numerical results reveal that the computation time of a spherical zonal band discretized using tesseroids is about 180/n (i.e. n is the grid size) times less than that of a spherical shell discretized using tesseroids in double and quadruple precision. The relative errors' mean values of the GP, GV, GGT, and GC for a spherical zonal band discretized using tesseroids are smaller than those for a spherical shell discretized using tesseroids. In short, the benefit of a spherical zonal band in comparison with a spherical shell discretized using tesseroids regarding both the computation time and errors is confirmed numerically. The numerical approach of a spherical zonal band discretized using tesseroids can be applied instead of the classical numerical strategy in numerical evaluation of a tesseroid or other spherical mass bodies in gravity field modelling. This study is supported by the project funded by China Postdoctoral Science Foundation (Grant No. 2021M691402).

How to cite: Deng, X.-L.: A comparison of gravitational effects between a spherical zonal band and a spherical shell discretized using tesseroids, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-875, https://doi.org/10.5194/egusphere-egu22-875, 2022.

The Laplace operator has a relatively simple structure in terms of spherical or ellipsoidal coordinates which are frequently used in geodesy. However, in treating the geodetic boundary value problem the physical surface of the Earth substantially differs from a sphere or an oblate ellipsoid of revolution, even if optimally approximated. Therefore, an alternative between the boundary complexity and the complexity of the coefficients of the Laplace partial differential equation governing the solution is discussed. The situation is more convenient in a system of general curvilinear coordinates such that the physical surface of the Earth (smoothed to a certain degree) is imbedded in the family of coordinate surfaces. The idea is close to concepts followed also in other branches of engineering and mathematical physics. A transformation of coordinates is applied. Subsequently, tensor calculus is used to express the Laplace operator in the system of new coordinates. The structure of the Laplacian is more complicated now, but in a sense it represents the topography of the physical surface of the Earth. Finally, 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 where useful and possible, modified by means of integration by parts. The iteration steps and their convergence are discussed and interpreted, numerically and in terms of functional analyses.


How to cite: Holota, P. and Nesvadba, O.: Structure of the Laplace operator, geometry of the Earth’s surface and successive approximations in the solution of the geodetic boundary value problem, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-9362, https://doi.org/10.5194/egusphere-egu22-9362, 2022.

EGU22-9610 | Presentations | G1.5

Combination of integral transforms by spectral weighting – an overview  

Martin Pitoňák, Michal Šprlák, and Pavel Novák

Geodetic boundary-value problems (BVPs) and their solutions represent an important tool for describing and modelling potential fields such as the Earth’s gravitational field. Solutions to spherical geodetic BVPs lead to spherical harmonic series or surface convolution integrals with Green’s kernel functions. New BVPs have recently been formulated reflecting development of sensors. BVPs have been also developed for observables measured by kinematic sensors on moving platforms, i.e., airplanes and satellites. Solutions to BVPs for higher-order derivatives of the gravitational potential as boundary conditions are represented by multiple integral transforms. For example, solutions to gravimetric, gradiometric and gravitational curvature BVPs are represented by two, three and four integral transforms, respectively. Theoretically, each of the nine transforms provides an identical value of the gravitational potential, but practically, when discrete noisy observations are exploited, they provide different estimates. Combination of solutions to the above mentioned geodetic BVPs in terms of surface integrals with Green’s kernel functions by a spectral method is investigated in this contribution. It is assumed that the first-, second- and third-order directional derivatives of the Earth’s gravitational potential can be measured at the satellite altitude. They are downward continued to the Earth’s surface and converted into height anomalies. Thus, the spectral combination method serves in our numerical procedure also as the downward continuation technique. The spectral combination method requires deriving corresponding spectral weights for all nine estimators. A generalized formula for evaluation of spectral weights for the estimators is formulated. Properties of spectral combinations are investigated in both spatial and spectral domains.

How to cite: Pitoňák, M., Šprlák, M., and Novák, P.: Combination of integral transforms by spectral weighting – an overview  , EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-9610, https://doi.org/10.5194/egusphere-egu22-9610, 2022.

EGU22-10246 | Presentations | G1.5

Some remarks about orthometric and normal height systems

Viktor Popadyev and Samandar Rakhmonov

Theoretically, solving the geodetic boundary-value problems, we don't need any height systems to include them into integral equations. E.g. so called telluroid and the normal gravity on it are determined not by the normal height itself, but by the curvilinear coordinates of the points with the normal geopotential difference equal to the real geopotential difference. The length of the normal forceline, determining normal height value, is secondary. Similarly, gravity anomalies include normal gravity, determined also by the same geopotential difference in normal field.

Practically, using of the measured geopotential differences in geodesy is uncomfortable, since the corresponding levelling staff would have the variable step of the measuring scale, depending on the position of the point on the earth's surface and in space. Comparison and standardization of that staff is impossible. Then all the height systems we introduce to convert the geopotential values into the linear measure are non-optimal.

To determine the geoid at the same time with the orthometric height, the three only practically ways are possible (first fig.).


First way is the vertical spirit levelling, when the gravimeter is lowered into a vertical well and readings are taken from it at equal distances (a). The point with the geopotential number equal to zero will show us the point “on” the geoid, the rope length is the orthometric height. The second way is similar to the first with the spirit levelling along the paths on the walls of the quarry (b). The third way is a mechanical construction of a tunnel, the floor of which starts from the sea level and is built at a constant zero elevation (c).

Even if we know the upper crust mass distribution (with accuracy we need we must consider it completely unknown), the difficult volume integrals must be calculated for any benchmark.

The normal height is determined when M. S. Molodensky (1945) formulate his integro-differential equation (p. 55 of the English translation): “we compute the [curvilinear] coordinate q corresponding to the known potential of the real Earth..., neglecting the disturbing potential and the deflection of the vertical – an obvious first approximation”. In other words we may reformulate this, that the normal height is the ortometric height in the normal field. Moreover, the role of the geoid in normal field plays the level ellipsoid, not the quasigeoid (second fig.)!

In general, we don't need in “quasigeoid” in any physical or geometrical meaning, e.g. for the height measuring, as a “brother” of the geoid or in the BVP solving. So, strictly speaking, the quasigeoid is not a “vertical reference surface”, and the normal heights they are counted/measured not from ellipsoid nor from quasigeoid. The height mark is calculated and assigned as a “passport value” to each point of the earth’s surface.

How to cite: Popadyev, V. and Rakhmonov, S.: Some remarks about orthometric and normal height systems, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-10246, https://doi.org/10.5194/egusphere-egu22-10246, 2022.

EGU22-6136 | Presentations | G1.5

New realization for European vertical reference system; a first attempt to include the hydrodynamic leveling data

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

A study by Afrasteh et al. (2021) has shown that combining model-based hydrodynamic leveling data with data of the Unified European Leveling Network (UELN) has great potential to improve the quality of the European Vertical Reference Frame (EVRF). In the current study, we made our first attempt to actually include the model-based hydrodynamic leveling data as new observations and compute a new realization for the European Vertical Reference System (EVRS). Please note, at this stage our results are provisional and should not be considered as an official realization for EVRS. For the spirit leveling data, we have used the potential differences from UELN, including the third leveling epoch in Great Britain. To generate the model-based hydrodynamic leveling data, 3D DCSM-FM hydrodynamic model that covers the North-east Atlantic Ocean including the North Sea is used to simulate the mean water level for January 1997 to January 2019. The tide gauges records covering the same period have been collected for the North Sea countries to compute the observed water level time series. The difference between observation- and the model-derived mean water level is used to generate the noise model for the hydrodynamic leveling data. We observe an improvement in the precision of the estimated heights in all coastal countries surrounding the 3D DCSM-FM domain. Moreover, our results show that adding model-based hydrodynamic leveling connections significantly reduces the south-north tilt in Great Britain, comparing the EVRF heights with the EGG2015 geoid model. Such a tilt in the British vertical datum, which is caused by a systematic error in the British leveling observations, has been reported in several studies. Our results show that using the model-based hydrodynamic leveling data could solve this problem in the British spirit leveling-based network and provide a stronger tie between Great Britain and other North Sea countries.


Y. Afrasteh, D. C. Slobbe, M. Verlaan, M. Sacher, R. Klees, H. Guarneri, L. Keyzer, J. Pietrzak, M. Snellen, and F. Zijl. The potential impact of hydrodynamic leveling on the quality of the European vertical reference frame. Journal of Geodesy, 95(8), 2021. doi: 10.1007/s00190-021-01543-3.

How to cite: Afrasteh, Y., Slobbe, C., Verlaan, M., Sacher, M., Klees, R., Guarneri, H., Keyzer, L., Pietrzak, J., Snellen, M., and Zijl, F.: New realization for European vertical reference system; a first attempt to include the hydrodynamic leveling data, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-6136, https://doi.org/10.5194/egusphere-egu22-6136, 2022.

We present nonlinear diffusion filtering of the GOCE-based satellite-only mean dynamic topography (MDT) based on the geodesic mean curvature flow (GMCF). GMCF represents a curvature-driven diffusion filtering, where the processed data are considered as a set of specific contour lines. A properly designed evolution of these contour lines corresponds to smoothing of the processed data. A main advantage is an adaptive smoothing of the contour lines while respecting significant values of gradients. This property can be beneficial for filtering the MDT models since it allows preserving important gradients along main ocean surface currents. We present numerical solution of the GMCF-based diffusion partial differential equations using the finite volume method (FVM) on regular grids. The derived numerical scheme is applied for filtering the satellite-only MDT models obtained as a combination of the DTU21_MSS model and the recent GOCE-based satellite-only global geopotential models. Then the filtered MDT models are used to derive velocities of the surface geostrophic currents over oceans.

How to cite: Čunderlík, R., Kollár, M., and Mikula, K.: Surface geostrophic currents derived from the nonlinear diffusion filtering of the GOCE-based satellite-only MDT using the geodesic mean curvature flow, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-2553, https://doi.org/10.5194/egusphere-egu22-2553, 2022.

The secular change in the flattening of Earth and its effect on global tectonics is a subject still to be investigated.

Tidal friction causes a constant despinning of the rotation of Earth. It happens at a rate of Δω = – (5.4 ± 0.5) ∙ 10-22s-2, resulting in a change of the length of day with ∆LOD = (2.3 ± 0.1) ms/century (Stacey, 1992). The slowly decreasing rotational speed creates a change in the flattening of the Earth, that produces a latitude dependent stress field. The meridional stress component is always positive (i.e. tensional), while the azimuthal stress is negative (i.e. compressional) from the equator, up to the critical latitudes (~ ±48.2°), and positive poleward. This means two major tectonic provinces: in the equatorial region a strike-slip province and towards the poles, a normal fault province (Denis & Varga, 1990).

From the 1960s reliable seismological catalogues are available. ISC GEM Catalogue contains re-computed moment magnitude (Mw) values, what is essential for calculating the released seismic energy, since at higher magnitudes, it doesn’t go into saturation. One can obtain the energy released by an event with the formula logE = 5.2 + 1.44Mw (Båth, 1966). Based on this catalogue, a 52-year period with moment magnitudes higher than 5.8, all in all 8799 events were used.

Our study shows that the effect of the despun Earth is reflected in the latitudinal distribution of earthquake energy, which is symmetric with respect to the equator and there are clear maxima at mid-latitudes. The distribution of seismic energy released by either normal fault or strike-slip earthquakes also follow a pattern previously described. Especially on the northern hemisphere normal fault events occur dominantly towards the poles while strike-slip earthquakes tend to happen at lower latitudes. We can conclude that tidal friction actually creates the proposed stress field on Earth, and is visible if we observe how global seismicity behaves with respect to latitude.


Båth, M. (1966). Earthquake energy and magnitude. Physics and Chemistry of the Earth, 7, 115-165.

Denis, C., Varga, P. (1990). Tectonic consequences of the Earth’s variable rotation, In: Brosche P, Sündermann J (eds.) Earth rotation from eons to days. Springer, pp. 146-162.

Stacey, F. D. (1992). Physics of the Earth, Brookfield Press, Australia, ISBN 0-646-09091-7.

How to cite: Fodor, C. and Varga, P.: Relationship between temporal variation of Earth's flattening and spatial distribution of global earthquake energy, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-2608, https://doi.org/10.5194/egusphere-egu22-2608, 2022.