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

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

How to cite: Macák, M., Minarechová, Z., Čunderlík, R., and Mikula, K.: Stable finite element method for solving the oblique derivative boundary value problems in geodesy, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-2614, https://doi.org/10.5194/egusphere-egu21-2614, 2021.

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

How to cite: Holota, P. and Nesvadba, O.: Laplacian structure mirroring surface topography in determining the gravity potential by successive approximations, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-11729, https://doi.org/10.5194/egusphere-egu21-11729, 2021.

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

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

How to cite: Albayrak, M., Hirt, C., Guillaume, S., Shum, C., Bevis, M., Zeray Öztürk, E., and Bildirici, I. Ö.: Validations of Three Global Gravity Field Models Using the QDaedalus System Observed Astrogeodetic Vertical Deflections in the Munich Region, Germany, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-128, https://doi.org/10.5194/egusphere-egu21-128, 2021.

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

How to cite: Pitoňák, M., Šprlák, M., Ophaug, V., Omang, O., and Novák, P.: Validation of calibrated GOCE gravity gradients GRD_SPW_2 by least-squares spectral weighting   , EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1112, https://doi.org/10.5194/egusphere-egu21-1112, 2021.

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

How to cite: Afrasteh, Y., Slobbe, C., Verlaan, M., Sacher, M., Klees, R., Guarneri, H., Keyzer, L., Pietrzak, J., Snellen, M., and Zijl, F.: Towards tide gauges selection for model-based hydrodynamic leveling connections; with application to assess the potential impact on the quality of the European Vertical Reference Frame, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-12598, https://doi.org/10.5194/egusphere-egu21-12598, 2021.

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

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

How to cite: Küreç Nehbit, P., Glaser, S., Balidakis, K., Sakic, P., Heinkelmann, R., Schuh, H., and Konak, H.: Improving the sensitivity levels generated from hypothesis testing by combining VLBI with GNSS data, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3116, https://doi.org/10.5194/egusphere-egu21-3116, 2021.

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

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

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

Reference: Varga P., Fodor Cs., 2021. About the energy and age of the plate tectonics, Terra Nova. (in print) https://doi.org/10.1111/ter.12518

How to cite: Fodor, C. and Varga, P.: Modelling moving force of tectonic plates with the use of length of day variation, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8401, https://doi.org/10.5194/egusphere-egu21-8401, 2021.

How to cite: Simons, F. J. and Reuber, G. S.: Investigation of a Coupled Deterministic Inversion for the Interior of the Earth by using Gravity-Anomaly, Acoustic-Wavefield and Geodetic Velocity measurements, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-6648, https://doi.org/10.5194/egusphere-egu21-6648, 2021.

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

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

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

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

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

How to cite: Uieda, L., Soler, S. R., Pesce, A., Perozzi, L., and Wieczorek, M. A.: Harmonica and Boule: Modern Python tools for geophysical gravimetry, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8291, https://doi.org/10.5194/egusphere-egu21-8291, 2021.

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

How to cite: Seoane, L., Ramillien, G., Darrozes, J., Frappart, F., Rouxel, D., Schmitt, T., and Salaun, C.: Seafloor topography variations mapped by regional gravity tensor analysis , EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-12570, https://doi.org/10.5194/egusphere-egu21-12570, 2021.

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

How to cite: Xie, Y., Shen, W., Han, J., and Deng, X.: Determining the height of Mount Everest using the shallow layer method, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1886, https://doi.org/10.5194/egusphere-egu21-1886, 2021.

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

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

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

How to cite: Ebbing, J., Szwillus, W., and Dilixiati, Y.: A Bayesian framework for simultaneous determination of susceptibility and magnetic thickness from magnetic data, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-10940, https://doi.org/10.5194/egusphere-egu21-10940, 2021.

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

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

How to cite: Brown, W., Beggan, C., Hammer, M., Finlay, C., and Cox, G.: Isolating internal secular variation in Geomagnetic Virtual Observatory time series using Principle Component Analysis, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1082, https://doi.org/10.5194/egusphere-egu21-1082, 2021.

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

How to cite: Gerhards, C., Kegeles, A., and Menzel, P.: Nonuniqueness and Uniqueness for Inverse Magnetization Problems, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3359, https://doi.org/10.5194/egusphere-egu21-3359, 2021.

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

How to cite: Faucher, F., Scherzer, O., and de Hoop, M. V.: Seismic imaging combining active and passive sources using distributed acoustic sensing, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-15142, https://doi.org/10.5194/egusphere-egu21-15142, 2021.

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

How to cite: Vishwakarma, B. D., Ziegler, Y., Royston, S., and Bamber, J. L.: A novel data-driven method to estimate GIA signal from Earth observation data, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8876, https://doi.org/10.5194/egusphere-egu21-8876, 2021.

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

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

How to cite: Turen, Y., Sanli, D. U., and Erol, T.: The quality of velocities from GNSS campaign measurements when gaps in data exist, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-7421, https://doi.org/10.5194/egusphere-egu21-7421, 2021.

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

How to cite: Klos, A., Kusche, J., Lenczuk, A., Leszczuk, G., and Bogusz, J.: Benchmarking GPS stations: an improved way to identify the GPS sensitivity, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-504, https://doi.org/10.5194/egusphere-egu21-504, 2021.

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

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

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

How to cite: Strasser, S., Banville, S., Kvas, A., Loyer, S., and Mayer-Gürr, T.: Comparison and generalization of GNSS satellite attitude models, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-7825, https://doi.org/10.5194/egusphere-egu21-7825, 2021.

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

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

How to cite: Villiger, A., Dach, R., Prange, L., and Jäggi, A.: Extension of the repro3 ANTEX file with BeiDou and QZSS satellite antenna pattern, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-6287, https://doi.org/10.5194/egusphere-egu21-6287, 2021.

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

How to cite: Kröger, J., Kersten, T., Breva, Y., and Schön, S.: Impact of Multi-GNSS Antenna-Receiver Calibrations in the Coordinate Domain, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8507, https://doi.org/10.5194/egusphere-egu21-8507, 2021.

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

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

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

How to cite: Zheng, H., Chang, H., Yuan, Y., Wang, Q., Li, Y., and Li, X.: An efficient solution for fast generation of multi-GNSS real-time products, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8306, https://doi.org/10.5194/egusphere-egu21-8306, 2021.

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

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

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

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

How to cite: Kazmierski, K., Zajdel, R., and Sośnica, K.: Multi-GNSS real-time orbit and clock quality changes over time , EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-7160, https://doi.org/10.5194/egusphere-egu21-7160, 2021.

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

How to cite: Diamantidis, P.-K., Kłopotek, G., Haas, R., and Johansson, J.: Assessment of geodetic products from Multi-GNSS analyses at the Onsala site, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-14343, https://doi.org/10.5194/egusphere-egu21-14343, 2021.

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

How to cite: Geng, J., Pan, Y., Yang, S., and Li, P.: Combining multi-GNSS phase bias products for improved undifferenced ambiguity resolution, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-2531, https://doi.org/10.5194/egusphere-egu21-2531, 2021.

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

How to cite: Wang, B., Li, X., Huang, J., Feng, G., Lv, H., Han, X., Zhong, Y., and Li, X.: Multi-frequency and multi-GNSS PPP-RTK for vehicle navigation in urban environments, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9039, https://doi.org/10.5194/egusphere-egu21-9039, 2021.

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

How to cite: Stressler, B., Bilich, A., Ogaja, C., and Heck, J.: Multi-GNSS Single-Difference Baseline Processing at NGS with newly developed M-PAGES software, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-5556, https://doi.org/10.5194/egusphere-egu21-5556, 2021.

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

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

How to cite: Durmus, F. C. and Erdogan, B.: The Effect of the State-of-the-Art Mapping Functions on Precise Point Positioning, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9976, https://doi.org/10.5194/egusphere-egu21-9976, 2021.

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

How to cite: Erol, S., Mutlu, B., Erol, B., and Çevikalp, M. R.: Static and Pseudo-Kinematic PPP-AR Performance in Antarctic Region, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-14144, https://doi.org/10.5194/egusphere-egu21-14144, 2021.

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

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

How to cite: Saraçoğlu, A. and Şanlı, D. U.: Climatic Effects on GPS PPP Accuracy, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8172, https://doi.org/10.5194/egusphere-egu21-8172, 2021.

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

How to cite: Paziewski, J., Fortunato, M., Mazzoni, A., Odolinski, R., Li, G., Debelle, M., Warnant, R., and Gong, X.: The quality analysis of GNSS observations tracked by Android smart devices and positioning performance assessment, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-334, https://doi.org/10.5194/egusphere-egu21-334, 2021.

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

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

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

How to cite: Glaner, M. F., Gutlederer, K., and Weber, R.: Potential and limitations of processing smartphone GNSS raw observation data in PPP, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3345, https://doi.org/10.5194/egusphere-egu21-3345, 2021.

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

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

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

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

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

Willi D., GNSS receiver synchronization and antenna calibration, PhD Thesis, ETH Zürich, 2019, https://www.research-collection.ethz.ch/handle/20.500.11850/308750

How to cite: Moeller, G., Piringer, F., Pérez Ortega, M., Presl, R., and Rothacher, M.: Absolute phase center calibration of low-cost GNSS patch antennas – Is it worth the effort?, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-5700, https://doi.org/10.5194/egusphere-egu21-5700, 2021.

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

How to cite: Zus, F. and Wickert, J.: Higher-Order Ionospheric Corrections derived from realistic electron density fields , EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-824, https://doi.org/10.5194/egusphere-egu21-824, 2021.

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

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

How to cite: Sieradzki, R. and Paziewski, J.: Statistical investigations of polar patch occurrence during high solar activity, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-7201, https://doi.org/10.5194/egusphere-egu21-7201, 2021.

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

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

How to cite: Duman, H. and Şanlı, D. U.: Heteroskedasticity between GNSS time-series repeatabilities and noise magnitudes, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-4702, https://doi.org/10.5194/egusphere-egu21-4702, 2021.

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

How to cite: Fazilova, D., Magdiev, H., and Sichugova, L.: GNSS network of Uzbekistan: achievements, prospects and challenges, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-842, https://doi.org/10.5194/egusphere-egu21-842, 2021.

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

Keywords: Land subsidence, GPS, InSAR, Gediz Graben

How to cite: Gül, Y., Duman, H., Hastaoğlu, K. Ö., Poyraz, F., Tiryakioğlu, İ., Erdoğan, H., Doğan, A., and Güler, S.: The first result of geodetic implications on intra-graben subsidence along the eastern part of the Gediz graben, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-12489, https://doi.org/10.5194/egusphere-egu21-12489, 2021.

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

How to cite: Kaselimi, M., Doulamis, N., and Delikaraoglou, D.: Recurrent Neural Networks for Ionospheric Time Delays Prediction Using Global Navigation Satellite System Observables, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-10267, https://doi.org/10.5194/egusphere-egu21-10267, 2021.

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

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

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

How to cite: Kiani Shahvandi, M. and Soja, B.: A new spatio-temporal graph neural network method for the analysis of GNSS geodetic data, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-545, https://doi.org/10.5194/egusphere-egu21-545, 2021.

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

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

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

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

How to cite: Gou, J., Kiani Shahvandi, M., Hohensinn, R., and Soja, B.: Ultra-short-term prediction of LOD using LSTM neural networks, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-2308, https://doi.org/10.5194/egusphere-egu21-2308, 2021.

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

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

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

How to cite: Rhyner, S., Jordan, D., Salvini, D., and Dach, R.: Application of Machine Learning for Evaluation of GNSS Processing Protocols, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-7178, https://doi.org/10.5194/egusphere-egu21-7178, 2021.

Multi-temporal interferometric synthetic aperture radar (MT-InSAR) technique has been effectively used to monitor deformation events over the last two decades. The processing steps generally involve pixel selection, phase unwrapping and displacement estimation. The pixel selection step takes most of the processing time, while a reliable method for phase unwrapping is still not available. This study demonstrates the effect of using deep learning (DL) architectures for MT-InSAR processing. The architectures are applied to reduce time computations and further to improve the quality of pixel selection. Some promising results for pixel selection have been shown earlier with the proposed architecture. In this study, we investigate the performance of the proposed architectures on newer datasets with larger temporal interval. To achieve this objective, the models are retrained with interferometric stacks covering larger temporal period and large time steps (for better estimation of interferometric phase components). Pixel selection results are compared with those obtained using open access algorithms used for MT-InSAR processing.

How to cite: Tiwari, A., Narayan, A. B., and Dikshit, O.: A deep learning approach for efficient multi-temporal interferometric synthetic aperture radar (MT-InSAR) processing, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-12784, https://doi.org/10.5194/egusphere-egu21-12784, 2021.

The Rudzki inversion gravimetric reduction maps the Earth’s topographic masses inside the geoid in such a way that the inverted masses produce exactly the same potential as the topographic masses on the geoid. In other words, the indirect effect to the geoid is zero so that its computation is not needed. This paper proposes a geoid computation scheme that combines the Bouguer reduction and Rudzki inversion reduction under the spherical approximation and constant density assumption. The proposed computation scheme works with the Bouguer gravity field that is smooth and theoretically legitimate for the harmonic downward continuation. Then the Bouguer potential is compensated by the potential of the inverted masses, ensuring zero indirect effect to the geoid. The direct effect of the Rudzki inversion gravimetric reduction is added to the Bouguer gravity disturbance, resulting in the reduced gravity disturbance for geoid computation. A spherical harmonic reference gravity model is also developed so that the kernel modification/truncation can be applied to the Hotine integral. If the density of the topographic masses becomes available, the effect of density anomalies can be computed separately and added to the geoid computed under the constant density assumption. The combined ellipsoidal effect of the Bouguer and Rudzki inversion reduction should be insignificant because of the canceling effect between them.

How to cite: Wang, Y. M.: The Bouguer-Rudzki-Hotine scheme for geoid computations , EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-10202, https://doi.org/10.5194/egusphere-egu21-10202, 2021.

Topographic reduction is one of the most imperative steps in geoid modeling, where the gravity field inside the masses needs to be modeled. This is quite challenging because no one can measure gravity inside the topography at a desired resolution (only a very limited number of borehole gravity measurements are available in the whole world). Therefore, topographic mass modeling is usually treated either by the residual terrain modeling (RTM) or by the Helmert’s 2^nd condensation among other alternative reduction schemes. All of these topographic reductions need intense computation efforts for the integration of topographic mass induced gravity effects. Currently, the most popular tool for topographic mass modeling is the ‘tc’ program available in the GRAVSOFT package. In this program, the mass elements provided by a digital terrain model (DTM) are treated as rectangular prisms which cannot directly take the Earth curvature into account and suffer from geometrical shape change due to meridian convergence. In this study, the tesseroids which are naturally obtained from a DTM are employed and their gravity effects are precisely evaluated by numerical integrations. Four topographic mass integration schemes are proposed and programmed in FORTRAN. Their computational performances in computing the RTM effect, terrain correction, and total topographic effect with and without using parallelizing technique are tested in the Colorado area. Then they are applied to local geoid modeling to see the geoid model differences among these various integration schemes in the RTM case. The numerical findings reveal that: (1) The application of parallelization techniques can greatly reduce the computation time without the loss of any computation accuracy; (2) Among the four integration schemes, the maximum absolute difference of RTM effect, terrain correction, and total topographic effect is about 3 mm, 6 cm, and 7.5 cm for the height anomaly, and 4 mGal, 3 mGal, and 40 mGal for the gravity anomaly; (3) In the RTM case, the geoid model difference can reach a maximum of 1 cm in the target area, and a larger difference should be expected in areas with rougher terrain; (4) The effects on geoid models from mass density anomalies is bigger than the counterparts from DTM errors.

How to cite: Lin, M. and Li, X.: Comparison of different topographic mass integration schemes in topographic reduction and its impact on geoid modeling: a case study in the Colorado area, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-6923, https://doi.org/10.5194/egusphere-egu21-6923, 2021.

For the upcoming North American-Pacific Geopotential Datum of 2022, the National Geodetic Survey (NGS), the Canadian Geodetic Survey (CGS) and the National Institute of Statistics and Geography of Mexico (INEGI) computed the first joint experimental gravimetric geoid model (xGEOID) on 1’x1’ grids that covers a region bordered by latitude 0 to 85 degree, longitude 180 to 350 degree east. xGEOID20 models are computed using terrestrial gravity data, the latest satellite gravity model GOCO06S, altimetric gravity data DTU15, and an additional nine airborne gravity blocks of the GRAV-D project, for a total of 63 blocks. In addition, a digital elevation model in a 3” grid was produced by combining MERIT, TanDEM-X, and USGS-NED and used for the topographic/gravimetric reductions. The geoid models computed from the height anomalies (NGS) and from the Helmert-Stokes scheme (CGS) were combined using two different weighting schemes, then evaluated against the independent GPS/leveling data sets. The models perform in a very similar way, and the geoid comparisons with the most accurate Geoid Slope Validation Surveys (GSVS) from 2011, 2014 and 2017 indicate that the relative geoid accuracy could be around 1-2 cm baseline lengths up to 300 km for these GSVS lines in the United States. The xGEOID20 A/B models were selected from the combined models based on the validation results. The geoid accuracies were also estimated using the forward modeling.

How to cite: Wang, Y. M., Li, X., Ahlgren, K., Krcmaric, J., Hardy, R., Veronneau, M., Huang, J., and Avalos, D.: The experimental geoid 2020 – the first joint geoid model for the North American and Pacific Geopotential Datum , EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-6011, https://doi.org/10.5194/egusphere-egu21-6011, 2021.

Within the GeoGravGOCE project, funded by the Hellenic Foundation for Research Innovation, one of the main goals is the investigation of downward continuation schemes for the GOCE Satellite Gravity Gradiometry (SGG) data. It is well known that once the original SGG observations have been filtered to the GOCE Measurement Band Width (MBW), in order to remove noise and long-wavelength correlated errors, a crucial point for gravity field and geoid determination refers to the combination of GOCE data with local gravity field information. One possible way to exploit GOCE data is to use them in a Spherical Harmonic Synthesis (SHS) to derive a GOCE-only and/or a combined Global Geopotential Model. Our aim is to overcome the inherent smoothing of SHS and use directly the SGG data in order to investigate their contribution to regional gravity field and geoid determination. For that, methods based on the input-output-system-theory (IOST) are used for the combination of heterogeneous data at the Earth’s surface and at the satellite altitude or a mean sphere. The GOCE Level 2 gradients are first processed, transformed and reduced to a mean orbit using the IOST methods and then are downward continued to the Earth’s surface with an iterative Monte Carlo method (simulated annealing - SA). In this work we present the theoretical background of the proposed methodology and key-concepts for its implementation.

How to cite: Tziavos, I. N., Natsiopoulos, D. A., Vergos, G. S., Pitenis, E. A., and Mamagiannou, E. G.: Theoretical frame for the application of IOST in the downward continuation of GOCE SGG data, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1968, https://doi.org/10.5194/egusphere-egu21-1968, 2021.

In the frame of the GeoGravGOCE project, funded by the Hellenic Foundation for Research Innovation, GOCE Satellite Gravity Gradiometry (SGG) data are to be used for regional geoid and gravity field refinement as well as for potential determination in the frame of the International Height Reference Frame (IHRF). An inherent step in the geoid computation with either stochastic or spectral methods is the reduction of the related disturbing potential functionals within the well-known Remove-Compute-Restore (RCR) procedure. In this work we evaluate the latest, Release 6 (R6), satellite only and combined Global Geopotential Models (GGMs) which rely solely on GOCE and on land gravity data. The evaluation is performed over the established network of 1542 GPS/Levelling benchmarks over Greece mainland (BMs), which have been used in the past for the evaluation of GOCE GGMs. We employ the spectral enhancement approach, during which the GOCE-based GGMs are evaluated every one degree to the maximum degree of expansion coupled by EGM2008 and high-frequency RTM effects. This synthesis resolves wavelengths corresponding to maximum degree 216,000, hence the omission error is at the few mm-level. TIM-R6, DIR-R6, GOCO06s and XGM2019e are evaluated using EGM2008 residuals to the GPS/Levelling as the ground truth. From the results achieved, the optimal combination degree of a GOCE-only GGM augmented with EGM2008 is selected to be used in the sequel as reference field for the practical determination of the gravimetric geoid over Greece.

How to cite: Vergos, G. S., Tziavos, I. N., Natsiopoulos, D. A., Mamagiannou, E. G., and Pitenis, E. A.: Evaluation of the latest GOCE GGMs in support of regional geoid modeling over Greece, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1648, https://doi.org/10.5194/egusphere-egu21-1648, 2021.

Whilst GOCE SGG data have been widely processed and used in geodetic research, one of the key points of their use is to have a one-stop software for their pre-processing and basic manipulations in terms of frame transformations and filtering operations. Within the GeoGravGOCE project, funded by the Hellenic Foundation for Research Innovation, the main goal is the optimal combination of GOCE Satellite Gravity Gradiometry (SGG) data with in-situ observations for geoid determination. During the project development, it became apparent that GOCE SGG data after using the GOCEPARSER, had to be pre- and post-processed via several own-developed routines in order to perform data quality checks, data consistency tests, reference frame transformations, data reductions and filtering. With that in mind, a standalone open-source software has been developed in MATLAB consisting of a Graphical User Interface (GUI) to perform the aforementioned operation. The software is divided in four tabs and is designed to process the original GOCE gravity gradients, which are the second-order derivatives of the gravitational potential. The first tab of the software is designed to allow the pre-processing of the Level 2 Electrostatic Gravity Gradiometer nominal gravity gradients (EGG_NOM) and Satellite to Satellite Tracking Precise Science Orbits (SST_PSO) products. The second tab enables the transformation of gravity gradients from a Global Geopotential Model (GGM) from the Local North Oriented Frame (LNOF) to the Gradiometer Reference Frame (GRF). The third tab provides filtering options for the reduced SGG observations and encompasses three different methods: Finite Impulse Response (FIR), Infinite Impulse Response (IIR), and Wavelet Multi-Resolution Analysis (WL-MRA). Finally, the fourth tab allows the transformation of SGG data from the GRF to the LNOF and vice versa. In this work, we present the basic software development procedure and outline its basic functionality and results.

How to cite: Mamagiannou, E. M. G., Pitenis, E. A., Natsiopoulos, D. A., Vergos, G. S., and Tziavos, I. N.: GeoGravGOCE: A GOCE SGG processing software for datum transformations and filtering, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1680, https://doi.org/10.5194/egusphere-egu21-1680, 2021.

Physical heights, e.g. orthometric and normal heights, are, so far, practically considered as static heights in the majority of land areas over the world. They were traditionally determined without considering the dynamic processes of the Earth induced from temporal mass variations within the Earth’s system. The Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) satellite missions provided unique data that allow the estimation of temporal variations of geoid heights and vertical deformations of the Earth’s surface, and thereby the dynamics of physical heights. They revealed that for the large river basin of a strong hydrological signal (e.g. the Amazon river basin), peak to peak variations of orthometric/normal height changes reach 8 cm. The objective of this research is to discuss the need of considering the dynamics of physical heights for the determination of accurate orthometric/normal heights. An approach to determine the dynamics of physical heights using the release 6 (RL06) GRACE-based Global Geopotential Models (GGMs) as well as load Love numbers from the Preliminary Reference Earth Model (PREM) was proposed. Then, the dynamics of orthometric/normal heights was modelled and predicted using the seasonal decomposition (SD) method. The proposed approach was tested over the area of Poland. The main findings reveal that the dynamics of orthometric/normal heights over the area investigated reach the level of a couple of centimetres and can be modelled and predicted with a millimetre accuracy using the SD method. Accurate orthometric/normal heights can be obtained by combining modelled dynamics of orthometric/normal heights with static orthometric/normal heights referred to a specific reference epoch.

Keywords: dynamics of physical heights, GRACE, accurate orthometric/normal heights, temporal variations of geoid/quasigeoid heights, vertical deformations of the Earth’s surface

How to cite: Godah, W., Szelachowska, M., and Krynski, J.: On the dynamics of physical heights and their use for the determination of accurate orthometric/normal heights, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-2110, https://doi.org/10.5194/egusphere-egu21-2110, 2021.

In the frame of the IAG Subcommission 2.4f “Gravity and Geoid in Antarctica” (AntGG) a first Antarctic-wide grid of ground-based gravity anomalies was released in 2016 (Scheinert et al. 2016). That data set was provided with a grid space of 10 km and covered about 73% of the Antarctic continent. Since then a considerably amount of new data has been made available, mainly collected by means of airborne gravimetry. Regions which were formerly void of any terrestrial gravity observations and have now been surveyed include especially the polar data gap originating from GOCE satellite gravimetry. Thus, it is timely to come up with an updated and enhanced regional gravity field solution for Antarctica. For this, we aim to improve further aspects in comparison to the AntGG 2016 solution: The grid spacing will be enhanced to 5 km. Instead of providing gravity anomalies only for parts of Antarctica, now the entire continent should be covered. In addition to the gravity anomaly also a regional geoid solution should be provided along with further desirable functionals (e.g. gravity anomaly vs. disturbance, different height levels).

We will discuss the expanded AntGG data base which now includes terrestrial gravity data from Antarctic surveys conducted over the past 40 years. The methodology applied in the analysis is based on the remove-compute-restore technique. Here we utilize the newly developed combined spherical-harmonic gravity field model SATOP1 (Zingerle et al. 2019) which is based on the global satellite-only model GOCO05s and the high-resolution topographic model EARTH2014. We will demonstrate the feasibility to adequately reduce the original gravity data and, thus, to also cross-validate and evaluate the accuracy of the data especially where different data set overlap. For the compute step the recently developed partition-enhanced least-squares collocation (PE-LSC) has been used (Zingerle et al. 2021, in review; cf. the contribution of Zingerle et al. in the same session). This method allows to treat all data available in Antarctica in one single computation step in an efficient and fast way. Thus, it becomes feasible to iterate the computations within short time once any input data or parameters are changed, and to easily predict the desirable functionals also in regions void of terrestrial measurements as well as at any height level (e.g. gravity anomalies at the surface or gravity disturbances at constant height).

We will discuss the results and give an outlook on the data products which shall be finally provided to present the new regional gravity field solution for Antarctica. Furthermore, implications for further applications will be discussed e.g. with respect to geophysical modelling of the Earth’s interior (cf. the contribution of Schaller et al. in session G4.3).

How to cite: Scheinert, M., Zingerle, P., Schaller, T., Pail, R., and Willberg, M.: Towards an updated, enhanced regional gravity field solution for Antarctica, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9873, https://doi.org/10.5194/egusphere-egu21-9873, 2021.

In the last decade, big efforts have been undertaken in terms of gravity surveys in the Southeast part of Brazil. First of all, São Paulo state has gravity data coverage quite completed in terms of 5’ resolution. Second, in the last few years, some field works have been carried out in Minas Gerais state. The purpose of gravity densification is not only to improve the quality of geoid (quasi-geoid) models in Brazil, but also to contribute to the geodetic infrastructure, in particular, at the moment, for the establishment of the International Height Reference Frame, where two of six planned stations are located in the densification area. These efforts resulted in the computation of two quasi-geoid models in the Southeast region of Brazil. The decision is to compute a quasi-geoid instead of a geoid model, once since 2018, the Brazilian vertical system is based on normal heights. The Minas Gerais model was computed using Least Squares Collocation, via Fast Collocation. The spectral decomposition was employed in the technique for quasi-geoid model computation, where the reference field was represented by XGM2019 up to degree and order 200. The model was compared with GNSS/leveling in order to check the consistency of two different data sets. Two quasi-geoidal models for the São Paulo state have been computed. Numerical integration through the Fast Fourier Transform (FFT) was used to perform the integral. The Molodensky gravity anomaly was determined in a 5’ grid, reduced and restored using the Residual Terrain Model (RTM) technique and the XGM2019 with the degree and order 250 and 720. The validation for the São Paulo quasi-geoid model is based on the GNSS measurements in the leveling network too.  The Digital Terrain Model SRTM15 plus was used in the continent and the ocean areas in both states.

How to cite: Silva, V., Guimarães, G., Blitkow, D., and Matos, A. C.: New geoid models computation in the Southeast part of Brazil, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3284, https://doi.org/10.5194/egusphere-egu21-3284, 2021.

The Global Geodetic Observing System (GGOS) is the contribution of Geodesy to the observation and monitoring of the Earth System. Geodesy is the science of determining and representing the shape of the Earth, its gravity field and its rotation as a function of time. A core element to reach this goal are stable and consistent geodetic reference frames, which provide the fundamental layer for the determination of time-dependent coordinates of points or objects, and for describing the motion of the Earth in space. Traditionally, geodetic reference frames have been used for surveying, mapping, and space-based positioning and navigation. With modern instrumentation and analytical techniques, Geodesy is now capable of detecting time variations ranging from large and secular scales to very small and transient deformations with increasing spatial and temporal resolution, high accuracy, and decreasing latency. GGOS has been working closely with components of International Association of Geodesy (IAG) to provide consistent and openly available observations of the spatial and temporal changes of the shape and gravity field of the Earth, as well as the temporal variations of the Earth’s rotation. These efforts make available a global picture of the surface kinematics of our planet, including the ocean, ice cover, continental water, and land surfaces, as well as estimates of mass anomalies, mass transport, and mass exchange in the System Earth. Surface kinematics and mass transport together are the key to global mass balance determination, and are an important contribution to understanding the energy budget of our planet. In order to play its vital role, GGOS has following missions; a) to provide the observations needed to monitor, map, and understand changes in the Earth’s shape, rotation, and mass distribution, b) to provide the global geodetic frame of reference that is the fundamental backbone for measuring and consistently interpreting key global change processes and for many other scientific and societal applications, c) to benefit science and society by providing the foundation upon which advances in Earth and planetary system science and applications are built. For the mission, GGOS works tighter with components of the IAG, more specifically, IAG Services, IAG Commissions and IAG Inter-Commission Committees. The IAG Services provide the infrastructure and products on which all contributions of GGOS are based, and the IAG Commissions and IAG Inter-Commission Committees provide expertise and support to address key scientific issues within GGOS. Together with the IAG components, GGOS provides the fundamental infrastructure underpinning Earth sciences and their applications.

How to cite: Miyahara, B., Sánchez, L., and Sehnal, M.: The Global Geodetic Observing System (GGOS) – infrastructure underpinning Earth science, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3927, https://doi.org/10.5194/egusphere-egu21-3927, 2021.

This presentation gives a summary of the role and the activities of the Bureau of Products and Standards (BPS) to support IAG’s Global Geodetic Observing System (GGOS) in its goal to provide observations and consistent geodetic products needed to monitor, map and understand changes in the Earth’s shape, rotation and mass distribution. In its present structure, the two Committees “Earth System Modeling” and “Essential Geodetic Variables” as well as the Working Group “Towards a consistent set of parameters for the definition of a new GRS” are associated with the BPS. A key objective of the BPS is to keep track and to foster homogenization of adopted geodetic standards and conventions across all IAG components as a fundamental basis for the generation of consistent geometric and gravimetric products. Towards this aim, an updated 2^nd version of the BPS inventory of standards and conventions used for the generation of IAG products has been published in the Geodesist’s Handbook 2020. In the framework of the renewing of the GGOS website, the BPS supports the GGOS Coordinating Office in particular regarding the representation of geodetic products. Furthermore, the BPS contributes to the rewriting of the IERS Conventions as Chapter Expert for Chapter 1 “General definitions and numerical standards” and interacts with external stakeholders regarding standards and conventions, such as ISO, IAU, BIPM, CODATA and the UN GGIM Subcommittee on Geodesy, including its Working Group “Data Sharing and Development of Geodetic Standards”.

How to cite: Angermann, D., Gruber, T., Gerstl, M., Heinkelmann, R., Hugentobler, U., Sanchez, L., and Steigenberger, P.: The GGOS Bureau of Products and Standards, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-4684, https://doi.org/10.5194/egusphere-egu21-4684, 2021.

In the correction for polar motion, terrestrial gravimetry and 3-D positioning follow different conventions. The 3-D positions were first corrected to refer to the "mean pole" (IERS Conventions up to 2010) and now to the "secular pole" (IERS Conventions update since 2018). In any case, the pole reference evolves in time and describes the track of secular or low-frequency polar wander. However, since 1988 terrestrial gravimetry follows the IAGBN (International Gravity Basestation Network) Processing Standards where the gravity values are corrected to refer to the IERS Reference Pole, a fixed quantity. This may lead to discrepancies when for instance gravity change rates from absolute gravity measurements are interpreted together with vertical velocities from GNSS. I discuss the size and geographical distribution of the possible discrepancies and how to account for them in geodynamical problems. The fixed reference of the IAGBN Processing Standards has served the gravity community well, by providing a stable system for terrestrial gravity for the last 30 years during which time the pole reference in the IERS Conventions has been revised several times. In fact, the recently proposed conventions for the International Gravity Reference System (IGRS) and the International Gravity Reference Frame (IGRF) maintain the IAGBN principle. However, it appears that with the adoption of the “secular pole” the reference in 3-D positioning may have become predictable for the foreseeable future. Therefore, it could be suggested that now is the time to harmonize terrestrial gravity with 3-D, by adopting the time-dependent secular pole as a reference for it as well, especially as this is already happening with satellite gravity. I argue that at present the practical drawbacks from such a change of reference would outweigh any theoretical advantages, and the harmonization, where necessary, can be simply performed a-posteriori to published gravity trends/values.

How to cite: Mäkinen, J.: On the correction for polar motion in gravimetry and in 3-D positioning, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1853, https://doi.org/10.5194/egusphere-egu21-1853, 2021.

The International Association of Geodesy (IAG), as the organisation responsible for advancing Geodesy, introduced in 2015 the International Height Reference System (IHRS) as the global conventional reference system for the determination of gravity field-related vertical coordinates. The definition of the IHRS is given in terms of potential parameters: the vertical coordinates are geopotential numbers (C_P = W₀ ‐ W_P) referring to an equipotential surface of the Earth's gravity field realised by the conventional value W₀ = 62 636 853.4 m²s^‐2. The spatial reference of the position P for the potential W_P = W(X) is given by coordinates X of the International Terrestrial Reference Frame (ITRF). At present, the main challenge is the realisation of the IHRS; i.e., the establishment of the International Height Reference Frame (IHRF): a global network with regional and national densifications, whose geopotential numbers referring to the global IHRS are known. According to the objectives of the IAG Global Geodetic Observing System (GGOS), the target accuracy of these global geopotential numbers is 3 x 10^-2 m²s^-2. In practice, the precise realisation of the IHRS is limited by different aspects; for instance, there are no unified standards for the determination of the potential values W_P; the gravity field modelling and the estimation of the position vectors X follow different conventions; the geodetic infrastructure is not homogeneously distributed globally, etc. This may restrict the expected accuracy of 3 x 10^-2 m²s^-2 to some orders lower (from 10 x 10^-2 m²s^-2 to 100 x 10^-2 m²s^-2). This contribution summarises advances and present challenges in the establishment of the IHRS/IHRF.

How to cite: Sanchez, L., Huang, J., Barzaghi, R., and Vergos, G. S.: Towards a Global Unified Physical Height System, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1500, https://doi.org/10.5194/egusphere-egu21-1500, 2021.

The maintenance of leveling benchmark is both laborious and costly due to distortions caused by geodynamic activities and local deformations. It is necessary to realize geoid-based vertical datum, which also enables calculation from ellipsoidal heights obtained from GNSS to orthometric heights that have physical meaning. It can be considered as an important step for height system unification as it eliminates the problems stem from the conventional vertical datum. The ongoing height modernization efforts in Turkey focus to improve quality and coverage of the gravity data, eliminate errors in existing terrestrial gravity measurements in order to achieve a precise geoid model. Accuracy of the geopotential model is crucial while realizing a geoid model based vertical datum as well as unifying the regional height systems with the International Heights Reference System. In this point of view, we assessed the accuracies of recently released global geopotential models including XGM2019e_2159, GECO, EIGEN-6C4, EGM2008, SGG-UGM-1, EIGEN-6C3stat, and EIGEN-6C2 using high order GNSS/leveling control benchmarks and terrestrial gravity data in Turkey. The reason for choosing these models in the validations is their relatively higher spatial resolutions and improved accuracies compared to other GGMs in published validation results with globally distributed terrestrial data. The GNSS/leveling data used in validations include high accuracy GNSS coordinates in ITRF datum with co-located Helmert orthometric heights in regional vertical datum. 100 benchmarks are homogeneously distributed in the country with the benchmarks along the coastlines. In addition, the terrestrial gravity anomalies with 5 arc-minute resolution were also used in the tests. In order to have comparable results, residual terrain effect has been restored to the GGM derived parameters. Numerical tests revealed significant differences in accuracies of the tested GGMs. The most accurate GGM has the comparable performance with official regional geoid model solutions in Turkey. The drawn results in the study were interpreted and discussed from practical applications and height system unification points in conclusion.

How to cite: Çevikalp, M. R., Erol, B., Mutlu, B., and Erol, S.: Accuracy Assessment of Recent High-Degree Global Geopotential Models Using Geodetic Control Points and Terrestrial Gravity Data in Turkey, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-11929, https://doi.org/10.5194/egusphere-egu21-11929, 2021.

The VLBI Global Observing System (VGOS) is the VLBI contribution to GGOS. During the last years, several VGOS stations have been established, the VGOS observation program has started, and by 2021 VGOS has achieved an operational state involving nine international VGOS stations. Further VGOS stations are currently being installed, so that the number of active VGOS stations will increase drastically in the near future. In the end of 2019 the International VLBI Service for Geodesy and Astrometry (IVS) decided to start a new and so-far experimental VGOS-Intensive series, called VGOS-B, involving Ishioka (Japan) and Onsala (Sweden). Both sites operate modern VGOS stations with 13.2~m diameter radio telescopes, i.e. ISHIOKA (IS) in Japan, and ONSA13NE (OE) and ONSA13SW (OW) in Sweden. In total 12 VGOS-B sessions were observed between December 2019 and February 2020, one every week, in parallel and simultaneously to legacy S/X INT1 Intensive sessions that involve the stations KOKEE (KK) on Hawaii and WETTZELL (WZ) in Germany. These 1-hour long VGOS-B sessions consist of more than fifty radio source observations, resulting in about 1.6 TB of raw data that are collected at each station. The scheduling of the VGOS-B sessions was done using VieSched++ and the subsequent steps (correlation, fringe-fitting, database creation) were carried out at the Onsala Space Observatory using DIFX and HOPS. The resulting VGOS databases were  analysed with several VLBI analysis software packages, involving nuSolve, c5++ and ASCOT. In this presentation, we give an overview on the VGOS-B series, present our experiences, and discuss the obtained results. The derived UT1-UTC results were compared to corresponding results from standard legacy S/X Intensive sessions (INT1/INT2), as well to the final values of the International Earth Rotation and Reference Frame Service (IERS), provided in IERS Bulletin~B. 
The VGOS-B series achieve 3-4 times lower formal uncertainties for the UT1-UTC results than standard legacy S/X INT series.  Furthermore, the root mean square (RMS) agreement with respect to the IERS Bulletin B is 30-40 % better for the VGOS-B results than for the INT1/INT2 results.

How to cite: Haas, R., Varenius, E., Diamantidis, P.-K., Matsumotu, S., Schartner, M., and Nilsson, T.: VGOS Intensives Ishioka-Onsala, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-12916, https://doi.org/10.5194/egusphere-egu21-12916, 2021.

Geospatial Information Authority of Japan has a VLBI antenna (ISHIOKA) and an IGS station (ISHI) at the Ishioka Geodetic Observing Station. The Ishioka VLBI antenna has participated in the IVS sessions and IGS station ISHI has continuously provided the GNSS data.

We conducted co-location surveys in November 2018 and September 2020 to determine a local tie vector between the Ishioka VLBI antenna and the IGS station ISHI. In the surveys, we determined the position of ISHI w.r.t. four surrounding reference pillars by angle/distance measurements and leveling. To determine the position of the VLBI antenna reference point w.r.t. the pillars, we adopted the “inside method” (Munekane, 2019), where the position of the VLBI reference point is determined by observing mirror installed inside the AZ cabin from the fixed point inside the cabin; its position is determined by angle/distance measurements from the pillars. We plan to finish the calculation early this year and submit the results to IERS ITRS Center so as to contribute to the ITRF2020.

In this presentation, we will outline the inside method and compare the results in 2018 and 2020.

How to cite: Takagi, Y., Ueshiba, H., Nakakuki, T., Matsumoto, S., Hayashi, K., Yutsudo, T., Mori, K., and Kobayashi, T.: VLBI-GNSS co-location survey at the Ishioka Geodetic Observing Station in 2018 and 2020, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-810, https://doi.org/10.5194/egusphere-egu21-810, 2021.

A growing number of geodetic VLBI stations participate in the VLBI Global Observing System (VGOS). Multiple sites operate both new VGOS telescopes and legacy S/X VLBI telescopes. At Onsala Space Observatory, Sweden, we operate two 13.2 m diameter VGOS radio telescopes, ONSA13NE (OE) and ONSA13SW (OW), as well as the 20~m legacy S/X telescope ONSALA60 (ON). Transitioning from the legacy system and providing continuity of the terrestrial and celestial reference frames necessitate establishing ties between S/X and VGOS telescopes. Since spring 2019, we have carried out more than 20 short-baseline (550 m) interferometric observations at X-band to establish local-tie vectors between ON, OE and OW. The obtained data were correlated at Onsala Space Observatory using DiFX, post-processed using HOPS and analysed with nuSolve and ASCOT. In this presentation we given an overview of the observations, analysis, and results of these local-tie experiments. We investigate the impact of modeling e.g. gravitational deformation, and the possibility of using phase-delays to improve the precision. Finally, we present a comparison with preliminary results from two other methods: global mixed-mode observations and classical local-tie measurements.

How to cite: Varenius, E., Haas, R., Diamantidis, P., and Nilsson, T.: Short-baseline interferometry at Onsala Space Observatory, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-14266, https://doi.org/10.5194/egusphere-egu21-14266, 2021.

Over the last years, ideas have been proposed to install a Very Long Baseline Interferometry (VLBI) transmitter on one or more satellites of the Galileo constellation. Satellites transmitting signals that can be observed by VLBI telescopes provide the opportunity of extending the current VLBI research with observations to geodetic satellites. These observations offer a variety of new possibilities such as high precision tying of space geodetic techniques but also the direct determination of the absolute orientation of the satellite constellation with respect to the International Celestial Reference Frame (ICRF) and have implications on the determination of long-term reference frames. 

This contribution provides a visibility study of the Galileo satellites from a VLBI network. The newly developed satellite scheduling module in VieSched++ is used to determine the time periods during which a satellite is observable from a VLBI network. The possible satellite observations are evaluated through the number of stations from which a satellite is observable. Moreover, the impact on determining the orientation of the satellite constellation, caused by the observation geometry, is investigated with using the UT1-UTC Dilution of Precision (UDOP) factor.

How to cite: Wolf, H., Böhm, J., Schartner, M., and Hugentobler, U.: Visibility study of Galileo satellites from a VLBI network, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-5824, https://doi.org/10.5194/egusphere-egu21-5824, 2021.

Recently, the GNSS-A (Global Navigation Satellite System – Acoustic combination technique) seafloor geodetic observation technology, developed in the Hydrographic and Oceanographic department in Japan Coast Guard (JCG), was upgraded to be able to monitor a subseafloor interplate coupling condition of about 1 cm/year and an interplate shallow slow slip event of about 5 cm (e.g., Yokota et al., 2018, Scientific Data; Ishikawa et al., 2020, Front. Ear. Sci.). By observing such small-scale seafloor crustal movements, GNSS-A technology makes a decisive contribution to subduction seismology and disaster prevention sciences (e.g., Yokota et al., 2016, Nature; Yokota and Ishikawa, 2020, Sci. Adv.). This technology was achieved by connecting high-precision underwater acoustic ranging technology and high-rate GNSS on a vessel at sea surface.

The GNSS-A, which is carried out all over the world, especially in the Pacific Rim, has been constructed for observation of plate boundary subduction processes and fault movement processes. Unlike the GNSS network, GNSS-A has never contributed to global geodesy within the framework of the Global Geodetic Observing System (GGOS). However, it can be a unique observation method for the construction of the International Terrestrial Reference Frame (ITRF). It can make an important contribution in determining the movement and Euler pole on an oceanic plate that have few land area.

In the future, if an extensive seafloor geodetic observation network as shown by Kato et al. (2018, JDR) will be established, there is a possibility of constructing a next-generation reference frame that completely explains the plate motion on the earth's surface. This presentation will present the current state of the GNSS-A ability and cost and future prospects for the contribution to global geodesy.

How to cite: Yokota, Y., Ishikawa, T., Watanabe, S., and Nakamura, Y.: GNSS-A seafloor geodetic observation capability in 2021 and its applicability to global geodesy, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-4527, https://doi.org/10.5194/egusphere-egu21-4527, 2021.

Atmospheric waves excited by strong surface explosions, both natural and anthropogenic, often disturb upper atmosphere. In this letter, we report an N-shaped pulse with period ~1.3 minutes propagating southward at ~0.8 km/s, observed as changes in ionospheric total electron content using continuous GNSS stations in Israel and Palestine, ~10 minutes after the August 4, 2020 chemical explosion in Beirut, Lebanon.  The peak-to-peak amplitude of the disturbance reached ~2% of the background electrons, comparable to recently recorded volcanic explosions in the Japanese Islands. We also succeeded in reproducing the observed disturbances assuming acoustic waves propagating upward and their interaction with geomagnetic fields.

Keywords: Chemical explosion, Beirut, N-shaped pulse, Total electron content

How to cite: Kundu, B., Senapati, B., Matsushita, A., and Heki, K.: Atmospheric wave energy of the 2020 August 4 explosion in Beirut, Lebanon, from ionospheric disturbances , EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1936, https://doi.org/10.5194/egusphere-egu21-1936, 2021.

The huge amount of water vapor in the atmosphere caused disastrous heavy rain and floods in early July 2018 in SW Japan. Here I present a comprehensive space geodetic study of water brought by this heavy rain done by using a dense network of Global Navigation Satellite System (GNSS) receivers. 

First, I reconstruct sea level precipitable water vapor above land region on the heavy rain. The total amount of water vapor derived by spatially integrating precipitable water vapor on land was ~25.8 Gt, which corresponds to the bucket size to carry water from ocean to land. I then compiled the precipitation measured with a rain radar network. The data showed the total precipitation by this heavy rain as ~22.11 Gt.

Next, I studied the crustal subsidence caused by the rainwater as the surface load. The GNSS stations located under the heavy rain area temporarily subsided 1-2 centimeters and the subsidence mostly recovered in a day. Using such vertical crustal movement data, I estimated the distribution of surface water in SW Japan. 

The total amount of the estimated water load on 6 July 2018 was ~68.2 Gt, which significantly exceeds the cumulative on-land rainfalls of the heavy rain day from radar rain gauge analyzed precipitation data. I consider that such an amplification of subsidence originates from the selective deployment of GNSS stations in the concave places, e.g. along valleys and within basins, in the mountainous Japanese Islands.

How to cite: Arief, S.: Topographic amplification of crustal subsidence by the rainwater load of the 2018 heavy rain in SW Japan, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-16260, https://doi.org/10.5194/egusphere-egu21-16260, 2021.

The Metadata Management and Distribution System for Multiple GNSS Networks (M³G, https://gnss-metadata.eu), hosted by the Royal Observatory of Belgium, is one of the services of the European Plate Observing System (EPOS, https://www.epos-eu.org) and EUREF (http://euref.eu).

M³G provides the scientific as well as the non-scientific community with a state-of-the-art archive of information on permanently tracking GNSS stations in Europe, including the station description, the GNSS networks the stations contribute to, whether station observation data are publicly available, and how to access them. 

Since its first public release (2018), M³G has been under continuous development, to respond to the evolving needs of the GNSS community, to progress towards FAIR data principles and comply with GDPR. 

M³G offers APIs and an interactive user interface where any GNSS station manager, after registration, can insert all information relative to its GNSS stations and make this information publicly available. Consequently, the commitment of station managers to insert GNSS station metadata in M³G and their willingness to keep the information up to date is crucial for the success of M³G.

At the moment, M³G is used by 127 GNSS agencies and includes data from more than 2500 GNSS stations all over Europe, and more still in the process of being collected.

We will illustrate the rationale underlying M³G, the data that it provides and how these data can be accessed.

How to cite: Fabian, A., Bruyninx, C., Miglio, A., and Legrand, J.: M3G: an expanding catalogue of permanently tracking GNSS stations in Europe, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-11655, https://doi.org/10.5194/egusphere-egu21-11655, 2021.

The Japan Coast Guard (JCG) operates Satellite Laser Ranging (SLR) and GNSS observation at the Shimosato Hydrographic Observatory (SHO) in Wakayama Prefecture, Japan. The SLR and GNSS observation results obtained at the SHO are submitted to the ILRS and the IGS, respectively, and have contributed to the development of the International Terrestrial Reference Frame (ITRF). The SHO, operating two types of global geodetic observation, is now one of the sites of the Global Geodetic Observing System (GGOS).

Observation sites such as the SHO that operate multiple geodetic techniques function as co-location sites, where the different geodetic techniques can be linked together by precisely determining the local tie between these techniques. In November 2020, the JCG and the Geospatial Information Authority of Japan (GSI) have performed a local tie survey at the SHO to determine the local tie between the SLR telescope and the GNSS station. In our survey, we mounted several targets on the SLR telescope, which we observed from four survey sites that were temporarily set in the SHO. During the survey, we rotated the telescope along the azimuth and the elevation axes at fixed intervals, observing the target positions for each rotation angle. The measured target positions form arcs, from which we can estimate the rotation axes of the telescope; the origin of the axes was determined as the center of the SLR telescope. For the calculation of the local tie, we used the software pyaxis, developed by Land Information New Zealand (LINZ).

In our presentation, we will show the methods of our survey and calculation described above, and the estimated local tie vector. As of January 2021, we are preparing to submit the co-location SINEX file to the IERS, to contribute to the construction of the upcoming ITRF2020.

How to cite: Watanabe, S., Nakamura, Y., Yokota, Y., Suzuki, A., Ueshiba, H., and Seo, N.: Local tie survey of the SLR and GNSS stations at the Shimosato Hydrographic Observatory, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-4544, https://doi.org/10.5194/egusphere-egu21-4544, 2021.

National Centre for Geodesy (NCG) has been established in IIT Kanpur, India with the vision of acting as a hub of excellence in geodetic research at the National and International level. Working towards its mission, it has initiated this state-of-the- art establishment for improving the space geodetic infrastructure of the country and encouraging more researches in the geodesy field. The presentation will discuss the current status of the planned core site and its future establishments. It will provide detailed description of all the facilities installed in the site right now, and the future extensions. This new core-site will house facilities for three technologies – Space, Time and Earth gravity domain. The main purpose of establishing this site is for improving the realization of terrestrial and celestial reference frames, Earth Orientation Parameters (EOPs) and other data products essential for understanding the Earth’s environment. This co-located site with four space geodetic techniques will help in the International campaign for determination of TRF with 1mm accuracy and 0.1 mm/yr. stability. Moreover, this site location will improve the uniformity in geographical distribution of the ITRF observatories and the necessity of this station has been confirmed by simulation modelling.

Keywords: NCG, India, Core site, TRF, stability, uniformity.

How to cite: Dhar, S., Tiwari, A., Balasubramanian, N., Devaraju, B., Dikshit, O., Prakash, J., Mishra, P., Agarwal, D., Sharma, V., Varade, D., Laha, A., Kumar, A., Singh, S., Bihari Narayan Singh, A., Goyal, R., and Kumar, V.: Establishment of State-of-the-Art Geodesy Village in India: Current status and Outlook, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-16068, https://doi.org/10.5194/egusphere-egu21-16068, 2021.

In recent years, the sensitivity of the GNSS station time series to the loading displacements is demonstrated by multiple studies, mainly for the non-tidal atmospheric loading (NTAL) and non-tidal ocean loading (NTOL). But the impact of the loading displacements is beyond the coordinate time series, including and not limited to geocenter motion, Earth Orientation Parameters, satellite orbits, etc. We extensively evaluate the impact on and the improvements of the reference frame products from reprocessed 25 years of GPS and GLONASS network solution with a consistent application of non-tidal loading and Continental Water Storage Loading (CWSL) displacement at the observational level. We also discussed the differences of correcting for the loading displacements at the observation level and correction at the product level on GNSS station coordinates and Geocenter motions, we elaborate the advantage of the inclusion of correction at the observational level.

Significant improvements are found in estimated coordinate time series, almost 90% of the station shows improved WRMS in North and Up directions and over 75% in East. CWSL dominates the contribution in the North direction. The annual Geocenter variations (over 80% of the x and y components) can be explained by the loading displacement. A small and consistent reduction of orbit disclosure is found among all 32 GPS satellites and most of the GLONASS satellites (23 out of 25) after the inclusion of all the loading displacements.  All the improvements demonstrate the urgent need for the adoption of loading displacements in the global GNSS analysis.

How to cite: Wang, L., Thaller, D., Susnik, A., and Dach, R.: Improving the products of global GNSS data analysis by correcting for loading displacements at the observation level, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-12920, https://doi.org/10.5194/egusphere-egu21-12920, 2021.