International Symposium on Earth and Environmental Sciences for Future Generations

In this study, we present a global terrestrial reference frame (TRF) from simulated very long baseline interferometry (VLBI) observations. In the time span from 2008 until 2014, 695 standard VLBI rapid turnaround (R1, R4) 24 h-sessions were simulated using a network of 28 globally distributed stations. Within the software VieVS@GFZ, we apply different measurement noise at the observation level and investigate the impact on the TRF and on the Earth rotation parameters. We find that the effect of varying only the noise applied within the simulation is not proportional to the changes in the estimates and their uncertainties. For instance, increasing the noise level from 15 ps to 300 ps increases the uncertainty of the station positions by a factor of 3.5, of station velocities by 5, of polar motion by 3.4, and of UT1-UTC by 1.5. A comparison with the VLBI-TRF derived from real observations within the same time span shows that the solution simulated with a noise level based on the formal errors of real observations is still too optimistic.

The assessment of the accuracy and the stability of the global Terrestrial Reference Frames (TRFs) is a matter of great importance for the geodetic community. The classical Helmert transformation plays a crucial role in terms of evaluating the datum related parameters of global TRFs (origin, scale, and orientation, and their associated rates). We discuss a new alternative approach for the assessment of TRFs temporal evolution and we compare it with the Helmert transformation. Our concept relies on the splitting of the velocities into two specified parts. The first one is referred to the reference system effect and the latter one to the deformation, respectively. This separation is done in order to create the necessary mathematical tools for the TRF assessment. The new approach is tested on the single-technique TRFs (VLBI, SLR, GPS and DORIS, respectively) of the DTRF2008. The novelty of the new methodology is its ability to treat individually the systematic errors of each TRF. This feature detects systematic effects that the Helmert transformation cannot. The results reveal that the new approach and the Helmert transformation show almost the same results in terms of rates of the datum parameters with an uncertainty of 0.1–0.3 mm/year for the four space geodetic techniques TRFs. The uncertainty refers to the estimated rate differences standard deviation between the new approach and the Helmert one.

Six campaigns with a total of twenty-four Very Long Baseline Array Calibrator Survey (VCS) observing sessions were carried out with ten radio telescopes located on U.S. territory from 1994 to 2007. The aim of those astrometric sessions was to estimate source positions and to make snapshot images of compact radio sources. Coordinates of about two thirds of the sources in the ICRF2 catalogue are estimated from VCS sessions, most of them from two scans in one session only. Moreover, there are systematic errors due to the deficiencies of a continent-wide network for the estimation of Earth orientation parameters (EOP) and the linking between the celestial and terrestrial frame. We investigate the impact of EOP estimation on source positions for those sessions and we use polar motion estimates from the analysis of Global Navigation Satellite Systems (GNSS) observations to strengthen the solution. We find that there is a systematic effect up to 1 mas in the estimated source coordinates between a solution with fixed EOP coming from the GNSS techniques and a solution where the EOP are estimated in the Very Long Baseline Interferometry analysis. Furthermore, we discuss analysis strategies for these sessions including the proper use of datum or “transfer sources”.

For many years, there has been a recognized discrepancy between the accuracies of absolute gravity determination and the hitherto valid gravity reference system of the International Association of Geodesy (IAG), the International Gravity Standardization Net 1971 (IGSN71).Scientists from metrology and geosciences agreed on a proposal to base a new absolute gravity reference upon repeated instrument comparisons under metrological rules for traceability to SI quantities. In a strategy paper, which originated from the lively discussion of a mixed working group in metrology and geodesy with the objective to define and harmonize the measurements at the highest accuracy level, it was proposed to continue the comparisons under the International Committee for Weights and Measures (CIPM) every four years at alternating locations with the aim to distribute comparison results over a global network of carefully observed gravity reference and comparison sites. Their gravity variations are recorded by a combination of repeated absolute gravity measurements and continuously operating superconducting gravimeters. The results of comparisons and the gravity variations of the reference stations will be documented in a registry, part of the AGrav database, maintained jointly by the International Gravimetric Bureau (BGI) and the Federal Agency for Cartography and Geodesy (BKG).By means of this network of comparison and gravity reference stations it will be possible to establish a global gravity reference system covering the needs of the geodetic and metrological communities and with capabilities to integrate observations of any new kind of absolute gravimeters including that based on cold atoms. Recorded gravity variations in an absolute reference system complement the Global Geodetic Reference Frame and will be used for combination with other geoscientific data and the investigation of mass transports and global change processes in the context of the Global Geodetic Observing System, GGOS. The implementation of the new gravity reference system will be based upon the international standards and conventions of the IAG. During the IUGG General Assembly in Prague 2015, the IAG adopted Resolution No. 2 and initiated the Establishment of a Global Absolute Gravity Reference System.

In this work, the linearized fixed gravimetric boundary value problem and its solution in spheroidal approximation is discussed. Input to the problem are gravity disturbances, using the known Earth’s topography as a boundary, so this corresponds to an oblique derivative problem. From the physical viewpoint, it has many advantages and can serve as the basis in establishing a world height system that supports geometrical and physical heights world-wide with high precision. Adopting the spheroidal approximation, an integral equation results which can be solved using successive approximations. The mathematical model becomes simpler and can be solved more easily by neglecting the Earth’s topography. On the other hand, adopting the spherical approximation, the solution corresponds to a normal derivative problem plus suitable corrections which include the topography. We conclude that the spheroidal approximation should be taken into account in order to achieve higher accuracy.

A geopotential model of the Earth is usually calculated using the Stokes coefficients. As computational power has increased, research is focusing more on new ways of gravity field modelling. The objective of this work is to study an application of the h-p finite element method for solving boundary value problems in physical geodesy. For the purpose of studying this method, we have formulated model boundary value problems with different boundary conditions. The algorithm for solving these test problems was designed and was subsequently implemented by the program. We derived a weak formulation for each model boundary value problem and also the corresponding finite element discretization. We used isoparametric reference elements with linear and quadratic shape functions. The authors present the application of the h and p methodologies for increasing the rate of convergence of our solution, discuss mesh generation for large domains, and also solve the model boundary value problem, which is similar to the geodetic boundary value problem.

The aim of this paper is to discuss the solution of the simple gravimetric boundary value problem by means of the method of successive approximations. A transformation of coordinates is used to express the relation between the description of the boundary of the solution domain and the structure of Laplace’s operator. The solution domain is carried onto the exterior of a sphere and the original oblique derivative boundary condition is given the form of Neumann’s boundary condition. Laplace’s operator expressed in terms of new coordinates involves topography-dependent coefficients. Effects caused by the topography of the physical surface of the Earth are treated as perturbations. Their internal structure is analyzed and modified by using integration by parts. As a result of the transformation a spherical mathematical apparatus may be applied at each iteration step, including the spherical form of Green’s function of the second kind, i.e. Neumann’s function, in the integral representation of the successive approximations.

A new Argentinean gravimetric geoid model named GEOIDEAR was developed using the remove-compute-restore technique and incorporating the GOCO05S satellite-only global geopotential model (GGM) together with 560,656 land and marine gravity measurements. Terrain corrections were calculated for all gravity observations using a combination of the SRTM_v4.1 and SRTM30_Plus_v10 digital elevation models. For the regions that lacked of gravity observations, the DTU13 gravity model was utilised. The residual gravity anomalies were gridded using the tensioned spline algorithm. The resultant gravity anomaly grid was applied in the Stokes’ integral using the spherical multi-band FFT approach and the deterministic kernel modification proposed by Wong and Gore. The accuracy of GEOIDEAR was assessed by comparing it with GPS-levelling derived geoid undulations at 1904 locations and the EGM2008 GGM. Results show that the new Argentinean geoid model has an accuracy of less than 10 cm.

Over the oceans, data from altimetry are currently the only input data for the latest global geoid models such as EGM08 or EIGEN6C. Over the Mediterranean sea, satellite altimetry does not give good results for gravity models. In particular because of the high ocean variability and in the vicinity of the coast in some areas. A marine gravity data compilation and screening was conducted as part of an international project GEOMED2 for calculating the geoid of the Mediterranean sea. In this paper, marine gravity data and their processing are described. The shipborne gravity data are validated and an estimation of the error is done. Then the cleaned data are used to validate the Global Geoid models (GGm).

The absolute measurement of g is currently realized through the laser interferometric measurement of a free falling retro-reflector. The Micro-g LaCoste FG5X is a free-fall gravimeter with a laser interferometer in Mach-Zehnder configuration which uses simultaneous time and distance measurements to calculate the absolute value of g. Because the instrument itself contains the necessary working standards for precise time and length measurements, it is considered independent of external references. The timing is kept with a 10 MHz rubidium oscillator with a stability of $$5 \times 10^{-10}$$ . The length unit is realized by the laser interferometer. The frequency calibrated and iodine stabilized helium-neon laser has a wavelength of 633 nm and an accuracy of $$2.5 \times 10^{-11}$$ .In 2012 the FG5-220 of the Institut für Erdmessung (IfE) was upgraded to the FG5X-220. The upgrade included a new dropping chamber with a longer free fall and new electronics including a new rubidium oscillator. The metrological traceability to measurement units of the Système International d’unités (SI unit) is ensured by two complementary and successive approaches: the comparison of frequencies with standards of higher order and the comparison of the measured g to a reference measured by absolute gravimeters defined as primary standards within the SI. A number of experiments to test the rubidium oscillator were performed. The oscillator showed a linear drift of $$0.2 \times 10^{-3}\,\mathrm{Hz}$$ per month (=  $$0.3\,\mathrm{nm}\,\mathrm{s}^{-2}$$ per month) in the first 18 months of use. A jump in the frequency of 0.01 Hz (=  $$20\,\mathrm{nm}\,\mathrm{s}^{-2}$$ ) was revealed recently and the drift rate changed to $$-0.4 \times 10^{-3}\,\mathrm{Hz}$$ /month.Since the upgrade of the absolute gravimeter the instrument participated in several international comparisons, which showed no significant measuring offset between the instrument prior and after the upgrade.

Robert Daublebsky von Sterneck, bohemian aristocrat, astronomer, geophysicist and geodesist, devoted part of his live to pendulum gravity measurements. More than one hundred Sterneck’s pendulum gravity observations were performed between 1889 and 1895 on the Czech territory (i.e Bohemia, Moravia and Czech Silesia). Until present, thorough evaluation of the accuracy of these measurements was not accomplished. On the basis of original Sterneck’s field books the station locations were investigated and their true positions identified. For this purpose, all available original handwritten notes were translated and often even puzzled out. The observed values have been compared with the actual knowledge of the Earth’s gravity field.

This paper is devoted to the problem of the ground-satellite comparison of time-variable gravity. We first review the different methods used to validate satellite gravity observations (ground truth experiment) and point out possible issues. We first show results obtained in Europe where a moderate amplitude hydrological signal exists using both satellite (GRACE) and surface gravity measurements from the GGP (Global Geodynamics Project) network of superconducting gravimeters. We show also the nice agreement between ground and GRACE observations in Djougou (West Africa) where hydrological changes due to monsoon are important. We finally present on-going projects for the so-called ‘null test’ which is related to observations in a region with no (or very small) hydrological contribution to gravity. First results for the Sahara (Algeria) are reported and future missions in Egypt and Saudi Arabia briefly introduced.

The launch of the GRACE mission brought a broad interest within the geophysical community in monitoring temporal gravity field variations. Due to the limited lifetime of GRACE, several studies have been conducted for the search of optimal GRACE follow-on and future satellite gravity missions. These studies mainly discuss the use of alternative formations like Pendulum, Cartwheel and LISA as well as the double inline pair missions with different orbits as a possible substitute of the current GRACE mission. The double satellite pair configuration in a so-called Bender constellation, however, is currently in the focus of research into time-variable gravity field recovery by future satellite missions, where the primary objective is to achieve higher temporal and spatial resolutions.When looking for optimal double inline missions, one important aspect is the impact of the groundtrack pattern of such missions on the quality of gravity recovery. The investigation of pattern distribution impact on the recovery quality may lead to a better understanding of orbital parameter optimization. This study, in particular, investigates the influence of relative differences between the ascending nodes (longitude) in a double pair mission. The research aims to show how the variations in ascending node difference change the quality of gravity solutions to the large extent. We also show the impact of the time-variable gravity field itself on the error level of the gravity solutions, i.e. how the quality of the gravity field changes simply by changing the signal being sampled, but holding the sampling constant.

Ocean tides cause notable aliasing errors in the gravity field from single pair space-borne gravimetry missions like GRACE. Several studies into future gravity missions have shown that constellations with two or more GRACE-like tandems lead to a significant reduction of aliasing error from all kinds of high-frequency signal sources. Despite such reduction, tidal aliasing will remain an error source. We here investigate the efficiency of tidal error de-aliasing in the post-processing mode for such future double-pair missions. To that purpose, we analyze how a certain satellite mission samples each tidal constituent. Given the repeat orbit patterns and the observation time span, we examine and model the alias periods and amplitudes constituent by constituent based on data-driven analysis. Results show that a double-pair formation has indeed better de-aliasing properties than a single-pair formation in terms of distribution and amplitude of ocean tide aliasing error. After least-squares (LS) spectral estimation of the tidal aliases at the derived alias periods, the aliasing error is reduced significantly.

We revisit the concept of scalar gravity anomaly determination by an airborne strapdown INS–GNSS system. We built on the previously investigated concepts (mainly within 1995–2005 period) while trying to decrease the error spectrum of the system caused by accelerometer biases at lower frequencies and GNSS-position/velocity noise at shorter wavelengths. We propose to determine the random long-term accelerometer bias through combination of −GRACE + GOCE data that provide an unbiased field with 80 km resolution while the decrease in velocity noise is expected by precise-point-positioning (PPP) method that merges satellite-phase observations from GPS and Galileo. In the absence of Galileo constellation we focus our practical demonstration on the gravity-anomaly determination via INS/GNSS data filtering. We present first the modeling of an extended Kalman filter/smoother that determines the gravity anomaly together with the trajectory, which is a preferred method over the cascade determination (i.e. separate estimation of trajectory and specific forces, GNSS acceleration and low-pass filtering of the merged signal). Second, we show how to incorporate the same modeling within the concept of dynamic networks. This approach allows imposing cross-over conditions on the state of gravity anomaly at trajectory intersections while estimating the sensor and trajectory errors at the same time. This is indeed rigorous formulation of the problem that is expected to surpass the conditioning via cross-over adjustment that in previous investigations followed the filtering-smoothing. Despite the remaining challenges of the method of dynamic network caused by large number of parameters (i.e. > 106), we present first assessment of such implementation that was obtained within European FP7 GAL project.

This paper is devoted to an overview of the use of hybrid gravimetry in Earth and Environmental Sciences. We first recall the concept of hybrid gravimetry which relies on the simultaneous use of different types of gravimeters either superconducting, absolute or relative spring gravimeters. This combination of instruments provides a complete tool for time-lapse gravimetry: while superconducting gravimeters and/or absolute gravimeters are used to obtain temporal gravity changes at one or several base stations, relative gravity surveys provide spatial differences with respect to these base stations, and allow to cover a much wider area than base stations only. Hybrid gravimetry therefore provides time-lapse gravity changes at a survey scale. We present here an overview of different published applications in hydrology, glaciology, volcanology and geothermics in order to point out that hybrid gravimetry is a powerful tool to monitor spatially and temporarily surface and underground mass changes.

We present a comparison in the various tidal bands, between two different spectral analyses of long gravimetric time series. The first one is performed using a long gravity series recorded by superconducting gravimeters at J9 Observatory (Strasbourg) and the second one uses a theoretical series of the same length, almost 28 years, computed for the same location according to the Hartmann and Wenzel tidal potential development.Long term gravity records are of great interest when performing spectral analysis. The length of the data series allows us to retrieve small amplitude waves in the major tidal groups (e.g. tides generated by the third-degree potential, as for example 3MO₁ in the diurnal, 3MO₂ in the semi-diurnal, and MN₃ in the ter-diurnal frequency band, with amplitudes respectively of 2.29, 5.97 and 1.44 nm/s2), to separate waves close in frequency, as the waves NO₁ and NO_1X which need more than 18 year data length to be separated and finally to detect very low-frequency signals such as the monthly, semiannual or annual waves. Several examples for each of these cases are shown in our series.

Since 2006 the gravity change at 17 points in Sweden has been observed with Lantmäteriet’s absolute gravimeter FG5-233. The main purpose of the observations is to study the postglacial rebound in Fennoscandia. In 2010, a suspected jump of a few μGal can be seen in the gravity time series that significantly affects the estimated gravity rate of changes. It is shown that if the jump is not considered, then the absolute value of the gravity rate of change is systematically underestimated compared to the land uplift model NKG2014LU_test. In this paper two different ways to estimate and apply corrections of the jump are demonstrated. The first is to estimate the jump from the observations themselves within a least squares adjustment, while the second is to assume the instrument bias obtained in international comparisons of absolute gravimeters. The best agreement between land uplift model and estimated rates of change of gravity is achieved by correcting the data with the official biases reported from the international comparisons.

We propose a comparison of the tidal analysis results obtained from the continuous records of time-varying surface gravity collected by a worldwide network of Superconducting Gravimeters with the analysis results of space nutation observed by the international Very Long Baseline Interferometry (VLBI) network. The length of the surface gravity time series (20 years for the longest) enables now to look for additional diurnal tides that were previously not analyzed. In parallel, we now possess 35 years of VLBI data permitting to look for additional nutation terms. We focus our analysis on the diurnal prograde frequency band in the search for a possible resonance effect linked to the Free Inner Core Nutation. This Earth’s normal mode has never been clearly observed. Its direct deformation effect at the Earth’s surface is theoretically predicted to be too small to be detected. However, the tidal forcing at a frequency close to its eigenfrequency could enhance some tidal or nutation amplitude resulting in the characterization of this mode through its resonance effect.

To study the Earth global deformation at periods ranging from a few hours to a few thousand years, we consider a homogeneous compressible Earth model with either a Maxwell or a Burgers rheology. First, we compute, for the harmonic degree ℓ = 2, the ratio between the gravity variation and the vertical surface displacement due to surface loading as a function of the forcing period. In the elastic domain, up to the relaxation time of the rheological model, which is 226 years, the ratio is almost constant and equal to − 0. 26 μGal/mm. In the viscoelastic domain, above 10,000 years, the ratio tends to − 0. 08 μGal/mm. In between, the transition is smooth. Second, we compute the period T_CW and quality factor Q_anel of the Chandler wobble as a function of the rheological parameters of a Burgers model. The influence of both the steady-state and transient viscosities on T_CW is significant only for viscosity values smaller than what can usually be found in the literature for the mantle viscosities and Q_anel is more sensitive than T_CW to the transient viscosity.

The contribution of the diurnal atmospheric S₁ tide to Earth’s wobble is assessed by tidally analyzing hourly polar motion (PM) estimates from approximately 25 years of geodetic Very Long Baseline Interferometry (VLBI) observations. Special emphasis is placed on the dependency of S₁ estimates on various settings in the a priori delay model and on the method of time series analysis in post-processing. The considered VLBI solutions differ with regard to the inclusion/exclusion of weak network geometries and the choice of a priori geophysical corrections such as thermal antenna deformation. Prograde PM coefficients $$\text{A}^{+} + i\text{B}^{+}$$ of S₁ are on the level of 9 + i10 μas (microarcseconds) for all solutions and none of the changes in the processing strategies perturbs this estimate beyond the twofold S₁ standard deviation ( $$\sim$$ 2.6 μas). An independent validation of the deduced harmonics against excitation estimates from atmosphere-ocean models shows that space geodetic and geophysical accounts of the S₁ effect in PM are still inconsistent by about 10 μas.

The resonance associated with the Free Core Nutation (FCN) has been widely studied in Very Long Base Interferometry (VLBI) network measurements and in superconducting gravity records, but few experiments have been done with tiltmeters. In this study we use records collected with a pair of about 100 m long hydrostatic silica tiltmeters, orthogonally installed in an abandoned silver mine at Sainte Croix aux Mines (Alsace, in North-Eastern France). Main difficulties in retrieving FCN parameters from tidal analysis arise from the weak amplitude of PSI1 tidal wave (the closest in frequency to the FCN), as well as from the inaccuracy of the available ocean loading correction. Moreover because of the closeness in frequency of the single constituents of the diurnal tidal band, long (>1 year) records are needed for resolving K1, PSI1 and PHI1 waves. Hence we analyze a 10-year dataset of tilt records, which has preliminarily required a critical review and a relevant editing for making records suitable for tidal analysis and subsequent inversion of the tidal parameters. A Bayesian inversion is used for a preliminary retrieval of the FCN parameters.

Space-Geodetic techniques are used to provide fundamental scientific products like the terrestrial and celestial reference frame or the Earth orientation parameters (EOPs). These parameters are typically determined in a least squares adjustment of redundant observations. Within this process, numerical issues materializing in the condition of the equation system as well as in insufficient stability of the solution play an important role. While bad condition numbers are an indicator of numerical problems having no connection to the solution strategy i.e., the algorithms used for solving the equation system, numerical stability refers to the algorithms which are used. This paper focuses on the impact of numerical conditioning on EOPs.Exemplarily for other space-geodetic techniques, we analyze the data analysis of Very Long Baseline Interferometry (VLBI) observations. For VLBI, the equation system of the least squares adjustment is apparently ill-conditioned. Thus, errors of the observations would be amplified during the adjustment process. However, we show that the conditioning is not that bad as it highly depends on the parametrization and we present options to improve the conditioning in VLBI data analysis. We present methods to reveal the relationship between numerical characteristics of the involved matrices and the EOPs.

Based on European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-Interim data we model displacements of global station coordinates due to non-tidal atmospheric loading based on Farrel’s theory. We compare these displacements to publicly available external displacements. We apply our displacements to Satellite Laser Ranging (SLR) data processing over a recent 6 years period of the LAGEOS, LARES, AJISAI, STARLETTE and STELLA geodetic satellites. We assess the impact of the loading model on the orbital fits of these missions. Indeed a tiny improvement shows up. We also quantify the impact of the non-tidal loading model on the large scale figure of the Earth expressed in terms of weekly C(2,0) harmonics. It turns out that here no effect is visible.

The requirement for the quantification of sea level rise and other global change phenomena are precise and stable reference frames. To accord with these science driven requirements, GGOS, the Global Geodetic Observing System, aims for reference frame accuracy of 1 mm, stability of 0.1 mm/year, and Earth Orientation Parameters accuracy of ∼ 30 μas. At this level of precision a variety of otherwise neglected effects has to be taken into account. In our article we investigate whether the use of meteorological data for the analysis of space geodetic techniques could be one of these effects that need to be considered. The article moves forward in finding an optimized meteorological data set in order to provide results at the required accuracy level. At the Very Long Baseline Interferometry (VLBI) stations of the International VLBI Service for Geodesy and Astrometry meteorological data are observed and are customarily applied for analyses. Observed data can contain outliers and inhomogeneities that have to be appropriately accounted for. We test the two blind models GPT and GPT2 as a replacement for locally observed data. We find that both cause small seasonal signals in the celestial pole offsets with an amplitude of ∼ 15 μas. We also assess whether the mean values as obtained by extrapolation of surface or near-surface data of ERA-Interim reanalysis product or of the World Meteorological Organization can be used as reference values for homogenization of the observed meteorological data. In particular at sites where the model surface height and the height of the space geodetic reference point differ significantly, very large differences were found. Hence, we cannot recommend shifting the mean value of the observed data to the mean values derived by hypsometrically adjusted surface data.

The history of monitoring Earth orientation goes back to the end of nineteenth century, when polar motion was discovered. Description of international efforts in organizing coordinated observations to determine Earth’s orientation is presented. The services, such as International Latitude Service (ILS), Bureau International de l’Heure (BIH), International Polar Motion Service (IPMS) and, finally, International Earth Rotation and Reference Systems Service (IERS), are described, as well as the observational techniques used by them. Each improvement of the techniques and their accuracies led to new discoveries and corresponding improvements of the theory of Earth’s rotation. From the very beginning of these efforts, classical astrometric observations were used for almost one century. Later on, as more precise modern data obtained by space geodesy appeared, new and more accurate theories of precession-nutation became necessary. Finally, to explain the differences between the observations and theory, more and more data from other sources (mainly of geophysical origin) became necessary to be considered. These data and their effects are also shortly commented. Here we concentrate on optical astrometry that dominated throughout the twentieth century; namely we present some important re-analyses of these observations. Special attention is devoted to the re-analyses done in 1998–2012 at the Astronomical Institute, Czech Academy of Sciences. Data covering 1899.7–1992.0 were used to derive Earth orientation parameters and to improve star positions and proper motions in the Hipparcos celestial reference frame.

In this contribution, we present full-rank observation equations of the network and user receivers, of mixed types, through an application of $$\mathcal{S}$$ -system theory. We discuss the important roles played by the inter system biases (ISBs), and we show how the three-component structure of PPP-RTK is affected by the inclusion of the ISBs as extra parameters in the model.

Real-time Precise Point Positioning (PPP) is expected to find more and more applications with various precise satellite orbit and clock products becoming more easily and reliably available. A crucial aspect for current real-time PPP system is the transmission of precise satellite orbit and clock correction data to the PPP users at a high update rate, typically 1–2 min for orbit corrections and 1–10 s for clock corrections. Such a high update rate is a challenge to many applications since it requires continuous data links for PPP users to timely receive the correction data. Therefore, latency and loss of the correction data incurred by the data links are major concerns in addition to communication cost. This paper describes a new correction update method with potential to address the concerns, which transmits initial parameters for orbit and clock to the users which can be at a much lower update rate. The preliminary numerical results have been provided with encouraging performance.

The China’s BeiDou system is the first global satellite navigation system to broadcast the three frequency signals for full constellation. A lot of studies have been done recently for positioning and navigation by using BeiDou three frequency signals, but mostly based on the GPS-like empirical stochastic model. This paper aims to study the stochastic modelling of BeiDou observations and then analyze its impact on the ambiguity resolution and precision positioning. To generalize the stochastic model, the satellite-dependent precisions, cross correlations between arbitrary two frequencies and time correlations for each frequency are set up. The results indicate that comparing with empirical stochastic model, the realistic stochastic model can improve the ambiguity resolution and positioning precision. Besides, the derived variance matrix of parameters with realistic stochastic model can objectively reflect the actual precisions of parameter estimates, which is rather important for solution evaluation in real applications.

Microwave space-geodetic observations such as Global Navigation Satellite Systems (GNSS) or Very Long Baseline Interferometry (VLBI) are delayed in the neutral atmosphere. In order to improve the quality of these techniques for precise applications like reference frame realisation, we need to get more knowledge about the temporal and spatial refractivity variations in the neutrosphere. In addition to the annually to hourly long periodic variations, which can be considered within the adjustment process, micro-scale meteorological phenomena in the range of minutes to sub-seconds affect space-geodetic observations as well. Thus, induced phase fluctuations of wavefronts passing through the turbulent medium form a significant error source for electromagnetic wave propagation.In order to identify high-frequency atmospheric effects, we analysed 1 Hz high-rate GPS observations from the continuous operating GNSS station at the Geodetic Observatory Wettzell and derived post-fit carrier phase residuals for several days with a Kalman-Filter based Precise Point Positioning (PPP) approach. Since undifferenced carrier phase observations contain a superposition of several effects, the computed power-law behaviour of the residuals might not follow the theoretically predicted stochastical behaviour for refractivity fluctuations. Hence, the influence of multipath was identified. A residual stacking was performed, and the reduced residuals were analysed with regard to turbulence characteristics.

Local ties are vectors that link reference points of different space geodetic instruments at co-located stations. Discrepancies between local ties and solutions from space geodetic techniques weaken the determination of reference frames. Terrestrially determined local ties and GPS-derived coordinates differences can disagree at the cm-level due to suboptimal GPS processing.In this paper, we propose a post-processing correction strategy to reduce apparent height differences which occur when, unnecessarily, tropospheric delay are estimated between co-located stations or tropospheric constraints between co-located stations are not taken into account. A site-dependent correction factor is determined which stays constant over time and thus can be calibrated. The correction strategy is successfully applied to co-located stations in the pillar network of our institute where the local tie is well-controlled. We find that height discrepancies between levelling survey and post-processed GPS results can be reduced from the centimeter-level to some millimeters. This holds also true for co-located GPS stations of the EUREF Permanent Network.

Evaluating the impact of receiver antenna phase centre corrections (PCCs) in geodetic positioning and timing applications in a general way is quite challenging, because several estimation concepts, implementation philosophies as well as different sets of PCCs exist and interact with each other and their contributions are not identifiable. In this paper, the authors present a methodology, based on investigations of Geiger (GPS-techniques applied to geodesy and surveying. Lecture notes in earth sciences, vol 19. Springer, New York, pp 210–222, 1988) and Santerre (Manuscr Geodaet 16:28–53, 1991), to classify PCCs and forecast their impact on all geodetic parameters, i.e. not only the position but also the receiver clock and troposphere parameter in a phase based precise point positioning (PPP) approach. In a first step, we introduce the mathematical model and generic PCC patterns. In the second step, simulation studies are carried out. Findings are evaluated by empirical studies using differences of PPP results to isolate the impact of different patterns. In parallel, the software impact is analysed since every software handles the observation modelling and parameter estimation differently, e.g., Kalman filter versus least squares approach. We show that all geodetic parameters are affected by PCC and that the impact on the parameters can be even amplified compared to the magnitude of the generic patterns.

Geodetic time series obtained via space-geodetic techniques, e.g. site displacements from continuous gps observations and aggregated basin water storages from grace, display a seasonal behavior. Much focus has been given to separate such periodic signal from other signals buried in the geodetic time series, e.g. linear or non-linear trends. Conventionally, these seasonal signals are retrieved with constant amplitudes by the classical least squares estimation approach. Recently, singular spectrum analysis (ssa) has been successfully applied to extract the time variable seasonal signals from the gps time series. This study aims to extend the application of ssa to other geodetic time series. Through two examples, i.e. water level time series from satellite altimetry and grace-derived basin averaged equivalent water height time series, the capabilities of ssa to separate the non-linear trend from seasonal signals are demonstrated. In addition, it is shown that the so-called w-correlation analysis is beneficial in determining the optimal embedding window size, which is a key parameter during ssa analysis.

The number of Global Navigation Satellite System (GNSS) satellites and their geometry directly affect the quality of positioning and derived satellite products. Accordingly, the International GNSS Service (IGS) recommends GNSS antennas to be installed away from natural and man-made surfaces and structures, which may affect the incoming signals through severe multipath or obstructions. Following these recommendations, continuous GNSS (cGNSS) stations are generally located in low multipath environments with minimal signal obstructions. However, some applications require GNSS antennas to be installed at specific locations in order to measure local processes. In support of sea level studies, cGNSS stations are established at or close to tide gauges in order to accurately monitor the local vertical land movements experienced by the sea level sensors. However, the environment at the tide gauge might not be optimal for GNSS observations due to the aforementioned station-specific effects, which may degrade the quality of coordinate solutions. This study investigates the impact of severe signal obstructions on long-term position time series for some selected stations. A masking profile from an actually obstructed site is extracted, simulated and applied to unobstructed IGS sites. To investigate these effects, we implemented a new feature called azimuth-dependent elevation masking in the Bernese GNSS Software version 5.2. We present our preliminary results on the use of this new feature to study the impact of different obstruction scenarios on long-term GNSS position time series and vertical land movement estimates. The results show that a certain obstruction, with the effect being highly dependent on its severity and azimuthal direction, affects all coordinate components with the effect being more significant for the Up component. Moreover, it causes changes in the rate estimates and increases the rate uncertainty with the effect being site-specific.

The generation of position time series in geodetic networks is often based on the successive forward implementation of the Helmert transformation (HT) to daily/weekly solutions using the transformation parameters obtained from a separate least-squares adjustment over a selected set of reference stations. An overlooked problem with this approach is that the noise of the daily/weekly solutions is fully absorbed into the transformed station positions, or even amplified if we consider the additional uncertainty of the estimated Helmert parameters. Its filtering is therefore a desirable task which could enhance the geophysical content of geodetic time series to be analyzed in a global secular frame. To accommodate the need for such filtering, we present in this paper an epoch-wise stacking approach for the HT-based alignment of a series of daily/weekly frames to a common secular frame via an integrated estimation process. The resulting transformation formulae differ from the classic HT solution in terms of Kalman-like corrections, and they lead to an improved solution in the sense of minimizing the error variances of the transformed positions in the target frame.

Although conventionally used for positioning, navigation, and timing, GNSS observations constitute a useful tool for atmospheric remote sensing. By quantifying and analyzing the influence of the atmosphere on the propagating electromagnetic signals, we can infer a significant amount of information for further understanding Earth’s atmosphere as well as its relationship with satellite positioning activities. For some industrial sectors that require high accuracy and reliability, such as oil exploration, dredging, and aviation, the understanding of how GNSS satellite signals propagate across the atmosphere is crucial information. Among several improvements related to GNSS, the increasing number of in-orbit Galileo satellites opens a new window of opportunities for atmospheric research. Users can achieve improved satellite geometry and take advantage of Galileo signal characteristics, such as improved signal strength. In this study, the usage of Galileo signals for neutral atmospheric delay (NAD) estimation is assessed along with its integration with signals from the already established GPS constellation. Using the University of New Brunswick’s GNSS Analysis and Positioning Software (GAPS) precise point positioning suite, the NAD values are estimated and integrated with in situ measurements of pressure, temperature, and humidity, allowing us to estimate the integrated water vapor (IWV) of the atmosphere above a GNSS station. As a reference for the estimation assessment, existing IWV values from radiosondes are used. Preliminary results show that the Galileo + GPS NAD estimations are close to those of GPS at the 2-centimeter level. The recently-released multi-GNSS processing online version of GAPS is now able to provide users with a useful tool for atmospheric research.

In this paper, we analyze the tropospheric delay observed on some ground-based CGPS stations in a dense small regional network and its time evolution during extreme weather conditions. In particular, we studied two severe weather events occurring in the Campanian Region (Italy) on October 12, 2012 and December 2, 2014, reaching 42 and 28 mm rainfall during about 1 h at Naples (MAFE) and Gragnano (GRAG) stations respectively. The main concern of this study is the retrieval of the precipitable water (PW) from co-located GPS and meteorological stations. We investigate the correlation between PW and rain amount at ground level. We analyse phase residuals for each visible GPS satellite using sky plots of the phase residuals along the GPS satellites tracks, showing that the two phenomena are shown in the phase residual plots. Moreover, we compare PW data retrieved from observed meteorological data and from models (GPT2 and ECMWF), evidencing that there is a need for co-located CGPS and weather stations to improve the assessment of water content in the troposphere.

We investigate the possibilities to use data from water vapor radiometers (WVR) to calibrate the wet tropospheric delays in geodetic Very Long Baseline Interferometry (VLBI) observations. We test three methods: (1) direct calibration using WVR measurements aquired in the directions of the VLBI observations, (2) estimating zenith wet delays and gradients from the WVR data and use these to correct the VLBI data, and (3) including the WVR measurements as additional observations in the VLBI data analysis. Furthermore, in all cases we model the WVR calibration errors in the data analysis. We test the three methods using data from the continuous VLBI campaigns CONT02–CONT14. We find clear improvements when applying methods 1 and 3 for CONT05 campaign, however, the results are degraded for the other campaigns.

The Nakagawa lowland is located in the central part of the Kanto Plain; the largest plain in Japan. During the 1960s, major land subsidence occurred, exceeding 10 cm/year, as a result of over pumping of shallow and deep groundwaters in this area. In recent times, following the regulation of pumping by national and local governments, the amount of land subsidence in this area has decreased sharply. However, in the Nakagawa lowland, subsidence exceeding 1 cm/year is still ongoing in some areas, and is more pronounced during dry years in which the amount of groundwater use increases. In this study, we examined the local characteristics of land subsidence through persistent scatterer interferometry using ALOS/PALSAR data obtained from April 2006 to April 2011. On the basis of this analysis, we confirmed that subsidence was concentrated along the western margin of an incised buried valley, in which average displacement rates exceed 10 mm/year. The characteristics of this subsidence zone are suggestive of a geological structure that is buried beneath the alluvial plains, which is affected by groundwater pumping that targets the basal gravel layers of buried valley-fills. In addition, we detected a patched zone of around 0.3 km2 in the study area, in which average displacement rates exceed 15 mm/year. We estimated that this zone was formed by consolidation settlement of soft ground as a result of residential landfill.

Greece is characterized by complex and intense geodynamics, because it is located between the collision boundaries of two tectonic plates (Africa-Nubia and Eurasia), with major active tectonic features such as the Hellenic Arc, the Anatolian fault in North Aegean Trough and the Kefalonia fault in the Ionian Sea. GPS is a well-established tool for geophysical research purposes, because it is able to provide continuous measurements for monitoring displacements of the Earth’s crust. The aim of the present study is to create a modern and improved geodetic velocity field for Greece using GPS observations from continuously operating reference stations. The new set of geodetic velocities is derived from the processing of 7 years (2008–2014) of daily GPS data, using 155 stations distributed in the broader Greek territory and 30 IGS-EPN GPS stations. The GAMIT/GLOBK software package was used to process the GPS measurements. The results are expressed in the ITRF2008 reference frame. The analysis showed that the northern region of Greece is the most stable and has identical movement with the Eurasian plate in contrast with the region of the southern part and the Aegean Sea. According to the results, the estimated horizontal geodetic velocities show completely different pattern between northern and southern Greece with significant differences both in magnitude and direction. The derived site values were used for a velocity grid creation in order to predict velocities within the Greek area and to enforce proper realization of GNSS reference systems in Greece.

As it is well known, GNSS data analysis is a powerful tool to study geodynamic processes. However, observational methodologies and data analysis results should be adapted to determine local or even regional effects. It is particularly important in tectonic plate boundary areas when looking for subduction zone limits.When using Continuous GNSS (CGNSS) observing receiver networks, a set of precise topocentric coordinates (e, n, u) for each place, will be available. Furthermore time series formed by the daily positions will produce the sites temporal variations. If those time series are long enough, horizontal components (e, n) use to show linear behaviors if there are no other geodynamic effect affecting the tectonic plates movement. Anyway the height component (u) uses to show periodical but not linear effects. But often time series are disturbed by different processes, as local subsidence, periodic dilatation compression effects, GNSS signal interferences, etc.This paper shows a detailed topocentric coordinates time series study for sites belonging to what we call the SPINA network, which stands for South of the Iberian Peninsula, North of Africa Region. To avoid the above mentioned local effects, a priori quality control is carefully performed. Solutions are obtained by processed positioning with respect to a IGS reference station and by PPP processing (Precise Point Positioning), using the Bernese software. Results will be compared and combined. Then, a designed methodology, using filter processes, harmonic adjustments and wavelets will be applied. As final product we expect to get horizontal displacement model to describe the regional geodynamic main characteristics.

Natural glacier events such as ice avalanches, debris flows or glacier lake outburst floods (GLOF) may have hazardous impacts on the downstream area of the glacier and can cause severe destructions. The Inylchek Glaciers in Kyrgyzstan, are one of the largest non-polar glacier systems in the world. Each year, an ice-dammed lake is formed (Lake Merzbacher) by melt-water which drains predominantly every year suddenly within a few days causing a destructive flood. To understand the mechanism of the GLOF, a network of continuously operating GPS stations at the Inylchek Glaciers provide daily horizontal and vertical positions of the ice-dam in front of the Merzbacher Lake. Irrespective of the general motion during the year, the ice-dam is strongly influenced by the formation and outburst of the lake. Especially the vertical position and surface velocities increase shortly before the GLOF supporting the assumption that the ice-dam adjacent to the lake becomes afloat. After the GLOF, e.g. in 2014, the elevation decreases rapidly by 20 m within 8 days. In 2015, the GLOF changes in timing, magnitude and available lake water volume but the motion pattern of the ice-dam is similar compared to the year before. These comparable results have the potential to develop an early warning system for the glacier-dammed lake outburst flood.

Water is a scarce resource in many regions of the world. In all Central Asian countries, the society depends on the availability of water either for hydro-power generation or irrigation. Since the collapse of the Soviet Union and the separation into independent countries, water resources management became a critical and political issue. Public information on water resources is now unavailable for many lakes and reservoirs and the data exchange about in- and outflows or actual storage volumes is limited. While the initial purpose of radar altimetry has been to measure sea surface topography and sea level changes, it proved to be a suitable tool for inland water body monitoring and to partially provide data about lake and reservoir level changes. Using this technology, the water levels of the Toktogul, Kairakum and Shardara Reservoirs and Lake Aydarkol have been extracted from 1995 onward. Using external information the derived water levels have been converted into water volume changes. This study shows that since 2011 the available water volume decreased and the water from the Toktogul and Shardara Reservoirs are overused. In 2015 the stored water volume of the Toktogul Reservoir was almost at its lowest possible amount. Merely the Kairakum Reservoir with a smaller storage capacity is replenished every year. Likewise, a decrease of water level and volume of Lake Aydarkol is clearly visible for the past years.