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Funding Information: We would like to thank Arthur Niell very much for the comments during the reviews. The results reported in this paper used the data coordinated by the International VLBI Service (IVS) and its international self‐funded member organizations. We are grateful to the IVS stations at Hartebeesthoek (South Africa Radio Astronomical Observatory), Ishioka (Geospatial Information Authority of Japan), Kokee Park (U.S. Naval Observatory and NASA GSFC, USA), Ny‐Ålesund (Norwegian Mapping Authority, Norway), Onsala (Onsala Space Observatory, Chalmers University of Technology, Sweden), Shanghai (Shanghai Astronomical Observatory, China), Wettzell (Bundesamt für Kartographie und Geodäsie and Technische Universität München, Germany), and Yebes (Instituto Geográfico Nacional, Spain), to the staff at the Bonn Correlator, the Washington Correlator, the Onsala Observatory Correlator, and the MIT Haystack Observatory correlator for performing the correlations and the fringe fitting of the data, to the NASA GSFC VLBI group and the BKG VLBI group for doing the geodetic solutions, and to the IVS Data Centers at BKG (Leipzig, Germany), Observatoire de Paris (France), and NASA CDDIS (Greenbelt, MD, USA) for the central data holdings. This research has made use of the Generic Mapping Tools package, the pgplot library, and the SAO/NASA Astrophysics Data System. The work was supported by the Academy of Finland project No. 315721. Open Access funding enabled and organized by Projekt DEAL. Funding Information: We would like to thank Arthur Niell very much for the comments during the reviews. The results reported in this paper used the data coordinated by the International VLBI Service (IVS) and its international self-funded member organizations. We are grateful to the IVS stations at Hartebeesthoek (South Africa Radio Astronomical Observatory), Ishioka (Geospatial Information Authority of Japan), Kokee Park (U.S. Naval Observatory and NASA GSFC, USA), Ny-Ålesund (Norwegian Mapping Authority, Norway), Onsala (Onsala Space Observatory, Chalmers University of Technology, Sweden), Shanghai (Shanghai Astronomical Observatory, China), Wettzell (Bundesamt für Kartographie und Geodäsie and Technische Universität München, Germany), and Yebes (Instituto Geográfico Nacional, Spain), to the staff at the Bonn Correlator, the Washington Correlator, the Onsala Observatory Correlator, and the MIT Haystack Observatory correlator for performing the correlations and the fringe fitting of the data, to the NASA GSFC VLBI group and the BKG VLBI group for doing the geodetic solutions, and to the IVS Data Centers at BKG (Leipzig, Germany), Observatoire de Paris (France), and NASA CDDIS (Greenbelt, MD, USA) for the central data holdings. This research has made use of the Generic Mapping Tools package, the pgplot library, and the SAO/NASA Astrophysics Data System. The work was supported by the Academy of Finland project No. 315721. Open Access funding enabled and organized by Projekt DEAL. Publisher Copyright: © 2023. The Authors. We report the results of position ties for short baselines at eight geodetic sites based on phase delays that are extracted from global geodetic very-long-baseline interferometry (VLBI) observations rather than dedicated short-baseline experiments. An analysis of phase delay observables at X band from two antennas at the Geodetic Observatory Wettzell, Germany, extracted from 107 global 24-hr VLBI sessions since 2019 yields weighted root-mean-square scatters about the mean baseline vector of 0.3, 0.3, and 0.8 mm in the east, north, and up directions, respectively. Position ties are also obtained for other short baselines between legacy antennas and nearby, newly built antennas. They are critical for maintaining a consistent continuation of the realization of the terrestrial reference frame, especially when including the new VGOS network. The phase delays of the baseline WETTZ13N–WETTZELL enable an investigation of sources of error at the sub-millimeter level. We found that a systematic variation of larger than1 mm can be introduced to the Up estimates of this baseline vector when atmospheric delays were estimated. Although the sub-millimeter repeatability has been achieved for the baseline vector WETTZ13N–WETTZELL, we conclude that long term monitoring should be conducted for more short baselines to assess the instrumental effects, in particular the systematic differences between phase delays and group delays, and to find common solutions for reducing them. This will be an important step toward the goal of global geodesy at the 1 mm level.

Very Long Baseline Interferometry (VLBI) intensive (INT) sessions are critical for the rapid determination and densification of Universal Time 1-Coordinate Universal Time (UT1-UTC), which plays an important role in satellite geodesy and space exploration missions and is not predictable over longer time scales. Due to the limited observation geometry of INT sessions with two to three stations observing about 1 hr, tropospheric gradients cannot be estimated, which degrades the UT1-UTC precision. We investigate the impact of tropospheric ties at Global Navigation Satellite Systems (GNSSs) and VLBI co-located stations in INT sessions from 2001 to 2021. VLBI and GNSS observations are combined on the observation level. The results are evaluated by using both UT1-UTC and Length of Day (LOD) from consecutive sessions. We demonstrate a better agreement of 10%–30% when comparing the derived LOD to GNSS LOD for INT1, INT2, and VGOS-2 sessions; whereas, the agreement is not improved when directly comparing UT1-UTC to the IERS Earth Orientation Parameters (EOPs) product, potentially because INT sessions also contribute to IERS EOP products. The major impact comes from tropospheric gradient ties, whereas applying zenith delay ties does not improve or even deteriorate UT1-UTC agreement. Gradient ties also introduce systematic biases in UT1-UTC by around −3 to −5 μs, except for the Russian INT sessions. Regression analysis shows that the east gradient introduces systematic effects in UT1-UTC for sessions involving Germany and USA (Hawaii), whereas for Germany–Japan and Russian sessions, the north gradient also contributes systematically.

The location of the Earth's principal axes of inertia is a foundation for all the theories and solutions of its rotation, and thus has a broad effect on many fields, including astronomy, geodesy, and satellite-based positioning and navigation systems. That location is determined by the second-degree Stokes coefficients of the geopotential. Accurate solutions for those coefficients were limited to the stationary case for many years, but the situation improved with the accomplishment of Gravity Recovery and Climate Experiment (GRACE), and nowadays several solutions for the time-varying geopotential have been derived based on gravity and satellite laser ranging data, with time resolutions reaching one month or one week. Although those solutions are already accurate enough to compute the evolution of the Earth's axes of inertia along more than a decade, such an analysis has never been performed. In this paper, we present the first analysis of this problem, taking advantage of previous analytical derivations to simplify the computations and the estimation of the uncertainty of solutions. The results are rather striking, since the axes of inertia do not move around some mean position fixed to a given terrestrial reference frame in this period, but drift away from their initial location in a slow but clear and not negligible manner.

This article focuses on the new generation of geodetic very long baseline interferometry (VLBI), the VLBI global observing system (VGOS), and measurements carried out during the CONT17 campaign. It uses broadband technology that increases both the number and precision of observations. These characteristics make VGOS a suitable tool for studying the atmosphere. This study focuses on the effects of the ionosphere on VGOS signals using a model that incorporates and extends ideas originally published in Hobiger et al. (2006, https://doi.org/10.1029/2005RS003297). Our investigation revealed that the differential total electron content (dTEC) data product calculated with the VGOS post-processing software had a sign error that fortunately, does not change the final values of the phase and group delay. Therefore, this study was a way to identify this problem within the dTEC product. After diagnosing and solving this problem, the underlying model was modified such that instead of considering a single unknown for the latitude gradient of the ionosphere, a time series of latitude gradients were considered that enhanced the resulting vertical total electron content (VTEC) estimates. For evaluation purposes, time series of VTEC at each station during the CONT17 campaign were compared with VTEC obtained from the global navigation satellite system (GNSS). The final agreement between VGOS and GNSS was between 1.1 and 5.9 TEC units (TECU).

Global Geodetic Observing System (GGOS) requires an accuracy of 1 mm and a stability of 1 mm/decade for the Terrestrial Reference Frame (TRF), which is not achieved yet. Global Navigation Satellite Systems (GNSS) play a critical role in TRF determination, thanks to its continuous observations collected from hundreds of globally distributed stations. GNSS observations at the user side are affected by antenna, receiver, and the local environment. The impact of the antenna is more significant to carrier-phase observations and handled with the phase center offset and variation corrections, meanwhile that of the receiver is more significant to the pseudo-range observations. In this study, we investigate the long-term agreement of station coordinates at co-located GNSS stations, i.e., more than one GNSS stations within a few hundreds of meters. We demonstrate that (1) the coordinate difference between co-located GNSS stations could have seasonal variations and long-term trends, (2) discontinuities are often observed after instrument changes, especially the antenna change, and (3) different receiver types could cause station coordinate bias up to 1 mm. A preliminary investigation of the possible reasons is carried out and addressed as well.

Tropospheric delay modeling is challenging in high-precision Very Long Baseline Interferometry (VLBI) analysis due to the rapid water vapor variation and imperfect observation geometry, where observations from Global Navigation Satellite Systems (GNSS) co-locations can enhance the VLBI analysis. We investigate the impact of tropospheric ties in the VLBI and GNSS integrated processing during the CONT05–CONT17 campaigns, and present a method that automatically handles the systematic tropospheric tie biases. Applying tropospheric ties at VLBI–GNSS co-locations enhances the observation geometry and improves the solution reliability. The VLBI network is stabilized, with station coordinate repeatability improved by 12% horizontally and by 28% vertically, and the network scale improved by 32%. The Earth Orientation Parameters (EOP) improve by up to 20%. Both zenith delay and gradient ties contribute to the improvement of EOP, whereas the gradient ties contribute mainly to the improvement of length of day and celestial pole offsets.

The international celestial and terrestrial reference frames (ICRF and ITRF) are two important realizations of the global geodetic reference frame (GGRF). As the basis for high-accuracy astrometry and space exploration, ICRF is currently determined by the Very Long Baseline Interferometry (VLBI) technique solely and independently from the ITRF, whereas a consistent determination of TRF and CRF by a combination of different techniques is highly desirable. We conduct the Global Navigation Satellite Systems (GNSS) and VLBI integrated processing on the observation level and investigate the impact of applying global ties (that is, Earth Orientation Parameters, EOP), local ties, and tropospheric ties on the precision of both TRF and CRF. The GNSS and VLBI observations in VLBI continuous campaigns from CONT05 to CONT17 are processed simultaneously in the common least-squares estimator using the Positioning And Navigation Data Analyst (PANDA) software. We present that the precision of the VLBI station coordinates is significantly improved in the integrated solution, such as the horizontal components by global ties and the vertical components by local and tropospheric ties. Focusing on the precision of active galactic nuclei (AGN) coordinates, we demonstrate that the global ties can slightly reduce the AGN coordinate formal errors by up to 4%, and the local ties mainly improve the declination precision by about 10%. As for the tropospheric ties, the formal error of AGN coordinate can be reduced by 10% on average, and the repeatability can also be improved, especially the declination (10%). Moreover, the southern AGN are more improved than the northern ones, due to the observation geometry of the VLBI ground station distribution.

The Continuous Very Long Baseline Interferometry (VLBI) campaign 2017 (CONT17) differs from previous CONT campaigns as there are three independent networks observing in parallel; two legacy VLBI networks observing in S/X band (Legacy-1 and Legacy-2) and one VGOS (the next generation VLBI system: VLBI2010) network observing in broadbrand. Co-located VLBI radio telescopes across the networks could be combined to strengthen the geodetic solutions from CONT17 by using local ties. Moreover, it is widely known that the co-located VLBI radio telescopes observe common effects such as the tropospheric delays in a similar way. Therefore, we can not only combine the station coordinates, but we can also combine the tropospheric parameters. In this work, we focused on the impact of combining the tropospheric parameters obtained at co-located VLBI telescopes on the estimated geodetic parameters during CONT17. We considered three case studies where we combined: (i) the Legacy-1 and the Legacy-2 networks, (ii) the Legacy-1 and the VGOS networks, and (iii) the Legacy-1, the Legacy-2, and the VGOS networks. The results show an improvement in station position repeatability when combining the tropospheric parameters w.r.t. applying only local ties by 28%, 15%, and 26% respectively. Station coordinates at the VLBI radio telescopes of the Legacy-1 network were not affected by this approach as they were used for the datum definition. In addition, the baseline length repeatabilities show no improvement when combining the tropospheric parameters. Moreover, the agreement between the tropospheric parameters from VLBI and tropospheric parameters from independent GNSS data analysis and ray-tracing through ERA5 improves due to the network combination.

The relationship between the length of day (LOD) and El-Niño Southern Oscillation (ENSO) has been well studied since the 1980s. LOD is the negative time-derivative of UT1-UTC, which is directly proportional to Earth Rotation Angle (ERA), one of the Earth Orientation Parameters (EOP). The EOP can be determined using Very Long Baseline Interferometry (VLBI), which is a space geodetic technique. In addition, satellite techniques such as the Global Navigation Satellite System (GNSS), Satellite Laser Ranging (SLR), Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) can provide Earth Rotation Parameters, i.e., polar motion and LOD. ENSO is a climate phenomenon occurring over the tropical eastern Pacific Ocean that mainly affects the tropics and the subtropics. Extreme ENSO events can cause extreme weather like flooding and droughts in many parts of the world. In this work, we investigated the effect of ENSO on the LOD from January 1979 to April 2022 using the wavelet coherence method. This method computes the coherence between the two non-stationary time-series in the time-frequency domain using the real-valued Morlet wavelet. We used the Multivariate ENSO index version 2 (MEI v.2) which is the most robust series as the climate index for the ENSO, and LOD time-series from IERS (EOP 14 C04 (IAU2000A)). We also used Oceanic Niño and Southern Oscillation index in this study for comparison. The results show strong coherence of 0.7 to 0.9 at major ENSO events for the periods 2–4 years between LOD and MEI.v2.

The real-time Earth orientation parameters (EOP) estimation is needed for many applications, including precise tracking and navigation of interplanetary spacecraft, climate forecasting, and disaster prevention. However, the complexity and time-consuming data processing always lead to time delays. Accordingly, several methods were developed and applied for the EOP prediction. However, the accuracy of EOP prediction is still not satisfactory even for prediction of just a few days in the future. Therefore, new methods or a combination of the existing approaches can be investigated to improve the predicted EOP. To assess the various EOP prediction capabilities, the international Earth rotation and reference systems service (IERS) established the working group on the 2nd Earth Orientation Parameters Prediction Comparison Campaign (2nd EOP PCC).Our EOP prediction team provides the full set of EOP predictions weekly for one year ahead. The SSA+Copula method and the empirical free core nutation (FCN) model (named B16) are used for Earth rotation parameters and celestial pole offsets (CPO) prediction, respectively. Our preliminary results illustrate an improvement in EOP prediction compared to the current EOP prediction methods, especially on CPO. Additionally, the comparison with other method results indicates that the proposed techniques can efficiently and precisely predict the EOP at different terms (short, mid, and long term).

We report the results of position ties for short baselines at eight geodetic sites based on phase delays that are extracted from global geodetic very-long-baseline interferometry (VLBI) observation...

Atmospheric ties are theoretically affected by the height differences between antennas at the same site and the meteorological conditions. However, there is often a discrepancy between the expected zenith delay differences and those estimated from geodetic analysis, potentially degrading a combined solution employing atmospheric ties. In order to investigate the possible effects on GNSS atmospheric delay, this study set up an experiment of four co-located GNSS stations of the same type, both antenna and receiver. Specific height differences for each antenna w.r.t the reference antenna are given. One antenna was equipped with a radome at the same height and type as a antenna close to the ground. In addition, a meteorological sensor was used for meteorological data recording. The results show that tropospheric ties from the analytical equation based on meteorological data from GPT3, Numerical Weather Model, and in-situ measurements, and ray-traced tropospheric ties, reduced the bias of zenith delay roughly by 72 %. However, the in-situ tropospheric ties yield the best precision in this study. These results demonstrate, that the instrument effects on GNSS zenith delays were mitigated by using the same instrument. In contrast, the radome causes unexpected bias of GNSS zenith delays in this study. Additionally, multipath effects at low-elevation observations degraded the tropospheric east gradients.

Atmospheric ties are the differences of atmospheric parameters between antennas or stations at the same site and meteorological conditions. However, there is often a discrepancy between the expected zenith delay differences and those estimated from geodetic analysis, potentially degrading a combined solution employing atmospheric ties to constrain atmospheric delay differences. To investigate the possible effects on GNSS atmospheric delay, this study set up an experiment with four co-located GNSS stations of the same type, both antenna and receiver. Specific height differences for each antenna w.r.t. one reference antenna have been measured. One antenna was equipped with a radome of the same height and type as an antenna close to the ground. Additionally, a meteorological sensor was used for meteorological data recording. The results show that tropospheric ties from the analytical equation based on meteorological data from Global Pressure and Temperature 3 (GPT3) model, Numerical Weather Models, in-situ measurements, and ray-traced tropospheric ties, reduced the bias of zenith delay roughly by 72 %. However, the in-situ tropospheric ties yielded the best precision in this study. These results demonstrate that the instrument effects on GNSS zenith delays were mitigated using the same instrument. In contrast, although the effects of the radome on atmospheric delays are well known, the magnitude of the effects determined in this study is unexpectedly large. Additionally, multipath effects at low-elevation observations degraded the tropospheric gradients. To extract the instrument effect, we set up another experiment with three GNSS stations and four different antennas. The height differences between the three stations were on one centimeter level. One of the three stations could be adjusted in height to control the height displacement after changing antenna. We succeeded in keeping the shift in the GNSS zenith delays within 2 mm level. The bias on GNSS zenith delays and tropospheric gradients agrees with the result of the previous experiment in this study. Moreover, we successfully detected the antenna-dependent effect on both the GNSS zenith delays and gradients from this experiment.

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.

The new data release of the Gaia satellite operated by the European Space Agency recently published its 3rd data release (Early Data Release 3, EDR3). The dataset contains astrometric data of about 1.8 billion objects detected at optical frequencies and therefore it outperforms any catalog of astrometric information up to date. The reference frame defined by Gaia EDR3 is aligned to the International Celestial Reference System by referring to counterparts in its realization, the third International Celestial Reference Frame (ICRF3), which is calculated from very long baseline interferometry (VLBI) observations of extragalactic objects at radio frequencies. The Gaia dataset is known to be magnitude-dependent in terms of astrometric calibration. As the objects in ICRF3, although bright at radio frequencies, are mostly faint at optical frequencies, the optically bright Gaia frame has to be linked to ICRF3 by additional counterparts besides objects in ICRF3. The non-rotation of the optically bright Gaia frame is especially important as optically bright objects can, besides astrophysical studies, be used for navigation in space, where other geodetic systems like global navigation satellite systems are out of reach. Suitable additional counterparts are radio stars which are observed by VLBI relative to extragalactic objects in ICRF3. We discuss the orientation and spin differences between the optically bright Gaia EDR3 and VLBI data of radio stars and their impact on the Gaia data usage.

The Potsdam Open Source Radio Interferometry Tool (PORT) is the very long baseline interferometry (VLBI) analysis software developed and maintained at the GFZ German Research Centre for Geosciences. Chiefly, PORT is tasked with the timely processing of VLBI sessions and post-processing activities supporting the generation of celestial and terrestrial reference frames. In addition, it serves as a framework for research and development within the GFZ's VLBI working group and is part of the tool set employed in educating young researchers. Starting out from VLBI group delays, PORT estimates station and radio sources positions, as well as Earth orientation parameters, tropospheric parameters, and station clock offsets and drifts. The estimation procedures take into account all the necessary data analysis models that were agreed on for contributing to the ITRF2020 processing activities. The PORT code base is implemented in the MATLAB (R) and Python programming languages. It is licensed under the terms of the GNU General Public License and available for download at GFZ's Git server ., Publications of the Astronomical Society of the Pacific, 133 (1028)

The next-generation, broadband geodetic very long baseline interferometry system, named VGOS, is developing its global network, and VGOS networks with a small size of 3--7 stations have already made broadband observations from 2017 to 2019. We made quality assessments for two kinds of observables in the 21 VGOS sessions currently available: group delay and differential total electron content ($\delta$TEC). Our study reveals that the random measurement noise of VGOS group delays is at the level of less than 2 ps (1 ps = 10$^{-12}$ s), while the contributions from systematic error sources, mainly source structure related, are at the level of 20 ps. Due to the significant improvement in measurement noise, source structure effects with relatively small magnitudes that are not overwhelming in the S/X VLBI system, for instance 10 ps, are clearly visible in VGOS observations. Another critical error source in VGOS observations is discrete delay jumps, for instance, a systematic offset of about 310 ps or integer multiples of that. The predominant causative factor is found to be related to source structure. The measurement noise level of $\delta$TEC observables is about 0.07 TECU, but the systematic effects are five times larger than that. A strong correlation between group delay and $\delta$TEC observables is discovered with a trend of 40 ps/TECU for observations with large structure effects; there is a second trend in the range 60 ps/TECU to 70 ps/TECU when the measurement noise is dominant., Comment: 25 pages, 11 figures, and accepted for publication in Journal of Geodesy

A new realization of the International Celestial Reference Frame (ICRF) is presented based on the work achieved by a working group of the International Astronomical Union (IAU) mandated for this purpose. This new realization, referred to as ICRF3, is based on nearly 40 years of data acquired by very long baseline interferometry. The ICRF3 includes positions at 8.4 GHz for 4536 sources, supplemented with positions at 24 GHz for 824 sources and at 32 GHz for 678 sources, for a total of 4588 sources. A subset of 303 sources among these, uniformly distributed on the sky, are identified as "defining sources" and as such serve to define the axes of the frame. Source positions are reported for epoch 2015.0 and must be propagated for observations at other epochs for the most accurate needs, accounting for the acceleration toward the Galactic center, which results in a dipolar proper motion field of amplitude 0.0058 milliarcsecond/yr (mas/yr). The frame shows a median positional uncertainty of about 0.1 mas in right ascension and 0.2 mas in declination, with a noise floor of 0.03 mas in the individual source coordinates. A subset of 500 sources is found to have extremely accurate positions at 8.4 GHz, in the range of 0.03 to 0.06 mas. Comparing ICRF3 with the Gaia Celestial Reference Frame 2 in the optical domain, there is no evidence for deformations larger than 0.03 mas between the two frames. Significant positional offsets between the three ICRF3 frequencies are detected for about 5% of the sources. Moreover, a notable fraction (22%) of the sources shows optical and radio positions that are significantly offset. There are indications that these positional offsets may be the manifestation of extended source structures. This third realization of the ICRF was adopted by the IAU at its 30th General Assembly in August 2018 and replaced the previous realization, ICRF2, on January 1, 2019., Comment: 28 pages, 22 figures

International audience; There has been growing interest in recent years in the use of homogeneously reprocessed ground-based GNSS, VLBI, and DORIS measurements for climate applications. Existing datasets are reviewed and the sensitivity of tropospheric estimates to the processing details is discussed. The uncertainty in the derived IWV estimates and linear trends is around 1 kg m−2 RMS and ± 0.3 kg m−2 per decade, respectively. Standardized methods for ZTD outlier detection and IWV conversion are proposed. The homogeneity of final time series is limited however by changes in the stations equipment and environment. Various homogenization algorithms have been evaluated based on a synthetic benchmark dataset. The uncertainty of trends estimated from the homogenized times series is estimated to ±0.5 kg m−2 per decade. Reprocessed GNSS IWV data are analysed along with satellites data, reanalyses and global and regional climate model simulations. A selection of global and regional reprocessed GNSS datasets and ERA-interim reanalysis are made available through the GOP-TropDB tropospheric database and online service. A new tropo SINEX format, providing new features and simplifications, was developed and it is going to be adopted by all the IAG services.

Atmospheric ties are affected by the differences of atmospheric parameters of space geodetic techniques at co-location sites. Similar to local ties, they could be applied along with local ties for a combination of space geodetic techniques to improve the realization of terrestrial reference frames (TRF). Theoretically, atmospheric ties are affected by the height differences between antennas at the same site and meteorological conditions. Therefore, atmospheric ties could be determined by analytical equation based on meteorological information from in situ measurements or weather model. However, there is often a discrepancy between the expected zenith delay differences and those estimated from geodetic analysis, thus potentially degrading a combined atmospheric ties solution. In this study, we analyse the time series of zenith delays from co-located GNSS antennas at Wettzell (height differences below 3 meters), for 11 years (2008–2018). GNSS observations were analyzed with Bernese GNSS software version 5.2 with double-differencing technique and relative tropospheric delay and gradients were estimated with L1, L2, and the ionosphere-free (L3) linear combination thereof. Atmospheric ties were derived analytically employing meteorological data from Global Pressure and Temperature model 3 (GPT3) and ERA5 reanalysis, as well as corrections derived from ray tracing (Potsdam Mapping Functions, PMF). The comparison shows that zenith delay differences are dominated by equipment changes. The discrepancies between atmospheric ties and estimated zenith delay differences are frequency dependent, with the L1 solutions being the least biased. For these small vertical differences, seasonal signals are not significant for all frequencies.

This report focuses on some selected scientific outcomes of the activities developed by the IAU/IAG Joint Working Group on Theory of Earth rotation and validation along the term 2015–2019. It is based on its end-of-term report to the IAG Commission 3 published in the Travaux de l’IAG 2015–2019, which in its turn updates previous reports to the IAG and IAU, particularly the triennial report 2015–2018 to the IAU Commission A2, and the medium term report to the IAG Commission 3 (2015–2017). The content of the report has served as a basis for the IAG General Assembly to adopt Resolution 5 on Improvement of Earth rotation theories and models. JMF, AE, and JG were partially supported by Spanish Project AYA2016-79775-P (AEI/FEDER, UE). The work of RSG described in this paper was performed at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. Support for that work was provided by the Earth Surface and Interior Focus Area of NASA’s Science Mission Directorate.

The exceptional situation of simultaneously observing a dedicated near-Earth orbiting satellite via the four main space geodetic techniques opens the unique opportunity to investigate the additional benefits on the realization of global terrestrial reference frame using co-location in space. Applying co-location in space requires a precise orbit determination (POD) of dedicated satellites for all techniques. In this regard, current VLBI infrastructure is extended by the observation to satellites and the impact of such observation concept on the VLBI estimates is assessed. Thus the main geodetic products including the terrestrial reference frame are investigated within the GGOS-SIM-II project. In this study, the potential influence of orbital errors on the estimates and capability of VLBI observations to satellites within the POD are investigated for different scenarios with varying networks, observation time and measurement noise.

The terrestrial and celestial reference frames, which serve as the basis for geodesy and astronomy, are mainly determined and maintained by space geodetic techniques such as Very Long Baseline Interferometry (VLBI), Satellite Laser Ranging (SLR), Global Navigation Satellite Systems (GNSS), and DORIS (Doppler Orbitography and Radiopositioning Integrated by Satellite). These techniques are also used together to determine the Earth Orientation Parameters (EOP), which are very important for precise positioning, navigation and timing. Currently, the combination of all these techniques is done on the parameter level (ITRF) or on the normal equation level (DTRF), which are well-known and convenient methods but may suffer from some inconsistency.Unlike the combination on the parameter or normal equation levels, the integrated processing at the observation level exploits the lengths and unique features of different techniques, and is valuable in determining homogeneous reference frames and EOP, and to connect the terrestrial, celestial, and dynamic frames. We are applying the integrated GNSS, VLBI and SLR data processing in the current Positioning And Navigation Data Analyst (PANDA) software, which aims on processing multi-geodetic techniques on the observation level. We present the strategy and current status of the integrated GNSS and VLBI processing and demonstrate the benefit of integrating GNSS for VLBI using 14 years of VLBI intensive sessions (2001-2014) and five CONT campaigns (2005-2017). We discuss the impact of applying tropospheric tie and local tie in the integrated processing.

The Earth precession-nutation model endorsed by resolutions of each the International Astronomical Union and the International Union of Geodesy and Geophysics is composed of two theories developed independently, namely IAU2006 precession and IAU2000A nutation. The IAU2006 precession was adopted to supersede the precession part of the IAU 2000A precession-nutation model and tried to get the new precession theory dynamically consistent with the IAU2000A nutation. However, full consistency was not reached, and slight adjustments of the IAU2000A nutation amplitudes at the micro arcsecond level were required to ensure consistency. The first set of formulae for these corrections derived by Capitaine et al. (Astrophys 432(1):355–367, 2005), which was not included in IAU2006 but provided in some standards and software for computing nutations. Later, Escapa et al. showed that a few additional terms of the same order of magnitude have to be added to the 2005 expressions to get complete dynamical consistency between the official precession and nutation models. In 2018 Escapa and Capitaine made a joint review of the problem and proposed three alternative ways of nutation model and its parameters to achieve consistency to certain different extents, although no estimation of their respective effects could be worked out to illustrate the proposals. Here we present some preliminary results on the assessment of the effects of each of the three sets of corrections suggested by Escapa and Capitaine (Proceedings of the Journées, des Systémes de Référence et de la Rotation Terrestre: Furthering our Knowledge of Earth Rotation, Alicante, 2018) by testing them in conjunction with the conventional celestial pole offsets given in the IERS EOP14C04 time series. The four first authors were partially supported by Spanish Project AYA2016-79775-P (AEI/FEDER, UE).

Very Long Baseline Interferometry (VLBI) plays an indispensable role in the realization of global terrestrial and celestial reference frames and in the determination of the full set of the Earth Orientation Parameters (EOP). The main goal of this research is to assess the quality of the VLBI observations based on the sensitivity and robustness criteria. Sensitivity is defined as the minimum displacement value that can be detected in coordinate unknowns. Robustness describes the deformation strength induced by the maximum undetectable errors with the internal reliability analysis. The location of a VLBI station and the total weights of the observations at the station are most important for the sensitivity analysis. Furthermore, the total observation number of a radio source and the quality of the observations are important for the sensitivity levels of the radio sources. According to the robustness analysis of station coordinates, the worst robustness values are caused by atmospheric delay effects with high temporal and spatial variability. During CONT14, it is determined that FORTLEZA, WESTFORD, and TSUKUB32 have robustness values changing between 0.8 and 1.3 mm, which are significantly worse in comparison to the other stations. The radio sources 0506-612, NRAO150, and 3C345 have worse sensitivity levels compared to other radio sources. It can be concluded that the sensitivity and robustness analysis are reliable measures to obtain high accuracy VLBI solutions.

On the impact of gravitational deformation on VLBI-derived parameters Sahar Shoushtari1,2, Susanne Glaser1, Kyriakos Balidakis1, Robert Heinkelmann1,2, James M. Anderson1,2, Harald Schuh1,2(1) GFZ German Research Centre for Geosciences, Section 1.1 Space Geodetic Techniques, Telegrafenberg, 14473 Potsdam, Germany(2) Technische Universität Berlin, Chair of Satellite Geodesy, Strasse des 17. Juni 135, 10623 Berlin, GermanyVery Long Baseline Interferometry (VLBI) is a highly accurate space geodetic technique that observes extragalactic radio sources to measure the time delay between arrival times of a plane wavefront at two distant radio telescopes. The gravitational deformation of the VLBI telescopes as a function of pointing direction, caused by gravitational forces acting on the massive telescope structures, mainly impacts the estimated station heights and can reach centimeter-level for large antennas. Thus far, this effect has not been considered in operational VLBI data analysis. In the next realization ITRF2020, it is envisaged to model this effect in an effort to reduce the persistent scale discrepancy in ITRF2014 between VLBI and Satellite Laser Ranging. Currently, there are models for only a minority of antennas available, six in total: Effelsberg, Gilcreek, Medicina, Noto, Onsala, and Yebes, which are provided by the International VLBI Service for Geodesy and Astrometry (IVS). In this study, the impact of the gravitational models on station positions, Earth orientation parameters and the network scale is assessed within VLBI data analysis. The standard 24-hours IVS-R1 and -R4 sessions are analyzed using the PORT (Potsdam Open-source Radio Interferometry Tool) software package. First results show that the gravitational models of the six antennas change the station heights by a few mm and the horizontal components by less than 1 mm (in case of Medicina).

The recent dramatic development of multi-GNSS (Global Navigation Satellite Systems) constellations brings great opportunities and potential for more enhanced precise positioning, navigation, timing, and other applications. Significant improvement on positioning accuracy, reliability, as well as convergence time with the multi-GNSS fusion can be observed in comparison with the single-system processing like GPS (Global Positioning System). In this study, we develop a numerical weather model (NWM)-constrained PPP processing system to improve the multi-GNSS precise positioning. Tropospheric delay parameters which are derived from the European Centre for Medium-Range Weather Forecasts (ECMWF) analysis are applied to the multi-GNSS PPP, a combination of four systems: GPS, GLONASS, Galileo, and BeiDou. Observations from stations of the IGS (International GNSS Service) Multi-GNSS Experiments (MGEX) network are processed, with both the standard multi-GNSS PPP and the developed NWM-constrained multi-GNSS PPP processing. The high quality and accuracy of the tropospheric delay parameters derived from ECMWF are demonstrated through comparison and validation with the IGS final tropospheric delay products. Compared to the standard PPP solution, the convergence time is shortened by 32.0 %, 37.5 %, and 25.0 % for the north, east, and vertical components, respectively, with the NWM-constrained PPP solution. The positioning accuracy also benefits from the NWM-constrained PPP solution, which gets improved by 2.5 %, 12.1 %, and 18.7 % for the north, east, and vertical components, respectively.

Terrestrial reference frames (TRF), such as the ITRF2008, are primary products of geodesy. In this paper, we present TRF solutions based on Kalman filtering of very long baseline interferometry (VLBI) data, for which we estimate steady station coordinates over more than 30 years that are updated for every single VLBI session. By applying different levels of process noise, non-linear signals, such as seasonal and seismic effects, are taken into account. The corresponding stochastic model is derived site-dependent from geophysical loading deformation time series and is adapted during periods of post-seismic deformations. Our results demonstrate that the choice of stochastic process has a much smaller impact on the coordinate time series and velocities than the overall noise level. If process noise is applied, tests with and without additionally estimating seasonal signals indicate no difference between the resulting coordinate time series for periods when observational data are available. In a comparison with epoch reference frames, the Kalman filter solutions provide better short-term stability. Furthermore, we find out that the Kalman filter solutions are of similar quality when compared to a consistent least-squares solution, however, with the enhanced attribute of being easier to update as, for instance, in a post-earthquake period.

Geodetic/astrometric very long baseline interferometry (VLBI) has been routinely observing using various global networks for 40 yr, and it has produced more than 10 million baseline group delay, phase, and amplitude observables. These group delay observables are analyzed worldwide for geodetic and astrometric applications, for instance, to create the International Celestial Reference Frame (ICRF). The phase and amplitude observables are used in this paper, by means of closure analysis, to study intrinsic source structures and their evolution over time. The closure amplitude rms, CARMS, indicating how far away a source is from being compact in terms of morphology, is calculated for each individual source. The overall structure-effect magnitudes for 3417 ICRF radio sources are quantified. CARMS values larger than 0.3 suggest significant source structures and those larger than 0.4 indicate very extended source structures. The 30 most frequently observed sources, which constitute 40% of current geodetic VLBI observables, are studied in detail. The quality of ICRF sources for astrometry is evaluated by examining the CARMS values. It is confirmed that sources with CARMS values larger than 0.30 can contribute residual errors of about 15 ps to geodetic VLBI data analysis and those with the CARMS values larger than 0.4 generally can contribute more than 20 ps. We recommend CARMS values as an indicator of the astrometric quality for the ICRF sources and the continuous monitoring of the ICRF sources to update CARMS values with new VLBI observations as they become available.

Local ties (LTs) at co-located sites are currently used to combine different single-technique solutions to determine global terrestrial reference frames (TRFs). We assess by simulations the impact of different LT standard deviations, biased LTs and a selection of LTs on the datum realization of global TRFs. The simulations are based on Global Positioning System (GPS), Satellite Laser Ranging, and Very Long Baseline Interferometry (VLBI) observations covering the time span 2008–2014. We find that LT standard deviations of 1 cm and better yield differences in the TRF-defining parameters below 1 mm. VLBI is most affected by altering the LT standard deviations, especially in the translations since VLBI is inherently not sensitive to the origin of the TRF. Altering the standard deviations of the LTs applied in ITRF2005, ITRF2008, ITRF2014 results in small differences reaching a maximum of 0.6 mm at the VLBI stations. Simulating technique-wise biased LT stations shows the largest differences in the TRF-defining parameters of more than 2 mm, if all GPS LT stations are biased by 1 cm, proving that GPS plays the major role in the connection of the three techniques. Simulating single biased LT stations by 1 cm in either the north, east, or height component indicates small differences of less than 0.8 mm in the TRF-defining parameters, the largest differences result at LT stations located on the southern hemisphere. The selection of LTs demonstrates that the southern hemisphere LTs are very important, especially for the realization of the scale.

The tropospheric horizontal gradients with high spatiotemporal resolutions provide important information to describe the azimuthally asymmetric delays and significantly increase the ability of ground-based GNSS (Global Navigation Satellite Systems) within the field of meteorological studies, like the nowcasting of severe rainfall events. The recent rapid development of multi-GNSS constellations has potential to provide such high-resolution gradients with a significant degree of accuracy. In this study, we develop a multi-GNSS process for the precise retrieval of high-resolution tropospheric gradients. The tropospheric gradients with different temporal resolutions, retrieved from both single-system and multi-GNSS solutions, are validated using independent numerical weather models (NWM) data and water vapor radiometer (WVR) observations. The benefits of multi-GNSS processing for the retrieval of tropospheric gradients, as well as for the improvement of precise positioning, are demonstrated. The multi-GNSS high-resolution gradients agree well with those derived from the NWM and WVR, especially for the fast-changing peaks, which are mostly associated with synoptic fronts. The multi-GNSS gradients behave in a much more stable manner than the single-system estimates, especially in cases of high temporal resolution, benefiting from the increased number of observed satellites and improved observation geometry. The high-resolution multi-GNSS gradients show higher correlation with the NWM and WVR gradients than the low-resolution gradients. Furthermore, the precision of station positions can also be noticeably improved by multi-GNSS fusion, and enhanced results can be achieved if the high-resolution gradient estimation is performed, instead of the commonly used daily gradient estimation in the multi-GNSS data processing.

The revitalized Russian GLONASS system provides new potential for real-time retrieval of zenith tropospheric delays (ZTD) and precipitable water vapor (PWV) in order to support time-critical meteorological applications such as nowcasting or severe weather event monitoring. In this study, we develop a method of real-time ZTD/PWV retrieval based on GLONASS and/or GPS observations. The performance of ZTD and PWV derived from GLONASS data using real-time precise point positioning (PPP) technique is carefully investigated and evaluated. The potential of combining GLONASS and GPS data for ZTD/PWV retrieving is assessed as well. The GLONASS and GPS observations of about half a year for 80 globally distributed stations from the IGS (International GNSS Service) network are processed. The results show that the real-time GLONASS ZTD series agree quite well with the GPS ZTD series in general: the RMS of ZTD differences is about 8 mm (about 1.2 mm in PWV). Furthermore, for an inter-technique validation, the real-time ZTD estimated from GLONASS-only, GPS-only, and the GPS/GLONASS combined solutions are compared with those derived from very long baseline interferometry (VLBI) at colocated GNSS/VLBI stations. The comparison shows that GLONASS can contribute to real-time meteorological applications, with almost the same accuracy as GPS. More accurate and reliable water vapor values, about 1.5---2.3 mm in PWV, can be achieved when GLONASS observations are combined with the GPS ones in the real-time PPP data processing. The comparison with radiosonde data further confirms the performance of GLONASS-derived real-time PWV and the benefit of adding GLONASS to stand-alone GPS processing.

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.

We performed Monte Carlo simulations of very-long-baseline interferometry (VLBI) observations of Earth-orbiting satellites incorporating co-located space-geodetic instruments in order to study how well the VLBI frame and the spacecraft frame can be tied using such measurements. We simulated observations of spacecraft by VLBI observations, time-of-flight (TOF) measurements using a time-encoded signal in the spacecraft transmission, similar in concept to precise point positioning, and differential VLBI (D-VLBI) observations using angularly nearby quasar calibrators to compare their relative performance. We used the proposed European Geodetic Reference Antenna in Space (E-GRASP) mission as an initial test case for our software. We found that the standard VLBI technique is limited, in part, by the present lack of knowledge of the absolute offset of VLBI time to Coordinated Universal Time at the level of microseconds. TOF measurements are better able to overcome this problem and provide frame ties with uncertainties in translation and scale nearly a factor of three smaller than those yielded from VLBI measurements. If the absolute time offset issue can be resolved by external means, the VLBI results can be significantly improved and can come close to providing 1 mm accuracy in the frame tie parameters. D-VLBI observations with optimum performance assumptions provide roughly a factor of two higher uncertainties for the E-GRASP orbit. We additionally simulated how station and spacecraft position offsets affect the frame tie performance.

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.