We investigated the suitability of the astronomical 15 GHz Very Long Baseline Array (VLBA) observing program MOJAVE-5 for estimation of geodetic parameters, such as station coordinates and Earth orientation parameters. We processed a concurrent dedicated VLBA geodesy program observed at 2.3 GHz and 8.6 GHz starting on September 2016 through July 2020 as reference dataset. We showed that the baseline length repeatability from MOJAVE-5 experiments is only a factor of 1.5 greater than from the dedicated geodetic dataset and still below 1 ppb. The wrms of the difference of estimated Earth orientation parameters with respect to the reference IERS C04 time series are a factor of 1.3 to 1.8 worse. We isolated three major differences between the datasets in terms of their possible impact on the geodetic results, i.e. the scheduling approach, treatment of the ionospheric delay, and selection of target radio sources. We showed that the major factor causing discrepancies in the estimated geodetic parameters is the different scheduling approach of the datasets. We conclude that systematic errors in MOJAVE-5 dataset are low enough for these data to be used as an excellent testbed for further investigations on the radio source structure effects in geodesy and astrometry.

Satellite altimetry and gravimetry are used to determine the mean seasonal cycle in relative sea level, a quantity relevant to coastal flooding and related applications. The main harmonics (annual, semiannual, terannual) are estimated from 25 years of gridded altimetry, while several conventional altimeter "corrections" (gravitational tide, pole tide, and inverted barometer) are restored. To transform from absolute to relative sea levels, a model of vertical land motion is developed from a high-resolution seasonal mass inversion estimated from satellite gravimetry. An adjustment for annual geocenter motion accounts for use of a center-of-mass reference frame in satellite orbit determination. A set of 544 test tide gauges, from which seasonal harmonics have been estimated from hourly measurements, is used to assess how accurately each adjustment to the altimeter data helps converge the results to true relative sea levels. At these gauges, the median annual and semiannual amplitudes are 7.1 cm and 2.2 cm, respectively. The root-mean-square differences with altimetry are 3.24 and 1.17 cm, respectively, which are reduced to 1.93 and 0.86 cm after restoration of corrections and adjustment for land motion. Example outliers highlight some limitations of present-day coastal altimetry owing to inadequate spatial resolution: upwelling and currents off Oregon and wave setup at Minamitori Island.

A long-term drift in polar motion (PM) has been observed for more than a century, and Glacial Isostatic Adjustment (GIA) has been understood as an important cause. However, observed PM includes contributions from other sources, including contemporary climate change and perhaps others associated with Earth's interior dynamics. It has been difficult to separate these effects, because there is considerable scatter among GIA models concerning predicted PM rates. Here we develop a new method to estimate GIA PM using data from the GRACE mission. Changes in GRACE degree 2, order 1 spherical harmonic coefficients are due both to GIA and contemporary surface mass load changes. We estimate the surface mass load contribution to degree 2, order 1 coefficients using GRACE data, relying on higher-degree GRACE coefficients that are dominantly affected by surface loads. Then the GIA PM trend is obtained from the difference between observed PM trend (which includes effects from GIA and surface mass loads) and the estimated PM trend mostly associated with surface mass loads. A previous estimate of the GIA PM trend from PM observations for the period 1900-1978 is toward 79.90° W at a speed of 3.53 mas/year (10.91 cm/year). Our new estimate for the GIA trend is in a direction of 61.77° W at a speed of 2.18 mas/year (6.74 cm/year), similar to the observed PM trend during the early twentieth century. This is consistent with the view that the early twentieth-century trend was dominated by GIA and that more recently there is an increasing contribution from contemporary surface mass load redistribution associated with climate change. Our GIA PM also agrees with the linear mean pole during 1900-2017. Contributions from other solid Earth process such as mantle convection would also produce a linear trend in PM and could be included in our GIA estimate.

We revisit the problem of modeling the ocean's contribution to rapid, non-tidal Earth rotation variations at periods of 2-120 days. Estimates of oceanic angular momentum (OAM, 2007-2011) are drawn from a suite of established circulation models and new numerical simulations, whose finest configuration is on a grid. We show that the OAM product by the Earth System Modeling Group at GeoForschungsZentrum Potsdam has spurious short period variance in its equatorial motion terms, rendering the series a poor choice for describing oceanic signals in polar motion on time scales of less than 2 weeks. Accounting for OAM in rotation budgets from other models typically reduces the variance of atmosphere-corrected geodetic excitation by 54% for deconvolved polar motion and by 60% for length-of-day. Use of OAM from the model does provide for an additional reduction in residual variance such that the combined oceanic-atmospheric effect explains as much as 84% of the polar motion excitation at periods < 120 days. Employing statistical analysis and bottom pressure changes from daily Gravity Recovery and Climate Experiment solutions, we highlight the tendency of ocean models run at a 1 grid spacing to misrepresent topographically constrained dynamics in some deep basins of the Southern Ocean, which has adverse effects on OAM estimates taken along the 90 meridian. Higher model resolution thus emerges as a sensible target for improving the oceanic component in broader efforts of Earth system modeling for geodetic purposes.

The satellite missions GRACE and GRACE Follow-On have undoubtedly been the most important sources to observe mass transport on global scales. Within the Combination Service for Time-Variable Gravity Fields (COST-G), gravity field solutions from various processing centers are being combined to improve the signal-to-noise ratio and further increase the spatial resolution. The time series of monthly gravity field solutions suffer from a data gap of about one year between the two missions GRACE and GRACE Follow-On among several smaller data gaps. We present an intermediate technique bridging the gap between the two missions allowing (1) for a continued and uninterrupted time series of mass observations and (2) to compare, cross-validate and link the two time series. We focus on the combination of high-low satellite-to-satellite tracking (HL-SST) of low-Earth orbiting satellites by GPS in combination with satellite laser ranging (SLR), where SLR contributes to the very low degrees and HL-SST is able to provide the higher spatial resolution at an lower overall precision compared to GRACE-like solutions. We present a complete series covering the period from 2003 to 2022 filling the gaps of GRACE and between the missions. The achieved spatial resolution is approximately 700 km at a monthly temporal resolutions throughout the time period of interest. For the purpose of demonstrating possible applications, we estimate the low degree glacial isostatic adjustment signal in Fennoscandia and North America. In both cases, the location, the signal strength and extend of the signal coincide well with GRACE/GRACE-FO solutions achieving 99.5% and 86.5% correlation, respectively.

Global geodetic VLBI is upgrading to its next-generation observing system, VGOS. This upgrade has turned out to be a process over multiple years, until VGOS reaches its full capabilities with the envisaged continuous observations. Until then, for the Australian stations, the upgrade means ceasing their legacy S/X observations, leaving a large gap in the global network as well as in the station time series. The Australian mixed-mode observing program is a series of sessions where the VGOS stations in Hobart and Katherine observe legacy S/X VLBI together with other stations in the region. This paper describes the technical details of these observations and their processing strategies and discusses their suitability for geodetic results by comparison with those of standard legacy S/X sessions. The presented mixed-mode sessions allow a continuation of the station time series, a benefit for the stations themselves as well as for future realisations of the terrestrial and celestial reference frames. A novel mode of observing is introduced and tested. The results are promising and it is suggested for acceptance into standard legacy S/X IVS observations, overcoming current gaps in the network due to VGOS upgrades and preventing a worsening of global results otherwise.

ESA's Gravity field and steady-state Ocean Circulation Explorer (GOCE) orbited the Earth between 2009 and 2013 for the determination of the static part of Earth's gravity field. The GPS-derived precise science orbits (PSOs) were operationally generated by the Astronomical Institute of the University of Bern (AIUB). Due to a significantly improved understanding of remaining artifacts after the end of the GOCE mission (especially in the GOCE gradiometry data), ESA initiated a reprocessing of the entire GOCE Level 1b data in 2018. In this framework, AIUB was commissioned to recompute the GOCE reduced-dynamic and kinematic PSOs. In this paper, we report on the employed precise orbit determination methods, with a focus on measures undertaken to mitigate ionosphere-induced artifacts in the kinematic orbits and thereof derived gravity field models. With respect to the PSOs computed during the operational phase of GOCE, the reprocessed PSOs show in average a 8-9% better consistency with GPS data, 31% smaller 3-dimensional reduced-dynamic orbit overlaps, an 8% better 3-dimensional consistency between reduced-dynamic and kinematic orbits, and a 3-7% reduction of satellite laser ranging residuals. In the second part of the paper, we present results from GPS-based gravity field determinations that highlight the strong benefit of the GOCE reprocessed kinematic PSOs. Due to the applied data weighting strategy, a substantially improved quality of gravity field coefficients between degree 10 and 40 is achieved, corresponding to a remarkable reduction of ionosphere-induced artifacts along the geomagnetic equator. For a static gravity field solution covering the entire mission period, geoid height differences with respect to a superior inter-satellite ranging solution are markedly reduced (43% in terms of global RMS, compared to previous GOCE GPS-based gravity fields). Furthermore, we demonstrate that the reprocessed GOCE PSOs allow to recover long-wavelength time-variable gravity field signals (up to degree 10), comparable to information derived from GPS data of dedicated satellite missions. To this end, it is essential to take into account the GOCE common-mode accelerometer data in the gravity field recovery.

The global navigation satellite system (GNSS) daily position time series are often described as the sum of stochastic processes and geophysical signals which allow to study global and local geodynamical effects such as plate tectonics, earthquakes, or ground water variations. In this work, we propose to extend the Generalized Method of Wavelet Moments (GMWM) to estimate the parameters of linear models with correlated residuals. This statistical inferential framework is applied to GNSS daily position time-series data to jointly estimate functional (geophysical) as well as stochastic noise models. Our method is called GMWMX, with X standing for eXogenous variables: it is semi-parametric, computationally efficient and scalable. Unlike standard methods such as the widely used maximum likelihood estimator (MLE), our methodology offers statistical guarantees, such as consistency and asymptotic normality, without relying on strong parametric assumptions. At the Gaussian model, our results (theoretical and obtained in simulations) show that the estimated parameters are similar to the ones obtained with the MLE. The computational performances of our approach have important practical implications. Indeed, the estimation of the parameters of large networks of thousands of GNSS stations (some of them being recorded over several decades) quickly becomes computationally prohibitive. Compared to standard likelihood-based methods, the GMWMX has a considerably reduced algorithmic complexity of order for a time series of length . Thus, the GMWMX appears to provide a reduction in processing time of a factor of 10-1000 compared to likelihood-based methods depending on the considered stochastic model, the length of the time series and the amount of missing data. As a consequence, the proposed method allows the estimation of large-scale problems within minutes on a standard computer. We validate the performances of our method via Monte Carlo simulations by generating GNSS daily position time series with missing observations and we consider composite stochastic noise models including processes presenting long-range dependence such as power law or Matérn processes. The advantages of our method are also illustrated using real time series from GNSS stations located in the Eastern part of the USA.

The GENESIS mission prepared for launch in 2027 integrates the four space-geodetic techniques on a single spaceborne platform in medium Earth orbit. With its unique observations and alternative tie concepts, the mission aims to contribute to an improved accuracy and homogeneity of future terrestrial reference system realizations. To assess the expected contribution of Global Navigation Satellite System (GNSS) tracking, a comprehensive GNSS coverage analysis is performed based on detailed link-budget simulations, taking into account the best available gain patterns and signal-specific transmit power estimates derived for this work from measurements of a high-gain dish antenna. The benefit of different receiver antenna concepts for the GENESIS spacecraft is assessed, and it is demonstrated that a single-antenna system with either a nadir-looking or side-looking boresight is a viable alternative to the dual-antenna configuration considered in initial mission studies. Compared to terrestrial users and missions in low Earth orbit, GENESIS will collect GNSS signals transmitted at up to two times larger off-boresight angles. Only limited information on the actual transmit antenna phase patterns is presently available in this region, which hampers a quantitative assessment of the expected measurement and orbit determination accuracy. As such, a comprehensive release of manufacturer calibrations is encouraged for all blocks of GPS and Galileo satellites. In parallel, a need for in-flight characterization and calibration of the GNSS transmit antennas for off-boresight angles of up to using observations of the GENESIS mission itself is expected. The impact of such calibrations on the overall quality of terrestrial reference frame parameters will need to be assessed in comprehensive simulations of global GNSS network solutions with joint processing of terrestrial and GENESIS GNSS observations.

Comparing measurements of absolute sea level by satellite altimetry and relative sea level by a tide gauge can reveal errors in either measurement system. Combining the measurements can determine vertical land motion (VLM) at the tide gauge. We here discuss ten case studies in which a tide gauge has likely experienced a small ( cm), discontinuous offset in the vertical, suggesting inadvertent loss of reference-level stability. Proper interpretation of offsets is helped if independent VLM measurements from nearby geodetic stations are available. In two cases, earthquake-induced VLM cannot be ruled out, although it appears unlikely. Offsets as small as 1-2 cm can be detected when both altimeter and tide gauge successfully observe the same ocean signal. This is most likely to occur for tide gauges located on small, open-ocean islands. Tide gauges near large land masses are typically more challenging owing to inadequacies of satellite altimetry near land and to differences between coastal and open-ocean sea levels. The case studies highlight the utility of satellite altimetry for tide-gauge quality control.

Two innovations are presented for coordinate time-series computation. First, an improved solution is given to a century-old problem, that is the non-iterative computation of conventional geodetic (CG: latitude, longitude, height) coordinates from geocentric Cartesian (GC: , , ) coordinates. The accuracy is 1 nm for heights < 500 km and < 10 rad for latitude at any point, terrestrial or outer space. This can be 3 orders of magnitude more accurate than published non-iterative methods. Secondly, CG time series are transformed into a practical system of "graticule distance" (GD: easting, northing, height) curvilinear coordinates that, unlike the commonly used system of topocentric Cartesian (TC: east, north, up) coordinates, is global in nature without arbitrary specification of GC reference coordinates for every geodetic station. Since 2011, Nevada Geodetic Laboratory has publicly produced time series for 20,000 GPS stations in GD form that have been cited by hundreds of studies. The GD system facilitates direct comparison of positions for co-located stations. Users of GD time series are able: (1) to resolve different historical station names that have been assigned to the same physical benchmark and (2) to resolve different physical benchmarks that have been assigned the same name. This benefits historical reconstruction of benchmark occupation and local site tie analysis for reference frame integrity. GD coordinates have archival value, in that inversion back to GC coordinates is practically exact. For geodetic stations, GD time series closely emulate TC time series with rates agreeing to 0.01 mm/yr, and so can be used interchangeably.

One of the main tasks of Very Long Baseline Interferometry (VLBI) is the rapid determination of the highly variable Earth's rotation expressed through the difference between Universal Time UT1 and Coordinated Universal Time UTC (dUT1). For this reason, dedicated one hour, single baseline sessions, called , are observed on a daily basis. Thus far, the optimal geometry of sessions was understood to include a long east-west extension of the baseline to ensure a dUT1 estimation with highest accuracy. In this publication, we prove that long east-west baselines are the best choice only for certain lengths and orientations. In this respect, optimal orientations may even require significant inclination of the baseline with respect to the equatorial plane. The basis of these findings is a simulation study with subsequent investigations in the partial derivatives of the observed group delays with respect to dUT1 . Almost 3000 baselines between artificial stations located on a regular degree grid are investigated to derive a global and generally valid picture about the best length and orientation of baselines. Our results reveal that especially equatorial baselines or baselines with a center close to the equatorial plane are not suited for although they provide a good east-west extension. This is explained by the narrow right ascension band of visible sources and the resulting lack of variety in the partial derivatives. Moreover, it is shown that north-south baselines are also capable of determining dUT1 with reasonable accuracy, given that the baseline orientation is significantly different from the Earth rotation axis. However, great care must be taken to provide accurate polar motion a priori information for these baselines. Finally, we provide a better metric to assess the suitability of baselines based on the effective spread of .

The precise estimation of geodetic parameters using single- and double-differenced SLR observations is investigated. While the differencing of observables is a standard approach for the GNSS processing, double differences of simultaneous SLR observations are practically impossible to obtain due to the SLR basic principle of observing one satellite at a time. Despite this, the availability of co-located SLR telescopes and the use of the alternative concept of allow the forming of SLR differences under certain assumptions, thus enabling the use of these processing strategies. These differences are in principle almost free of both, satellite- and station-specific error sources, and are shown to be a valuable tool to obtain relative coordinates and range biases, and to validate local ties. Tested with the two co-located SLR telescopes at the Geodetic Observatory Wettzell (Germany) using SLR observations to GLONASS and LAGEOS, the developed differencing approach shows that it is possible to obtain single- and double-difference residuals at the millimetre level, and that it is possible to estimate parameters, such as range biases at the stations and the local baseline vector with a precision at the millimetre level and an accuracy comparable to traditional terrestrial survey methods. The presented SLR differences constitute a valuable alternative for the monitoring of the local baselines and the estimation of geodetic parameters.

We measured the components of the 31-m-long vector between the two very-long-baseline interferometry (VLBI) antennas at the Kokee Park Geophysical Observatory (KPGO), Hawaii, with approximately 1 mm precision using phase delay observables from dedicated VLBI observations in 2016 and 2018. The two KPGO antennas are the 20 m legacy VLBI antenna and the 12 m VLBI Global Observing System (VGOS) antenna. Independent estimates of the vector between the two antennas were obtained by the National Geodetic Survey (NGS) using standard optical surveys in 2015 and 2018. The uncertainties of the latter survey were 0.3 and 0.7 mm in the horizontal and vertical components of the baseline, respectively. We applied corrections to the measured positions for the varying thermal deformation of the antennas on the different days of the VLBI and survey measurements, which can amount to 1 mm, bringing all results to a common reference temperature. The difference between the VLBI and survey results are 0.2 ± 0.4 mm, -1.3 ± 0.4 mm, and 0.8 ± 0.8 mm in the East, North, and Up topocentric components, respectively. We also estimate that the Up component of the baseline may suffer from systematic errors due to gravitational deformation and uncalibrated instrumental delay variations at the 20 m antenna that may reach ± 10 and -2 mm, respectively, resulting in an accuracy uncertainty on the order of 10 mm for the relative heights of the antennas. Furthermore, possible tilting of the 12 m antenna increases the uncertainties in the differences in the horizontal components to 1.0 mm. These results bring into focus the importance of (1) correcting to a common reference temperature the measurements of the reference points of all geodetic instruments within a site, (2) obtaining measurements of the gravitational deformation of all antennas, and (3) monitoring local motions of the geodetic instruments. These results have significant implications for the accuracy of global reference frames that require accurate local ties between geodetic instruments, such as the International Terrestrial Reference Frame (ITRF).

We present results from observation, correlation and analysis of interferometric measurements between the three geodetic very long baseline interferometry (VLBI) stations at the Onsala Space Observatory. In total, 25 sessions were observed in 2019 and 2020, most of them 24 h long, all using X band only. These involved the legacy VLBI station ONSALA60 and the Onsala twin telescopes, ONSA13NE and ONSA13SW, two broadband stations for the next-generation geodetic VLBI global observing system (VGOS). We used two analysis packages: to pre-process the data and solve ambiguities, and to solve for station positions, including modelling gravitational deformation of the radio telescopes and other significant effects. We obtained weighted root mean square post-fit residuals for each session on the order of 10-15 ps using group-delays and 2-5 ps using phase-delays. The best performance was achieved on the (rather short) baseline between the VGOS stations. As the main result of this work, we determined the coordinates of the Onsala twin telescopes in VTRF2020b with sub-millimetre precision. This new set of coordinates should be used from now on for scheduling, correlation, as a priori for data analyses, and for comparison with classical local-tie techniques. Finally, we find that positions estimated from phase-delays are offset  mm in the up-component with respect to group-delays. Additional modelling of (elevation dependent) effects may contribute to the future understanding of this offset.

The primary goal of the geodetic Very Long Baseline Interferometry (VLBI) technique is to provide highly accurate terrestrial and celestial reference frames as well as Earth orientation parameters. In compliance with the concept of VLBI, additional parameters reflecting relative offsets and variations of the atomic clocks of the radio telescopes have to be estimated. In addition, reality shows that in many cases significant offsets appear in the observed group delays for individual baselines which have to be compensated for by estimating so-called baseline-dependent clock offsets (BCOs). For the first time, we systematically investigate the impact of BCOs to stress their importance for all kinds of VLBI data analyses. For our investigations, we concentrate on analyzing data from both legacy networks of the CONT17 campaign. Various aspects of BCOs including their impact on the estimates of geodetically important parameters, such as station coordinates and Earth orientation parameters, are investigated. In addition, some of the theory behind the BCO determination, e.g., the impact of changing the reference clock in the observing network on the BCO estimate is introduced together with the relationship between BCOs and triangle delay closures. In conclusion, missing channels, and here in particular at S band, affecting the ionospheric delay calibration, are identified to be the dominant cause for the occurrence of significant BCOs in VLBI data analysis.

The troposphere is considered as one of the major error sources in space geodetic techniques. Thus, accurate troposphere delay models are essential to provide high-quality products, such as reference frames, satellite orbits, or Earth rotation parameters. In this paper, a new troposphere delay model for satellite laser ranging, the Vienna Mapping Functions 3 for optical frequencies (VMF3o), is introduced. The model parameters are derived from ray-traced delays generated by an in-house ray-tracing software. VMF3o comprises not only zenith delays and mapping functions, but also linear horizontal gradients, which are not part of the standard SLR analysis yet. The model parameters are dedicated to a signal wavelength of 532 nm. Since some SLR stations operate also with other wavelengths, VMF3o provides a correction formula to transform the model parameters to any requested wavelength between 350 and 1064 nm. A test demonstrates that the correction formula approximates slant delays calculated at different wavelengths very accurately. The remaining error for slant delays at a wavelength of 1064 nm adds up to only a few millimetres at elevation angle. A comparison study of the modelled delays that are derived from VMF3o and ray-traced delays was carried out to examine the quality of the model approach. The remaining differences of modelled and ray-traced delays are expressed as mean absolute error. At elevation angle, the mean absolute error is only a few millimetres. At elevation angle, it is at the 1 mm level. The results of the comparison also reveal that introducing linear horizontal gradients reduces the mean absolute error by more than 80% for low elevation angles.

Accurate positioning using the Global Positioning System relies on accurate modeling of tropospheric delay. Estimated tropospheric delay must vary sufficiently to capture true variations; otherwise, systematic errors propagate into estimated positions, particularly the vertical. However, if the allowed delay variation is too large, the propagation of data noise into all parameters is amplified, reducing precision. Here we investigate the optimal choice of tropospheric constraints applied in the GipsyX software, which are specified by values of random walk process noise. We use the variability of 5-min estimated positions as a proxy for tropospheric error. Given that weighted mean 5-min positions closely replicate 24-h solutions, our ultimate goal is to improve 24-h positions and other daily products, such as precise orbit parameters. The commonly adopted default constraint for the zenith wet delay (ZWD) is 3 mm/√(hr) for 5-min data intervals. Using this constraint, we observe spurious wave-like patterns of 5-min vertical displacement estimates with amplitudes ~ 100 mm coincident with Winter Storm Ezekiel of November 27, 2019, across the central/eastern USA. Loosening the constraint suppresses the spurious waves and reduces 5-min vertical displacement variability while improving water vapor estimates. Further improvement can be achieved when optimizing constraints regionally, or for each station. Globally, results are typically optimized in the range of 6-12 mm/√(hr). Generally, we at least recommend loosening the constraint from the current default of 3 mm/√(hr) to 6 mm/√(hr) for ZWD every 300 s. Constraint values must be scaled by √(/300) for alternative data intervals of seconds.