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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: x, y, z) coordinates. The accuracy is 1 nm for heights < 500 km and < 10-15 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.

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This article discusses the ways in which nineteenth-century geodesists reflected on precision as an epistemic virtue in their measurement practice. Physical geodesy is often understood as a quintessential nineteenth-century precision science, stimulating advances in instrument making and statistics, and generating incredible quantities of data. Throughout most of the nineteenth century, geodesists indeed pursued their most prestigious research problem - the exact determination of the earth's polar flattening - along those lines. Treating measurement errors as random, they assumed that remaining discordances could be overcome by manufacturing better instruments and extending statistical analysis to a larger amount of data. In the second half of the nineteenth century, however, several German geodesists developed sophisticated methodological critiques of their discipline, in which they diagnosed a too-narrow focus on precision among their peers. On their account, geodesists urgently needed to identify and anticipate the causes of the remaining measurement errors that arose from the earth's little understood interior constitution. While mostly overlooked in the literature, these critiques paved the way for many empirical successes in late nineteenth- and early twentieth-century geodesy, including the first convergent measurements of the earth's polar flattening.

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Land water storage plays a key role for the Earth's climate, natural ecosystems, and human activities. Since the launch of the first Gravity Recovery and Climate Experiment (GRACE) mission in 2002, spaceborne observations of changes in terrestrial water storage (TWS) have provided a unique, global perspective on natural and human-induced changes in freshwater resources. Even though they have become much used within the broader Earth system science community, space-based TWS datasets still incorporate important and case-specific limitations which may not always be clear to users not familiar with the underlying processing algorithms. Here, we provide an accessible and illustrated overview of the measurement concept, of the main available data products, and of some frequently encountered technical terms and concepts. We summarize concrete recommendations on how to use TWS data in combination with other hydrological or climatological datasets, and guidance on how to avoid possible pitfalls. Finally, we provide an overview of some of the main applications of GRACE TWS data in the fields of hydrology and climate science. This review is written with the intention of supporting future research and facilitating the use of satellite-based terrestrial water storage datasets in interdisciplinary contexts.

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Derived measurements involve problems of coordination. Conducting them often requires detailed theoretical assumptions about their target, while such assumptions can lack sources of evidence that are independent from these very measurements. In this paper, I defend two claims about problems of coordination. I motivate both by a novel case study on a central measurement problem in the history of physical geodesy: the determination of the earth's ellipticity. First, I argue that the severity of problems of coordination varies according to scientists' predictive and experimental control over perturbations of the measurement process. Second, I identify a methodology by which scientists can solve hard problems of coordination and gradually increase their predictive control over perturbations. I dub this methodology 'operational pluralism' since it is driven by the introduction of alternative measurement operations that involve different physical indicators.

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GeoGateway (http://geo-gateway.org) is a web-based interface for analysis and modeling of geodetic imaging data and to support response to related disasters. Geodetic imaging data product currently supported by GeoGateway include Global Navigation Satellite System (GNSS) daily position time series and derived velocities and displacements and airborne Interferometric Synthetic Aperture Radar (InSAR) from NASA's UAVSAR platform. GeoGateway allows users to layer data products in a web map interface and extract information from various tools. Extracted products can be downloaded for further analysis. GeoGateway includes overlays of California fault traces, seismicity from user selected search parameters, and user supplied map files. GeoGateway also provides earthquake nowcasts and hazard maps as well as products created for related response to natural disasters. A user guide is present in the GeoGateway interface. The GeoGateway development team is also growing the user base through workshops, webinars, and video tutorials. GeoGateway is used in the classroom and for research by experts and non-experts including by students.

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Gravity Recovery and Climate Experiment and its Follow On (GRACE (-FO)) missions have resulted in a paradigm shift in understanding the temporal changes in the Earth's gravity field and its drivers. To provide continuous observations to the user community, missing monthly solutions within and between GRACE (-FO) missions (33 solutions) need to be imputed. Here, we modeled GRACE (-FO) data (196 solutions) between 04/2002-04/2021 to infer missing solutions and derive uncertainties in the existing and missing observations using Bayesian inference. First, we parametrized the GRACE (-FO) time series using an additive generative model comprising long-term variability (secular trend + interannual to decadal variations), annual, and semi-annual cycles. Informative priors for each component were used and Markov Chain Monte Carlo (MCMC) was applied to generate 2,000 samples for each component to quantify the posterior distributions. Second, we reconstructed the new data (229 solutions) by joining medians of posterior distributions of all components and adding back the residuals to secure the variability of the original data. Results show that the reconstructed solutions explain 99% of the variability of the original data at the basin scale and 78% at the one-degree grid scale. The results outperform other reconstructed data in terms of accuracy relative to land surface modeling. Our data-driven approach relies only on GRACE (-FO) observations and provides a total uncertainty over GRACE (-FO) data from the data-generation process perspective. Moreover, the predictive posterior distribution can be potentially used for "nowcasting" in GRACE (-FO) near-real-time applications (e.g., data assimilations), which minimize the current mission data latency (40-60 days).

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Climate change, of which sea level change is one component, is seldom out of the news. This paper reviews developments in the measurement and understanding of changes in sea level and tides, focusing on the changes during the past century. The main aim has been to demonstrate how sea level and tidal science are now connected intimately with the fields of climate change and geodesy.

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This paper presents the new cable delay measurement system (CDMS) designed at Yebes Observatory (IGN, Spain), which is required for the VLBI Global Observing System (VGOS) stations. This system measures the phase difference between the 5 MHz reference signal from the hydrogen maser and the 5 MHz signal that reaches the broadband receiver through a coaxial cable, for the generation of calibration tones. As a result, the system detects the changes in the length of that coaxial cable due to temperature variations along the cable run and flexures caused by VGOS radio telescope movements. This CDMS outperforms the previous versions: firstly, it does not require a frequency counter for phase/delay measurements; secondly, it largely reduces the use of digital circuits; hence, reducing digital noise; and thirdly, it has a remotely controlled automatic calibration subsystem. The system was tested in the laboratory and in the radio telescope, and the measurements of both set-ups are shown. These measurements include the total noise, accuracy, hysteresis, and stability. The results in the radio telescope can be correlated with the different factors that affect the cable, such as temperature and flexures. The system allows to achieve an RMS noise of less than 0.5 ps, significantly improving the requirements established in VGOS. The system is currently installed in the Red Atlántica de Estaciones Geodinámicas y Espaciales (RAEGE)Yebes VGOS 13.2 m radio telescope, and will be installed in the Norwegian Mapping Authority (NMA) twin VGOS radio telescopes, in the Finnish Geospatial Research Institute (FGI) VGOS station and in the RAEGE Santa María VGOS radio telescope (Açores, Portugal).

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This paper presents the results of an orbital analysis of satellite laser ranging data performed by the Borowiec SLR station (7811) in the period from July 1993 to December 2019, including the determination of the station positions and velocity. The analysis was performed using the GEODYN-II orbital program for the independent monthly orbital arcs from the results of the LAGEOS-1 and LAGEOS-2 satellites. Each arc was created from the results of the laser observations of a dozen or so selected stations, which were characterized by a large number of normal points and a good quality of observations. The geocentric and topocentric coordinates of the station were analyzed. Factors influencing the uncertainty of the measurements were determined: the number of the normal points, the dispersion of the normal points in relation to the orbits, and the long-term stability of the systematic deviations. The position leap at the end of 2002 and its interpretation in ITRF2014 were analyzed. The 3D stability of the determined positions throughout the period of study was equal to 12.7 mm, with the uncertainty of determination being at the level of 4.3 mm. A very high compliance of the computed velocity of the Borowiec SLR station (24.9 mm/year) with ITRF2014 (25.0 mm/year) was found.

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In a text (1892) on light, Jules Henri Poincaré introduced a geometrical device for tracking the polarization of state of light interacting with matter. Poincaré first mapped all polarization ellipses onto the surface of sphere and changes of state were represented as rotations from one point to another about prescribed axes depending on linear optical properties of the medium. Here, we consider how Poincaré, the mathematician, invented his sphere. Poincaré's professional activities in the service of geodesy appear at first glance to provide a borrowed geometry for his one-to-one mapping of polarization ellipses to global lines of latitude and longitude. However, this association falls apart in the face of a close reading of Poincaré's biography and his influences, especially the research interests of his teachers from the École Polytechnique and the Écoles de Mines. The work of Tissot and Mallard on distortion ellipses in cartography and the etiology of optical activity in crystals, respectively, together with Poincaré's own study of the qualitative theory of differential equations, provide the iconography of, and motivation for, the sphere. Whether Poincaré's mentors were unwitting partners in the invention of the sphere-it is impossible to be sure-Poincaré's otherworldly geometric sensibilities carried him through isometries (rotations) on hyperbolic planes and beyond. The apparent ingenuity behind Poincaré's sphere is diminished in comparison to his fulsome achievements. Moreover, Poincaré's considerations of the psychology of invention further emphasize that sometimes great ideas arrive to those fortunate to receive them by mechanisms that resist interpretation.

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The development of nineteenth-century geodetic measurement challenges the dominant coherentist account of metric success. Coherentists argue that measurements of a parameter are successful if their numerical outcomes convergence across varying contextual constraints. Aiming at numerical convergence, in turn, offers an operational aim for scientists to solve problems of coordination. Geodesists faced such a problem of coordination between two indicators of the earth's polar flattening, which were both based on imperfect ellipsoid models. While not achieving numerical convergence, their measurements produced novel data that grounded valuable theoretical hypotheses. Consequently, they ought to be regarded as epistemically successful. This insight warrants a dynamic revision of coherentism, which allows to judge the success of a metric based on both its coherence and fruitfulness. On that view, scientific measurement aims to coordinate theoretical definitions and produce novel data and theoretical insights.

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This paper shows a simultaneous tri-band (S: 2.2-2.7 GHz, X: 7.5-9 GHz and Ka: 28-33 GHz) low-noise cryogenic receiver for geodetic Very Long Baseline Interferometry (geo-VLBI) which has been developed at Yebes Observatory laboratories in Spain. A special feature is that the whole receiver front-end is fully coolable down to cryogenic temperatures to minimize receiver noise. It was installed in the first radio telescope of the Red Atlántica de Estaciones Geodinámicas y Espaciales (RAEGE) project, which is located in Yebes Observatory, in the frame of the VLBI Global Observing System (VGOS). After this, the receiver was borrowed by the Norwegian Mapping Autorithy (NMA) for the commissioning of two VGOS radiotelescopes in Svalbard (Norway). A second identical receiver was built for the Ishioka VGOS station of the Geospatial Information Authority (GSI) of Japan, and a third one for the second RAEGE VGOS station, located in Santa María (Açores Archipelago, Portugal). The average receiver noise temperatures are 21, 23, and 25 Kelvin and the measured antenna efficiencies are 70%, 75%, and 60% in S-band, X-band, and Ka-band, respectively.

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Surface deformation in California's Central Valley (CV) has long been linked to changes in groundwater storage. Recent advances in remote sensing have enabled the mapping of CV deformation and associated changes in groundwater resources at increasingly higher spatiotemporal resolution. Here, we use interferometric synthetic aperture radar (InSAR) from the Sentinel-1 missions, augmented by continuous Global Positioning System (cGPS) positioning, to characterize the surface deformation of the San Joaquin Valley (SJV, southern two-thirds of the CV) for consecutive dry (2016) and wet (2017) water years. We separate trends and seasonal oscillations in deformation time series and interpret them in the context of surface and groundwater hydrology. We find that subsidence rates in 2016 (mean -42.0 mm/yr; peak -345 mm/yr) are twice that in 2017 (mean -20.4 mm/yr; peak -177 mm/yr), consistent with increased groundwater pumping in 2016 to offset the loss of surface-water deliveries. Locations of greatest subsidence migrated outwards from the valley axis in the wetter 2017 water year, possibly reflecting a surplus of surface-water supplies in the lowest portions of the SJV. Patterns in the amplitude of seasonal deformation and the timing of peak seasonal uplift reveal entry points and potential pathways for groundwater recharge into the SJV and subsequent groundwater flow within the aquifer. This study provides novel insight into the SJV aquifer system that can be used to constrain groundwater flow and subsidence models, which has relevance to groundwater management in the context of California's 2014 Sustainable Groundwater Management Act (SGMA).

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We recompute the 26-yr weekly Geocentre Motion (GCM) time-series from 1994 to 2020 through the network shift approach using Satellite Laser Ranging (SLR) observations to LAGEOS1/2. Then the Singular Spectrum Analysis (SSA) is applied for the first time to separate and investigate the geophysical signals from the GCM time-series. The Principal Components (PCs) of the embedded covariance matrix of SSA from the GCM time-series are determined based on the w-correlation criterion and two PCs with large w-correlation are regarded as one periodic signal pair. The results indicate that the annual signal in all three coordinate components and semi-annual signal in both X and Z components are detected. The annual signal from this study agrees well in both amplitude and phase with those derived by the Astronomical Institute of the University of Bern and the Center for Space Research, especially for the Y and Z components. Besides, the other periodic signals with the periods of (1043.6, 85, 28), (570, 280, 222.7) and (14.1, 15.3) days are also quantitatively explored for the first time from the GCM time-series by using SSA, interpreting the corresponding geophysical and astrodynamic sources of aliasing effects of K1/O1, T2 and Mm tides, draconitic effects, and overlapping effects of the ground-track repeatability of LAGEOS1/2.

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The LARES (LAser RElativity Satellite) was built by the Italian Space Agency (ASI) and launched on 13 February 2012 by the European Space Agency. It is intended for studying the Lense-Thirring effect resulting from general relativity as well as for geodynamic studies and satellite geodesy. The satellite is observed by most ground laser stations. The task of this work is to determine the station coordinates and to assess the quality of their determination by comparison with the results from the LAGEOS-1 and LAGEOS-2 satellites. Observation results in the form of normal points (396,105 normal points in total) were downloaded from the EUROLAS Data Center for the period from 29 February 2012 to 31 December 2015. Seven-day orbital arcs were computed by the NASA GSFC GEODYN-II software, determining the coordinates of seventeen selected measuring stations. The average Root Mean Square (RMS) (15.1 mm) of the determined orbits is nearly the same as for LAGEOS (15.2 mm). The stability of the coordinates of each station (3DRMS) is from 9 mm to 46 mm (for LAGEOS, from 5 mm to 15 mm) with the uncertainty of determining the coordinates of 3-11 mm (LAGEOS 2-7 mm). The combined positioning for the LARES + LAGEOS-1 + LAGEOS-2 satellites allows for the stability of 5-18 mm with an uncertainty of 2-6 mm. For most stations, this solution is slightly better than the LAGEOS-only one.

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Geodetic observations on volcanoes can reveal important aspects of crustal magma chambers. The rate of decay of deformation with distance reflects the centroid depth of the chamber. The amplitude of the deformation is proportional to the product of the pressure change and volume of the reservoir. The ratio of horizontal to vertical displacement is sensitive to chamber shape: sills are efficient at generating vertical displacement, while stocks produce more horizontal deformation. Geodesy alone cannot constrain important parameters such as chamber volume or pressure; furthermore, kinematic models have no predictive power. Elastic response combined with influx proportional to pressure gradient predicts an exponentially decaying flux, leading to saw-tooth inflation cycles observed at some volcanoes. Yet many magmatic systems exhibit more complex temporal behaviour. Wall rock adjacent to magma reservoirs cannot behave fully elastically. Modern conceptual models of magma chambers also include cumulate and/or mush zones, with potentially multi-level melt lenses. A viscoelastic shell surrounding a spherical magma chamber significantly modifies the predicted time-dependent response; post-eruptive inflation can occur without recharge if the magma is sufficiently incompressible relative to the surrounding crust (Segall P. 2016 J. Geophys. Res. Solid Earth, 121, 8501-8522). Numerical calculations confirm this behaviour for both oblate and prolate ellipsoidal chambers surrounded by viscoelastic aureoles. Interestingly, the response to a nearly instantaneous pressure drop during an explosive eruption can be non-monotonic as the rock around the chamber relaxes at different rates. Pressure-dependent recharge of a non-Newtonian magma in an elastic crust leads to an initially high rate of inflation which slows over time; behaviour that has been observed in some magmatic systems. I close by discussing future challenges in volcano geodesy. This article is part of the Theo Murphy meeting issue 'Magma reservoir architecture and dynamics'.

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NASA maintains and operates a global network of Very Long Baseline Interferometry (VLBI), Satellite Laser Ranging (SLR), and Global Navigation Satellite System (GNSS) ground stations as part of the NASA Space Geodesy Program. The NASA Space Geodesy Network (NSGN) provides the geodetic products that support Earth observations and the related science requirements as outlined by the US National Research Council (NRC 2010, 2018). The Global Geodetic Observing System (GGOS) and the NRC have set an ambitious goal of improving the Terrestrial Reference Frame (TRF) to have an accuracy of 1 millimeter and stability of 0.1 millimeters per year, an order of magnitude beyond current capabilities. NASA and its partners within GGOS are addressing this challenge by planning and implementing modern geodetic stations co-located at existing and new sites around the world. In 2013, NASA demonstrated the performance of its next-generation systems at the prototype next-generation core site at NASA's Goddard Geophysical and Astronomical Observatory in Greenbelt, Maryland. Implementation of a new broadband VLBI station in Hawaii was completed in 2016. NASA is currently implementing new VLBI and SLR stations in Texas and is planning the replacement of its other aging domestic and international legacy stations. In this article, we describe critical gaps in the current global network and discuss how the new NSGN will expand the global geodetic coverage and ultimately improve the geodetic products. We also describe the characteristics of a modern NSGN site and the capabilities of the next-generation NASA SLR and VLBI systems. Finally, we outline the plans for efficiently operating the NSGN by centralizing and automating the operations of the new geodetic stations.

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Our understanding of plate boundary deformation has been enhanced by transient signals observed against the backdrop of time-independent secular motions. We make use of a new analysis of displacement time series from about 1,000 continuous Global Positioning System (GPS) stations in California from 1999 to 2018 to distinguish tectonic and nontectonic transients from secular motion. A primary objective is to define a high-resolution three-dimensional reference frame (datum) for California that can be rapidly maintained with geodetic data to accommodate both secular and time-dependent motions. To this end, we compare the displacements to those predicted by a horizontal secular fault slip model for the region and construct displacement and strain rate fields. Over the past 19 years, California has experienced 19 geodetically detectable earthquakes and widespread postseismic deformation. We observe postseismic strain rate variations as large as 1,000 nstrain/year with moment releases equivalent up to an Mw6.8 earthquake. We find significant secular differences up to 10 mm/year with the fault slip model, from the Mendocino Triple Junction to the southern Cascadia subduction zone, the northern Basin and Range, and the Santa Barbara channel. Secular vertical uplift is observed across the Transverse Ranges, Coastal Ranges, Sierra Nevada, as well as large-scale postseismic uplift after the 1999 Mw7.1 Hector Mine and 2010 Mw7.2 El Mayor-Cucapah earthquakes. We also identify areas of vertical land motions due to anthropogenic, natural, and magmatic processes. Finally, we demonstrate the utility of the kinematic datum by improving the accuracy of high-spatial-resolution 12-day repeat-cycle Sentinel-1 Interferometric Synthetic Aperture Radar displacement and velocity maps.

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Recent progress in the domain of time and frequency (T/F) standards requires important improvements of existing time distribution links. Among these, the accuracy of time transfer is actually an important part of the concerns in order to establish and maintain time & space references from ground and/or space facilities. Several time transfers by laser link projects have been carried out over the past 10 years with numerous scientific and metrological objectives. Satellite Laser ranging (SLR) has proven to be a fundamental tool, offering a straightforward, conceptually simple, highly accurate and unambiguous observable. Depending on the mission, LR is used to transmit time over two-way or one-way distances from 500 to several millions of km. The following missions and their objectives employed this technique: European Laser Timing (ELT) at 450 km, Time Transfer by Laser Link (T2L2) at 1,336 km, Laser Time Transfer (LTT) at 36,000 km, Lunar Reconnaissance Orbiter (LRO) at 350,000 km, and MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) at tens of million km. This article describes the synergy between SLR and T/F technologies developed on the ground and in space and as well as the state of the art of their exploitation. The performance and sources of limitation of such space missions are analyzed. It shows that current and future challenges lie in the improvement of the time accuracy and stability of the time for ground geodetic observatories. The role of the next generation of SLR systems is emphasized both in space and at ground level, from the point of view of GGOS and valuable exploitation of the synergy between time synchronization, ranging and data transfer.

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The following article presents a new isometric transformation algorithm based on the transformation in the newly normed Hilbert type space. The presented method is based on so-called virtual translations, already known in advance, of two relative oblique orthogonal coordinate systems-interior and exterior orientation of sensors-to a common, known in both systems, point. Each of the systems is translated along its axis (the systems have common origins) and at the same time the angular relative orientation of both coordinate systems is constant. The translation of both coordinate systems is defined by the spatial norm determining the length of vectors in the new Hilbert type space. As such, the displacement of two relative oblique orthogonal systems is reduced to zero. This makes it possible to directly calculate the rotation matrix of the sensor. The next and final step is the return translation of the system along an already known track. The method can be used for big rotation angles. The method was verified in laboratory conditions for the test data set and measurement data (field data). The accuracy of the results in the laboratory test is on the level of 10-6 of the input data. This confirmed the correctness of the assumed calculation method. The method is a further development of the author's 2017 Total Free Station (TFS) transformation to several centroids in Hilbert type space. This is the reason why the method is called Multi-Centroid Isometric Transformation-MCIT. MCIT is very fast and enables, by reducing to zero the translation of two relative oblique orthogonal coordinate systems, direct calculation of the exterior orientation of the sensors.