Satellite Laser Ranging (SLR) is an established technique providing very accurate position measurements of satellites in Earth orbit. However, despite decades of development, it remains a complex and expensive technology, which impedes its further growth to new applications and users. The miniSLR implements a complete SLR system within a small, transportable enclosure. Through this design, costs of ownership can be reduced significantly, and the process of establishing a new SLR site is greatly simplified. A number of novel technical solutions have been implemented to achieve a good laser ranging performance despite the small size and simplified design. Data from the initial six months of test operation have been used to generate a first estimation of the system performance. The data include measurements to many of the important SLR satellites, such as Lageos, Etalon and most of the geodetic and Earth observation missions in LEO. It is shown that the miniSLR achieves sub-centimetre accuracy, comparable with conventional SLR systems. The miniSLR is an engineering station in the International Laser Ranging Service and supplies data to the community. Continuous efforts are undertaken to further improve the system operation and stability.

Various aspects of gravity field modeling rely upon analytical mathematical functions for calculating spherical harmonic coefficients. Such functions allow quick and efficient evaluation of cumbersome convolution integrals defined on the sphere. In this work, we present a new analytical method for determining spherical harmonic coefficients of isotropic polynomial functions. This method in computationally flexible and efficient, since it makes use of recurrence relations. Also, its use is universal and could be extended to piecewise polynomials and polynomials with compact support. Our numerical investigation of the proposed method shows that certain recurrence relations lose accuracy as the order of implemented polynomials increases because of accumulation of numerical errors. Propagation of these errors could be mitigated by hybrid methods or using extended precision arithmetic. We demonstrate the relevance of our method in gravity field modeling and discuss two areas of application. The first one is the design of B-spline windows and filter kernels for the low-pass filtering of gravity field functionals (e.g., GRACE Follow-On monthly geopotential solutions). The second one is the calculation of spherical harmonic coefficients of isotropic polynomial covariance functions.

The accuracy assessment of terrestrial reference frames (TRFs) at coordinate system level is a key task to ensure their successful use in Earth studies, satellite navigation and other geodetic positioning applications. Currently, the TRF quality specifications for the most demanding users dictate that the origin, orientation and scale should be determined at an accuracy level of 1 mm, and they should remain stable over time at a rate of 0.1 mm/yr. To evaluate the conformity of the internal accuracy of modern TRFs to such requirements, an appropriate mapping is needed to convert frame coordinate errors (and their CV matrix) in a terrestrial network to matching errors (and their CV matrix) in the realized coordinate system. Several projection schemes may be considered for this mapping problem, all of which aim at extracting the correlated part of the estimation error in TRF coordinates that is describable by small random perturbations in their coordinate system. The goal of the present paper is to investigate the inference problem of frame accuracy at coordinate system level, and to discuss not only the theoretical aspects of the required covariance projectors, but also the practical impact on the results obtained by their implementation in space geodetic solutions. For this purpose, a relevant case study is performed to evaluate the accuracy of the realized origin, orientation and scale in the ITRF frame series based on the formal CV matrices for their estimated positions and velocities in the four technique subnetworks (DORIS, SLR, VLBI, GNSS).

We describe the new global land water storage data set GLWS2.0, which contains total water storage anomalies (TWSA) over the global land except for Greenland and Antarctica with a spatial resolution of 0.5^circ , covering the time frame 2003 to 2019 without gaps, and including monthly uncertainty quantification. GLWS2.0 was derived by assimilating monthly GRACE/-FO mass change maps into the WaterGAP global hydrology model via the ensemble Kalman filter, taking data and model uncertainty into account. TWSA in GLWS2.0 is then accumulated over several hydrological storage variables. In this article, we describe the methods and data sets that went into GLWS2.0, how it compares to GRACE/-FO data in terms of representing TWSA trends, seasonal signals, and extremes, as well as its validation via comparing to GNSS-derived vertical loading and its comparison with a version of the NASA Catchment Land Surface Model GRACE Data Assimilation (CLSM-DA). We find that, in the average over more than 1000 stations globally, GLWS2.0 correlates better with GNSS observations of vertical loading at short-term, seasonal, and long-term temporal bands than GRACE/-FO. While some differences exist, overall GLWS2.0 agrees reasonably well with CLSM-DA in terms of TWSA trends and annual amplitudes and phases.HighlightsWe describe the new global land water storage data set GLWS2.0, which contains total water storage anomalies over the global land with a spatial resolution of 0.5^circ , covering the period 2003 to 2019 without gaps, and including uncertainty quantification.GLWS2.0 synthesizes monthly GRACE/-FO mass change maps with daily precipitation and radiation data via the WaterGAP model framework, taking data and model uncertainty into account.Here we describe the methods and data sets that went into GLWS2.0 and its validation from a geodetic applications perspective. We find that, in the global average, GLWS2.0 fits better than GRACE/-FO to GNSS observations of vertical loading.

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.

Seafloor deformation monitoring is now routinely performed in the marine sector of the Campi Flegrei volcanic area (Southern Italy). The MEDUSA infrastructure is formed by four buoys deployed at a water depth ranging from 40 to 96 m, and equipped with cGPS receivers, accelerometers and magnetic compasses to monitor the buoy status and a seafloor module with a bottom pressure recorder and other onboard instruments. The analysis of the time series data acquired by the MEDUSA monitoring infrastructure system allows to study the seafloor deformation in the Campi Flegrei caldera with geodetic accuracy. In a previous work, we show that the time series acquired by the Campi Flegrei cGPS onland network and MEDUSA over the period 2017–2020 are in good agreement with the ground deformation field predicted by a Mogi model which is widely used to describe the observed deformation of an active volcano in terms of magma intrusion. Only for one of the buoys, CFBA (A), the data differ significantly from the model prediction, at a level of simeq 6.9 sigma and of simeq 23.7 sigma for the seafloor horizontal speed and direction, respectively. For this reason, we devised a new method to reconstruct the horizontal sea bottom displacement considering in the analysis both cGPS and compass data. The method, applied to the CFBA buoy measurements and validated also on the CFBC (C) buoy, uses compass data to correct cGPS positions accounting for the pole inclination. Including also systematic errors, the internal consistency, always within sim 3 sigma for the speed and sim 2 sigma for the angle, between the results derived for different maximum inclinations of the buoy pole (up to 3.5^{circ }) indicates that the method allows to significantly reduce the impact of the pole inclination which, if not properly taken into account, can alter the estimation of the horizontal seafloor deformation. In particular, we find a good convergence of the retrieved velocity and deformation angle as we include in the analysis data from increasing values of the buoy pole inclination. Taking the result derived assuming the maximum allowed cutoff and accounting for statistical and systematic errors, we found a speed v = (3.521 ± 0.039 (stat) ± 0.352 (syst)) cm/yr and a deformation direction angle alpha = (-115.159 ± 0.670 (stat) ± 7.630 (syst))^{circ } (statistical errors at 1 sigma quoted from the rms of their values, main systematic errors added linearly). The relative impact of the main potential systematic (statistical) effects increases (decreases) with the cutoff. Our analysis provides a horizontal speed consistent with the model at a level of simeq 5.2 sigma (stat only) or of simeq 0.5 sigma (stat and syst added linearly), and a deformation angle consistent with the model at simeq 4.3 sigma level (stat only) or at simeq 0.3 sigma level (stat and syst added linearly). Correspondingly, the module of the vectorial difference between the velocity retrieved from the data and the velocity of the adopted Mogi model diminishes by a factor of simeq 7.65 ± 1.23 (stat) or ± 5.78 (stat + syst) with respect to the previous work. A list of potential improvements to be implemented in the system and instruments is also discussed.