Journal of Geodesy最新文献

The gravimetry measurements from the Gravity Recovery and Climate Experiment (GRACE) and its follow-on (GRACE-FO) mission provide an essential way to monitor changes in ocean bottom pressure ((p_b)), which is a critical variable in understanding ocean circulation. However, the coarse spatial resolution of the GRACE(-FO) fields blurs important spatial details, such as (p_b) gradients. In this study, we employ a self-supervised deep learning algorithm to downscale global monthly (p_b) anomalies derived from GRACE(-FO) observations to an equal-angle 0.25 ( ^{circ }) grid in the absence of high-resolution ground truth. The optimization process is realized by constraining the outputs to follow the large-scale mass conservation contained in the gravity field estimates while learning the spatial details from two ocean reanalysis products. The downscaled product agrees with GRACE(-FO) solutions over large ocean basins at the millimeter level in terms of equivalent water height and shows signs of outperforming them when evaluating short spatial scale variability. In particular, the downscaled (p_b) product has more realistic signal content near the coast and exhibits better agreement with tide gauge measurements at around 80% of 465 globally distributed stations. Our method presents a novel way of combining the advantages of satellite measurements and ocean models at the product level, with potential downstream applications for studies of the large-scale ocean circulation, coastal sea level variability, and changes in global geodetic parameters.

The Gravity field and steady-state Ocean Circulation Explorer (GOCE) mission, launched by the European Space Agency, provided high-quality gravitational gradient data with near-global coverage, excluding polar regions. These data have been instrumental in regional gravity field modelling through various methods. One approach involves a mathematical model based on Fredholm’s integral equation of the first kind, which relates surface gravity anomalies to satellite gradient data. Solving this equation requires discretising a surface integral and applying further regularisation techniques to stabilise the numerical solution of a resulting system of linear equations. This study examines four methods for modifying the system of linear equations derived by discretising the Fredholm integral equation. The methods include direct inversion, remove-compute-restore, truncation reduction of the integral formula, and inversion of a modified integral for estimating surface gravity anomalies from satellite gradient data over a test area in Central Europe. Since the system of linear equations is ill-conditioned, the Tikhonov regularisation is applied to stabilise its numerical solution. To assess the precision and reliability of the estimated gravity anomalies, the study introduces mathematical models for estimation of biased and de-biased noise variance–covariance matrices of estimated surface gravity anomalies. The results indicate that the signal-to-noise ratio of reduced satellite gradient data in the remove-compute-restore method is smaller compared to other methods in the study, necessitating stronger stabilisation of the model to recover surface gravity anomalies. This, in turn, leads to a more optimistic uncertainty propagation than the other considered methods.

While integer ambiguity resolution (IAR) enables GNSS to achieve real-time sub-centimeter-level positioning in open-sky environments, it can be easily hindered if the involved receivers are situated in areas with limited satellite visibility, such as in dense city environments. In such GNSS-challenged cases, commercial Low Earth Orbit (LEO) communication satellites can potentially augment GNSS by providing additional measurements. However, LEO satellites often lack code measurements, mainly transmitting satellite-specific frequency-varying carrier phase signals. This contribution aims to study the ambiguity-resolved baseline positioning performance of such phase-only signals, addressing the extent to which LEO constellations can realize near real-time positioning in standalone and GNSS-combined modes. Through a simulation platform, we analyze the distinct response of each LEO constellation (Iridium, Globalstar, Starlink, OneWeb, and Orbcomm) to IAR under various circumstances. Although achieving single-receiver high-precision positioning can be challenged by inaccuracies in the LEO satellite orbit products, the relative distance between two receivers can help overcome this limitation. As a result, centimeter-level relative positioning over short baselines can be made possible, even with a satellite elevation cut-off angle of 50 degrees, making it suitable for GNSS-challenged environments. This can be achieved with high-grade receiver clocks over very short baselines ((sim )5 km) and access to decimeter-level orbit products.

The stochastic representation of an uncertain shape model allows the dynamic evaluation of its induced gravity signal. This can be also applied for representing a time variable gravity field to model mass changes. The algorithm for estimating variations in gravitational potential is extended for the case of second-order derivatives. Two different harmonic synthesis formulas are used to derive the sought variations: one expressed in spherical coordinates using the traditional associated Legendre functions (ALF) and their derivatives up to the second order, while the other expressed in Cartesian coordinates by including the derived Legendre functions (DLF). The obtained variations are compared in terms of convergence with gravity signal differences referring to the specific shape changes using the line integral analytical approach for three asteroid shape models. Both approaches provide results that differ from the analytical method at a 1E−1 level, while the differences between them are at the 1E−15 level. The obtained results are highly influenced by the geometry of the examined shape model, with the ALF approach providing variations with closer agreement with the analytical method only for the almost spherical shape. Both harmonic synthesis expressions can be used to derive accurate results, as they differ at a very low level, and one can choose based on the convenience of their algorithmic characteristics.

Effective angular momentum (EAM) forecasts are widely used as an important input for predicting both polar motion and dUT1. So far, model predictions for atmosphere, ocean, and terrestrial hydrosphere utilized in Earth rotation research reach only 6-days into the future. GFZ’s oceanic and land-surface model forecasts are forced with operational 6-day high-resolution deterministic numerical weather predictions provided by the European Centre for Medium-range Weather Forecasts. Those atmospheric forecasts extend also further into the future with a reduced sampling rate of just 6 h but the prediction skill decreases rapidly after roughly one week. To decide about publishing 10-day instead of 6-day model-based EAM forecasts, we generated a test set of 454 individual 10-day forecasts and used it with GFZ’s EAM Predictor method to calculate Earth rotation predictions. Using 10-day instead of 6-day EAM forecasts leads to slight improvements in y-pole and dUT1 predictions for 10 to 30 days ahead. By introducing additional neural network models trained on the errors of the EAM forecasts when compared to their subsequently available analysis runs, Earth rotation prediction can be enhanced even further. A reduction of the mean absolute errors for polar motion and length-of-day prediction at a forecast horizon of 10 days of 26.8% in x-pole, 15.5% in y-pole, 27.6% in dUT1, and 47.1% in (Delta )LOD is achieved. This test application successfully demonstrates the potential of the extended EAM forecasts for Earth rotation prediction although the success rate has to be further improved to arrive at robust routine predictions. GFZ publishes from October 2024 onwards raw uncorrected 10-day instead of 6-day EAM forecasts at www.gfz-potsdam.de/en/esmdata for the individual contributions of atmosphere, ocean, and terrestrial hydrosphere. Users interested in the summarized effect of all subsystems are advised to use the 90-day combined EAM forecast product that also makes use of the presented corrections to the EAM forecasts.

The geodetic community commonly challenges the composite hypotheses in the statistical testing of mathematical models. Since the composite hypotheses are not specified as opposed to their simple counterparts, they require a prior estimation of the model parameters. However, if the mathematical models are ill-conditioned, the regularized estimation is often applied for the parameters of interest. Due to the biased property, the regularized estimation does not rigorously originate in the principle of maximum likelihood (ML) estimation, which was the base for developing the theory of the generalized likelihood ratio (GLR) test. Since the regularized estimator of the parameters of interest is consequently inconsistent with the ML one, one cannot construct the GLR test, which is the uniformly most powerful invariant (UMPI) test. So far, only the bias correction approach has been suggested to solve this problem. In this contribution, an implicit representation of the regularized mathematical model is proposed. It eliminates the complete impact of regularized estimation on a mathematical model and delivers the misclosures analytically free from the influence of regularization. Thus, one can construct the GLR test, which belongs to the UMPI family, and then formulate the test statistic in terms of misclosures.

As a critical parameter in meteorological monitoring, precipitable water vapor (PWV) is widely used in short-term extreme weather forecasting and long-term climate change research. However, as PWV exhibits significant vertical attenuation, especially within 2 km, achieving accurate vertical interpolation is essential for comparisons and fusion across different measurement techniques, such as sampling water vapor at different heights. PWV vertical adjustment relies only on the empirical or time-varying lapse rate models (e.g., GPWV-H). The non-uniform vertical distribution of PWV and the uncertain variation trend in the low-latitude region still limit the accuracy. To address these issues, we propose the Spatially enhanced Vertical Adjustment Model for PWV (SPWV-H), taking into account the non-uniform distribution in the vertical direction based on the fifth-generation European Centre for Medium-Range Weather Forecasts Atmospheric Reanalysis (ERA5) products. The assessment, validated against the ERA5 benchmark, highlights the SPWV-H model’s superior performance with an RMSE of 1 mm and a bias of 0.03 mm, especially pronounced in the low-latitude region. Compared to global radiosonde datasets, the SPWV-H model achieves notable reductions in RMSE of 12%, 11%, and 18% when evaluated against the EPWV-H, GPWV-H, and GPT3-1 models, respectively. In spatial interpolation, the SPWV-H model achieves an RMSE of 1.22 mm, indicating an improvement of 10%, 9%, and 14% compared to the EPWV-H, GPWV-H, and GPT3-1 models, respectively. Therefore, the SPWV-H model can provide a reliable service for multi-source PWV fusion and real-time PWV monitoring by GNSS.

In February 2023, the International Laser Ranging Service started the tracking of additional medium Earth orbit satellites from the global BeiDou navigation satellite system (BDS) constellation, increasing the total number of tracked BDS satellites to 27. As an optical space geodesy technique, the Satellite Laser Ranging (SLR) provides another important measurement for BDS other than the microwave (L-band) one. Based on three years of data from June 2021 to May 2024, the potential benefits of introducing SLR data into BDS processing and analysis are investigated from three key aspects: orbit validation, precise orbit determination, and geodetic parameters estimation. The independent SLR validations of BDS precise orbit products from four analysis centers show that using the a priori box-wing model for solar radiation pressure (SRP) modeling can achieve superior performance than purely empirical models. The results also indicate the existence of SRP modeling deficiencies for some satellites such as C45 and C46 with Search and Rescue payloads. Given a sparse ground network with 5 stations, the introduction of SLR significantly stabilizes the SRP parameter estimates and improves the orbit accuracy by 44.4%. In terms of geodetic parameter estimation, the scatter of the Z-component geocenter motion can be effectively reduced with the inclusion of SLR data, presenting 10.9–15.3% smaller root mean square (RMS) values during February 2023 and May 2024, depending on the SRP models. In addition, the annual amplitudes of the Z-component geocenter motion are reduced by 7.2–48.2%. The improvement is more pronounced with a limited number of microwave stations, due to the greater strength of SLR observations in geocenter motion estimation. On the other hand, since the SLR observations are unhomogeneously distributed in both space and time, the incorporation of SLR does not evidently enhance the accuracy of Earth rotation parameters, and may even to some extent contaminate the results when the number of microwave stations is limited.

Trends in the deep-ocean M(_2) barotropic tide, deduced from nearly three decades of satellite altimetry and recently presented by Opel et al. (Commun Earth Environ 5:261, https://doi.org/10.1038/s43247-024-01432-5, 2024), are here updated with a slightly longer time series and with a focus on potential systematic errors. Tidal changes are very small, of order 0.2 mm/year or less, with a tendency for decreasing amplitudes, which is evidently a response to the ocean’s increasing stratification and an increasing energy loss to baroclinic motion. A variety of systematic errors in the satellite altimeter system potentially corrupt these small trend estimates. The Dynamic Atmosphere Correction (DAC), derived from an ocean model and used for de-aliasing, introduces a spurious trend (exceeding 0.1 mm/year in places) caused by changes in ECMWF atmospheric tides. Both operational and reanalysis atmospheric tides have spurious trends over the altimeter era. Tidally coherent errors in satellite orbits, including from use of inconsistent tidal geocenter models, are more difficult to bound, although differences between two sets of satellite ephemerides are found to reach 0.1 mm/year for M(_2). Orbit errors are more deleterious for some other constituents, including the annual cycle. Tidal leakage in the “mesoscale correction,” needed here to suppress non-tidal ocean variability, is a known potential problem, and if the leakage changes over time, it impacts ocean-tide trend estimation. Tests show the error is likely small in the open ocean ((<0.04) mm/year) but large in some marginal seas ((>0.2) mm/year). Potential contamination from other altimeter corrections (e.g., ionospheric path delay) is likely negligible for M(_2) but can be difficult to bound.