Journal of Geodesy最新文献

Combining the Liouville equations for polar motion (PM) with forecasted geophysical effective angular momentum (EAM) functions can significantly improve the accuracy of Earth's PM predictions. These predictions rely on deconvolution and convolution methods. Deconvolution derives the geodetic EAM function from the PM observations, while convolution uses both the geodetic and geophysical EAM functions to reproduce and predict the PM values. However, there are limitations in existing numerical realisations of deconvolution and convolution that must be addressed. These limitations include low-frequency biases, high-frequency errors, and edge errors, which can negatively impact the accuracy of PM prediction. To overcome these concerns, we develop the Convolution Least Squares (Conv-LS) scheme through a multi-perspective analysis in the frequency domain, PM domain, and EAM domain. By comparing representative approaches for reproducing three different PM series (IERS C01, IERS C04, and IGS) with varying sampling intervals (18.25 days, daily, and 6 h), we demonstrate that the Conv-LS scheme can effectively eliminate the usually present spurious signals and also integrate high-accuracy deconvolution algorithms to reduce reproduced errors further. Compared to the traditional approacsh (using a low-accuracy discrete PM equation for deconvolution and numerical integration for convolution), our new approach (utilising a high-accuracy deconvolution algorithm along with the Conv-LS scheme for convolution) reduces the standard deviations of the residuals' x-component by 31.0%, 60.1%, and 13.7% for C01, C04, and IGS PM series, respectively, while also reducing the y-component by 17.3%, 47.0%, and 14.0%, respectively. These results highlight the superiority of the Conv-LS scheme, leading us to recommend it for practical applications.

The truncation coefficient is widely utilized in non-global coverage computations of geophysics and geodesy and is always altitude dependent. As the two commonly used calculation methods for truncation coefficients, i.e., the spectral form and the recursive formula, both suffer from decreasing precision caused by high-altitude, leading to slow convergence for the former and numerical instability recursion for the latter. The asymptotic expansion mathematically converges with increasing degree and can precisely compensate for the shortcomings of the two methods. This study introduces asymptotic expansion to accurately compute the truncation coefficient for the spectral gravity forward modeling to a high degree. The evaluation at the whole altitudes and whole integral radii indicates that the proposed method has the following advantages: (i) The calculation precision increases with increasing degree and is altitude independent; (ii) the accurate calculation can be supported by a double-precision format; and (iii) the calculation can be conducted nearly without extra time cost with increasing degree. Generally, asymptotic expansion is used to calculate the high degree truncation coefficients, while the truncation coefficients at low degrees can be calculated using spectral form or recursive formulas in multiprecision format as a supplement; and the available range of asymptotic expansion is provided in the appendix.

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 √(x/300) for alternative data intervals of x seconds.

Differential code bias (DCB) is widely used to achieve consistency between global navigation satellite system (GNSS) observations at different frequencies. Since a strong correlation exists between satellite DCBs at different frequencies and the satellite clock offset, the DCB products need to be aligned with the corresponding clock products. This paper proposes a satellite’s DCB conversion model between different clock products released by the International GNSS Service (IGS) via the uncombined method. First, a one-step uncombined approach with a simplified ionospheric processing model is proposed for multi-frequency DCB estimation. In the second step, a linear function model is applied to represent the relationship between the initial satellite clock bias and the DCB estimates at different frequencies. To test the proposed model, BeiDou global system (BDS-3) multi-frequency data collected from 60 multi-GNSS experiment stations and precise clock products released by four IGS analysis centers are used to estimate the DCB. The DCB estimates are compared to the DCB products released by the Chinese Academy of Sciences (CAS) and the Deutsches Zentrum für Luft-und Raumfahrt (DLR). The average root-mean-square (RMS) values of the differences between the DCB estimates and the two DCB products are 0.61 ns and 0.52 ns, which are significantly larger than the corresponding monthly standard deviations. This indicates that systematic bias exists between the DCB estimates and the two DCB products. Additionally, systematic biases are also observed in the DCB estimation when different clock products are used, with the maximum value reaching 4 ns. In order to study the propagation of parameter errors between the DCB estimates and the clock products, regression analysis is conducted to determine the linear model coefficients of the DCB conversion model. The results show that the model coefficients for the four frequency pairs C2I-C6I, C2I-C1X, C2I-C5X and C2I-C7Z are 0.394, 0.237, 0.238, and 0.238, respectively. Kinematic precision point positioning is conducted for model verification. During the first 6-h period, the average three-dimensional RMS of the positioning errors is 13.5 cm when the DCB estimates are corrected by the conversion model, which is improved by 32.5%, 14.6%, and 11.3% compared with the usage of the CAS and DLR products and those without model conversion, respectively.

Very-long-baseline interferometry (VLBI) networks have historically lacked enough antennas to densify the southern hemisphere adequately. This situation not only impacts directly the realization of the Celestial Reference System but also the determination of the Earth Orientation Parameters (EOP). In the last years, a significant step in the modernization of the VLBI infrastructure has been taken with the VLBI Global Observing System (VGOS). However, the distribution of VGOS antennas is still far from being homogeneous. In this work, we used the software VieSched++ for VLBI scheduling to simulate nine new VGOS arrays. These networks, which are more dense in the southern hemisphere and focus on South America, were planned considering existing geodetic sites where a VGOS antenna could be added and new sites where the installation is feasible. We compared the statistical performance of the proposed networks with that of a simulated standard VGOS network and the actual VGOS performance for the last 2 years. A more uniform station distribution does not seem to be associated with better repeatabilities for station coordinates, but the results for EOP and source coordinates improve as expected.

Like many geophysical observations, relative gravity (RG) measurements are affected by random errors, systematic errors, and occasional blunders. When RG measurements are used to build large gravity networks in remote areas under adverse environmental or logistical conditions (such as extreme temperatures, heavy precipitation, rugged terrain, difficult or dangerous roads, and high altitudes), it is more likely for significant errors to occur and accumulate. Therefore, obtaining accurate gravity estimates at regional gravity networks largely depends on defensive data collection protocols and robust adjustment techniques. In this work, we present a measurement field protocol based on highly redundant observation patterns, and a two-step least squares adjustment scheme implemented as a MATLAB package. This software helps us identify blunders, mitigates the impact of random errors, and downweights or removes outlier observations. The methodology also guarantees that adjusted gravity values have well-constrained standard error estimates. We illustrate the capabilities of our approach through the case study of the Bolivian gravity network, where we determined the acceleration due to gravity at 2548 stations that spread over difficult and sometimes extreme environments, with a typical level of uncertainty of 0.10–0.15 mGal.

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.

In this contribution, we introduce the ambiguity-resolved (AR) detector and study its distributional characteristics. The AR-detector is a new detector that lies in between the commonly used ambiguity-float (AF) and ambiguity-known (AK) detectors. As the ambiguity vector can seldomly be known completely, usage of the AK-detector is questionable as reliance on its distributional properties will then generally be incorrect. The AR-detector resolves the shortcomings of the AK-detector by treating the ambiguities as unknown integers. We show how the detector improves upon the AF-detector, and we demonstrate that the, for ambiguity-resolved parameter estimation, commonly required extreme success rates can be relaxed for detection, thus showing that improved model validation is also possible with smaller success rates. As such, the AR-detector is designed to work for mixed-integer GNSS models.

In recent years, significant progress has been in ionospheric modeling research through data ingestion and data assimilation from a variety of sources, including ground-based global navigation satellite systems, space-based radio occultation and satellite altimetry (SA). Given the diverse observing geometries, vertical data coverages and intermission biases among different measurements, it is imperative to evaluate their absolute accuracies and estimate systematic biases to determine reasonable weights and error covariances when constructing ionospheric models. This study specifically investigates the disparities among the vertical total electron content (VTEC) derived from SA data of the Jason and Sentinel missions, the integrated VTEC from the Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC) and global ionospheric maps (GIMs). To mitigate the systematic bias resulting from differences in satellite altitudes, the vertical ranges of various VTECs are mapped to a standardized height. The results indicate that the intermission bias of SA-derived VTEC remains relatively stable, with Jason-1 serving as a benchmark for mapping other datasets. The mean bias between COSMIC and SA-derived VTEC is minimal, suggesting good agreement between these two space-based techniques. However, COSMIC and GIM VTEC exhibit remarkable seasonal discrepancies, influenced by the solar activity variations. Moreover, GIMs demonstrate noticeable hemispheric asymmetry and a degradation in accuracy ranging from 0.7 to 1.7 TECU in the ocean-dominant Southern Hemisphere. While space-based observations effectively illustrate phenomena such as the Weddell Sea anomaly and longitudinal ionospheric characteristics, GIMs tend to exhibit a more pronounced mid-latitude electron density enhancement structure.