Journal of Geodesy最新文献

In recent years, the fundamental quantity of the gravitational field has been extended from gravitational potential, gravitational vector, and gravitational gradient tensor to gravitational curvature with its first measurement along the vertical direction in laboratory conditions. Previous studies numerically identified the near-zone and polar-region problems for gravitational curvature of a tesseroid, but these issues remain unresolved. In this contribution, we derive the new third-order central and single-sided difference formulas with one, two, and three arguments using the finite difference method. To solve these near-zone and polar-region problems, we apply a numerical approach combining the conditional split, finite difference, and double exponential rule based on these newly derived third-order difference formulas when the computation point is located below, inside, and outside the tesseroid. Numerical experiments with a spherical shell discretized into tesseroids reveal that the accuracy of gravitational curvature is about 4–8 digits in double precision. Numerical results confirm that when the computation point moves to the surface of the tesseroid, the relative and absolute errors of gravitational curvature do not change much, i.e., the near-zone problem can be adequately solved using the numerical approach in this study. When the latitude of the computation point increases, the relative and absolute errors of gravitational curvature do not increase, which solves the polar-region problem with this stable numerical approach. The provided Fortran codes at https://github.com/xiaoledeng/xtessgc-xqtessgc will help with potential applications for the gravitational field of different celestial bodies in geodesy, geophysics, and planetary sciences.

The paper presents 3D numerical modelling of the altimetry-derived marine gravity data with the high horizontal resolution 1 × 1 arc min. The finite volume method (FVM) as a numerical method is used to solve the altimetry–gravimetry boundary-value problem. Large-scale parallel computations result in the disturbing potential in every finite volume of the discretized 3D computational domain between an ellipsoidal approximation of the Earth’s surface and an upper boundary chosen at altitude of 200 km. Afterwards, the first, second or higher derivatives of the disturbing potential in different directions can be numerically derived using the finite differences. A crucial impact on achieved accuracy has the process of preparing the Dirichlet boundary conditions over oceans/seas. It is based on nonlinear filtering of the geopotential generated on a mean sea surface (MSS) from a GRACE/GOCE-based satellite-only global geopotential model. The paper presents different types of the altimetry-derived marine gravity data obtained on the DTU21_MSS as well as at higher altitudes of the 3D computational domain. The altimetry-derived gravity disturbances on the DTU21_MSS are compared with those from recent datasets like DTU21_GRAV or SS_v31.1. Standard deviations of the residuals are about 2.7 and 2.9 mGal, respectively. The obtained altimetry-derived gravity disturbances at higher altitudes are compared with airborne gravity data from the GRAV-D campaign in US showing accuracy about 3 mGal. In addition, the gravity disturbing gradients as the second derivatives or the third derivatives are provided with the same high resolution on the DTU21_MSS as well as at different altitudes.

In urban canyons or natural valleys, diffraction effect occurs when the signal of Global Navigation Satellite Systems (GNSS) transmits to the edge of obstructions, such as buildings, trees, and slopes, resulting in large diffraction error, which is one of the important error sources in carrier-phase-based precise positioning. However, the theoretical formula derivation and numerical modeling of the diffraction error have been rarely studied. In this study, we derived the theoretical formula of the diffraction error based on the geometrical structure of the signal propagation path in satellite-obstruction-antenna geometry. Then, the diffraction error extraction and modeling method were proposed to study the time-varying characteristics of diffraction error and verify the validity of the theoretical formula of the diffraction error. Based on the GNSS data collected in occlusion environment, a designed experiment was carried out. The results show that the diffraction error generally increases or decreases monotonically, and mostly the amplitude of it could be larger than 50 mm and even reach 200 mm. The time-varying characteristics of diffraction error can be precisely simulated with the vertical and horizontal diffraction formulas developed, and the diffraction error model established could be applied in sidereal filtering method to correct the diffraction error. From the experiment, the fixed rate of ambiguity resolution can be improved from 76.8 to 98.87%, and the positioning reliability is improved from 80 to over 98% with the diffraction correction. The results of this paper provided theoretical basis and experience for the processing of GNSS diffraction error and show the significance in applications of high-precision positioning.

Spectral gravity forward modelling delivers gravitational fields of mass distributions by evaluating Newton’s integral in the spectral domain. We generalize its spherical harmonic variant to 3D variable densities and to any integration radius. The former is achieved by expressing the density function as an infinite-degree polynomial in the radial direction with polynomial coefficients varying laterally as a bounded function. The latter generalization builds on Molodensky’s truncation coefficients and allows to evaluate gravitational contribution of masses found up to and beyond some integration radius. In a numerical study, we forward-model lunar topographic masses by first assuming constant and then 3D variable density. Our validation with respect to GRAIL-based models shows that the 3D density model yields superior gravitational field compared to the constant density model. Thanks to the efficiency of FFT-based spherical harmonic transforms, the new technique can be employed in high-resolution modelling of topographic potentials. A numerical implementation is made available through CHarm, which is a C/Python library for high-degree spherical harmonic transforms accessible at https://github.com/blazej-bucha/charm.

The Surface Water and Ocean Topography (SWOT) altimeter mission provides a significant opportunity to improve the accuracy of geoid gradients (GGs) and marine gravity fields. This paper presents a new method, namely LSA3, to determine the north and east ((xi ) and (eta )) components of GGs from simulated and real SWOT data in the northern South China Sea. To fully use SWOT’s fine-scale sea surface height (SSH) measurements, LSA3 first determines GGs in SWOT along-, cross- and oblique-track directions and constructs a grid for each gradient. Least-squares adjustment (LSA), accounting for correlations of the GGs in three directions, is then employed to point-wisely estimate (xi ) and (eta ) components at grid points. The accuracy of estimated (xi ) and (eta ) components is assessed using those computed by numerical differentiations. For comparison, GG components are also estimated using least-squares collocation (LSC) and weighted LSA (WLSA) methods with empirically determined data window sizes and without accounting for correlations. Simulated results show that LSA3-estimated GG components achieve the root-mean-square deviation (RMSD) values of 0.43 and 0.47 microrad for (xi ) and (eta ), respectively, outperforming LSC (0.82 and 0.86 microrad) and WLSA (0.49 and 0.54 microrad). The results from the real SWOT data indicate that LSA3 is comparable to LSC with a mean RMSD of 1.88 mgal for marine gravity anomalies when compared to shipborne gravity data, but LSA3 is more computationally efficient than LSC. Compared to the Sandwell V32.1 gravity field, SWOT improves gravity accuracy by an average of 12.0%, with a maximum improvement of 44.3% for a single ship trajectory.

In this contribution, we introduce some new theory for the classical GNSS ambiguity function (AF) method. We provide the probability model by means of which the AF-estimator becomes a maximum likelihood estimator, and we provide a globally convergent algorithm for computing the AF-estimate. The algorithm is constructed from combining the branch-and-bound principle, with a special convex relaxation of the multimodal ambiguity function, to which the projected-gradient-descent method is applied to obtain the required bounds. We also provide a systematic comparison between the AF-principle and that of integer least-squares (ILS). From this comparison, the conclusion is reached that the two principles are fundamentally different, although there are identified circumstances under which one can expect AF- and ILS-solutions to behave similarly.

This paper presents a study on depth modernization, paralleling height modernization for land elevations. Depth modernization integrates mean sea surface (MSS) models, ocean tide models, and precise ship positioning to achieve accurate seafloor depth measurements. Conventional methods rely on tidal corrections and chart datum from temporary tide gauges, which can be challenging in regions with complex tidal patterns and inconsistent chart datums. For depth modernization, we developed (1) a hybrid MSS model using satellite altimeter data, tide gauge records, and a regional geoid model, and (2) a hydrodynamic-driven ocean model with 26 tidal constituents to determine separations between the hybrid MSS and five tidal surfaces, resulting in five ellipsoid-based surfaces analogous to a geoid model for height modernization. Precise ship positioning is demonstrated using GNSS data collected by the Legend research ship in the Pacific Ocean east of Taiwan and the Canadian spatial reference system precise point positioning toolbox. We used measurements in the Taiwan Strait to show how modern depth is implemented. Comparisons of depths in four regions from the conventional and modern methods show small (a few cm) to moderate (a few dm) differences with some variability depending on the region and equipment. Discontinuities in depths from the conventional method are analyzed. Depth modernization has significantly benefited rapid and accurate bathymetric mapping for electronic navigation charts. Future work in MSS and ocean tide models and the availability of PPP tools for depth modernization are discussed. For mapping agencies worldwide, depth modernization should be prioritized alongside height modernization to ensure rapid and accurate depth data provision.

The gravitational field of a planetary body is most often modeled by an exterior spherical harmonic series, which is uniformly convergent outside the smallest mass-enclosing sphere centered at the origin of the coordinate system, known as the Brillouin sphere. The model can become unstable inside the spherical boundary. Rarely deliberated or emphasized is an obvious fact that the radius of the Brillouin sphere, which is the maximum radius coordinate of the body, changes with the origin. The sphere can thus be adjusted to fit a certain convex portion of irregular body shape via an appropriate coordinate translation, thereby maximizing the region of model stability above the body. We demonstrate that it is, while perhaps counterintuitive, rational to displace the coordinate origin from the center of figure, or even off the body entirely. We review concisely the theory and a method of spherical harmonic translation. We consider some textbook examples that illuminate the physical meaning and the practical advantage of the transformation, the discussion of which, as it turns out, is not so easily encountered. We provide seminormalized as well as fully normalized version of the algorithms, which are compact and easy to work with for low-degree applications. At little cost, the proposed approach enables the spherical harmonics to be comparable with the far more complicated ellipsoidal harmonics in performance in the case of two small objects, Phobos and 433 Eros.

For a rapid retrieval of zenith wet delay (ZWD) and multi-global navigation satellite system (GNSS) precise point positioning (PPP) enhancement, a lightweight ZWD retrieval model was constructed by combining ground-based GNSS observations and precipitable water vapor (PWV) data provided by the European Center for Medium-Range Weather Forecasts Reanalysis (ERA5). The proposed model can rapidly produce ZWD without relying on the meteorological profile parameters. The proposed ZWD retrieval model achieved an RMSE and STD of 1.74 cm, with a correlation coefficient of 0.98. The enhanced performance of PWV-generated ZWD in GNSS PPP was tested in this study. The results showed that the ZWD constraint in GNSS PPP mainly affects the convergence time of the standard PPP solution, with the most significant effect in the U-direction. The PPP convergence time can be shortened by a maximum of 43%, with an average reduction of 24% for the eight sites over the four seasons. In the PPP-ambiguity resolution solution, the time to first fix (TTFF) was shorter for all sites with ZWD enhancement than for those without ZWD enhancement. The TTFF of the eight sites was significantly shortened in all four seasons, with an average improvement of 31%. The ZWD retrieval method based on the ERA5 PWV proposed in this study can quickly generate ZWD with high accuracy and resolution over a large area and significantly enhance GNSS PPP. The methodology proposed in this study is valuable for utilizing multi-source PWV-generated ZWD services for GNSS PPP enhancement.

Global Navigation Satellite System (GNSS) products are an integral part of a wide range of scientific and commercial applications. The creation of such products requires processing software capable of solving a combined station position and GNSS satellite orbit estimation by least squares adjustment, also known as global GNSS processing. Such processing is routinely performed by the International GNSS Service (IGS) and its Analysis Centers. For the IGS Reprocessing Campaign 3 (repro3), Graz University of Technology (TUG) participated as an AC using the raw observation approach, which uses all measurements as observed by the receivers. However, a common feature of almost all global multi-GNSS processing strategies is the use of diagonal covariance matrices as stochastic models for simplicity. This implies that any spatial or temporal correlations are ignored. However, numerous studies have shown that GNSS processing is indeed affected by spatial and temporal correlations. For global GNSS processing, research on stochastic modeling and its challenges is rather scarce. In this work, a detailed insight into the problems of stochastic modeling in global GNSS processing using the raw observation approach is given along with a detailed overview of the intended TUG approach. An analysis of the impact of temporal correlation modeling on the resulting GNSS products and GNSS frame estimation is also given.