Global Gravity Field Solutions Research Articles

A combined regional Geopotential Model using optimized global Gravity Field Solutions

To develop a gravimetric geoid, a Global Geopotential Model (GGM) is required to minimise the truncation error arising from using the Stokes integral with a limited number of gravity data points. The choice of a best-fitting GGM determines the accuracy of a gravimetric geoid solution. Selecting a suitable GGM is a rigorous process, requiring both internal and external evaluation of all GGMs available at the International Center for Globa Earth Models (ICGEM). Moreover, GGMs perform differently depending on the wavelength, and it is difficult to obtain a GGM that performs best across the full harmonic spectrum. In this study, a combined GGM is developed from a selection of the most recent and high-resolution GGMs covering Peninsular Malaysia. The selected models are first synthesized harmonically to obtain geoid undulations at collocated GNSS-levelled points, and free air anomalies at randomly sampled points across the study area. These quantities are compared with the observed geoid undulations and point gravity anomalies interpolated from a grid of free air anomalies. The best performing GGMs are then used to produce a combined GGM, by selecting the spherical harmonic coefficients with the best characteristics for every degree. The signal and error spectra of the new GGM are compared with the selected geopotential models. The combined GGM produced a higher cumulative signal to noise ratio (SNR) of 4402.669 compared to all the selected GGMs, with XGM2016 and Eigen-6C following suit with SNR of 4139.561 and 4092.462, respectively. Besides, the new combined GGM performed better across the whole harmonic spectrum than all selected GGMs. The use of combined GGMs in geoid modelling, instead of a single GGM may be more desirable because they can improve the quality of results.


 On Testing Frame-Dragging with LAGEOS and a Recently Announced Geodetic Satellite

Recently, Ciufolini and coworkers announced the forthcoming launch of a new cannonball geodetic satellite in 2019. It should be injected in an essentially circular path with the same semimajor axis a of LAGEOS (Laser Geodynamics Satellite), in orbit since 1976, and an inclination I of its orbital plane supplementary with respect to that of its existing cousin. According to their proponents, the sum of the satellites’ precessions of the longitudes of the ascending nodes Ω should allow one to test the general relativistic Lense–Thirring effect to a ≃0.2% accuracy level, with a contribution of the mismodeling in the even zonal harmonics Jl, l = 2, 4, 6, . . . of the geopotential to the total error budget as little as 0.1%. Actually, such an ambitious goal seems to be hardly attainable because of the direct and indirect impact of, at least, the first even zonal J2. On the one hand, the lingering scatter of the estimated values of such a key geophysical parameter from different recent GRACE/GOCE-based (Gravity Recovery and Climate Experiment/Gravity field and steady-state Ocean Circulation Explorer) global gravity field solutions is representative of an uncertainty which may directly impact the summed Lense–Thirring node precessions at a ≃70–80% in the worst scenarios, and to a ≃3–10% level in other, more favorable cases. On the other hand, the phenomenologically measured secular decay à of the semimajor axis of LAGEOS (and, presumably, of the other satellite as well), currently known at a σà≃0.03 m yr–1 level after more than 30 yr, will couple with the sum of the J2-induced node precessions yielding an overall bias as large as '20–40% after 5–10 yr. A further systematic error of the order of ≃2–14% may arise from an analogous interplay of the secular decay of the inclination I˙ with the oblateness-driven node precessions.

Modeling of present-day atmosphere and ocean non-tidal de-aliasing errors for future gravity mission simulations

A realistically perturbed synthetic de-aliasing model consistent with the updated Earth System Model of the European Space Agency is now available over the period 1995–2006. The dataset contains realizations of (1) errors at large spatial scales assessed individually for periods 10–30, 3–10, and 1–3 days, the S1 atmospheric tide, and sub-diurnal periods; (2) errors at small spatial scales typically not covered by global models of atmosphere and ocean variability; and (3) errors due to physical processes not represented in currently available de-aliasing products. The model is provided in two separate sets of Stokes coefficients to allow for a flexible re-scaling of the overall error level to account for potential future improvements in atmosphere and ocean mass variability models. Error magnitudes for the different frequency bands are derived from a small ensemble of four atmospheric and oceanic models. For the largest spatial scales up to $$\hbox {d/o} = 40$$ and periods longer than 24 h, those error estimates are approximately confirmed from a variance component estimation based on GRACE daily normal equations. Future mission performance simulations based on the updated Earth System Model and the realistically perturbed de-aliasing model indicate that for GRACE-type missions only moderate reductions of de-aliasing errors can be expected from a second satellite pair in a shifted polar orbit. Substantially more accurate global gravity fields are obtained when a second pair of satellites in an moderately inclined orbit is added, which largely stabilizes the global gravity field solutions due to its rotated sampling sensitivity.

Different radial basis functions and their applicability for regional gravity field representation on the sphere

Global gravity field solutions are commonly modelled in spherical harmonic basis functions. Additionally, radial basis functions on the sphere with quasi-local support are used to model regional refinements of gravity fields. However, these functions are usually not orthogonal on a sphere, which makes the modelling process more complex. In this paper we study and compare different radial basis functions and their performance in regional gravity field modelling on the sphere by making use of simulated data. In addition to the type of radial basis function also the size of the study area on the sphere, the point grid, the margins and the method which is used to solve the singular system have to be taken into account. The synthetic signal, which we use in our simulation, is a residual signal in a bandwidth which corresponds to the bandwidth of GOCE satellite gravity observations.

Precise estimation of in situ geopotential differences from GRACE low‐low satellite‐to‐satellite tracking and accelerometer data

The precise determination of in situ geopotential differences at satellite altitude was demonstrated by simultaneously adjusting the orbits of the coorbiting GRACE satellites with intersatellite low‐low range rate measurements. The results agree well (correlation coefficients 0.5–0.8) with the monthly solutions of the spherical harmonic coefficients estimated using contemporary methods of precise orbit determination and parameter recovery. Higher correlation (>0.8 in general) was found for the in situ estimates over the continents than over the oceans. The analysis of 4 months of GRACE satellite‐to‐satellite tracking data from July 2003 to October 2003 indicated a significant migration of mass over the Amazon basin (hydrological effect), which agreed well with the predictions from the published monthly mean global gravity field solutions. Our results demonstrate the validity and utility of this alternative technique for global and especially regional modeling of the gravity field and its variation with temporal and spatial resolutions finer than monthly and 1000 km, respectively.

Estimation of the Earth's tensor of inertia from recent global gravity field solutions

The dynamic figure of the Earth, characterized by the principal axes and principal moments of inertia, is estimated from satellite-derived gravitational harmonic coefficients of second degree in recent global Earth gravity models and from the dynamic ellipticity resulting from the precession constant observed through very-long-baseline interferometry (VLBI). Closed, exact formulae for the determination of these parameters of the Earth's tensor of inertia are developed based on the exact solution of the eigenvalue–eigenvector problem, including a rigorous error propagation. These formulae are applied to determine (a) static components and accuracy of the Earth's tensor of inertia at epoch and (b) the variation with time of the Earth's tensor of inertia and its accuracy. The best-fitting principal moments of inertia and second-degree harmonic coefficients in the principal-axes system are found from an adjustment involving four global gravity field models and six different values for the dynamic ellipticity. The evolution with time of the dynamic figure of the Earth is determined from the mean pole path and the observed secular rate of change in the second-degree zonal coefficient. It is found that differences in the principal moments of inertia change significantly over the time interval from 1962 to 2000, whereas changes in the absolute values cannot be reliably resolved due to the uncertainty in the dynamic ellipticity.