Evaluation of the third- and fourth-generation GOCE Earth gravity field models with Australian terrestrial gravity data in spherical harmonics

In March 2013 the fourth generation of ESA’s (European Space Agency) global gravity field models, DIR4 (Bruinsma et al, 2010b) and TIM4 (Pail et al, 2010), generated from the GOCE (Gravity field and steady-state Ocean Circulation Explorer) gravity observation satellite were released. We evaluate the models using an independent ground truth data set of gravity anomalies over Australia. Combined with GRACE (Gravity Recovery and Climate Experiment) satellite gravity, a new gravity model is obtained that is used to perform comparisons with GOCE models in spherical harmonics. Over Australia, the new gravity model proves to have significantly higher accuracy in the degrees below 120 as compared to EGM2008 and seems to be at least comparable to the accuracy of this model between degree 150 and degree 260. Comparisons in terms of residual quasi-geoid heights, gravity disturbances, and radial gravity gradients evaluated on the ellipsoid and at approximate GOCE mean satellite altitude (h=250 km) show both fourth generation models to improve significantly w.r.t. their predecessors.Relatively, we find a root-mean-square improvement of 39 % for the DIR4 and 23 % for TIM4 over the respective third release models at a spatial scale of 100 km (degree 200). In terms of absolute errors TIM4 is found to perform slightly better in the bands from degree 120 up to degree 160 and DIR4 is found to perform slightly better than TIM4 from degree 170 up to degree 250. Our analyses cannot confirm the DIR4 formal error of 1 cm geoid height (0.35 mGal in terms of gravity) at degree 200. The formal errors of TIM4, with 3.2 cm geoid height (0.9 mGal in terms of gravity) at degree 200, seem to be realistic. Due to combination with GRACE and SLR data, the DIR models, at satellite altitude, clearly show lower RMS values compared to TIM models in the long wavelength part of the spectrum (below degree and order 120). Our study shows different spectral sensitivity of different functionals at ground level and at GOCE satellite altitude and establishes the link among these findings and the Meissl scheme (Rummel and van Gelderen in Manuscripta Geodaetica 20:379–385, 1995)

Kombinace řešení okrajové úlohy pro gravitační křivosti

V globálních studiích je gravitační pole Země popsáno pomocí sférických harmonických funkcí. Řešení okrajové úlohy pro gravitační křivosti je formulováno pro vertikální-vertikální-vertikální, vertikální-vertikální-horizontální, vertikální-horizontální-horizontální a horizontální-horizontální komponenty. Každá rovnice poskytuje nezávislý soubor sférických harmonických koeficientů, protože každá složka gravitačního tenzoru třetího řádu je citlivá na gravitační změny v jiném směru. V tomto příspěvku jsou odhady sférických harmonických koeficientů prováděny kombinací čtyř řešení okrajové úlohy pro gravatační křivosti pomocí tří metod, a to aritmetického průměru, váženého průměru a modelu podmíněného nastavení. Vzhledem k tomu, že směrové derivace gravitačního potenciálu třetího řádu nejsou dosud pozorovány satelitními senzory, syntetizujeme je v nadmořské výšce 250 km z globálního gravitačního modelu až do stupně 360 při současném přidávání Gaussova šumu. Výsledky numerické analýzy ukazují, že aritmetický průměr poskytuje nejlepší řešení dle RMS shody mezi predikovanými a referenčními hodnotami. Tento výsledek vysvětlíme tím, že podmínky vytvářejí pouze další stochastické vazby mezi odhadovanými parametry.In global studies, the Earth's gravitational field is conveniently described in terms of spherical harmonics. The solution to a gravitational curvature boundary-value problem canould formally be formulated for the vertical-vertical-vertical, vertical-vertical-horizontal, vertical-horizontal-horizontal and horizontal-horizontal-horizontal components. Each equation provides an independent set of spherical harmonic coefficients because each component of the third-order gravitational tensor is sensitive to gravitational changes in the different direction. In this contribution, estimations of spherical harmonic coefficients are carried out by combining four solutions components of the gravitational curvature boundary-value problem based on using three methods, namely an arithmetic mean, a weighted mean and a conditional adjustment model. Since the third-order gradients directional derivatives of the gravitational potential are not yet observed by satellite sensors, we synthesise them at thea satellite altitude of 250 km from a global gravitational model up to the degree 360 of spherical harmonics, while adding a Gaussian noise with thea standard deviation of m-1 s-2. Results of the numerical analysis reveal that an arithmetic mean provides the best solution in terms by means of of the RMS fit between predicted and referenceobserved values. We explain this resultfinding by the fact that the conditions only create additional stochastic bindings between estimated parameters

Integral inversion of GRAIL inter-satellite gravitational accelerations for regional recovery of the lunar gravitational field

© 2019 COSPAR We present an integral-based approach for high-resolution regional recovery of the gravitational field in this article. We derive rigorous remove-compute-restore integral estimators relating the line-of-sight gravitational acceleration to an arbitrary order radial derivative of the gravitational potential. The integral estimators are composed of three terms, i.e., the truncated integration, the low-frequency line-of-sight gravitational acceleration, and the high-frequency truncation error (effect of the distant zones). We test the accuracy of the integral transformations and of the integral estimators in a closed-loop simulation over the Montes Jura region on the nearside of the Moon. In this way, we determine optimal sizes of integration radii and grid discretisation. In addition, we investigate the performance of the regional integral inversion with synthetic and realistic GRAIL observations. We demonstrate that the regional inversion results of the disturbing gravitational potential and its first order radial derivative in the Montes Jura mountain range are less contaminated by high-frequency noise than the global spherical harmonic models