Time-Variable Gravity Field from the Combination of HLSST and SLR

The Earth’s time-variable gravity field is of great significance to study mass change within the Earth’s system. Since 2002, the NASA-DLR Gravity Recovery and Climate Experiment (GRACE) and its successor GRACE follow-on mission provide observations of monthly changes in the Earth gravity field with unprecedented accuracy and resolution by employing low-low satellite-to-satellite tracking (LLSST) measurements. In addition to LLSST, monthly gravity field models can be acquired from satellite laser ranging (SLR) and high-low satellite-to-satellite tracking (HLSST). The monthly gravity field solutions HLSST+SLR were derived by combining HLSST observations of low earth orbiting (LEO) satellites with SLR observations of geodetic satellites. Bandpass filtering was applied to the harmonic coefficients of HLSST+SLR solutions to reduce noise. In this study, we analyzed the performance of the monthly HLSST+SLR solutions in the spectral and spatial domains. The results show that: (1) the accuracies of HLSST+SLR solutions are comparable to those from GRACE for coefficients below degree 10, and significantly improved compared to those of SLR-only and HLSST-only solutions; (2) the effective spatial resolution could reach 1000 km, corresponding to the spherical harmonic coefficient degree 20, which is higher than that of the HLSST-only solutions. Compared with the GRACE solutions, the global mass redistribution features and magnitudes can be well identified from HLSST+SLR solutions at the spatial resolution of 1000 km, although with much noise. In the applications of regional mass recovery, the seasonal variations over the Amazon Basin and the long-term trend over Greenland derived from HLSST+SLR solutions truncated to degree 20 agree well with those from GRACE solutions without truncation, and the RMS of mass variations is 282 Gt over the Amazon Basin and 192 Gt in Greenland. We conclude that HLSST+SLR can be an alternative option to estimate temporal changes in the Earth gravity field, although with far less spatial resolution and lower accuracy than that offered by GRACE. This approach can monitor the large-scale mass transport during the data gaps between the GRACE and the GRACE follow-on missions.

Mirror Symmetry of Life

Functioning in the Earth gravity field imposes on living organisms a necessity to read directions. The characteristic feature of their bodies, regardless unicellular or multicellular, is axial symmetry. The development of body plan orchestrated by spatiotemporal changes in gene expression patterns is based on formation of the vertical and radial axes. Especially for immobile plants, anchored to the substrate, vertical axis is primary and most important. But also in animals the primary is the axis, which defines the anterior and posterior pole of the embryo. There are many little known chiral processes and structures that are left- or right oriented with respect to this axis. Recent developments indicate the role of intrinsic cell chirality that determines the direction of developmental chiral processes in living organisms. The still enigmatic events in cambia of trees and handedness of phyllotaxis as well as plant living crystals are in focus of the chapter.

Determination of static and time-varying Earth gravity field by quantum measurements: the MOCAST+ study

<p>In the ongoing MOCAST+ study (funded by the Italian Space Agency), the use of an enhanced cold atom interferometer is proposed for a satellite gravity mission. The instrument consists of an interferometric gravitational gradiometer with Strontium atoms, on which an optical frequency measurement is implemented by means of an ultra-stable laser, in order to also provide time measurements. The study is investigating whether this combination can give the possibility of improving the estimation of gravity models even at low harmonic degrees with inherent advantages in the modeling of mass transport and its global variations: this would represent fundamental information, e.g. in the study of variations in the hydrological cycle and relative mass exchange between atmosphere, oceans, cryosphere and solid Earth.</p><p>The main lines of the MOCAST+ proposal are: two satellites on a polar orbit (reference altitude 342 km) at a distance of about 100 km with atomic samples on board interrogated by the same clock laser (noise of the local oscillator in common). The atom interferometer should allow to collect observations of differences of the gravitational potential (which will contribute to the estimate of the low frequencies of the Earth gravity field model) and of second derivatives of the gravitational potential along one or more orthogonal directions, which will be not necessarily the same for the two satellites</p><p>In this presentation, the mathematical model for the application of the space-wise approach to the simulated data will be described, consisting in a filter - gridding - harmonic analysis scheme that is to be repeated for several Monte Carlo samples extracted for the same simulated scenario, in order to produce a sample estimate of the error covariance matrix of the harmonic coefficients.</p><p>The data analysis based on the formulated mathematical model will be applied to both static and time-variable gravity field, performing simulations over a limited time span and extending the resulting accuracy to a longer period by covariance propagation, assuming to have other independent solutions with the same accuracy. In particular, the time-variable analysis will be mainly dedicated to assessing the accuracy in estimating the rate of change in geodynamic processes for which a linear variation in time can be reasonably assumed.</p><p> </p>

Effect of the Gravitational Aberration on the Earth Gravity Field

Discussing the problem of the external gravitational potential of the rotating Earth, we have to consider the fundamental postulate of the finite speed of the propagation of gravitation. This can be done using the expressions for the gravitational aberration compared to the Liénard–Wiechert solution of the retarded potentials. The term gravitational counter-aberration or co-aberration is introduced to describe the pattern of the propagation of the gravitational signal emitted by the rotating Earth. It is proved that in the first approximation, the classic theory of the aberration of light can be applied to calculate this effect. Some effects of the gravitational aberration on the external gravity field of the rotating Earth may influence the orbit determination of the Earth artificial satellites.

Precise LEO satellite orbit determination and Earth gravity field modeling with carrier-range method

<p>Precise LEO satellite orbit determination(OD) and Earth gravity field modeling are researched in this study.</p><p>Firstly, on the basis of Precise Point Positioning Ambiguity Resolution(PPPAR), a kinematic LEO satellite OD algorithm based on the epoch-difference and post-facto iteration is introduced, which plays a vital rule in the detection of the phase cycle slip to achieve the best orbit accuracy. The experiments of GRACE satellite OD with zero-difference IF combination observations spanning one year of 2010 show that, compared to the JPL reference orbits, the daily average 3D RMS is generally below 5.0cm for the float solution, while that is below 4.0cm for the fixed solution.</p><p>Secondly, to solve the problem that specific a-priori information like earth gravity field model must be involved in LEO’ reduced dynamic OD, the simultaneous solution method, which is specially on the relation with the kinematic OD and reduced dynamic OD, is used and the carrier-range, which can be recovered from phase observations once the kinematic OD process using Integer Ambiguity Resolution (IAR) technology is carried out, is naturally applied to this method. With the experiments based on the data over a period of the year of 2010, comes some evacuations, including the external checks on the accuracy of the orbits and the analysis on the earth gravity model. The numerical results show that, compared to the JPL reference orbits, the 3D RMS is below 3.0cm and the RMS is below 2.0cm for each component. As for the accuracy of gravity field model, compared to some contemporary significant earth gravity model, the model of the single month solution behaves very well below the 60 degree of the gravity field’s coefficients, while over the 60 degree, only the UTCSR model quite corresponds to the model computed by this method. Therefore, due to the promotion of the orbital accuracy and gravity field model, we suggest that the recovered carrier-range should be implemented in the simultaneous method for the better product solution of the LEO’s missions.</p>

An Assessment of the GOCE High-Level Processing Facility (HPF) Released Global Geopotential Models with Regional Test Results in Turkey

The launch of dedicated satellite missions at the beginning of the 2000s led to significant improvement in the determination of Earth gravity field models. As a consequence of this progress, both the accuracies and the spatial resolutions of the global geopotential models increased. However, the spectral behaviors and the accuracies of the released models vary mainly depending on their computation strategies. These strategies are briefly explained in this article. Comprehensive quality assessment of the gravity field models by means of spectral and statistical analyses provides a comparison of the gravity field mapping accuracies of these models, as well as providing an understanding of their progress. The practical benefit of these assessments by means of choosing an optimal model with the highest accuracy and best resolution for a specific application is obvious for a broad range of geoscience applications, including geodesy and geophysics, that employ Earth gravity field parameters in their studies. From this perspective, this study aims to evaluate the GOCE High-Level Processing Facility geopotential models including recently published sixth releases using different validation methods recommended in the literature, and investigate their performances comparatively and in addition to some other models, such as GOCO05S, GOGRA04S and EGM2008. In addition to the validation statistics from various countries, the study specifically emphasizes the numerical test results in Turkey. It is concluded that the performance improves from the first generation RL01 models toward the final RL05 models, which were based on the entire mission data. This outcome was confirmed when the releases of different computation approaches were considered. The accuracies of the RL05 models were found to be similar to GOCO05S, GOGRA04S and even to RL06 versions but better than EGM2008, in their maximum expansion degrees. Regarding the results obtained from these tests using the GPS/leveling observations in Turkey, the contribution of the GOCE data to the models was significant, especially between the expansion degrees of 100 and 250. In the study, the tested geopotential models were also considered for detailed geoid modeling using the remove-compute-restore method. It was found that the best-fitting geopotential model with its optimal expansion degree (please see the definition of optimal degree in the article) improved the high-frequency regional geoid model accuracy by almost 15%.