Variable Gravity Field Research Articles

Numerical modelling of post-seismic rupture propagation after the Sumatra 26.12.2004 earthquake constrained by GRACE gravity data

In the last decades, the development of the surface and satellite geodetic and geophysical observations brought a new insights into the seismic cycle, documenting new features of inter-, co-, and post-seismic processes. In particular since 2002 satellite mission GRACE provides monthly models of the global gravity field with unprecedented accuracy showing temporal variations of the Earth's gravity field, including those caused by mass redistribution associated with earthquake processes. When combined with GPS measurements, these new data have allowed to assess the relative importance of afterslip and viscoelastic relaxation after the Sumatra 26.12.2004 earthquake. Indeed the observed post-seismic crustal displacements were fitted well by a viscoelastic relaxation model assuming Burgers body rheology for the asthenosphere (60–220 km deep) with a transient viscosity as low as 4 × 10^17 Pas and constant ~ 10^19 Pas steady state viscosity in the 60–660-km depth range. However, even the low-viscosity asthenosphere provides the amplitude of strain which gravity effect does not exceed 50 per cent of the GRACE gravity variations, thus additional localized slip of about 1 m was suggested at downdip extension of the coseismic rupture. Post-seismic slip at coseismic rupture or its downdip extension has been suggested by several authors but the mechanism of the post-seismic fault propagation has never been investigated numerically. Depth and size of localized slip area as well as rate and time decay during the post-seismic stage were either assigned a priory or estimated by fitting real geodesy or gravity data. In this paper we investigate post-seismic rupture propagation by modelling two consequent stages. First, we run a long-term, geodynamic simulation to self-consistently produce the initial stress and temperature distribution. At the second stage, we simulate a seismic cycle using results of the first step as initial conditions. The second short-term simulation involves three substeps, including additional stress accumulation after part of the subduction channel was locked; spontaneous coseismic slip; formation and development of damage zones producing afterslip. During the last substep post-seismic stress leads to gradual ~1 m slip localized at three faults around ~100-km downdip extension of the coseismic rupture. We used the displacement field caused by the slip to calculate pressure and density variations and to simulate gravity field variations. Wavelength of calculated gravity anomaly fits well to that of the real data and its amplitude provides about 60 per cent of the observed GRACE anomaly. Importantly, the surface displacements caused by the estimated afterslip are much smaller than those registered by GPS networks. As a result cumulative effect of Burgers rheology viscoelastic relaxation (which explains measured GPS displacements and about a half of gravity variations) plus post-seismic slip predicted by damage rheology model (which causes much smaller surface displacements but provides another half of the GRACE gravity variations) fits well to both sets of the real data. Hence, the presented numerical modelling based on damage rheology supports the process of post-seismic downdip rupture propagation previously hypothesized from the GRACE gravity data.

Coriolis Effect on Convection in a Rotating Porous Layer Subjected to Variable Gravity

We consider the effects of rotation in a porous layer heated from below and subjected to a variable gravity field. The study is presented for large Vadasz numbers where no oscillatory convection is possible. It is demonstrated that the Coriolis acceleration stabilizes the convection in a variable gravity field, whilst the effect of gravity parameter stabilses the convection when reduced and destabilizes the convection when increased.

Combined geological and gravimetric mapping and modelling for an improved understanding of observed high-resolution gravity variations: a case study for the Global Geodynamics Project (GGP) station Moxa, Germany

Geodynamic observatories around the globe continuously monitor signals like gravity, tilt and strain as a function of time. However, global signals are often masked by local effects, caused by the direct surroundings of the station, including the local geological setting. This link is well established for superconducting gravimeters (SG) that observe the gravity field variations at very high resolution. An enhancement of the SG time series by the application of local correction is exemplarily shown here in a very practicable procedure for the Geodynamic Observatory Moxa, Germany. We show how the combination of geological and gravimetrical mapping and modelling around Moxa results in a significant correction of the original gravity data, as can be proven by comparison with the satellite-derived gravity field. Detailed geological mapping of the observatory surroundings, including measurements of fold axes, foliations and joints, was the basis of the present study. The fold structure in the area of interest was interpreted by geometrical 3D modelling. The complete representation of different rock types in space also provides a better understanding of the local hydro-geological situation. Using a combination of the 3D geological model with the high-resolution Bouguer map of the observatory surroundings, we developed a 3D density model. This model enables the correction of small gravity effects caused by mass variations close to the SG, in particular local hydro-geological mass changes. Thus, the procedure presented here, based on a close connection of geology and gravimetry, is a powerful tool for the reduction of local gravity effects on SG recordings. It should be applicable to SG stations worldwide, where similar hydrologically driven mass changes can be assumed.

Thermoslutal Convection in Walters’ (Model B') Rotating Fluid Permeated with Suspended Particles and Variable Gravity Field in Porous Medium in Hydromagnetics

The thermosolutal convection in Walters’ (Model B') elastico-viscous rotating fluid permeated with suspended particles (fine dust) and variable gravity field in porous medium in hydromagnetics is considered. By applying normal mode analysis method, the dispersion relation has been derived and solved numerically. It is observed that the rotation, magnetic field, gravity field, suspended particles and viscoelasticity introduce oscillatory modes. For stationary convection, Walters’ (Model B') elastico-viscous fluid behave like an ordinary Newtonian fluid and it is observed that rotation and stable solute gradient has stabilizing effects and suspended particles are found to have destabilizing effect on the system, whereas the medium permeability has stabilizing or destabilizing effect on the system under certain conditions. The magnetic field has destabilizing effect in the absence of rotation, whereas in the presence of rotation, magnetic field has stabilizing or destabilizing effect under certain conditions. The effect of rotation, suspended particles, magnetic field, stable solute gradient and medium permeability has also been shown graphically. AMS subject classifications are 76A10, 76E07, 76E25 and 76S05.

The ANU GRACE visualisation web portal

The launch of the Gravity Recovery and Climate Experiment (GRACE) space gravity mission opened new horizons to the scientific community for environmental monitoring. Through the provision of estimates of temporal changes in the Earth's gravity field, the products generated from the GRACE mission have enabled studies of mass balance changes in polar regions, deformation caused by very large earthquakes, glacial isostatic adjustment and quantification of water exchanges through various hydrological processes. International analysis centres provide estimates of the Earth's temporally varying gravity field in the form of spherical harmonic coefficients which are then used to quantify the geophysical processes that have caused the changes in the Earth's gravity field. We have designed an online, publicly available web application that performs the computations to convert the spherical harmonic representations (of the French Groupe de Recherche en Géodesie Spatiale) of the gravity field into estimates of crustal deformation and/or water loads, and provides users with the ability to visualise the estimates. Derived products are also available to download as numerical values for further analysis. This paper describes the scientific basis and technical approaches used by the web portal (grace.anu.edu.au/evasph.php).

Annual and seasonal water storage changes detected from GRACE data in the La Plata Basin

The gravity does not remain constant, but changes over time depending on the redistribution of the masses.Aquatic environments, like a river basin, perform important functions in nature such as control of climate, floods and nutrients; and they also provide goods and services for humanity. To monitor these environments at large spatial scales, the satellite gravity mission GRACE provides time-variable gravity field models that reflect the Earth’s gravity field variations due to mass transport processes, like continental water storage variations.The La Plata Basin is the second largest in South America and is a sample of the abundance, variety and quality of natural resources and possibilities offered in connection with the production of goods and services.The objective of this work is to analyze GRACE capability to monitor the water storage variations in the La Plata Basin. Firstly, GRACE solutions from four different processing centers are used to estimate the gravity trend and gravity amplitude over this basin. Afterwards, the calculated hydrological signal is used to obtain mass change models over this hydrographic system’s area, using two different methods and for the period from 2002 to 2009. Next, the annual and seasonal water storage changes from GRACE solutions are validated in Argentina by rainfall data over the time periods where extreme weather conditions took place.The results indicate that GRACE detected the variations of the continental water storage in the La Plata Basin, and particularly, it detected the important decrease in the South of the basin. Moreover, a coherency between the estimates of water mass changes and rainfall data was found, which shows that GRACE also detected extreme weather events (such as drought and intense rain episodes) that occurred in the 2004–2009 period in Argentina.

Combination of gravimetric and altimetric space observations for estimating oceanic polar motion excitations

Global dynamic processes cause variations in the Earth's rotation, which are monitored by various geometric observation techniques such as Global Navigation Satellite Systems (GNSS), Satellite Laser Ranging (SLR), and Very Long Baseline Interferometry (VLBI) with millimeter accuracy. The integral effect on Earth rotation of mass displacements and motion is therefore precisely known, but the separation of contributions from particular geodynamic processes remains a challenge. Here we show that the oceanic mass effect on Earth rotation can be derived from both time variable gravity field solutions from the Gravity Recovery And Climate Experiment (GRACE) and sea level anomalies (SLA) observed from satellite altimeter missions. The GRACE solutions require filtering and the application of an ocean mask, whereas the SLA need to be corrected for the steric effect as polar motion is only affected by mass redistributions. We assess the accuracy of our oceanic polar motion excitations by using GRACE and SLA solutions from different processing centers. In addition, we compare polar motion excitations from GRACE, satellite altimeter data and their combinations with excitations estimated from ocean models. We show that the combination of gravimetric and altimetric solutions reduces systematic errors of the individual solutions. The combined solutions are about 2 times more accurate than ocean model results and about 3 times more accurate than the so‐called reduced geodetic excitation functions. We anticipate our analysis to be valuable input for improved modeling of oceanic mass redistributions.

On regularized time varying gravity field models based on grace data and their comparison with hydrological models

Determination of spherical harmonic coefficients of the Earth's gravity field is often an ill-posed problem and leads to solving an ill-conditioned system of equations. Inversion of such a system i ...

Monthly gravity field solutions based on GRACE observations generated with the Celestial Mechanics Approach

The main objective of the Gravity Recovery And Climate Experiment (GRACE) satellite mission consists of determining the temporal variations of the Earth's gravity field. These variations are captured by time series of gravity field models of limited resolution at, e.g., monthly intervals. We present a new time series of monthly models, which was computed with the so-called Celestial Mechanics Approach (CMA), developed at the Astronomical Institute of the University of Bern (AIUB).The secular and seasonal variations in the monthly models are tested for statistical significance. Calibrated errors are derived from inter-annual variations. The time-variable signal can be extracted at least up to degree 60, but the gravity field coefficients of orders above 45 are heavily contaminated by noise. This is why a series of monthly models is computed up to a maximum degree of 60, but only a maximum order of 45. Spectral analysis of the residual time-variable signal shows a distinctive peak at a period of 160 days, which shows up in particular in the C20 spherical harmonic coefficient.Basic filter- and scaling-techniques are introduced to evaluate the monthly models. For this purpose, the variability over the oceans is investigated, which serves as a measure for the noisiness of the models. The models in selected regions show the expected seasonal and secular variations, which are in good agreement with the monthly models of the Helmholtz Centre Potsdam, German Research Centre for Geosciences (GFZ). The results also reveal a few small outliers, illustrating the necessity for improved data screening. Our monthly models are available at the web page of the International Centre for Global Earth Models (ICGEM).

Drought indicators based on model‐assimilated Gravity Recovery and Climate Experiment (GRACE) terrestrial water storage observations

The Gravity Recovery and Climate Experiment (GRACE) twin satellites observe time variations in Earth's gravity field which yield valuable information about changes in terrestrial water storage (TWS). GRACE is characterized by low spatial (>150,000 km2) and temporal (>10 days) resolution but has the unique ability to sense water stored at all levels (including groundwater) systematically and continuously. The GRACE Data Assimilation System (DAS), based on the Catchment Land Surface Model (CLSM), enhances the value of the GRACE water storage data by enabling spatial and temporal downscaling and vertical decomposition into moisture components (i.e., groundwater, soil moisture, and snow), which individually are more useful for scientific applications. In this study, GRACE DAS was applied to North America, and GRACE‐based drought indicators were developed as part of a larger effort to investigate the possibility of more comprehensive and objective identification of drought conditions by integrating spatially, temporally, and vertically disaggregated GRACE data into the U.S. and North American Drought Monitors. Previously, the drought monitors lacked objective information on deep soil moisture and groundwater conditions, which are useful indicators of drought. Extensive data sets of groundwater storage from U.S. Geological Survey monitoring wells and soil moisture from the Soil Climate Analysis Network were used to assess improvements in the hydrological modeling skill resulting from the assimilation of GRACE TWS data. The results point toward modest, but statistically significant, improvements in the hydrological modeling skill across major parts of the United States, highlighting the potential value of a GRACE‐assimilated water storage field for improving drought detection.

Simulation of the effects of microtubules in the cortical rotation of amphibian embryos in normal and zero gravity

This paper reports the results of computer modeling of microtubules that end up in the cortical region of a one-cell amphibian embryo, prior to the first cell division. Microtubules are modeled as initially randomly oriented semi-flexible rods, represented by several lines of point-masses interacting with one another like masses on springs with longitudinal and transverse stiffness. They are also considered to be space-filling rods floating in a viscous fluid (cytoplasm) experiencing drag forces and buoyancy from the fluid under a variable gravity field to test gravitational effects. Their randomly distributed interactions with the surrounding spherical container (the cell membrane) have a statistical nonzero average that creates a torque causing a rotational displacement between the cytoplasm and the rigid cortex. The simulation has been done for zero and normal gravity and it validates the observation that cortical rotation occurs in microgravity as well as on Earth. The speed of rotation depends on gravity, but is still substantial in microgravity.

Accuracy of scaled GRACE terrestrial water storage estimates

We assess the accuracy of global‐gridded terrestrial water storage (TWS) estimates derived from temporal gravity field variations observed by the Gravity Recovery and Climate Experiment (GRACE) satellites. The TWS data set has been corrected for signal modification due to filtering and truncation. Simulations of terrestrial water storage variations from land‐hydrology models are used to infer relationships between regional time series representing different spatial scales. These relationships, which are independent of the actual GRACE data, are used to extrapolate the GRACE TWS estimates from their effective spatial resolution (length scales of a few hundred kilometers) to finer spatial scales (∼100 km). Gridded, scaled data like these enable users who lack expertise in processing and filtering the standard GRACE spherical harmonic geopotential coefficients to estimate the time series of TWS over arbitrarily shaped regions. In addition, we provide gridded fields of leakage and GRACE measurement errors that allow users to rigorously estimate the associated regional TWS uncertainties. These fields are available for download from the GRACE project website (available at http://grace.jpl.nasa.gov). Three scaling relationships are examined: a single gain factor based on regionally averaged time series, spatially distributed (i.e., gridded) gain factors based on time series at each grid point, and gridded‐gain factors estimated as a function of temporal frequency. While regional gain factors have typically been used in previously published studies, we find that comparable accuracies can be obtained from scaled time series based on gridded gain factors. In regions where different temporal modes of TWS variability have significantly different spatial scales, gain factors based on the first two methods may reduce the accuracy of the scaled time series. In these cases, gain factors estimated separately as a function of frequency may be necessary to achieve accurate results.

The Gauss–Listing geopotential value W 0 and its rate from altimetric mean sea level and GRACE

In geopotential space, the fundamental geodetic parameter W 0 defines the Gauss–Listing geoid which can be used to best represent the Earth’s mean sea level (MSL) and hence specifies a conventional zero height level to unify vertical datums employed by mapping agencies throughout the world. Further, W 0 cannot be considered invariant as the parameter varies temporally as a direct response to sea level change and mass redistributions. This study determines W 0 and its rate, dW 0/dt, by utilizing altimetric MSL models and an independent mean dynamic topography (MDT) model to define points on the geoid. W 0 and dW 0/dt are estimated by two approaches: (i) by means of a global gravity field model (GGM) and (ii) within normal gravity field space as the geopotential value of the best fitting reference ellipsoid. The study shows that uncertainty in W 0 is mainly influenced by MDT while the choice of methodology, GGM and MSL data coverage are not significant within reason. Our estimate W 0 = 62636854.2 ± 0.2 m2 s−2 at epoch 2005.0 differs by 1.8 m2s−2 from the International Astronomical Union reference value. This study shows that, at a sub-decadal time scale, the time variation dW 0/dt stems mainly from sea level change with negligible effect from gravity field variations. dW 0/dt = (−2.70 ± 0.03) × 10−2 m2 s−2 year−1, corresponding to a MSL rise of 2.9 mm year−1, is evaluated from sea level change based on 16 years of TOPEX and Jason-1 data.

Noniterative Instantaneous Impact Point Prediction Algorithm for Launch Operations

T HE instantaneous impact point (IIP) in launch operations is defined as the touchdown point of a rocket with an assumption of an immediate end of the propelled flight [1–3]. The IIP is very important information to judge whether the flight is normal or not, and it should be continuously monitored during the whole flight so that proper actions be taken in an emergency to protect human life and property. Therefore, the real-time prediction and monitoring of the IIP is one of the key safety requirements. The IIP prediction problem seeks for the intersection point between the Earth’s surface and the free-flight trajectory of a rocket subject to gravity and other disturbing forces. The current position and velocity vectors are given as inputs to the problem. A numerical integration of the dynamicmodel including all force elementswith an initial position and velocity could yield a very accurate answer to the problem with relative ease. But when the real-time calculation is considered as a constraint, the numerical integration that requires a lot of computational resources is not a feasible option in the majority of launch operations. There has been some research on developing the IIP prediction algorithm that provides the real-time solution within acceptable accuracy with limited computational resources. To calculate the IIP for shortto midrange rockets, simplified models in the localvertical–local-horizontal frame are frequently used [3–6]. These assume that the trajectory of a rocket is parabolic subject to the constant vertical downward gravitational acceleration and often add correction terms to compensate for the modeling errors. Montenbruck and Markgraf [6] developed a linearized IIP calculation algorithm and implemented it for the launch operation of the Maxus-5 sounding rocket. Their algorithm was based on a simple parabolic flight model, and its prediction accuracy was improved by considering the effects of the Earth curvature, the Coriolis force, and the gravity field variation. The Keplerian algorithm predicts the IIP using the equations describing the motion of a rocket under the inverse-square law of gravity. Regan and Anandakrishnan [4] and Zarchan [7] developed a series of formulations that can be used as the base of theKeplerian IIP prediction, such as the expressions for the flight angle and the flight time. Currently, an iterativeKeplerian algorithm is frequently used to predict the IIP for long-range space vehicles [8,9]. The iterative Keplerian algorithm can calculate the true IIP solution for the Keplerian motion of a rocket using an iterative procedure (e.g., successive substitution) to find parameters such as Kepler’s f and g series expansions, the eccentric anomaly of the impact point, and the surface radius at impact. Considering that the IIP prediction for an actual launch operation should be carried out in real time, the iterative procedure that has the risk of computational overload is not very desirable to be included in the prediction algorithm. Especially when the algorithm is implemented in an onboard computer that has limited computing resources but is responsible for multiple mission-critical tasks such as event sequencing, navigation, and attitude control, the potential damage associated with the risk is significantly increased. This engineering Note presents a Keplerian IIP prediction algorithm that does not require any iterative procedure and is thus remarkably faster than the iterative Keplerian algorithm. First, an exact and closed solution for the Keplerian IIP with the spherical Earth model is developed. Then, a noniterative procedure to compensate for the effect of the oblateness of the Earth is added. Finally, the validity of the proposed algorithm is proved through the performance comparison with the iterative algorithm in terms of computational efficiency and the prediction accuracy.

Time-variations of equivalent water heights'from Grace Mission and in-situ river stages in the Amazon basin

Gravity Recovery and Climate Experiment (GRACE) mission is dedicated to measuring temporal variations of the Earth's gravity field. In this study, the Stokes coefficients made available by Groupe de Recherche en Géodésie Spatiale (GRGS) at a 10-day interval were converted into equivalent water height (EWH) for a ~4-year period in the Amazon basin (from July-2002 to May-2006). The seasonal amplitudes of EWH signal are the largest on the surface of Earth and reach ~ 1250mm at that basin's center. Error budget represents ~130 mm of EWH, including formal errors on Stokes coefficient, leakage errors (12 ~ 21 mm) and spectrum truncation (10 ~ 15 mm). Comparison between in situ river level time series measured at 233 ground-based hydrometric stations (HS) in the Amazon basin and vertically-integrated EWH derived from GRACE is carried out in this paper. Although EWH and HS measure different water bodies, in most of the cases a high correlation (up to ~80%) is detected between the HS series and EWH series at the same site. This correlation allows adjusting linear relationships between in situ and GRACE-based series for the major tributaries of the Amazon river. The regression coefficients decrease from up to down stream along the rivers reaching the theoretical value 1 at the Amazon's mouth in the Atlantic Ocean. The variation of the regression coefficients versus the distance from estuary is analysed for the largest rivers in the basin. In a second step, a classification of the proportionality between in situ and GRACE time-series is proposed.

Improved daily GRACE gravity field solutions using a Kalman smoother

Different GRACE data analysis centers provide temporal variations of the Earth's gravity field as monthly, 10-daily or weekly solutions. These temporal mean fields cannot model the variations occurring during the respective time span. The aim of our approach is to extract as much temporal information as possible out of the given GRACE data. Therefore the temporal resolution shall be increased with the goal to derive daily snapshots. Yet, such an increase in temporal resolution is accompanied by a loss of redundancy and therefore in a reduced accuracy if the daily solutions are calculated individually. The approach presented here therefore introduces spatial and temporal correlations of the expected gravity field signal derived from geophysical models in addition to the daily observations, thus effectively constraining the spatial and temporal evolution of the GRACE solution. The GRACE data processing is then performed within the framework of a Kalman filter and smoother estimation procedure.The approach is at first investigated in a closed-loop simulation scenario and then applied to the original GRACE observations (level-1B data) to calculate daily solutions as part of the gravity field model ITG-Grace2010. Finally, the daily models are compared to vertical GPS station displacements and ocean bottom pressure observations.From these comparisons it can be concluded that particular in higher latitudes the daily solutions contain high-frequent temporal gravity field information and represent an improvement to existing geophysical models.

Gravity Field Variations Associated with the Buried Geological Structures: San Marcos Fault (NE Mexico) Case Study

Gravity data are sensitive to local vertical offsets across high-angle faults, where rocks with different densities are juxtaposed. Yet high densities in some Mesozoic sedimentary rocks just above the basement may smear out the subtle gravity signatures of basement faults. At this study the gravity data processing tends to avoid ill-described “black-box” techniques. The study area is situated in the Palomas site, Cuatrociénegas region, Coahuila, NE Mexico. The San Marcos Fault is at least 300 km long and has WNW-ESE trend from the central part of Nuevo León State through Coahuila, and finally to the eastern part of Chihuahua State. Gravimetric data shows that the lowest values of free air and Bouguer anomalies are in the southern part of the area, and the highest values are in the western and central part of the area. Between these parts exists a zone of high horizontal gravity gradient. Configuration of linear elements of gravity field (gradient zones) delimited the San Marcos Fault in the San Marcos valley below thickness of recent sedimentary cover. Two density models were carried out, which showed that the Cretaceous rocks are in discordant contact with the Paleo- zoic rocks that can be related to the San Marcos Fault. The density was determinate using to Nettleton’s method, which results highlight the presence of the San Marcos Fault. Density models showed that the Quaternary sediments are in direct contact with the San Marcos Fault.

Tackling mass redistribution phenomena by time-dependent GRACE- and terrestrial gravity observations

Time variable gravity field models derived from the satellite mission GRACE have been demonstrated to be consistent with water mass variations in the global hydrological cycle. Independent observations are provided by terrestrial measurements. In order to achieve a maximum of reliability and information gain, ground-based gravity observations may be deployed for comparison with the gravity field variations derived from the GRACE satellite mission. In this context, the data of the network of superconducting gravimeters (SG) of the ‘Global Geodynamics Project’ (GGP) are of particular interest. This study is focused on the dense SG network in Central Europe with its long-term gravity observations. It is shown that after the separation and reduction of local hydrological effects in the SG observations especially for subsurface stations, the time-variable gravity signals from GRACE agree well with the terrestrial observations from the SG station cluster.Station stability of the SG sites with respect to vertical deformations was checked by GNSS based observations. Most of the variability can be explained by loading effects due to changes in continental water storage, and, in general, the stability of all stations has been confirmed.From comparisons based on correlation and coherence analyses in combination with the root mean square (RMS) variability of the time series emerges, that the maximum correspondence between the SG and GRACE time series is achieved when filtering the GRACE data with Gaussian filters of about 1000km filter length, which is in accordance with previous publications.Empirical Orthogonal Functions (EOF) analysis was applied to the gravity time series in order to identify common characteristic spatial and temporal patterns. The high correspondence of the first modes for GRACE and SG data implies that the first EOF mode represents a large-scale (Central European) time-variable gravity signal seen by both the GRACE satellites and the SG cluster.

Simulation of the time-variable gravity field by means of coupled geophysical models

Abstract. Time variable gravity fields, reflecting variations of mass distribution in the system Earth is one of the key parameters to understand the changing Earth. Mass variations are caused either by redistribution of mass in, on or above the Earth's surface or by geophysical processes in the Earth's interior. The first set of observations of monthly variations of the Earth gravity field was provided by the US/German GRACE satellite mission beginning in 2002. This mission is still providing valuable information to the science community. However, as GRACE has outlived its expected lifetime, the geoscience community is currently seeking successor missions in order to maintain the long time series of climate change that was begun by GRACE. Several studies on science requirements and technical feasibility have been conducted in the recent years. These studies required a realistic model of the time variable gravity field in order to perform simulation studies on sensitivity of satellites and their instrumentation. This was the primary reason for the European Space Agency (ESA) to initiate a study on ''Monitoring and Modelling individual Sources of Mass Distribution and Transport in the Earth System by Means of Satellites''. The goal of this interdisciplinary study was to create as realistic as possible simulated time variable gravity fields based on coupled geophysical models, which could be used in the simulation processes in a controlled environment. For this purpose global atmosphere, ocean, continental hydrology and ice models were used. The coupling was performed by using consistent forcing throughout the models and by including water flow between the different domains of the Earth system. In addition gravity field changes due to solid Earth processes like continuous glacial isostatic adjustment (GIA) and a sudden earthquake with co-seismic and post-seismic signals were modelled. All individual model results were combined and converted to gravity field spherical harmonic series, which is the quantity commonly used to describe the Earth's global gravity field. The result of this study is a twelve-year time-series of 6-hourly time variable gravity field spherical harmonics up to degree and order 180 corresponding to a global spatial resolution of 1 degree in latitude and longitude. In this paper, we outline the input data sets and the process of combining these data sets into a coherent model of temporal gravity field changes. The resulting time series was used in some follow-on studies and is available to anybody interested.

Determination of Seasonal Variations of Low-Degree Earth Gravity Field from CHAMP Geometric Orbits

Based on satellite dynamics, 1 year’s CHAMP geometric precise orbit data are used in this paper to fit the satellite orbits by Cowell II numerical integral and partitioned Bayesian least square parameter estimation. Time series of low degree geopotential coefficients and are respectively calculated, which reflects obviously seasonal variations of and . The results / month, /month indicate the geodynamical shape of the earth is getting rounder and rounder and at the same time its pear-shaped component adds gradually.