Time-variable Gravity Research Articles

Seasonal and static gravity field of Mars from MGS, Mars Odyssey and MRO radio science

We present a spherical harmonic solution of the static gravity field of Mars to degree and order 120, GMM-3, that has been calculated using the Deep Space Network tracking data of the NASA Mars missions, Mars Global Surveyor (MGS), Mars Odyssey (ODY), and the Mars Reconnaissance Orbiter (MRO). We have also jointly determined spherical harmonic solutions for the static and time-variable gravity field of Mars, and the Mars k2 Love numbers, exclusive of the gravity contribution of the atmosphere. Consequently, the retrieved time-varying gravity coefficients and the Love number k2 solely yield seasonal variations in the mass of the polar caps and the solid tides of Mars, respectively. We obtain a Mars Love number k2 of 0.1697 ± 0.0027 (3-σ). The inclusion of MRO tracking data results in improved seasonal gravity field coefficients C30 and, for the first time, C50. Refinements of the atmospheric model in our orbit determination program have allowed us to monitor the odd zonal harmonic C30 for ∼1.5 solar cycles (16 years). This gravity model shows improved correlations with MOLA topography up to 15% larger at higher harmonics (l = 60–80) than previous solutions.

The development of the GSFC DORIS contribution to ITRF2014

The NASA GSFC DORIS analysis center has processed data from January 1993 to December 2014 and provided 1141 weekly solutions in the form of normal equations for incorporation into the DORIS solution for ITRF2014. The solution time series, designated as gscwd26, were based on tracking data to eleven DORIS satellites divided generally into seven-day arcs. With respect to the ITRF2008 submission (Le Bail et al., 2010), the measurement model was updated to model the beacon frequency variations at certain DORIS sites, to apply the DORIS antenna phase law for the Starec and Alcatel antennae, and to apply the antenna offset corrections in the NASA GSFC orbit determination software rather than using the data-supplied corrections. We show that computing the antenna offset corrections in the orbit determination software is superior to using the offset corrections that are supplied with the DORIS data, and that this improves the RMS of fit for SPOT-2, Envisat, SPOT-4, and SPOT-5. The updates for the force model included: (1) the development of improved nonconservative force modeling for SPOT-2, SPOT-3, SPOT-5, Envisat, and HY-2A, and (2) the application of an updated static gravity model based on GRACE and GOCE data, and weekly models of the variations in the low degree gravity field deduced independently from tracking by Satellite Laser Ranging (SLR) and DORIS. The post-ITRF2008 DORIS coordinate WRMS after the launch of Envisat and SPOT-5 is improved from 11.20 to 12.45mm with ITRF2008 (Le Bail et al., 2010), to between 8.50 and 9.99mm with the gscwd26 SINEX solution. The application of the DORIS antenna phase laws shifts the DORIS scale wrt DPOD2008 by +6.0mm from 1993/01/03 to 2002/06/06, and by +11.4mm from 2002/06/13 to 2011/10/30. The application of more detailed models of time-variable gravity reduces the slopes in the Helmert transformation parameters Tx, and Ty (w.r.t. DPOD2008) after 2005. The annual amplitude in these parameters is reduced from 3.2mm (for Tx), 4.1mm (for Ty), to 1.7mm (for Tx) and 2.8mm (for Ty).

EIGEN-6S4: A time-variable satellite-only gravity field model to d/o 300 based on LAGEOS, GRACE and GOCE data from the collaboration of GFZ Potsdam and GRGS Toulouse

EIGEN-6S4: A time-variable satellite-only gravity field model to d/o 300 based on LAGEOS, GRACE and GOCE data from the collaboration of GFZ Potsdam and GRGS Toulouse

First analyses of the iOSG-type superconducting gravimeter at the low noise underground laboratory (LSBB URL) of Rustrel, France

In the last few years, the performance of the cryogenic gravity instruments has been further improved by the development of a new generation of superconducting gravimeter (SG): the so-called iOSG which is a superconducting gravimeter designed for observatory purpose with a heavier sphere than previous SGs. The first iOSG (iOSG-024) has been installed in July 2015 at the LSSB low background noise underground research laboratory in Rustrel (France), funded by the EQUIPEX MIGA (Matter wave-laser based Interferometer Gravitation Antenna) project and by the European FEDER 2006-2013 PFM LSBB – Developpement des qualites environnementales du LSBB . This instrument is operational since September 2015. We present the first tidal analyses of the 7-month time-varying gravity records of this newly installed instrument as well as the calibration results performed by parallel FG5 absolute gravity measurements. We also show the performances of iOSG-024 in terms of noise levels in the seismic (in the millihertz frequency range) band using a standardized procedure based on the computation of the residual power spectral densities over a quiet time period. The obtained noise levels are compared with other SG sites and with seismological reference noise models. The combination of the instrumental performance of the iOSG with the LSBB site properties makes this gravimetric station one of the quietest in the world, comparable to the lower sensor of the OSG-56 at BFO, at seismic frequencies.

The International DORIS Service contribution to the 2014 realization of the International Terrestrial Reference Frame

In preparation of the 2014 realization of the International Terrestrial Reference Frame (ITRF2014), the International DORIS Service delivered to the International Earth Rotation and Reference Systems Service a set of 1140 weekly solution files including station coordinates and Earth orientation parameters, covering the time period from 1993.0 to 2015.0. The data come from eleven DORIS satellites: TOPEX/Poseidon, SPOT2, SPOT3, SPOT4, SPOT5, Envisat, Jason-1, Jason-2, Cryosat-2, Saral and HY-2A. In their processing, the six analysis centers which contributed to the DORIS combined solution used the latest time variable gravity models and estimated DORIS ground beacon frequency variations. Furthermore, all the analysis centers but one excepted included in their processing phase center variations for ground antennas. The main objective of this study is to present the combination process and to analyze the impact of the new modeling on the performance of the new combined solution. Comparisons with the IDS contribution to ITRF2008 show that (i) the application of the DORIS ground phase center variations in the data processing shifts the combined scale upward by nearly 7–11mm and (ii) thanks to estimation of DORIS ground beacon frequency variations, the new combined solution no longer shows any scale discontinuity in early 2002 and does not present unexplained vertical discontinuities in any station position time series. However, analysis of the new series with respect to ITRF2008 exhibits a scale increase late 2011 which is not yet explained. A new DORIS Terrestrial Reference Frame was computed to evaluate the intrinsic quality of the new combined solution. That evaluation shows that the addition of data from the new missions equipped with the latest generation of DORIS receiver (Jason-2, Cryosat-2, HY-2A, Saral), results in an internal position consistency of 10mm or better after mid-2008.

Towards the 1-cm SARAL orbit

We have investigated the quality of precise orbits for the SARAL altimeter satellite using Satellite Laser Ranging (SLR) and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) data from March 14, 2013 to August 10, 2014. We have identified a 4.31±0.14cm error in the Z (cross-track) direction that defines the center-of-mass of the SARAL satellite in the spacecraft coordinate system, and we have tuned the SLR and DORIS tracking point offsets. After these changes, we reduce the average RMS of the SLR residuals for seven-day arcs from 1.85 to 1.38cm. We tuned the non-conservative force model for SARAL, reducing the amplitude of the daily adjusted empirical accelerations by eight percent. We find that the best dynamic orbits show altimeter crossover residuals of 5.524cm over cycles 7–15. Our analysis offers a unique illustration that high-elevation SLR residuals will not necessarily provide an accurate estimate of radial error at the 1-cm level, and that other supporting orbit tests are necessary for a better estimate. Through the application of improved models for handling time-variable gravity, the use of reduced-dynamic orbits, and through an arc-by-arc estimation of the C22 and S22 coefficients, we find from analysis of independent SLR residuals and other tests that we achieve 1.1–1.2cm radial orbit accuracies for SARAL. The limiting errors stem from the inadequacy of the DPOD2008 and SLRF2008 station complements, and inadequacies in radiation force modeling, especially with respect to spacecraft self-shadowing and modeling of thermal variations due to eclipses.

The European way to gravimetry: From GOCE to NGGM

The European gravity mission GOCE (Gravity field and steady-state Ocean Circulation Explorer), which flew between 2009 and 2013 with extraordinary success, was the result of more than 20years of system studies and technology developments directed by the European Space Agency (ESA). Already while GOCE was being developed, ESA started preparatory studies for a Next Generation Gravity Mission (NGGM). While GOCE aimed to provide a high resolution static map of the Earth’s gravity, the objective of NGGM is long-term monitoring of the time-variable gravity field with high temporal and spatial resolution, by satellite-to-satellite tracking, a technique flown with the US–German mission GRACE for the first time. With respect to GOCE, the new mission implies new measurement techniques and instrumentation, a new mission scenario and different spacecraft design drivers. Despite the differences, however, several achievements of GOCE (e.g. demonstration of long-duration wide-band drag compensation, ultra-sensitive accelerometers, stable non-cryogenic temperature control in low Earth orbit) stand as the basis upon which NGGM is being defined. Technologies and techniques specific of the new mission (laser metrology, multi-task control architectures, high performance propulsion) are undergoing parallel developments in anticipation of the NGGM implementation phase. The paper recalls the GOCE mission and heritage, and introduces the objectives, scenarios, concepts and challenges of the NGGM, highlighting commonalities and differences between the two missions.

Monitoring Atlantic overturning circulation and transport variability with GRACE-type ocean bottom pressure observations – a sensitivity study

Abstract. The Atlantic Meridional Overturning Circulation (AMOC) is a key mechanism for large-scale northward heat transport and thus plays an important role for global climate. Relatively warm water is transported northward in the upper layers of the North Atlantic Ocean and, after cooling at subpolar latitudes, sinks down and is transported back south in the deeper limb of the AMOC. The utility of in situ ocean bottom pressure (OBP) observations to infer AMOC changes at single latitudes has been characterized in the recent literature using output from ocean models. We extend the analysis and examine the utility of space-based observations of time-variable gravity and the inversion for ocean bottom pressure to monitor AMOC changes and variability between 20 and 60° N. Consistent with previous results, we find a strong correlation between the AMOC signal and OBP variations, mainly along the western slope of the Atlantic Basin. We then use synthetic OBP data – smoothed and filtered to resemble the resolution of the GRACE (Gravity Recovery and Climate Experiment) gravity mission, but without errors – and reconstruct geostrophic AMOC transport. Due to the coarse resolution of GRACE-like OBP fields, we find that leakage of signal across the step slopes of the ocean basin is a significant challenge at certain latitudes. Transport signal rms is of a similar order of magnitude as error rms for the reconstructed time series. However, the interannual AMOC anomaly time series can be recovered from 20 years of monthly GRACE-like OBP fields with errors less than 1 sverdrup in many locations.

Assessment of conservative force models from GRACE accelerometers and precise orbit determination

The accuracy of the conservative force-models is not clear and the new space accelerometers provide a unique opportunity for their validation. In this paper, the conservative-force model deficiencies are investigated via Principal Component Analysis (PCA) using 4 years of GRACE measurements (2006–2009). The deficiencies are assessed by comparing the accelerometer readouts with the differences between the conservative force-model and the precise orbit accelerations. Within this scheme, the spatiotemporal data analysis is synthesized in a time-series of grids whose latitudinal and longitudinal variations are respectively influenced by the half orbital period and the equatorial orbit shift. With maximum amplitude of 50 nm/s2, the mean map shows a positive overestimation in Canada and Brazil and negative in Greenland. Explaining the 74% of the variability, the two first pairs of PCA modes show un-modeled patterns with amplitudes maxima of 80 nm/s2 and 50 nm/s2. Their periodic behavior and wave-length of degree-6 and degree-11s spherical harmonics strongly suggest an additional modeling and improvement. As for the long-term variations, our results show a latitudinal variation of 15 nm/s2 maximum amplitude correlated with the day-night periods. Performing a combined analysis of ascending and descending orbits, a trend of 3 nm/s2yr in the Indian Ocean is also observed. Our new approach for orbital force-models validation can be considered crucial for the current state-of-the-art of precise orbit determination (POD) and Time–Varying Gravity (TVG) modeling.

Use of GRACE time-variable data and GLDAS-LSM for estimating groundwater storage variability at small basin scales: a case study of the Nzoia River Basin

This study integrates time-variable Gravity Recovery and Climate Experiment (GRACE) gravimetric measurements and Global Land Data Assimilation System (GLDAS) land surface models (LSM) in order to understand the inter-annual variations and groundwater storage changes (GWSC) in the Nzoia River Basin in Kenya, using the water balance equation and parameters. From averaged GRACE and GWSC data, the results showed that over the 10-year period, the basin experienced a groundwater depth gain of 6.38 mm year−1, which is equivalent to aquifer recharge of 298 million cubic metres (mcm) year−1. The deseasonalized groundwater variation analysis gave a net gain in groundwater storage of 6.21 mm year−1 that is equal to a groundwater recharge gain of 290 mcm year−1. The observed results are comparable to the groundwater safe yield of 330 mcm year−1 as estimated by the Water Resource Management Authority in Kenya. Through cross-plotting and analysis with averaged satellite altimetry data and in situ measurements from rainfall and streamflow discharge, the total water storage change (TWSC) and GWSC in the basin were consistent and closely correlated in variation trends. The inter-annual standard deviation of groundwater change was determined as ±0.24 mm year−1, which is equivalent to 85% degree of confidence in the obtained results. The results in this study show that GRACE gravity-variable solutions and GLDAS-LSM provide reliable data sets suitable for the study of small to large basin groundwater storage variations, especially in areas with scarce and sparsely available in situ data.

Re-estimation of glacier mass loss in Greenland from GRACE with correction of land–ocean leakage effects

The Gravity Recovery and Climate Experiment (GRACE) satellites can estimate the high-precision time-varying gravity field and the changes of Earth's surface mass, which have been widely used in water cycle and glacier mass balance. However, one of larger errors in GRACE measurements, land–ocean leakage effects, restricts high precision retrieval of ocean mass and terrestrial water storage variations along the coasts, particularly estimation of mass loss in Greenland. The land–ocean leakage effect along the coasts in Greenland will contaminate the mass loss signals with significant signal attenuation. In this paper, the precise glacier mass loss in Greenland from GRACE is re-estimated with correction of land–ocean leakage effects using the forward gravity modeling. The loss of Greenland ice-sheets is −102.8±9.01Gt/a without removing leakage effect, but −183.0±19.91Gt/a after removing the leakage effect from September 2003 to March 2008, which has a good agreement with ICESat results of −184.8±28.2Gt/a. From January 2003 to December 2013, the total Greenland ice-sheet loss is at −261.54±6.12Gt/a from GRACE measurements with removing the leakage effect by 42.4%, while two-thirds of total glacier melting in Greenland occurred in southern Greenland in the past 11years. The secular leakage effects on glacier melting estimate is mainly located in the coastal areas, where larger glacier signals are significantly attenuated due to leaking out into the ocean. Furthermore, the leakage signals also have remarkable effects on seasonal and acceleration variations of glacier mass loss in Greenland. More significantly accelerated loss of glacier mass in Greenland is found at −26.19Gt/a2 after correcting for leakage effects.

Swarm kinematic orbits and gravity fields from 18 months of GPS data

The Swarm mission consists of three satellites orbiting the Earth at low orbital altitudes. The onboard GPS receivers, star cameras, and laser retro-reflectors make the Swarm mission an interesting candidate to explore the contribution of Swarm GPS data to the recovery of both the static and time-variable gravity fields. We use 1.5years of Swarm GPS and attitude data to generate kinematic positions of high quality to perform gravity field determination using the Celestial Mechanics Approach. The generated gravity fields reveal severe systematic errors along the geomagnetic equator. Their size is correlated with the ionospheric density and thus strongly varying over the analyzed time period. Similar to the findings of the GOCE mission, the systematic errors are related to the Swarm GPS carrier phase data and may be reduced by rejecting GPS data affected by large ionospheric changes. Such a measure yields a strong reduction of the systematic errors along the geomagnetic equator in the gravity field recovery. Long wavelength signatures of the gravity field may then be recovered with a similar quality as achieved with GRACE GPS data, which makes the Swarm mission well suited to bridge a potential gap between the current GRACE and the future GRACE Follow-On mission.

GRACE time-variable gravity field recovery using an improved energy balance approach

This Report was prepared for and submitted to the Graduate School of the Ohio State University as a dissertation in partial fulfillment of the requirements for the PhD degree.

What Can be Expected from the GRACE-FO Laser Ranging Interferometer for Earth Science Applications?

The primary objective of the gravity recovery and climate experiment followon (GRACE-FO) satellite mission, due for launch in August 2017, is to continue the GRACE time series of global monthly gravity field models. For this, evolved versions of the GRACE microwave instrument, GPS receiver, and accelerometer will be used. A secondary objective is to demonstrate the effectiveness of a laser ranging interferometer (LRI) in improving the satellite-to-satellite tracking measurement performance. In order to investigate the expected enhancement for Earth science applications, we have performed a full-scale simulation over the nominal mission lifetime of 5 years using a realistic orbit scenario and error assumptions both for instrument and background model errors. Unfiltered differences between the synthetic input and the finally recovered time-variable monthly gravity models show notable improvements with the LRI, on a global scale, of the order of 23 %. The gain is realized for wavelengths smaller than 240 km in case of Gaussian filtering but decreases to just a few percent when anisotropic filtering is applied. This is also confirmed for some typical regional Earth science applications which show randomly distributed patterns of small improvements but also degradations when using DDK4-filtered LRI-based models. Analysis of applied error models indicates that accelerometer noise followed by ocean tide and non-tidal mass variation errors are the main contributors to the overall GRACE-FO gravity model error. Improvements in these fields are therefore necessary, besides optimized constellations, to make use of the increased LRI accuracy and to significantly improve gravity field models from next-generation gravity missions.

Rosborough approach for the determination of regional time variability of the gravity field from satellite gradiometry data

It is well-known that Rosborough approach, based on spherical harmonics, can be efficiently applied to determine the unknown global gravitational field parameters in the framework of the so-called space-wise approach. Usually, for regional gravity field modeling radial basis functions instead of spherical harmonics are used as basis functions. Using the strong relationship between radial basis functions and spherical harmonics, the Rosborough counterparts of radial basis functions are developed. Based on these regionally supported Rosborough basis functions, all components of gravity-gradient tensor are expressed as series in regionally supported Rosborough basis functions. In a simulation study the feasibility of regional static and time-variable gravity field recovery from satellite gradiometry data using regionally supported Rosborough functions is tested.

Groundwater Storage Changes: Present Status from GRACE Observations

Satellite gravity measurements from the Gravity Recovery and Climate Experiment (GRACE) provide quantitative measurement of terrestrial water storage (TWS) changes with unprecedented accuracy. Combining GRACE-observed TWS changes and independent estimates of water change in soil and snow and surface reservoirs offers a means for estimating groundwater storage change. Since its launch in March 2002, GRACE time-variable gravity data have been successfully used to quantify long-term groundwater storage changes in different regions over the world, including northwest India, the High Plains Aquifer and the Central Valley in the USA, the North China Plain, Middle East, and southern Murray–Darling Basin in Australia, where groundwater storage has been significantly depleted in recent years (or decades). It is difficult to rely on in situ groundwater measurements for accurate quantification of large, regional-scale groundwater storage changes, especially at long timescales due to inadequate spatial and temporal coverage of in situ data and uncertainties in storage coefficients. The now nearly 13 years of GRACE gravity data provide a successful and unique complementary tool for monitoring and measuring groundwater changes on a global and regional basis. Despite the successful applications of GRACE in studying global groundwater storage change, there are still some major challenges limiting the application and interpretation of GRACE data. In this paper, we present an overview of GRACE applications in groundwater studies and discuss if and how the main challenges to using GRACE data can be addressed.

A new GPS-based calibration of GRACE accelerometers using the arc-to-chord threshold uncovered sinusoidal disturbing signal

In order to guarantee an unbiased solution in accelerometer measurements, calibration parameters have been finally calculated without using any kind of regularization or constraint. In this paper, a better calibration of the GRACE accelerometers is achieved from the instantaneous GPS-based non-gravitational accelerations. The first derivatives of the precise-orbit velocity are computed under an a priori arc-to-chord threshold, while the modelled time-varying forces of gravitational origin and reference-system rotations are computed according to current conventions (including sub-daily tide variations). After subtracting the modelled time-varying gravity from the GPS-based accelerations, cross-track axes of both GRACE satellites seem to be affected by a periodic error of unknown source. With the purpose of extracting the underlying information from the resulting data, the systematic error is modelled and subtracted successfully. According to this approach, the resulting accelerations serve as a reliable reference for accelerometer calibration.

Effectiveness of empirical orthogonal function used in decorrelation of GRACE time-variable gravity field

Empirical orthogonal function (EOF) was used to process the spherical harmonic coefficient (SHC) of 115 Gravity Recovery and Climate Experiment (GRACE) RL05 monthly gravity field models from March 2003 to February 2013 released by CSR (Center for Space Research). We analyzed the effectiveness of EOF in decorrelation of gravity field. Results show that only a small Gaussian smoothing radius was needed by EOF to significantly weaken the north–south stripes compared with the empirical moving-window filtering algorithm. The comparative experiments with a Global Land Data Assimilation System (GLDAS) hydrological model also show that EOF did not much affect the real geophysical signals, and that the removed signals were nearly uncorrelated with the real geophysical signals. As the Gravity Recovery and Climate Experiment (GRACE) missions continue, EOF can be used to significantly remove the correlated errors from monthly gravity fields and reserve rich effective signals.

Terrestrial water storage anomalies of Yangtze River Basin droughts observed by GRACE and connections with ENSO

Two severe drought events occurred in the Yangtze River Basin (YRB) of China in the summer of 2006 and the spring of 2011. We examine terrestrial water storage (TWS) changes in the YRB for these events using time-variable gravity data from the GRACE satellite mission, in combination with observations made by TRMM satellite and in situ river gauges, along with hydrological models GLDAS and WGHM. GRACE TWS deficit estimates clearly quantify these YRB droughts, and a normalized GRACE-based TWS anomaly provides an alternative and useful hydro-climatological index in the YRB. We find that an El Niño (La Niña) event is significantly correlated with high (low) TWS in the YRB with a phase lead of ~7–8months, and the lower YRB is more sensitive to ENSO variability than the upper basin. The possible linkage between TWS anomaly and ENSO is raised in terms of physical mechanisms of influencing the precipitation over the YRB.

The updated ESA Earth System Model for future gravity mission simulation studies

A new synthetic model of the time-variable global gravity field is now available based on realistic mass variability in atmosphere, oceans, terrestrial water storage, continental ice-sheets, and the solid Earth. The updated ESA Earth System Model is provided in Stokes coefficients up to degree and order 180 with a temporal resolution of 6 h covering the time period 1995–2006, and can be readily applied as a source model in future gravity mission simulation studies. The model contains plausible variability and trends in both low-degree coefficients and the global mean eustatic sea level. It depicts reasonable mass variability all over the globe at a wide range of frequencies including multi-year trends, year-to-year variability, and seasonal variability even at very fine spatial scales, which is important for a realistic representation of spatial aliasing and leakage. In particular on these small spatial scales between 50 and 250 km, the model contains a range of signals that have not been reliably observed yet by satellite gravimetry. In addition, the updated Earth System Model provides substantial high-frequency variability at periods down to a few hours only, thereby allowing to critically test strategies for the minimization of temporal aliasing.