Gravimetry Missions Research Articles

Influence of GIA Uncertainty on Climate Model Evaluation With GRACE/GRACE‐FO Satellite Gravimetry Data

AbstractGlobal coupled climate models are in continuous need for evaluation against independent observations to reveal systematic model deficits and uncertainties. Changes in terrestrial water storage (TWS) as measured by satellite gravimetry missions GRACE and GRACE‐FO provide valuable information on wetting and drying trends over the continents. Challenges arising from a comparison of observed and modelled water storage trends are related to gravity observations including non‐water related variations such as, for example, glacial isostatic adjustment (GIA). Therefore, correcting secular changes in the Earth's gravity field caused by ongoing GIA is important for the monitoring of long‐term changes in terrestrial water from GRACE in particular in former ice‐covered regions. By utilizing a new ensemble of 56 individual realizations of GIA signals based on perturbations of mantle viscosities and ice history, we find that many of those alternative GIA corrections change the direction of GRACE‐derived water storage trends, for example, from gaining mass into drying conditions, in particular in Eastern Canada. The change in the sign of the TWS trends subsequently impacts the conclusions drawn from using GRACE as observational basis for the evaluation of climate models as it influences the dis‐/agreement between observed and modelled wetting/drying trends. A modified GIA correction, a combined GRACE/GRACE‐FO data record extending over two decades, and a new generation of climate model experiments leads to substantially larger continental areas where wetting/drying trends currently observed by satellite missions coincide with long‐term predictions obtained from climate model experiments.

High-resolution temporal gravity field data products: Monthly mass grids and spherical harmonics from 1994 to 2021

Since April 2002, Gravity Recovery and Climate Experiment (GRACE) and GRACE-FO (FollowOn) satellite gravimetry missions have provided precious data for monitoring mass variations within the hydrosphere, cryosphere, and oceans with unprecedented accuracy and resolution. However, the long-term products of mass variations prior to GRACE-era may allow for a better understanding of spatio-temporal changes in climate-induced geophysical phenomena, e.g., terrestrial water cycle, ice sheet and glacier mass balance, sea level change and ocean bottom pressure (OBP). Here, climate-driven mass anomalies are simulated globally at 1.0° × 1.0° spatial and monthly temporal resolutions from January 1994 to January 2021 using an in-house developed hybrid Deep Learning architecture considering GRACE/-FO mascon and SLR-inferred gravimetry, ECMWF Reanalysis-5 data, and normalized time tag information as training datasets. Internally, we consider mathematical metrics such as RMSE, NSE and comparisons to previous studies, and externally, we compare our simulations to GRACE-independent datasets such as El-Nino and La-Nina indexes, Global Mean Sea Level, Earth Orientation Parameters-derived low-degree spherical harmonic coefficients, and in-situ OBP measurements for validation.

Benefit of enhanced electrostatic and optical accelerometry for future gravimetry missions

Twenty years of gravity observations from various satellite missions have provided unique data about mass redistribution processes in the Earth system, such as melting of Greenland’s ice shields, sea level changes, ground and underground water depletion, droughts, floods, etc. The ongoing climate change underlines the urgent need to continue this kind of observations with future gravimetry missions using enhanced concepts and sensors. This paper studies the benefit of enhanced electrostatic and novel optical accelerometers and gradiometers for future gravimetry missions.One of the limiting factors in the current space gravimetry missions is the drift of the Electrostatic Accelerometers (EA) which dominates the error contribution at low frequencies (<1mHz). This study focuses on the modeling of enhanced EAs with laser-interferometric readout, so-called optical accelerometers, and on evaluating their performance for gravity field recovery in future satellite missions.In this paper, we simulate gravimetry missions in multiple scopes, applying various software modules for satellite dynamics integration, accelerometer (ACC) and gradiometer simulation and gravity field recovery. The total noise budgets of the modeled enhanced electrostatic and optical ACCs show a similar sensitivity as the ACC concepts from other research groups. Parametrization w.r.t. the weight of the test mass (TM) of ACCs and the gap between the TM and the surrounding electrode housing confirmed the fact known from previous results that an ACC with a heavier TM and a larger gap will perform better. Our results suggest that the anticipated gain of novel ACCs might at some point be potentially limited by noise from the inter-satellite laser ranging interferometry.In order to present the advantage of the novel sensors, time-variable background models and associated aliasing errors were not considered in our simulations. The utilization of enhanced EAs and optical ACCs shows a significant improvement of accuracy compared to the currently used GRACE-like EA. In addition, their benefit in double satellite pairs in a so-called Bender constellation as well as in the combination of low-low satellite-to-satellite tracking with cross-track gradiometry has been investigated.

The Temporal Improvement of Earth's Mass Transport Estimated by Coupling GRACE‐FO With a Chinese Polar Gravity Satellite Mission

AbstractOver the past 20 years, the Gravity Recovery and Climate Experiment (GRACE), and its successor mission, GRACE‐Follow On (GRACE‐FO) have made significant contributions to time‐variable gravity field modeling. A Chinese low‐low satellite‐to‐satellite tracking gravimetry mission (i.e., Chinese future gravimetry mission) has been confirmed to be selected as the polar‐orbiting satellite gravimetry mission for China, because of the capability to collect gravity data globally. However, the analysis of potential contributions to geosciences from GRACE‐FO coupling with the Chinese future gravimetry mission is still limited. This study combines GRACE‐FO and Chinese future gravimetry missions as the Dual GRACE‐like Polar satellite Constellation (DGPC). By carefully choosing the initial orbit parameters of the Chinese future gravimetry mission with the differential evolution algorithm, the DGPC is expected to mitigate the temporal aliasing effects by improving the temporal resolution of time‐variable gravity solutions (i.e., 1‐day and 3‐day solutions). Regarding the spectral‐domain evaluation, zonal, tesseral, and sectorial coefficients estimated by the DGPC show approximately 6.01%–13.42% noise reductions compared with GRACE‐FO. Regarding the spatial‐domain evaluation, the DGPC can suppress noises of about 39.44% and 31.12% in annual amplitude and long‐term trend, respectively. On this basis, this paper analyzes the effectiveness of the DGPC in potential contributions to geosciences (e.g., hydrology, glaciology, and seismology). Specifically, the DGPC can improve accuracy by about 36.96%, 25.85%, and 33.16% with respect to GRACE‐FO for signals in the subhumid basin, signals of ice‐sheet mass balance over Greenland, and coseismic displacement of the fault zone, respectively. In general, the potential capability for high‐frequency signals recovery of the DGPC would facilitate contributions of satellite gravimetry to geosciences.

A global analysis of water storage variations from remotely sensed soil moisture and daily satellite gravimetry

Abstract. Water storage changes in the soil can be observed on a global scale with different types of satellite remote sensing. While active or passive microwave sensors are limited to the upper few centimeters of the soil, satellite gravimetry can detect changes in the terrestrial water storage (TWS) in an integrative way, but it cannot distinguish between storage variations in different compartments or soil depths. Jointly analyzing both data types promises novel insights into the dynamics of subsurface water storage and of related hydrological processes. In this study, we investigate the global relationship of (1) several satellite soil moisture products and (2) non-standard daily TWS data from the Gravity Recovery and Climate Experiment/Follow-On (GRACE/GRACE-FO) satellite gravimetry missions on different timescales. The six soil moisture products analyzed in this study differ in the post-processing and the considered soil depth. Level 3 surface soil moisture data sets of the Soil Moisture Active Passive (SMAP) and Soil Moisture and Ocean Salinity (SMOS) missions are compared to post-processed Level 4 data products (surface and root zone soil moisture) and the European Space Agency Climate Change Initiative (ESA CCI) multi-satellite product. On a common global 1∘ grid, we decompose all TWS and soil moisture data into seasonal to sub-monthly signal components and compare their spatial patterns and temporal variability. We find larger correlations between TWS and soil moisture for soil moisture products with deeper integration depths (root zone vs. surface layer) and for Level 4 data products. Even for high-pass filtered sub-monthly variations, significant correlations of up to 0.6 can be found in regions with a large, high-frequency storage variability. A time shift analysis of TWS versus soil moisture data reveals the differences in water storage dynamics with integration depth.

Small satellite formations and constellations for observing sub-daily mass changes in the Earth system

SUMMARY Satellite gravity missions so far are medium size satellites consisting of one or a pair of satellites flying in near-polar or sun-synchronous orbital planes. Due to the limited observation geometry and the related space–time sampling, high-frequency non-tidal mass variation signals from atmosphere and ocean cannot be observed and cause temporal aliasing. For current single-pair satellite gravimetry missions as GRACE and GRACE Follow-On (GRACE-FO) temporal aliasing is the limiting factor and represents the major error source in the gravity field time-series. Adding a second inclined satellite pair to a GRACE-like polar pair (Bender constellation) currently is the most promising solution to increase the spatio-temporal resolution and to significantly reduce the temporal aliasing error. This shall be implemented with the MAGIC mission in future. With the ongoing developments in miniaturization of satellites and gravity-relevant instruments (accelerometers and intersatellite ranging), in future constellations of multiple small satellite pairs may solve this problem even beyond the capabilities of a Bender constellation. Therefore, in this study the capabilities of such constellations flying in specific formations are investigated in order to enable a retrieval of the temporal gravity field on short time scales. We assess the performance of up to 18 satellite pairs. The satellite configurations cover satellite pairs in polar and inclined orbits flying in pair-wise or pearl-string formation with varying mean anomalies and right ascensions of the ascending node (RAAN). As future potential miniaturized instruments optomechanical accelerometers with similar performance as those flying on GRACE-FO are a candidate, while for the intersatellite ranging instrument still some technological development is required. Therefore, in this study a microwave ranging system equivalent to the GRACE and GRACE-FO instruments performance is taken as baseline assuming that such instruments can be miniaturized in future as well. In numerical closed-loop simulations, up to nine different satellite configurations with up to 18 satellite pairs are evaluated based on the retrieval of the non-tidal temporal gravity field on a monthly basis. From the simulation results it is concluded that the best-performing satellite constellation of 18 polar satellite pairs already is outperformed by a typical Bender-like constellation of 1 polar and 1 inclined pair. In general, we identify that increasing the number of satellite pairs leads to an improved gravity field retrieval, either at low spherical harmonic degree and order (d/o) by the shift in RAAN or at high d/o by the shift in mean anomaly. By a two-step simulation approach, co-estimating also (sub-)daily gravity fields for selected configurations with a large number of satellite pairs distributed equally over the globe, it is possible to retrieve stand-alone gravity fields at 24, 12 and 6 hr temporal resolution. Ultimately it is concluded that a network of miniaturized satellites with instrument performances similar to GRACE-FO and flying in a well-defined constellation has the potential to observe (sub-)daily mass variations and therefore could drastically reduce the problem of temporal aliasing due to high frequency mass variations in the Earth system.

Revisiting the global mean ocean mass budget over 2005–2020

Abstract. We investigate the performances of Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) satellite gravimetry missions in assessing the ocean mass budget at the global scale over 2005–2020. For that purpose, we focus on the last years of the record (2015–2020) when GRACE and GRACE Follow-On faced instrumental problems. We compare the global mean ocean mass estimates from GRACE and GRACE Follow-On to the sum of its contributions from Greenland, Antarctica, land glaciers, terrestrial water storage and atmospheric water content estimated with independent observations. Significant residuals are observed in the global mean ocean mass budget at interannual timescales. Our analyses suggest that the terrestrial water storage variations based on global hydrological models likely contribute in large part to the misclosure of the global mean ocean mass budget at interannual timescales. We also compare the GRACE-based global mean ocean mass with the altimetry-based global mean sea level corrected for the Argo-based thermosteric contribution (an equivalent of global mean ocean mass). After correcting for the wet troposphere drift of the radiometer on board the Jason-3 altimeter satellite, we find that mass budget misclosure is reduced but still significant. However, replacing the Argo-based thermosteric component by the Ocean Reanalysis System 5 (ORAS5) or from the Clouds and the Earth's Radiant Energy System (CERES) top of the atmosphere observations significantly reduces the residuals of the mass budget over the 2015–2020 time span. We conclude that the two most likely sources of error in the global mean ocean mass budget are the thermosteric component based on Argo and the terrestrial water storage contribution based on global hydrological models. The GRACE and GRACE Follow-On data are unlikely to be responsible on their own for the non-closure of the global mean ocean mass budget.

A parallel numerical algorithm by combining MPI and OpenMP programming models with applications in gravity field recovery

Satellite gravimetry missions have enabled the calculation of high-accuracy and high-resolution Earth gravity field models from satellite-to-satellite tracking data and gravitational gradients. However, calculating high maximum degree/order (e.g., 240 or even higher) gravity field models using the least squares method is time-consuming due to the vast amount of gravimetry observations. To improve calculation efficiency, a parallel algorithm has been developed by combining Message Passing Interface (MPI) and Open Multi-Processing (OpenMP) programming models to calculate and invert normal equations for the Earth gravity field recovery. The symmetrical feature of normal equations has been implemented to speed up the calculation progress and reduce computation time. For example, the computation time to generate the normal equation of an IGGT_R1 test version of degree/order 240 was reduced from 88 h to 27 h by considering the symmetrical feature. Here, the calculation was based on the high-performance computing cluster with 108 cores in the School of Geodesy and Geomatics, at Wuhan University. Additionally, the MPI parallel Gaussian-Jordan elimination method was modified to invert normal equation matrices and scaled up to 100 processor cores in this study while the traditional method was limited in a certain number of processors. Furthermore, the Cholesky decomposition from the ScaLAPACK library was used to compare with the parallel Gauss-Jordan elimination method. The numerical algorithm has effectively reduced the amount of calculation and sped up the calculation progress, and has been successfully implemented in applications such as building the gravity field models IGGT_R1 and IGGT_R1C.

Inter-Annual Variability in the Antarctic Ice Sheets Using Geodetic Observations and a Climate Model

Quantifying the mass balance of the Antarctic Ice Sheet (AIS), and the resulting sea level rise, requires an understanding of inter-annual variability and associated causal mechanisms. Very few studies have been exploring the influence of climate anomalies on the AIS and only a vague estimate of its impact is available. Changes to the ice sheet are quantified using observations from space-borne altimetry and gravimetry missions. We use data from Envisat (2002 to 2010) and Gravity Recovery And Climate Experiment (GRACE) (2002 to 2016) missions to estimate monthly elevation changes and mass changes, respectively. Similar estimates of the changes are made using weather variables (surface mass balance (SMB) and temperature) from a regional climate model (RACMO2.3p2) as inputs to a firn compaction (FC) model. Elevation changes estimated from different techniques are in good agreement with each other across the AIS especially in West Antarctica, Antarctic Peninsula, and along the coasts of East Antarctica. Inter-annual height change patterns are then extracted using for the first time an empirical mode decomposition followed by a principal component analysis to investigate for influences of climate anomalies on the AIS. Investigating the inter-annual signals in these regions revealed a sub-4-year periodic signal in the height change patterns. El Niño Southern Oscillation (ENSO) is a climate anomaly that alters, among other parameters, moisture transport, sea surface temperature, precipitation, in and around the AIS at similar frequency by alternating between warm and cold conditions. This periodic behavior in the height change patterns is altered in the Antarctic Pacific (AP) sector, possibly by the influence of multiple climate drivers, like the Amundsen Sea Low (ASL) and the Southern Annular Mode (SAM). Height change anomaly also appears to traverse eastwards from Coats Land to Pine Island Glacier (PIG) regions passing through Dronning Maud Land (DML) and Wilkes Land (WL) in 6 to 8 years. This is indicative of climate anomaly traversal due to the Antarctic Circumpolar Wave (ACW). Altogether, inter-annual variability in the SMB of the AIS is found to be modulated by multiple competing climate anomalies.

Revisiting the light time correction in gravimetric missions like GRACE and GRACE follow-on

The gravity field maps of the satellite gravimetry missions Gravity Recovery and Climate Experiment (GRACE ) and GRACE Follow-On are derived by means of precise orbit determination. The key observation is the biased inter-satellite range, which is measured primarily by a K-Band Ranging system (KBR) in GRACE and GRACE Follow-On. The GRACE Follow-On satellites are additionally equipped with a Laser Ranging Interferometer (LRI), which provides measurements with lower noise compared to the KBR. The biased range of KBR and LRI needs to be converted for gravity field recovery into an instantaneous range, i.e. the biased Euclidean distance between the satellites’ center-of-mass at the same time. One contributor to the difference between measured and instantaneous range arises due to the nonzero travel time of electro-magnetic waves between the spacecraft. We revisit the calculation of the light time correction (LTC) from first principles considering general relativistic effects and state-of-the-art models of Earth’s potential field. The novel analytical expressions for the LTC of KBR and LRI can circumvent numerical limitations of the classical approach. The dependency of the LTC on geopotential models and on the parameterization is studied, and afterwards the results are compared against the LTC provided in the official datasets of GRACE and GRACE Follow-On. It is shown that the new approach has a significantly lower noise, well below the instrument noise of current instruments, especially relevant for the LRI, and even if used with kinematic orbit products. This allows calculating the LTC accurate enough even for the next generation of gravimetric missions.

Hybrid-precision arithmetic for numerical orbit integration towards future satellite gravimetry missions

The precision of numerical orbit integration is crucial in precise orbit determination and gravity field recovery, especially in the context of future satellite gravimetry missions where nanometer-level inter-satellite measurements are provided by laser ranging interferometer. In this paper, we propose a hybrid-precision arithmetic in both Cowell’s and Encke’s formulations for numerical orbit integration after comprehensive analyses on the computational time costs and numerical errors by dividing the integration process into two parts, namely the increment calculation and the orbit propagation. Based on such a separation, we find that the round-off errors basically occur in the least time-consuming orbit propagation part while the more time-demanding increment calculation part is less sensitive to the round-off due to its small numerical magnitude. Therefore, it is natural in the hybrid-precision arithmetic to use the double- and quadruple-precision arithmetic in the increment calculation part and orbit propagation part, respectively. Numerical results demonstrate that the hybrid-precision arithmetic is as efficient as the double-precision method, while far better than its double-precision counterparts in terms of both accuracy and relative precision. In consideration of the ultra-high precision inter-satellite range and range rate measurements of future satellite gravimetry missions, the currently widely-used double-precision arithmetic cannot meet the numerical requirements of one-day arc orbit integration for the inter-satellite range measurement, in which numerical errors should be at least the same level of the measurement precision and had better be one-order magnitude smaller to fully avoid their contaminations, while for the inter-satellite range rate the double-precision Gauss-Jackson integrator is qualified. Instead, by implementation of hybrid-precision arithmetic the range rate precision is easily achieved at 10−12 m/s in terms of the maximum absolute error of the one-day arc by either Cowell’s or Encke’s formulation. Furthermore, the sub-nanometer-level range precision is obtainable in the Encke’s formulation with reference orbit selected as the best-fit one. Therefore, it is recommended to adopt the hybrid-precision arithmetic for orbit integration to fully exploit the ultra-high precise measurement from the pure numerical data processing point of view.

Earth\u2019s gravity from space

Satellite gravimetry began with the launch of the satellites Sputnik 1 and 2 in 1957. During the following 43 years, more and more details were discovered and the models of the Earth’s gravity could be refined. Methods improved and more and more satellite orbits and ground stations were added in the analysis, employing more advanced and precise measuring techniques. A new era started with the dedicated gravimetry missions CHAMP (2000–2010), GRACE (2002–2017), and GOCE (2009–2013). The methods of satellite-to-satellite tracking and satellite gradiometry resulted in a substantial improvement of our knowledge of the Earth’s gravity field in terms of accuracy and its spatial and temporal variations. There are three basic ways of using gravity and geoid models in Earth sciences and geodesy. First, in solid Earth physics, the highs and lows of the field are investigated in comparison with an idealized Earth, e.g., a hydrostatic equilibrium figure. In particular, in South America, Africa, Himalaya and Antarctica the gravity field is known much better now, due to GOCE and lead to an improved understanding of the continental crust and lithosphere. Second, in oceanography, the geoid serves as surface in equilibrium, a hypothetical ocean at rest. The ocean topography is the deviation of the actual ocean surface, measured by satellite altimetry, from this reference. The ocean topography serves as a new and independent input to ocean circulation modeling and leads to an improved understanding of ocean transport of mass, heat, and nutrients. Similarly, geodetic heights of the land surface will soon be referred to the geoid, leading to globally consistent heights and enabling the removal of existent systematic deformations and offsets of national and continental height systems. Third, the GRACE time series of monthly gravity models, reflecting seasonal, inter-annual and long-term gravity changes, became one of the most valuable data sources of climate change studies.

Simulation-based evaluation of a cold atom interferometry gradiometer concept for gravity field recovery

The prospects of future satellite gravimetry missions to sustain a continuous and improved observation of the gravitational field have stimulated studies of new concepts of space inertial sensors with potentially improved precision and stability. This is in particular the case for cold-atom interferometry (CAI) gradiometry which is the object of this paper. The performance of a specific CAI gradiometer design is studied here in terms of quality of the recovered gravity field through a closed-loop numerical simulation of the measurement and processing workflow. First we show that mapping the time-variable field on a monthly basis would require a noise level below 5mE/Hz. The mission scenarios are therefore focused on the static field, like GOCE. Second, the stringent requirement on the angular velocity of a one-arm gradiometer, which must not exceed 10-6 rad/s, leads to two possible modes of operation of the CAI gradiometer: the nadir and the quasi-inertial mode. In the nadir mode, which corresponds to the usual Earth-pointing satellite attitude, only the gradient Vyy, along the cross-track direction, is measured. In the quasi-inertial mode, the satellite attitude is approximately constant in the inertial reference frame and the 3 diagonal gradients Vxx,Vyy and Vzz are measured. Both modes are successively simulated for a 239 km altitude orbit and the error on the recovered gravity models eventually compared to GOCE solutions. We conclude that for the specific CAI gradiometer design assumed in this paper, only the quasi-inertial mode scenario would be able to significantly outperform GOCE results at the cost of technically challenging requirements on the orbit and attitude control.

Treatment of temporal aliasing effects in the context of next generation satellite gravimetry missions

AbstractTemporal aliasing effects have a large impact on the gravity field accuracy of current gravimetry missions and are also expected to dominate the error budget of Next Generation Gravimetry Missions (NGGMs). This paper focuses on aspects concerning their treatment in the context of Low‐Low Satellite‐to‐Satellite Tracking NGGMs. Closed‐loop full‐scale simulations are performed for a two‐pair Bender‐type Satellite Formation Flight (SFF), by taking into account error models of new generation instrument technology. The enhanced spatial sampling and error isotropy enable a further reduction of temporal aliasing errors from the processing perspective. A parameterization technique is adopted where the functional model is augmented by low‐resolution gravity field solutions coestimated at short time intervals, while the remaining higher‐resolution gravity field solution is estimated at a longer time interval. Fine‐tuning the parameterization choices leads to significant reduction of the temporal aliasing effects. The investigations reveal that the parameterization technique in case of a Bender‐type SFF can successfully mitigate aliasing effects caused by undersampling of high‐frequency atmospheric and oceanic signals, since their most significant variations can be captured by daily coestimated solutions. This amounts to a “self‐dealiasing” method that differs significantly from the classical dealiasing approach used nowadays for Gravity Recovery and Climate Experiment processing, enabling NGGMs to retrieve the complete spectrum of Earth's nontidal geophysical processes, including, for the first time, high‐frequency atmospheric and oceanic variations.

Expansion and Improvement of the Israeli Geoid Model by Shipborne GNSS Measurements

AbstractThe geoid is the equipotential surface that coincides with the sea level in the absence of such dynamic effects as tides, wind, ocean currents, and other disturbing forces. On land, geoid models are determined by using precise leveling, Global Navigation Satellite System (GNSS) measurements, and gravimetry measurements. However, in coastal areas, where performing precise leveling is not possible, geoid modeling relies solely on gravity measurements. Spaceborne gravimetry missions provide gravimetric measurements with global coverage. These measurements have low spatial resolution, which can reach distances of tens and hundreds of kilometers between tracks. Airborne and shipborne gravity measurements can be used to fill the gaps between tracks. In the absence of airborne and shipborne gravity measurements to densify the measuring data, shipborne GNSS measurements may provide a low-cost method for overcoming this problem in coastal areas. After applying several corrections to the raw GNSS measuremen...

DETERMINISTICALLY-MODIFIED INTEGRAL ESTIMATORS OF GRAVITATIONAL TENSOR

The Earth's global gravity field modelling is an important subject in Physical Geodesy. For this purpose different satellite gravimetry missions have been designed and launched. Satellite gravity gradiometry (SGG) is a technique to measure the second-order derivatives of the gravity field. The gravity field and steady state ocean circulation explorer (GOCE) is the first satellite mission which uses this technique and is dedicated to recover Earth's gravity models (EGMs) up to medium wavelengths. The existing terrestrial gravimetric data and EGM scan be used for validation of the GOCE data prior to their use. In this research, the tensor of gravitation in the local north-oriented frame is generated using deterministically-modified integral estimators involving terrestrial data and EGMs. The paper presents that the SGG data is assessable with an accuracy of 1-2 mE in Fennoscandia using a modified integral estimatorby the Molodensky method. A degree of modification of 100 and an integration cap size of for integrating terrestrial data are proper parameters for the estimator.

Comparisons of atmospheric data and reduction methods for the analysis of satellite gravimetry observations

The Gravity Recovery and Climate Experiment (GRACE) derived gravity solutions contain errors mostly due to instrument noise, anisotropic spatial sampling, and temporal aliasing. Improving the quality of satellite gravimetry observations, in terms of using more sensitive sensors and/or increasing the spatial isotropy, has been discussed in the context of the designed scenarios of future satellite gravimetry missions. Temporal aliasing caused by incomplete reducing of background models, however, is still a factor that affects the quality of the gravity field solutions. This paper specifically explores the possible physical, geometrical, and numerical modifications of the three‒dimensional (3‒D) integration approach to eliminate the high‒frequency atmospheric effects from satellite gravimetry observations. The new modified 3‒D approach is then applied to compute new sets of atmospheric dealiasing products, using atmospheric fields from the European Centre for Medium‒Range Weather Forecasts (ECMWF) operational analysis model and ERA‒Interim reanalysis. Impacts of modifications are compared to the prelaunch baseline and the current error‒curve of GRACE as well as an error‒curve of a Bender‒type multiorbit satellite configuration. Specifically, we found that using latitude‒dependent radius, latitude‒ and altitude‒dependent gravity accelerations along with numerical modifications have a considerable impact on the 3‒D integral. Comparing the new products to those of GRACE Atmosphere and Ocean Dealiasing level‒1B shows a nonnegligible difference with respect to the prelaunch baseline of GRACE and a possible Bender‒type mission up to harmonic degrees 13 and 50, respectively. A big difference is also found between the derived dealiasing products from ECMWF operational analysis and ERA‒Interim indicating the importance of input parameters on the final atmospheric dealiasing products.

Analytical error analysis for satellite gravity field determination based on two-dimensional Fourier method

The time-wise and space-wise approaches are generally applied to data processing and error analysis for satellite gravimetry missions. But both the approaches, which are based on least-squares collocation, address the whole effect of measurement errors and estimate the resolution of gravity field models mainly from a numerical point of indirect view. Moreover, requirement for higher accuracy and resolution gravity field models could make the computation more difficult, and serious numerical instabilities arise. In order to overcome the problems, this study focuses on constructing a direct relationship between power spectral density of the satellite gravimetry measurements and coefficients of the Earth's gravity potential. Based on two-dimensional Fourier transform, the relationship is analytically concluded. By taking advantage of the analytical expression, it is efficient and distinct for parameter estimation and error analysis of missions. From the relationship and the simulations, it is analytically confirmed that the low-frequency noise affects the gravity field recovery in all degrees for the instance of satellite gradiometer recovery mission. Furthermore, some other results and suggestions are also described.

Earth System Mass Transport Mission (e.motion): A Concept for Future Earth Gravity Field Measurements from Space

In the last decade, satellite gravimetry has been revealed as a pioneering technique for mapping mass redistributions within the Earth system. This fact has allowed us to have an improved understanding of the dynamic processes that take place within and between the Earth’s various constituents. Results from the Gravity Recovery And Climate Experiment (GRACE) mission have revolutionized Earth system research and have established the necessity for future satellite gravity missions. In 2010, a comprehensive team of European and Canadian scientists and industrial partners proposed the e.motion (Earth system mass transport mission) concept to the European Space Agency. The proposal is based on two tandem satellites in a pendulum orbit configuration at an altitude of about 370 km, carrying a laser interferometer inter-satellite ranging instrument and improved accelerometers. In this paper, we review and discuss a wide range of mass signals related to the global water cycle and to solid Earth deformations that were outlined in the e.motion proposal. The technological and mission challenges that need to be addressed in order to detect these signals are emphasized within the context of the scientific return. This analysis presents a broad perspective on the value and need for future satellite gravimetry missions.

Triangulated spherical splines for geopotential reconstruction

We present an alternate mathematical technique than contemporary spherical harmonics to approximate the geopotential based on triangulated spherical spline functions, which are smooth piecewise spherical harmonic polynomials over spherical triangulations. The new method is capable of multi-spatial resolution modeling and could thus enhance spatial resolutions for regional gravity field inversion using data from space gravimetry missions such as CHAMP, GRACE or GOCE. First, we propose to use the minimal energy spherical spline interpolation to find a good approximation of the geopotential at the orbital altitude of the satellite. Then we explain how to solve Laplace’s equation on the Earth’s exterior to compute a spherical spline to approximate the geopotential at the Earth’s surface. We propose a domain decomposition technique, which can compute an approximation of the minimal energy spherical spline interpolation on the orbital altitude and a multiple star technique to compute the spherical spline approximation by the collocation method. We prove that the spherical spline constructed by means of the domain decomposition technique converges to the minimal energy spline interpolation. We also prove that the modeled spline geopotential is continuous from the satellite altitude down to the Earth’s surface. We have implemented the two computational algorithms and applied them in a numerical experiment using simulated CHAMP geopotential observations computed at satellite altitude (450 km) assuming EGM96 (nmax = 90) is the truth model. We then validate our approach by comparing the computed geopotential values using the resulting spherical spline model down to the Earth’s surface, with the truth EGM96 values over several study regions. Our numerical evidence demonstrates that the algorithms produce a viable alternative of regional gravity field solution potentially exploiting the full accuracy of data from space gravimetry missions. The major advantage of our method is that it allows us to compute the geopotential over the regions of interest as well as enhancing the spatial resolution commensurable with the characteristics of satellite coverage, which could not be done using a global spherical harmonic representation.