GRACE Gravity Field Research Articles

A comparative study on the parametrization of a time-variable geopotential model from GRACE monthly solutions

The gravity field of the Earth is time-dependent due to several types of mass variations which take place on different time scales. Usually, the time-variability of the gravitational potential of the Earth is expressed by the monthly determination of a static geopotential model based on data from gravity field missions. In this paper, the variability of the potential is parameterized by a functional approach which contains a polynomial trend and periodic contributions. The respective parameters are estimated based on the monthly solutions derived from the GRACE and GRACE-FO gravity field mission up to a maximum degree of expansion nmax=96\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_\ ext {max}=96$$\\end{document}. As a preliminary data analysis, a Fourier analysis is performed on selected potential coefficients from the available monthly solutions of the GFZ. The indicated frequency components are then used to formulate a time-dependent analytical approach to describe each Stokes coefficient’s temporal behaviour. Different approaches are presented that include both polynomial and periodic components. The respective parameters for modelling the temporal variability of the coefficients are estimated in a Gauss-Markov model and tested for significance by statistical methods. Extensive comparative numerical studies are carried out between the newly generated model variants and the existing monthly GRACE, GRACE-FO and the existing time dependent EIGEN-6S4 solutions. The numerical comparisons make it clear that estimated models based on all available monthly solutions describe the essential periods very well, but such monthly events that deviate strongly from the mean behaviour of the signal show less precision in the space domain. Models that are estimated based on fourteen consecutive monthly solutions, covering one selected year, represent the amplitudes much more precise. The statements made apply to four initial data used, which are filtered to varying degrees. In particular, DDK2, DDK5 and DDK8, as well as unfiltered coefficients were used. For all the model approaches used, it can be seen that the potential coefficients contain up to about n≈40\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n\\approx 40$$\\end{document} in case of DDK5 periodically signals with annual, semi-annual or quarterly, as well as Luna nodal periods and do not vary significantly beyond that degree. Only an offset can be estimated significantly for all Stokes coefficients.

Combination of geometric and gravimetric data sets for the estimation of high-resolution mass balances of the Greenland ice sheet

SUMMARY In this study, we develop a model that allows to combine gravimetric and geometric data. By the combination, we improve the spatial resolution of the resulting mass balance estimate compared to a purely gravimetric one. The equivalent ice or firn density of the changing ice volume is estimated within a mathematical inversion model, which includes geometric information about the volumetric change of the ice sheet and the resulting gravity change. This gravity change is computed from monthly GRACE gravity fields. They have a limited spatial resolution of a few 100 km, but allow direct conclusions about the true mass changes over Greenland. The ice-volume changes are described by a product by the Climate Change Initiative of European Space Agency, which is based on altimetry data. They have a very fine spatial resolution (down to a few km), but are not directly sensitive to mass changes. By combining both data sets in a common mathematical model, the advantages of both data types (direct sensitivity to mass versus high spatial resolution) are made use of. In this way, we improve the spatial resolution of mass balance estimates over Greenland. This leads to a map of mass trends, which has the same spatial resolution as the input map of geometric changes, but which is consistent with the input gravity fields. It will enable improving the localization of mass change signals of ice sheets and glaciers, which are usually rather small-scale. We compare our estimates to the results of complementary studies regarding the total mass loss of the Greenland ice sheet and its surrounding land surface. Our study leads to a value of $-213\pm 37\, \text{Gt}\,\text{a}^{-1}$ in the time span from 2011 to 2015. We also discuss the problem of separating the mass contribution of the Greenland ice sheet itself and its surrounding region.

A decorrelation filter based on the full error covariance of GRACE gravity field solutions

A decorrelation filter based on the full error covariance of GRACE gravity field solutions

Influence of Three Gorges Dam on earthquakes based on GRACE gravity field

Abstract After the completion of the Three Gorges Dam, it increases the risk of inducing an earthquake. We use the GRACE Gravity Field Model to analyze the relationship between the operation of the Three Gorges Reservoir and the change of gravity field in western Sichuan. The research results indicate that the reservoir water level and the western Sichuan gravitational field are positively correlated. In the early stage of rising water level, the change of gravity field is not apparent, and the change of gravity field gradually increases with time. Therefore, the change of reservoir water level affects the gravity field in western Sichuan. The dynamic changes of the gravity field can reflect the Earth’s material change and deformation process and are closely related to earthquakes. Consequently, the Three Gorges Dam will indirectly affect the seismicity in western Sichuan by affecting the gravity field. The research provides valuable information for studying regional reservoir earthquake disasters and supports related policy decisions.

Revisiting Force Model Error Modeling in GRACE Gravity Field Recovery

Revisiting Force Model Error Modeling in GRACE Gravity Field Recovery

The new CNES-CLS18 global mean dynamic topography

Abstract. The mean dynamic topography (MDT) is a key reference surface for altimetry. It is needed for the calculation of the ocean absolute dynamic topography, and under the geostrophic approximation, the estimation of surface currents. CNES-CLS mean dynamic topography (MDT) solutions are calculated by merging information from altimeter data, GRACE, and GOCE gravity field and oceanographic in situ measurements (drifting buoy velocities, hydrological profiles). The objective of this paper is to present the newly updated CNES-CLS18 MDT. The main improvement compared to the previous CNES-CLS13 solution is the use of updated input datasets: the GOCO05S geoid model is used based on the complete GOCE mission (November 2009–October 2013) and 10.5 years of GRACE data, together with all drifting buoy velocities (SVP-type and Argo floats) and hydrological profiles (CORA database) available from 1993 to 2017 (instead of 1993–2012). The new solution also benefits from improved data processing (in particular a new wind-driven current model has been developed to extract the geostrophic component from the buoy velocities) and methodology (in particular the computation of the medium-scale GOCE-based MDT first guess has been revised). An evaluation of the new solution compared to the previous version and to other existing MDT solutions show significant improvements in both strong currents and coastal areas.

Geophysical Signal Detection in the Earth’s Oblateness Variation and Its Climate-Driven Source Analysis

This study analyzes the geophysical signals in J2 time series from 1976 to 2020 by using singular spectrum analysis (SSA) and the Lomb-Scargle (L-S) periodogram for the first time. The results of SSA indicate that the secular trend is characterized by a superposition of the secular linear decrease with a rate of approximately (−5.80 ± 0.08) × 10−11/yr and an obvious quadratic rate of (2.38 ± 0.02) × 10−13/yr2. Besides, the annual, semi-annual, and 10.6-year signals with determining for the first time its amplitude of 5.01 × 10−11, are also detected by SSA, where their stochastic behavior can be maintained to the greatest extent. The 18.6-year signal cannot be detected by SSA even when the window size of 18.6 years was selected, while L-S periodogram can detect the signal of 18.6 years after removing the 18.6-year tidal theoretical value and the linear trend, proving the existence of the tidal variations of 18.6 years in the residual time series. Nevertheless, the 10.6-year signal can be found only after removing the secular trend. This fact suggests that the advantages of different methods used will lead to different sensitivity to the particular signals hard to be detected. Finally, the reconstructed ΔJ2 time series through the sum of the climate-driven contributions from glacial isostatic adjustment (GIA), Antarctic ice sheets (ANT), atmosphere (ATM), continental glaciers (GLA), Greenland ice sheets (GRE), ocean bottom pressure (OBP), and terrestrial water storage (TWS) by using GRACE gravity field solution and geophysical models agrees very well with that of the observed ΔJ2 from SLR in terms of the amplitude and phase. About 81.5% of observed ΔJ2 can be explained by the reconstructed value. ATM, TWS, and OBP are the most significant contributing sources for seasonal signals in ΔJ2 time series, explaining up to 40.1%, 31.9%, and 26.3% of the variances of observed ΔJ2. These three components contribute to the annual and semi-annual variations of the observed ΔJ2 up to 30.1% and 1.6%, 30.8% and 1.0%, as well as 25.4% and 0.7%, respectively. GRE, ANT, and GLA have ~3 to ~7-year periodic fluctuations and a positive linear trend, excluding GIA.

The construction of high precision geostrophic currents based on new gravity models of GOCE and satellite altimetry data

The new gravity field models of gravity field and steady-state ocean circulation explorer (GOCE), TIM_R6 and DIR_R6, were released by the European Space Agency (ESA) in June 2019. The sixth generation of gravity models have the highest possible signal and lowest error levels compared with other GOCE-only gravity models, and the accuracy is significantly improved. This is an opportunity to build high precision geostrophic currents. The mean dynamic topography and geostrophic currents have been calculated by the 5th (TIM_R5 and DIR_R5), 6th (TIM_R6 and DIR_R6) release of GOCE gravity field models and ITSG-Grace2018 of GRACE gravity field model in this study. By comparison with the drifter results, the optimal filtering lengths of them have been obtained (for DIR_R5, DIR_R6, TIM_R5 and TIM_R6 models are 1° and for ITSG-Grace2018 model is 1.1°). The filtered results show that the geostrophic currents obtained by the GOCE gravity field models can better reflect detailed characteristics of ocean currents. The total geostrophic speed based on the TIM_R6 model is similar to the result of the DIR_R6 model with standard deviation (STD) of 0.320 m/s and 0.321 m/s, respectively. The STD of the total velocities are 0.333 m/s and 0.325 m/s for DIR_R5 and TIM_R5. When compared with ITSG-Grace2018 results, the STD (0.344 m/s) of total geostrophic speeds is larger than GOCE results, and the accuracy of geostrophic currents obtained by ITSG-Grace2018 is lower. And the absolute errors are mainly distributed in the areas with faster speeds, such as the Antarctic circumpolar circulation, equatorial region, Kuroshio and Gulf Stream areas. After the remove-restore technique was applied to TIM_R6 MDT, the STD of total geostrophic speeds dropped to 0.162 m/s.

The impact of error covariance matrix structure of GRACE’s gravity solution on the mass flux estimates of Greenland ice sheet

The error variance-covariance matrices of the monthly GRACE gravity field models are usually well-structured (e.g., order-leading) to contain the error information of the monthly gravity field models, and they are important information to further improve the accuracy of the estimated mass transportation by a post-processing scheme. Intensive studies have been performed to understand the impact of different approximations of the full error variance-covariance matrix on the mass estimates obtained with the conventional GRACE-post processing methods (e.g., the de-striping method). In this study, based on the variants of the mascon approach which treat monthly GRACE solutions as input, we consider four different structures to the error variance-covariance matrix, (i) full matrix, (ii) block diagonal matrix, (iii) diagonal matrix, and (iv) identity matrix, and examine their impact on the mass transport estimates in Greenland. Using both synthetic and real data, we analyze the results at four temporal scales: (i) the long-term decadal scale, (ii) the inter-annual scale, (iii) the seasonal scale, and (iv) the monthly scale. Based on the synthetic study, we find that for the recovery of the long-term trend, the application of the diagonal structure obtains the best estimates. This is caused by the amplification of the model error in the mascon approach when considering the full and block diagonal structures of error variance-covariance matrix, not due to any imperfection of them. Therefore, we emphasize that one should be aware of mascon model deficiency in the mascon approach. Furthermore, the best inter-annual, seasonal and monthly mass estimates are derived by considering the block diagonal and full structures. This is caused by the behavior of the bias and the unique parameterization error in the case of different structures. A similar finding is also presented in the real data case. Finally, our analysis denotes the necessity of releasing the block diagonal structure together with the official monthly gravity field model for the GRACE Follow-On mission, instead of releasing only the diagonal structure as done for the GRACE mission.

GRACE gravity field recovery with background model uncertainties

In this article, we present a computationally efficient method to incorporate background model uncertainties into the gravity field recovery process. While the geophysical models typically used during the processing of GRACE data, such as the atmosphere and ocean dealiasing product, have been greatly improved over the last years, they are still a limiting factor of the overall solution quality. Our idea is to use information about the uncertainty of these models to find a more appropriate stochastic model for the GRACE observations within the least squares adjustment, thus potentially improving the gravity field estimates. We used the ESA Earth System Model to derive uncertainty estimates for the atmosphere and ocean dealiasing product in the form of an autoregressive model. To assess our approach, we computed time series of monthly GRACE solutions from L1B data in the time span of 2005 to 2010 with and without the derived error model. Intercomparisons between these time series show that noise is reduced on all spatial scales, with up to 25% RMS reduction for Gaussian filter radii from 250 to 300 km, while preserving the monthly signal. We further observe a better agreement between formal and empirical errors, which supports our conclusion that used uncertainty information does improve the stochastic description of the GRACE observables.

GOCE gradiometer data calibration

The GOCE mission provides a unique gravity gradient dataset, which is used by most state-of-the-art global gravity field models. The quality of the gravity gradients of previous data releases degraded during the mission lifetime, which was often attributed to the increasing drag forces towards the end of the mission due to the approaching solar maximum and also, starting in August 2012, a sequence of five orbit lowerings. An imperfect calibration of the gravity gradiometer data was often suspected as root cause for the degradation. We present the novel method for the calibration of the GOCE gravity gradiometer data that was used for the official reprocessing of the GOCE gravity gradients in 2018. It is based on a comprehensive calibration model that includes quadratic factors and angular acceleration couplings as new calibration parameters. The calibration parameters are estimated from star tracker angular rates, gravity gradients calculated from a GRACE gravity field model and the condition that the three gradiometer arms measure the same non-gravitational acceleration. In addition to the GOCE data generated during science mode operations, we also use the data collected during satellite shaking mode operations. We demonstrate that applying the new method removes systematic errors to a large extent and, consequently, yields gravity gradients of superior and constant quality compared to previous data releases.

SLR, GRACE and Swarm Gravity Field Determination and Combination

Satellite gravimetry allows for determining large scale mass transport in the system Earth and to quantify ice mass change in polar regions. We provide, evaluate and compare a long time-series of monthly gravity field solutions derived either by satellite laser ranging (SLR) to geodetic satellites, by GPS and K-band observations of the GRACE mission, or by GPS observations of the three Swarm satellites. While GRACE provides gravity signal at the highest spatial resolution, SLR sheds light on mass transport in polar regions at larger scales also in the pre- and post-GRACE era. To bridge the gap between GRACE and GRACE Follow-On, we also derive monthly gravity fields using Swarm data and perform a combination with SLR. To correctly take all correlations into account, this combination is performed on the normal equation level. Validating the Swarm/SLR combination against GRACE during the overlapping period January 2015 to June 2016, the best fit is achieved when down-weighting Swarm compared to the weights determined by variance component estimation. While between 2014 and 2017 SLR alone slightly overestimates mass loss in Greenland compared to GRACE, the combined gravity fields match significantly better in the overlapping time period and the RMS of the differences is reduced by almost 100 Gt. After 2017, both SLR and Swarm indicate moderate mass gain in Greenland.

Mitigation of ionospheric signatures in Swarm GPS gravity field estimation using weighting strategies

Abstract. Even though ESA's three-satellite low-earth orbit (LEO) mission Swarm is primarily a magnetic field mission, it can also serve as a gravity field mission. Located in a near-polar orbit with initial altitudes of 480 km for Swarm A and Swarm C and 530 km for Swarm B and equipped with geodetic-type dual frequency Global Positioning System (GPS) receivers, it is suitable for gravity field computation. Of course, the Swarm GPS-only gravity fields cannot compete with the gravity fields derived from the ultra-precise Gravity Recovery And Climate Experiment (GRACE) K-band measurements. But for various reasons like the end of the GRACE mission in October 2017, data gaps in the previous months due to battery aging, and the gap between GRACE and the recently launched GRACE Follow-On mission, Swarm gravity fields became important to maintain a continuous time series and to bridge the gap between the two dedicated gravity missions. By comparing the gravity fields derived from Swarm kinematic positions to the GRACE gravity fields, systematic errors have been observed in the Swarm results, especially around the geomagnetic equator. These errors are already visible in the kinematic positions as spikes up to a few centimeters, from where they propagate into the gravity field solutions. We investigate these systematic errors by analyzing the geometry-free linear combination of the GPS carrier-phase observations and its time derivatives using a combination of a Gaussian filter and a Savitzky–Golay filter and the Rate of Total Electron Content (TEC) Index (ROTI). Based on this, we present different weighting schemes and investigate their impact on the gravity field solutions in order to assess the success of different mitigation strategies. We will show that a combination of a derivative-based weighting approach with a ROTI-based weighting approach is capable of reducing the geoid rms from 21.6 to 12.0 mm for a heavily affected month and that almost 10 % more kinematic positions can be preserved compared to a derivative-based screening.

Daily GRACE gravity field solutions track major flood events in the Ganges–Brahmaputra Delta

Abstract. Two daily gravity field solutions based on observations from the Gravity Recovery and Climate Experiment (GRACE) satellite mission are evaluated against daily river runoff data for major flood events in the Ganges–Brahmaputra Delta (GBD) in 2004 and 2007. The trends over periods of a few days of the daily GRACE data reflect temporal variations in daily river runoff during major flood events. This is especially true for the larger flood in 2007, which featured two distinct periods of critical flood level exceedance in the Brahmaputra River. This first hydrological evaluation of daily GRACE gravity field solutions based on a Kalman filter approach confirms their potential for gravity-based large-scale flood monitoring. This particularly applies to short-lived, high-volume floods, as they occur in the GBD with a 4–5-year return period. The release of daily GRACE gravity field solutions in near-real time may enable flood monitoring for large events.

Using GRACE and climate model simulations to predict mass loss of Alaskan glaciers through 2100

ABSTRACTGlaciers in Alaska are currently losing mass at a rate of ~−50 Gt a−1, one of the largest ice loss rates of any regional collection of mountain glaciers on Earth. Existing projections of Alaska's future sea-level contributions tend to be divergent and are not tied directly to regional observations. Here we develop a simple, regional observation-based projection of Alaska's future sea-level contribution. We compute a time series of recent Alaska glacier mass variability using monthly GRACE gravity fields from August 2002 through December 2014. We also construct a three-parameter model of Alaska glacier mass variability based on monthly ERA-Interim snowfall and temperature fields. When these three model parameters are fitted to the GRACE time series, the model explains 94% of the variance of the GRACE data. Using these parameter values, we then apply the model to simulated fields of monthly temperature and snowfall from the Community Earth System Model, to obtain predictions of mass variations through 2100. We conclude that mass loss rates may increase between −80 and −110 Gt a−1 by 2100, with a total sea-level rise contribution of 19 ± 4 mm during the 21st century.

GRACE-based estimates of water discharge over the Yellow River basin

As critical component of hydrologic cycle, basin discharge is a key issue for understanding the hydrological and climatologic related to water and energy cycles. Combining GRACE gravity field models with ET from GLDAS models and precipitation from GPCP, discharge of the Yellow River basin are estimated from the water balance equation. While comparing the results with discharge from GLDAS model and in situ measurements, the results reveal that discharge from Mosaic and CLM GLDAS model can partially represent the river discharge and the discharge estimation from water balance equation could reflect the discharge from precipitation over the Yellow River basin.

An improved GRACE monthly gravity field solution by modeling the non-conservative acceleration and attitude observation errors

The main contribution of this study is to improve the GRACE gravity field solution by taking errors of non-conservative acceleration and attitude observations into account. Unlike previous studies, the errors of the attitude and non-conservative acceleration data, and gravity field parameters, as well as accelerometer biases are estimated by means of weighted least squares adjustment. Then we compute a new time series of monthly gravity field models complete to degree and order 60 covering the period Jan. 2003 to Dec. 2012 from the twin GRACE satellites’ data. The derived GRACE solution (called Tongji-GRACE02) is compared in terms of geoid degree variances and temporal mass changes with the other GRACE solutions, namely CSR RL05, GFZ RL05a, and JPL RL05. The results show that (1) the global mass signals of Tongji-GRACE02 are generally consistent with those of CSR RL05, GFZ RL05a, and JPL RL05; (2) compared to CSR RL05, the noise of Tongji-GRACE02 is reduced by about 21 % over ocean when only using 300 km Gaussian smoothing, and 60 % or more over deserts (Australia, Kalahari, Karakum and Thar) without using Gaussian smoothing and decorrelation filtering; and (3) for all examples, the noise reductions are more significant than signal reductions, no matter whether smoothing and filtering are applied or not. The comparison with GLDAS data supports that the signals of Tongji-GRACE02 over St. Lawrence River basin are close to those from CSR RL05, GFZ RL05a and JPL RL05, while the GLDAS result shows the best agreement with the Tongji-GRACE02 result.

The pole tide and its effect on GRACE time‐variable gravity measurements: Implications for estimates of surface mass variations

AbstractGravity Recovery and Climate Experiment (GRACE) provides monthly solutions for the Earth's gravity field in the form of spherical harmonic coefficients. These can be used to infer changes in mass at the Earth's surface. The pole tide (the response of the Earth and oceans to polar motion) causes gravity signals dominated by harmonics of degree 2, order 1. If the pole tide is not removed from GRACE data, it affects the coefficients of those harmonics (C21, S21) and introduces errors when using those coefficients to determine surface mass variations. The pole tide is partially removed by GRACE processing centers before solving for the gravity field. But long‐period pole tide signals are not usually included in the GRACE pole tide correction, and so those signals are still present in the GRACE coefficients. We discuss this issue from the standpoint of somebody who uses the GRACE gravity fields to infer changes in surface mass. We arrive at a recommendation for an optimal GRACE pole tide correction. We describe how to modify the C21, S21 coefficients provided by the processing centers, so that they conform with our recommendation. We discuss the size of the pole tide contributions to C21, S21, compared to those of the direct load‐induced contributions. As an example, we show how an incompletely removed pole tide can impact GRACE results for the trend in ocean mass. We consider the impact of mantle anelasticity on long‐period pole tide corrections and conclude that it is unlikely to affect those corrections by more than 20%.

Comparison of GOCE-GPS gravity fields derived by different approaches

Several techniques have been proposed to exploit GNSS-derived kinematic orbit information for the determination of long-wavelength gravity field features. These methods include the (i) celestial mechanics approach, (ii) short-arc approach, (iii) point-wise acceleration approach, (iv) averaged acceleration approach, and (v) energy balance approach. Although there is a general consensus that—except for energy balance—these methods theoretically provide equivalent results, real data gravity field solutions from kinematic orbit analysis have never been evaluated against each other within a consistent data processing environment. This contribution strives to close this gap. Target consistency criteria for our study are the input data sets, period of investigation, spherical harmonic resolution, a priori gravity field information, etc. We compare GOCE gravity field estimates based on the aforementioned approaches as computed at the Graz University of Technology, the University of Bern, the University of Stuttgart/Austrian Academy of Sciences, and by RHEA Systems for the European Space Agency. The involved research groups complied with most of the consistency criterions. Deviations only occur where technical unfeasibility exists. Performance measures include formal errors, differences with respect to a state-of-the-art GRACE gravity field, (cumulative) geoid height differences, and SLR residuals from precise orbit determination of geodetic satellites. We found that for the approaches (i) to (iv), the cumulative geoid height differences at spherical harmonic degree 100 differ by only $${\approx }10~\%$$ ; in the absence of the polar data gap, SLR residuals agree by $${\approx }96~\%$$ . From our investigations, we conclude that real data analysis results are in agreement with the theoretical considerations concerning the (relative) performance of the different approaches.

Equivalent water height extracted from GRACE gravity field model with robust independent component analysis

The Level-2 monthly GRACE gravity field models issued by Center for Space Research (CSR), GeoForschungs Zentrum (GFZ), and Jet Propulsion Laboratory (JPL) are treated as observations used to extract the equivalent water height (EWH) with the robust independent component analysis (RICA). The smoothing radii of 300, 400, and 500 km are tested, respectively, in the Gaussian smoothing kernel function to reduce the observation Gaussianity. Three independent components are obtained by RICA in the spatial domain; the first component matches the geophysical signal, and the other two match the north-south strip and the other noises. The first mode is used to estimate EWHs of CSR, JPL, and GFZ, and compared with the classical empirical decorrelation method (EDM). The EWH STDs for 12 months in 2010 extracted by RICA and EDM show the obvious fluctuation. The results indicate that the sharp EWH changes in some areas have an important global effect, like in Amazon, Mekong, and Zambezi basins.