Spherical and ellipsoidal surface mass change from GRACE time-variable gravity data

2020 ◽  
Author(s):  
Michal Šprlák ◽  
Khosro Ghobadi-Far ◽  
Shin-Chan Han ◽  
Pavel Novák
Keyword(s):  
Gravity Field ◽  
Gravitational Potential ◽  
Gravity Data ◽  
Time Variable ◽  
Mass Change ◽  
Spherical Approximation ◽  
Surface Mass ◽  
Time Variable Gravity ◽  
The Earth ◽  
Variable Gravity

<p>The problem of estimating mass redistribution from temporal variations of the Earth’s gravity field, such as those observed by GRACE, is non-unique. By approximating the Earth’s surface by a sphere, surface mass change can be uniquely determined from time-variable gravity data. Conventionally, the spherical approach of Wahr et al. (1998) is employed for computing the surface mass change caused, for example, by terrestrial water and glaciers. The accuracy of the GRACE Level 2 time-variable gravity data has improved due to updated background geophysical models or enhanced data processing. Moreover, time series analysis of ∼15 years of GRACE observations allows for determining inter-annual and seasonal changes with a significantly higher accuracy than individual monthly fields. Thus, the improved time-variable gravity data might not tolerate the spherical approximation introduced by Wahr et al. (1998).</p><p>A spheroid (an ellipsoid of revolution) represents a closer approximation of the Earth than a sphere, particularly in polar regions. Motivated by this fact, we develop a rigorous method for determining surface mass change on a spheroid. Our mathematical treatment is fully ellipsoidal as we concisely use Jacobi ellipsoidal coordinates and exploit the corresponding series expansions of the gravitational potential and of the surface mass. We provide a unique one-to-one relationship between the ellipsoidal spectrum of the surface mass and the ellipsoidal spectrum of the gravitational potential. This ellipsoidal spectral formula is more general and embeds the spherical approach by Wahr et al. (1998) as a special case. We also quantify the differences between the spherical and ellipsoidal approximations numerically by calculating the surface mass change rate in Antarctica and Greenland.</p><p> </p><p>References:</p><p>Wahr J, Molenaar M, Bryan F (1998) Time variability of the Earth’s gravity field: Hydrological and oceanic effects and their possible detection using GRACE. Journal of Geophysical Research: Solid Earth, 103(B12), 30205-30229.</p>

scholarly journals Determination of ellipsoidal surface mass change from GRACE time-variable gravity data

2019 ◽  
Vol 219 (1) ◽  
pp. 248-259
Author(s):  
Khosro Ghobadi-Far ◽  
Michal Šprlák ◽  
Shin-Chan Han
Keyword(s):  
Time Variable ◽  
Mass Change ◽  
Lower Latitude ◽  
Spherical Approximation ◽  
Polar Regions ◽  
Surface Mass ◽  
Time Variable Gravity ◽  
The Earth ◽  
Mass Redistribution ◽  
Variable Gravity

SUMMARY The problem of determining mass redistribution within the Earth system from time-variable gravity (TVG) data is non-unique. Over seasonal and decadal time-scales, mass redistribution likely takes place on the Earth’s surface. By approximating the Earth’s surface by a sphere, surface mass variation can be uniquely determined from TVG data. Recently, using the improved GRACE TVG data, Li et al. and Ditmar found that such spherical approximation is no longer tenable and suggested practical approaches to accommodate the elliptical shape of the Earth. In this study, we develop a rigorous method of determining surface mass change on the Earth’s reference ellipsoid. We derive a unique one-to-one relationship between ellipsoidal spectra of surface mass and gravitational potential for the ellipsoidal geometry. In conjunction with our ellipsoidal formulation, the linear transformation between spherical and ellipsoidal harmonic coefficients of the geopotential field enables us to determine mass redistribution on the ellipsoid from GRACE TVG data. Using the Release 6 of GRACE TVG data to degree 60, we show that the ellipsoidal approach reconciles surface mass change rate significantly better than the spherical computation by 3–4 cm yr−1, equivalent to 10–15  per cent increase of total signal, in Greenland and West Antarctica. We quantify the spherical approximation error over the polar regions using GRACE Level-2 TVG data as well as mascon solutions, and demonstrate that the systematic error increases linearly with the maximum degree used for the synthesis. The terrestrial water storage computation is less affected by the spherical approximation because of geographic location of major river basins (lower latitude) and signal characteristics. The improvement of TVG data from GRACE and its Follow-On necessitates the ellipsoidal computation, particularly for quantifying mass change in polar regions.

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

2011 ◽  
Vol 4 (1) ◽  
pp. 27-70 ◽  
Author(s):  
Th. Gruber ◽  
J. L. Bamber ◽  
M. F. P. Bierkens ◽  
H. Dobslaw ◽  
M. Murböck ◽  
...  
Keyword(s):  
Time Series ◽  
Gravity Field ◽  
Mass Distribution ◽  
Time Variable ◽  
Data Sets ◽  
Earth System ◽  
Time Variable Gravity ◽  
The Earth ◽  
Gravity Fields ◽  
Variable Gravity

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

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

2021 ◽  
Vol 13 (17) ◽  
pp. 3491
Author(s):  
Luping Zhong ◽  
Krzysztof Sośnica ◽  
Matthias Weigelt ◽  
Bingshi Liu ◽  
Xiancai Zou
Keyword(s):  
Gravity Field ◽  
Spatial Resolution ◽  
Amazon Basin ◽  
Satellite Tracking ◽  
Time Variable ◽  
Earth Gravity Field ◽  
Time Variable Gravity ◽  
Earth Gravity ◽  
The Earth ◽  
Variable Gravity

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

scholarly journals Time-variable gravity field recovery from kinematic positions of Low Earth Orbiting satellites

2021 ◽  
Author(s):  
Thomas Grombein ◽  
Martin Lasser ◽  
Daniel Arnold ◽  
Ulrich Meyer ◽  
Adrian Jäggi
Keyword(s):  
Time Series ◽  
Gravity Field ◽  
Time Variable ◽  
Kinematic Orbit ◽  
Time Variable Gravity ◽  
Gravity Field Recovery ◽  
The Earth ◽  
Leo Satellites ◽  
Variable Gravity ◽  
Gnss Data

<p>For the monitoring of mass transport and mass distribution in the Earth’s system, the gravity field and its temporal variations provide an important source of information. Dedicated satellite missions like GRACE and GRACE-FO allow to resolve the Earth’s time-variable gravity field based on ultra-precise inter-satellite ranging. In addition, any (non-dedicated) Low Earth Orbiting (LEO) satellite equipped with an on-board GNSS receiver may also serve as a gravity field sensor. For this purpose, the collected GNSS data is used to derive kinematic LEO orbit positions that can subsequently be utilized as pseudo-observations for gravity field recovery. Although this technique is less sensitive and restricted to the long wavelength part of the gravity field, it provides valuable information, particularly for those months where no inter-satellite ranging measurements are available from GRACE or GRACE-FO. Furthermore, the increasing number of operational LEO satellites makes it attractive to produce combined Multi-LEO gravity field solutions that will take advantage of the variety of complementary orbital configurations and can offer additional sensitivities to selected coefficients of solutions based on inter-satellite ranging.</p><p>At the Astronomical Institute of the University of Bern (AIUB) GPS-based kinematic orbits are routinely processed for various LEO satellites like missions dedicated to gravity (GOCE, GRACE/-FO), altimetry (Jason, Sentinel), or further constellations of Earth-observing satellites like SWARM. Beside conventional ambiguity-float orbits, also ambiguity-fixed orbits are recently being computed based on new phase bias and clock products of the Center for Orbit Determination in Europe (CODE). The kinematic orbit positions offer the opportunity to derive time series of monthly gravity field solutions for the different LEO satellites that are eventually combined on the level of normal equations.</p><p>In this contribution, we will present first results of our effort to generate a combined time series of monthly gravity field solutions based on the kinematic orbits of multiple LEO satellites. In a first step, the focus is laid on the GRACE/-FO missions that provide the longest time series in terms of collected GNSS data and that will therefore serve as a backbone for future combinations. We analyze the impact of accelerometer data on the recovery of time-variable mass variations. This will be particularly important for the handling of non-dedicated gravity missions, for which accelerometer measurements are usually not available. Furthermore, we study and compare the performance of gravity field recoveries based on ambiguity-float and ambiguity-fixed kinematic orbit solutions. We assess our results with respect to superior gravity field models based on inter-satellite ranging for selected areas with strong mass change signals like in Greenland, West-Antarctica or the Amazon river basin.</p>

Intercomparison of signals and noise in time variable gravity field releases from an ice sheet perspective

2020 ◽  
Author(s):  
Andreas Groh ◽  
Ulrich Meyer ◽  
Martin Lasser ◽  
Christoph Dahle ◽  
Andreas Kvas ◽  
...  
Keyword(s):  
Time Series ◽  
Gravity Field ◽  
Regional Integration ◽  
Noise Level ◽  
Ice Sheets ◽  
Product Evaluation ◽  
Time Variable ◽  
Mass Change ◽  
Time Variable Gravity ◽  
Variable Gravity

<p align="justify">The International Combination Service for Time-variable Gravity Fields (COST-G), a product center of IAG’s International Gravity Field Service, aims on the combination of monthly global gravity field models. A consolidated gravity field series is derived from individual releases provided by different analysis centres (AC). COST-G’s Product Evaluation Group (PEG) assesses the combined gravity field series as well as the series provided by the ACs regarding their suitability for studying mass changes in the Earth’s subsystems (e.g. oceans, cryosphere, continental hydrosphere). Here we present results from the PEG’s assessment regarding mass changes of the ice sheets. Our study focuses on the COST-G RL01 series and the contributing releases AIUB RL02, GFZ RL06, ITSG-Grace2018, CSR RL06 and an unconstrained variant of GRGS RL05.</p> <p align="justify">Based on residual variations of the spherical harmonic (SH) coefficients with respect to a long-term and seasonal model, we quantify the noise level of the latest GRACE/GRACE-FO solutions series provided by COST-G and the contributing ACs. This assessment is performed both in the SH domain and in the space domain, focusing on the polar regions. A regional integration approach using tailored sensitivity kernels is applied to derive mass change time series for individual drainage basins and the entire ice sheets in Greenland (GIS) and Antarctica (AIS). A measure for the noise level of the different mass change time series is inferred from the residuals with respect to a climatology, corrected for remaining inter-annual mass changes. In this way we are able to assess if and to which extent mass change products for GIS and AIS can benefit from the combination of different solution series. Furthermore, we also quantify the signal content inherent to the individual mass change time series in terms of the seasonal signal and the linear trend (i.e. mass balance). Differences in the signal content between the releases are further investigated with respect to contributions from different parts of the SH spectrum. In addition to selected SH coefficients (e.g. C<sub>21</sub>, S<sub>21</sub>), we systematically attribute the differences to each SH degree and the corresponding SH orders.</p>

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

2011 ◽  
Vol 3 (1) ◽  
pp. 19-35 ◽  
Author(s):  
Th. Gruber ◽  
J. L. Bamber ◽  
M. F. P. Bierkens ◽  
H. Dobslaw ◽  
M. Murböck ◽  
...  
Keyword(s):  
Time Series ◽  
Gravity Field ◽  
Mass Distribution ◽  
Time Variable ◽  
Data Sets ◽  
Earth System ◽  
Time Variable Gravity ◽  
The Earth ◽  
Gravity Fields ◽  
Variable Gravity

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

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