Using Swarm For Gravity Field Determination – An Overview After 3+ Years In Orbit
1GFZ German Research Centre for Geosciences, Germany; 2Astronomical Institute, University of Bern, Switzerland
Besides its primary objective, observing the Earth’s magnetic field and the ionosphere, the Swarm Mission can also be regarded as a gravity field mission. Its payload, in particular GPS receivers and star trackers, allows to estimate the long-wavelength part of the Earth’s gravity field and its variations in time by means of high-low satellite-to-satellite tracking (hl-SST). This capability has gained even more relevance since the dedicated gravity field mission GRACE will soon reach the end of its nominal mission and the successor GRACE-FO will not be launched before December 2017. Thinking of ways to bridge the gap between GRACE and GRACE-FO in a best possible manner, the Swarm satellites will likely play an essential role.
At the Astronomical Institute of the University of Bern (AIUB), kinematic Swarm orbits are routinely processed and gravity field solutions are derived thereof. Their quality has significantly improved since the first results have been presented. Most prominently, first Swarm gravity fields were degraded by systematic errors along the Earth’s geomagnetic equator caused by ionospheric disturbances which affect the GPS observations. Initially, this degradation has been minimized by a crude GPS data screening procedure. However, recent investigations have shown that updated tracking loop settings of the GPS receivers onboard Swarm are also very beneficial for gravity field recovery allowing for a less aggressive GPS data screening or even making it obsolete. In this presentation, we give an overview of Swarm gravity field processing at AIUB and present the latest results of the (currently more than 3 years long) AIUB Swarm gravity field time-series. Special focus is set on the influence of the various tracking loop updates as well as on the GPS data screening. Concerning the latter, an optimal screening threshold depending on factors like ionospheric activity and GPS receiver settings is investigated.
Fully independent of AIUB, Swarm Level-1b GPS observations are directly used in a dynamic orbit and gravity field determination approach at the German Research Centre for Geosciences (GFZ). The sensitivity of the resulting gravity field solutions to the ionospheric disturbances as mentioned before is investigated and the GFZ solutions are compared to the ones from AIUB.
Estimation of Mass Variations in Greenland Using Leakage-Reduced GRACE Data
University of Calgary, Canada
In this study, the CSR Release 05 GRACE monthly models are used to estimate and monitor mass variations over Greenland. The data span the period from January 2003 to December 2014. The methodology for estimating mass variations focuses on the correction of leakage effects due to the implementation of smoothing filters in GRACE monthly solutions. The error due to leakage effects is reduced by taking into account the contribution of leaked masses in the extended area of Greenland. Using forward modeling techniques with tesseroid mass elements, the potential of the leakage-reduced masses is calculated.
After correcting the leakage effect, two approaches are used to derive mass variations over Greenland. For the first approach, global spherical harmonic analysis is implemented to derive the Stokes coefficients of the leakage-reduced potential, which are later converted into equivalent water height using Love numbers. The second approach uses inverse modeling and Tikhonov regularization of the leakage-reduced potential to directly derive surface density information over Greenland and convert it into equivalent water height. The second approach corresponds to a flat tesseroid mascon solution.
Two data sets of mass variations over Greenland are produced for the 11-year period of GRACE data. The first data set is in the form of Stokes coefficients, while the second data set is in the form of a spatial grid. Results indicate that the first method tends to overestimate the mass variations, providing amplified equivalent water height with 10% greater magnitude than the second method. The second method provides a smoother solution that agrees better with the results of the forward modeling and, therefore, is recommended.
Geoid Requirements for Height Systems and their Unification
Technical University of Munich, Germany
Tide gauge stations define the origin of height systems around the world and therefore are key points for height system unification as well as sea level determination. Because tide gauges are only able to measure the relative motion of the sea to a zero marker one needs on-site connection to the global geometric reference frame (e.g. GNSS or SAR) for the actual sea change rate. To get the absolute sea level or compare station heights globally, the equipotential surface of the tide gauges zero marker needs to be known as well.
With the results of GOCE it becomes possible to define a globally consistent geoid with centimeter accuracy and a spatial resolution of 80-100 km, but this still differs from a true equipotential surface due to omission and commission errors. The fine structure of the Earth gravity field (omission error), which mainly depends on the topography, can be taken into account with local geoid modelling using terrestrial and/or airborne gravity data. After an optimal combination of these measurements with the available satellite data it is possible to determine physical heights and make them compatible in an absolute sense.
This paper introduces the importance of the geoid on the definition of height systems and their unification. For the combination of satellite and terrestrial data, the impacts of omission and commission error are examined and evaluated. Furthermore, we investigate the influence of data density, distribution and accuracy from which we can define requirements for the data basis that is necessary for height systems unification.
Low-Degree Temporal Gravity Field Solution from SWARM Constellation of Satellites Using the Energy Balance Approach
1The Ohio State University, United States of America; 2Astronomical Institute, Czech Academy of Sciences, Czech Republic; 3Institute of Geodesy, Istanbul Technical University, Turkey; 4Delft Univ. of Technology, The Netherlands; 5School of Earth & Ocean Science, Cardiff Univ., Cardiff, UK; 6Dept. of Geomatics, National Cheng Kung Univ., Taiwan; 7European Space Agency, ESRIN, Italy; 8Institute of Geodesy & Geophysics, Chinese Academy of Sciences, Wuhan, China; 9Center for Space Research, Univ. of Texas at Austin, USA
ESA’s SWARM constellation of three near-polar satellites was launched on 22 November 2013, with the primary scientific objective to map the Earth’s magnetic field and its variations. Although not among its primary scientific objectives, the specific orbital formation geometry of the three identical SWARM accelerometer-equipped satellites allows recovery for more accurate low-degree temporal gravity field. Equipped with satellite laser ranging retro-reflectors, accelerometers and geodetic-quality GPS receivers, data from the SWARM satellites have been used to estimate low-degree temporal gravity field based on the acceleration, short-arc, and celestial mechanics approaches, with geopotential solutions complete to degree and order 15. Here we will use the improved formulation for the energy balance approach (EBA) to estimate the temporal gravity field using data from the SWARM satellites. The improved energy balance approach to generate in situ geopotential difference measurements using the GRACE KBR data has achieved the measurement accuracy by more than 3 orders of magnitude compared to previous studies. Specifically, we will: (1) assess the accuracy of SWARM temporal gravity field EBA solutions by comparing with solutions using other approaches and versus GRACE solutions using GPS and using KBR; (2) assess the impact on low-degree temporal gravity field EBA solutions using kinematic or dynamic SWARM GPS orbits; (3) evaluate low-degree temporal gravity solutions with or without accelerometer-corrections for data from individual SWARM satellite or from the combined constellation of SWARM satellites; (4) evaluate and confirm the maximum achievable degree and order of temporal gravity field model using data from the SWARM constellation of satellites, and (5) investigate the fidelity of the estimated SWARM second degree zonal geopotential coefficients and other approaches, as well as the solutions using other data, including SLR, other GPS, and GRACE KBR solutions.
Time Variable Gravity Field and Ocean Mass Change From SWARM Data
1University of Bonn, Germany; 2University of Hanover, Germany
Variations of ocean mass and bottom pressure changes are still not sufficiently understood on long time scales. The observation of these signals at the global scale has only become possible since the advent of the GRACE mission. Within the project “Consistent Ocean Mass Time Series from LEO Potential Field Missions” (CONTIM), we investigate how time series of gravity changes and ocean mass variations can be extended beyond and before the GRACE mission lifespan, making use of geodetic measurements of Low Earth Orbiters (LEO), and how these may be used for gap-filling of the GRACE time series.
Here, we use different kinematic orbits from SWARM, including orbits computed in this project, to estimate gravity fields of low spherical harmonic degree and order. We show how these fields compare to the more accurate GRACE solutions, and how the choice of non-conservative force modelling, solution parameterization, and other pre- and post-processing steps affect the solutions.
Continental Grids of Disturbing Gravity Tensor Components over North America
Slovak University of Technology, Slovak Republic
The GOCE (Gravity field and steady-state Ocean Circulation Explorer) mission resulted in 20 measurement cycles which more-or-less completely, except of the polar gaps and some short periods of missing data, covered the Earth. Most of the cycles were performed at the mean altitude of 254.9 km and the orbital resonance 979:61 but the last 4 cycles were gradually lowered down to 223.9 km and the orbital resonance 2311:143. GOCE Consortium and also several other scientific teams compiled the global grids of particular components of disturbing gravity tensor and pointed out that they contain additional high-frequency signal comparing to GOCE global gravity field models based on spherical harmonics. This contribution presents the new methodology of preparation of tile-like continental grids based on 2 dimensional local empirical covariance
functions. Our first practical experiences with this approach have been presented at Living Planet Symposium 2016 in Prague. Based on these experiences we produced the continental grid of disturbing gravity tensor components over the North-America at 2 different altitudes. The question of mutual connection and discrepancies between the sub-areas (tiles) and reliability of our results at different altitudes are discussed.
Impact Of Wiese-Approach In The Mitigation Of Ocean-Tide Aliasing Errors In Monthly GRACE Gravity Field Solutions
Leibniz University of Hannover, Germany
The aliasing of tidal and non-tidal geophysical signals with frequencies of less than one month into the monthly time-variable GRACE gravity field solutions is an often observed but only partially understood phenomenon. With the increasing sensor accuracy, the aliasing errors have been identified as the major stumbling blocks for the geophysical applications of satellite gravimetry data. While aliasing affects all the spherical harmonic coefcients, their impact on the higher harmonic degrees and orders can be reduced via parameter pre-elimination of low-degree sub-monthly (two-day) solutions often denoted as the Wiese approach. In this study, we specifically look at how the ocean-tide aliasing errors affect the sub-monthly and monthly solutions by using simulated data. Only the static gravity field and an ocean-tide model are used for simulating a GRACE-like mission scenario. This allows us to specify upper bounds for the ocean-tide aliasing errors, which we provide for the major diurnal and semi-diurnal ocean-tides. In addition to this, we investigate the possibility of the use of nuisance parameters to absorb the ocean-tide aliasing errors.
Combined Swarm/Sentinel Gravity Fields
1Astronomical Institute, University of Bern, Switzerland; 2GFZ German Research Centre for Geosciences, Potsdam, Germany
With their geodetic-grade on-board GPS receivers and star trackers the satellites of the Swarm mission can serve as probes for the long-wavelength part of the Earth gravity field by means of high-low satellite-to-satellite tracking (hl-SST). This is also true for the satellites of the ESA Sentinel mission, even if their slightly higher orbital altitude degrades their sensitivity to the high-frequency part of the gravity field. These gravity field solutions are of special interest in the view of a potential gap between the dedicated gravity missions GRACE and GRACE-FO.
In this contribution we present gravity fields based on the hl-SST of the three Swarm, as well as the Sentinel-1A, -2A, and -3A satellites. Based on different combination schemes we show that the Sentinel satellites are well suited to contribute to the longest-wavelength part of the Earth gravity field. We show that, unlike Swarm prior to the GPS tracking loop updates of May and October 2015, the Sentinel GPS data is not affected by systematic degradations along the geomagnetic equator. The addition of Sentinel data for the gravity field recovery has, therefore, the potential to improve the low degrees of the Swarm gravity fields. This can especially be interesting for times during which the omission of corrupted GPS data is mandatory for the mitigation of the systematic spurious features in the recovered Swarm gravity fields along the geomagnetic equator.