Using GPS and Gravity to Infer Ice Mass Changes in Greenland

There are strong indications that the global mean sea level rise is accelerating. The IPCC reports a mean sea level rise of ~0.17m (or 1.7 mm/year) during the previous century [1]. Recent satellite altimeter data indicate almost a doubling in this rate since 1993 (3.2 mm/year over 1993-2005 [2]) Roughly half the sea level rise is attributed to thermal expansion of ocean water. The rest of the sea-level rise is due to the addition of water to the oceans (from melting of mountain glaciers and polar ice). Model projections for the 21st century show a wide range of estimates varying from 0.22 m to 0.50 m. However some scientists believe these are conservative estimates. They predict a sea-level rise of 1 m for this century. A sea level rise of this magnitude will have significant consequences for coastal communities around the globe.
The mass balance and equilibrium state of an ice sheet is a complex function of external climate forcing and internal dynamical processes. During the last two decades scientists have witnessed large and rapid changes on the Greenland ice sheet. Large outlet glaciers thinned more rapidly than could be explained by increased summer melting alone. This observation therefore supports the theory that dynamical changes in ice flow have occurred [3]. Southeast Greenland, in particular, seemed to be affected by these dynamical changes. Indeed glacier flow there increased significantly and some glaciers doubled or nearly tripled in velocity: Kangerdlugssuaq glacier, a large outlet glacier in southeast Greenland, accelerated from 5 km yr-1 to 14 km yr¬-1 in only a few years [4], becoming perhaps the fastest glacier in the world. More recently, the sudden speed-up of glacier flow appears to have ceased [5]. Nonetheless, the sudden and near-synchronous dynamic changes of Greenland’s largest outlet glaciers suggest that the ice sheet is able to respond rapidly to environmental changes. Monitoring these changes and fluctuations has therefore become a key focus for climate scientists.
The most efficient way to assess contemporary ice mass changes on a large and remote ice sheet such as Greenland is to use remote sensing. Modern geodetic techniques that measure the mass balance of the Greenland Ice Sheet, such as time variable gravity (e.g. GRACE), must be corrected for postglacial rebound (PGR). PGR is the visco-elastic response of the earth to changes in ice loading caused by melting of the great ice sheets after the last glacial maximum.
The Geophysics Laboratory from the University of Luxembourg collaborates with researchers from the USA and Denmark in a project called GNET. The main goal of GNET is to determine PGR adjustments necessary to correct satellite measurements. As part of GNET more then 30 continuously operating GPS receivers have been placed at the edge of the Greenland Ice Sheet. The GPS antennas are placed on metal rods that are anchored firmly in the bedrock. The instruments can measure the vertical uplift rate of the earth’s crust very precisely. We analyze the GPS data and combine this with in-situ gravity measurements to separate changes in crustal uplift resulting from PGR and present day ice mass changes. The results of this study will contribute to better estimates of the current mass imbalance of the Greenland Ice Sheet and its contribution to global sea level rise.


GPS and Gravity in Luxembourg

In order to study trends and patterns of crustal motion in Luxembourg, detailed geodetic GPS measurements are carried out by the Administration du Cadastre et de la Topographie in collaboration with the University of Luxembourg. A network of continuous GPS stations is installed at 7 geologically stable sites across the country (see figure). The GPS stations record data continuously and data is processed at the Geophysics Laboratory. Using a wide network of reference stations in Europe the vertical movement of the Luxembourg sites is determined very accurate. We analyze the GPS data and combine this with absolute gravity measurements and rain gauge data to evaluate seasonal changes in ground height resulting from rainfall and groundwater variations.

Locations of permanent GPS stations in Luxembourg.


International Intercomparison of Absolute Gravimeters

In 2000, a laboratory dedicated to the intercomparison of absolute gravimeters was built within the Walferdange Underground Laboratory of Geodynamics with the power and space requirements that it is able to accommodate up 16 instruments operating simultaneously.

The WULG has the additional advantage of environmental stability (i.e. constant temperature and humidity within the lab), as well as being isolated from anthropogenic noise. International comparison of absolute gravimeter are organized every 4 years on alternate with the comparison organized at the Bureau International des Poids et Mesures in Sèvres, France. These comparisons are the only way to check that the gravimeters work properly.


Measurement of Newton’s Constant Using a Free-Fall Gradiometer

Although Newton’s Constant, G, is the second fundamental physical constant ever measured, it remains the constant with the highest uncertainty. While the velocity of light, c, which was first measured by Ole Romer in the 17th century, could be determined to a relative uncertainty of several parts in 10-9 in 1972 (Evenson, K.M., PRL, 1972)1), the value of G is still uncertain to 1.0x10-4 (CODATA, 2006). Other constants are even better determined, like i.e. the Rydberg constant, R, which is known to 6.6x10-12 (see figure).

The determination of G turned out to be very difficult. A reason is that the gravitational force is the weakest of the four fundamental forces. Compared to the electromagnetic force, the gravitational force is on the order of 10-36 times weaker. The measurement of G hence requires very sophisticated setups, to be able to distinguish the gravitational signal from other effects.
The most frequently used method for the measurement of G is the torsion balance. By means of such a setup G was determined in 1982 (Luther, G.G. & Towler, W.R., PRL, 1982) to a relative uncertainty of 75 ppm. This value was the basis for the CODATA-1986 recommended value of 6.672 59(85) x 10-11 m3 kg-1 s-2. Its relative uncertainty of 128 ppm (12.8 x 10-5) was assigned by the Committee on Data for Science and Technology after critical analysis. In the following years however, something unexpected happened. A group of the Physikalisch Technische Bundesanstalt (PTB, Germans national metrology institute) performed a measurement (Michaelis et al., Metrologia, 1995) with a lower uncertainty (83 ppm), but an absolute value which disagreed by 0.6 % from the CODATA-1986 recommended value. The setup however, was different from former ones. Instead of a torsion wire, the group used a mercury pool to support the test mass. The disagreement in the measured value gave rise to a further investigation of possible systematic errors. And indeed, Kuroda (Kuroda, PRL, 1995) showed that the spring constant of a torsion wire depends on the swing frequency, a fact which was neglected in torsion balance experiments so far.
The wide spread of the G values of later measurements opened the discussion to readjust the CODATA recommended value. As a consequence, the value recommended in 1998 was set to 6.673(10) x 10-11 m3 kg-1 s-2. Its relative uncertainty of 1.5 x 10-3 was by a factor 12 higher than the value recommended in 1986. This “readjustment” in the uncertainty was unique in the history of metrology.
This example shows that hidden systematic effects in a measurement principle can only be discovered when new measurement principles are developed and applied.

Recent measurements

During past years different methods were applied to determine Newton’s constant. In the following some of them are listed:
In 1999 for instance, a group of the University Wuppertal (Kleinevoß et al., Meas. Sci. Technol., 1999) determined G by measuring the influence of a field mass of 576 kg on the resonance frequency of a Fabry-Pérot resonator. The obtained relative uncertainty was 435 ppm.
In 1995 a group from the ETH Zürich (Arnet et al., Tech. Report, 241, ETH Zürich, 1995) measured the gravitational change due to the seasonal change of water in a storage lake by means of relative gravimeters. The relative uncertainty was 5700 ppm.
At the same University in Switzerland in 2002 (Schlamminger et al., PRL, 2002) an experiment was performed to determine G by means of a beam balance. To this purpose two field masses with a total mass of almost 14 tons were used to measure its attraction on two 1.1 kg test masses. The measurements were performed in a differential mode, so that most common mode effects were cancelled. A revised uncertainty budget published in 2006 (Schlamminger et al., PRD, 2006) assessed a relative uncertainty of 19 ppm. This is the second best measurement ever done.
In 2007 (Fixler et al., Science, 2007) and one year later (Lamporesi et al., PRL, 2008) the Gravitational Constant was measured by means of atomic interferometers. The test masses were clouds of atoms which were falling freely. Their acceleration due to external artificial field masses was extracted from the phase of the wavefunction of the atoms. While Fixler et al. used only one field mass, Lamporesi et al. employed two identical field masses to avoid common mode effects. Lamporesi et al. reached a relative uncertainty of 1800 ppm in comparison to Fixler et al. who reached 5200 ppm.
Another method was applied by Schwarz et al. (Schwarz et al., Science, 1998). The group used the commercial free fall absolute gravimeter FG-5, from MicroG-LaCoste. In comparison to the apparatus used by Fixler or Lamporesi, those free fall gravimeters employ macroscopic test masses (corner cube retro reflectors) rather than atoms. Schwarz employed, as Fixler did, only one field mass, which was alternately placed at two different heights. The differential acceleration on the test mass was measured and the value of G was obtained by comparing the theoretical calculated trajectory with the experimental measured one. The relative uncertainty obtained by Schwarz was 1410 ppm.
The today’s best measurement (lowest uncertainty) was performed by Gundlach and Merkowitz from the University of Washington (Gundlach & Merkowitz, PRL, 2000). They obtained a relative uncertainty of only 13.8 ppm. Although they used a torsion balance, they could avoid the high uncertainty due to the non-linearity of the spring constant of the torsion wire by applying a feed back loop. So the wire was not twisted at all. Furthermore they invented a new balance which is much less sensitive to the density distribution of the field masses. They figured out that by using a thin plate as a test mass the measurement can practically be made independent of the shape, mass distribution and the mass of the pendulum. All these factors formed the main uncertainty sources in former torsion balance experiments.
The following graph shows the values listed above. The red line gives the CODATA-2006 value. The error bars are the respective combined standard uncertainties.

It is interesting to see that the measurements with the smallest uncertainties (Gundlach & Merkowitz and Schlamminger et al.) agree very well within their standard error of the mean.

Our setup

Our group started just recently (end of 2008) on a project to measure Newton’s Constant, G. We will use a free-fall gradiometer with macroscopic test masses. This is essentially a combination of to free-fall gravimeters (like FG-5 from MicroG-LaCoste), however the reference mirror, which in the case of the gravimeter is vibration isolated (SuperSpring®), will be replaced by a second free falling test mass. Common mode effects, like ground vibrations are hence cancelled. It is basically a further development of the experiment made by Schwarz in 1998.
1) Today the speed of light is defined. Its exact value is 299 792 458 m s-1.