POST GLACIAL REBOUND DISCUSSION

WHAT IS OFFERED HERE

In order to compute mass trends from GRACE and interpret them as changes in the water content of hydrologic basins, or ocean bottom pressure, or ice sheet mass, one must remove the effect of Glacial Isostatic Adjustment (GIA or PGR) of the lithosphere and mantle.

The GRACE-derived grids described elsewhere in this website have had a reasonable PGR model of secular trends removed, in terms of mass changes expressed as cm of equivalent water thickness per year. Grids of that correction are offered here for users who wish to undo the correction and apply their own PGR model to the GRACE data. By 'popular demand' we also offer grids of the rates of lithospheric uplift and of geoid change with the same PGR model. The model used is that of A, G., J. Wahr, and S. Zhong, 2013. See also Chambers et al, 2010.

WHAT IS POST GLACIAL REBOUND?

Ice ages are periods of long-term reduction in the temperature of Earth's climate, resulting in an expansion of the continental and polar ice sheets and mountain glaciers (see Wikipedia article on ice ages for more details). They are related to but not fully explained by the three Milankovich cycles describing the eccentricity, precession (about the same as the Earth-Sun distance on June 21st), and tilt of the Earth relative to the ecliptic (http://www-istp.gsfc.nasa.gov/stargaze/Sprecess.htm). The most recent global deglaciation event, which marked the end of the most recent 100 kyr ice age cycle of the late Quaternary period began only 21,000 calendar years ago (Peltier, 2004), just before the Milankovitch cycle, and was essentially complete by 6000 years ago, but relative sea level have continued to change, essentially everywhere on the earth's surface, due to this cause. This continuing variation of land and sea levels exists as a consequence of the earth's delayed viscoelastic response to the redistribution of mass on its surface that accompanied deglaciation. In regions that were previously glaciated, such as Canada and Northwestern Europe, relative sea level continues to fall at a rate that is primarily determined by the ongoing post-glacial rebound of the crust and which may exceed 1 cm/yr (in the southeast Hudson Bay region of Canada, this rate is near 1.1 cm/yr). Even at sites that are well removed from the centres of glaciation, however, the rates of relative sea level change that exist as a consequence of ongoing glacial isostatic adjustment are nonnegligible. (e.g., Peltier, 1999).

HOW DOES PGR AFFECT THE EARTH GRAVITATIONAL FIELDS?

The redistribution of lithospheric masses, 'rebounding' from the glacial loading of the last ice age, produces long term ('secular') trends in the Earth's gravity field. These signals literally appear as trends when viewed over 5 to 10 year time periods.

IS PGR AN ERROR IN GRACE DATA?

No, it is not an error, it is a signal of great scientific interest in itself. But if one is studying a hydrologic basin, and wants to know whether or not an apparent trend of decreasing water content measured by GRACE indeed indicates that the basin is drying out, then it is necessary to remove some estimate of the PGR trend. This is precisely what, for example, Velicogna and Wahr (2006) had to do to estimate trends of Antarctica ice loss.

WHICH PGR SOLUTION SHOULD I REMOVE FROM THE DATA?

If you download the data from this site, NO PGR CORRECTION IS NEEDED. We have selected for you a reasonable one, and removed it from the data. We offer the PGR water equivalent grids for those who would like to add back the PGR model in order to substract their preferred model.

WHY ARE THERE THREE TYPES OF PGR GRIDS ?

PGR causes a change in the gravity field, so it can be expressed as a rate of change in the geoid, It can also be expressed as changes in the surface mass distribution that would cause the changes in gravity if the mass were concentrated at the surface, in mm/yr of equivalent water thickness, just as the GRACE grids. . Since PGR causes a physical deformation of the lithosphre, it can be expressed as trends in lithospheric height also in mm/yr. While the units are the same, the physical quantiities they represent is quite different.

IS THIS THE BEST PGR MODEL?

PGR is an area of active research. In fact, GRACE is providing additional constraints to retrieve PGR.

The two main ingredients in any PGR model are

the ice (deglaciation) history

the viscosity profile of the mantle

The A et al (2013) model here has a compressible Earth, and uses the ICE-5G deglaciation history and VM2 viscosity profile, and the same PREM-based elastic structure as Peltier (2004). The model includes polar wander feedback (computed as described in Mitrovica et al, 2005), uses the self-consistent sea level equation to distribute meltwater into the ocean, and includes degree-one terms when computing the uplift rate. (though the degree-one terms are zero for the geoid rate, since the computations are done in a center-of-mass frame). The difference between these results and the previous version presented here (by Paulson et al, 2007, which was available here until Jan 15, 2013), is that (1) these results are compressible, and (2) they use an elastic structure and a viscosity profile that vary continuously with radius throughout the mantle (they use exactly the same radial dependency that Peltier (2004) uses), rather than having them organized into a few homogeneous layers.

As newer versions of the deglaciation history become available, especially for Antarctica, we plan to update these GIA model outputs.

WHAT IS THE UNCERTAINTY IN THIS PGR MODELPGR MODEL?

The uncertainty is about +/- 20%.

The 20% value is somewhat ad-hoc, and comes from looking at results for various viscosity values and alternative deglaciation models for Antarctica and Greenland. This +/-20% probably over-estimates the uncertainty in northern Canada, where the deglaciation history is reasonably well-known; and it probably underestimates the uncertainty in Antarctica and Greenland, where the ice history is not as well-known. Plus, if you happen to be looking at a region where the model is close to zero because it is a transition region from large positive values to large negative values, then +/-20% of near-zero values is likely to underestimate the uncertaint

WHY ARE THERE THREE SMOOTHINGS

The results were smoothed using Gaussian smoothers with the same radii as our ocean and our land GRACE grids, as well as an unfiltered version. The mass estimates are provided on a 1 x 1 degree grid, centered at the half-degree.

The following three figures depict the GIA mass variability in terms of equivalent water thickness, using the 3 filters we offer, two of which are the same as used in our ocean grids and our land grids, respectively, and third one being the unfiltered sum (click on the figures to display them with a larger size). Images of the effect of GIA in terms of litospheric deformation or

These PGR rates in mm/yr of equivalent water HAVE ALREADY BEEN REMOVED (SUBTRACTED) from mass rates in mm/yr of equivalent water retrieved from GRACE to obtain corrected trends. If you are happy with the specific model described above, you need do nothing. If you prefer to use another model, then you must first add back the PGR model we applied with the same filter.

The data and browse images can be downloaded here.

ACKNOWLEDGEMENT and CITATION

When using these data, please acknowledge receiving the data from "http://grace.jpl.nasa.gov", and cite

A, G., J. Wahr, and S. Zhong (2013) "Computations of the viscoelastic response of a 3-D compressible Earth to surface loading: an application to Glacial Isostatic Adjustment in Antarctica and Canada", Geophys. J. Int., 192, 557–572, doi: 10.1093/gji/ggs030

REFERENCES:

Chambers, D. P., J. Wahr, M. E. Tamisiea, and R. S. Nerem (2010), Ocean mass from GRACE and glacial isostatic adjustment, J. Geophys. Res., 115, B11415, doi:10.1029/2010JB007530

Chambers, D. P., J. Wahr, M. E. Tamisiea, and R. S. Nerem (2012), Reply to comment by W. R. Peltier et al. on
“Ocean mass from GRACE and glacial isostatic adjustment,” J. Geophys. Res., 117, B11404, doi:doi:10.1029/2012JB009441

Dickey, J.O et al: Satellite Gravity and the Geosphere. National Research Council, 1997.

Dickey, J.O. et al, Recent Earth oblateness variations: Unraveling climate and postglacial rebound effects Science 298 (5600): 1975-1977, 2002.

Mitrovica, J.X., J. Wahr, I. Matsuyama, and A. Paulson. The rotational stability of an Ice Age Earth, Geophys. J. Int., 161, 491-506, 2005.

Paulson, A., S. Zhong, and J. Wahr. Inference of mantle viscosity from GRACE and relative sea level data, Geophys. J. Int. (2007) 171, 497–508. doi: 10.1111/j.1365-246X.2007.03556.x

Peltier, W.R., Ice-Age paleotopographie, Science 265 (5169): 195-201, 1994.

Peltier, W.R., Global sea level rise and glacial isostatic adjustment, Global and Planetary Change 20 (1999): 93-123, 1999.

Peltier, W.R., 2004. Global Glacial Isostasy and the Surface of the Ice-Age Earth: The ICE-5G(VM2) model and GRACE, Ann. Rev. Earth Planet. Sci., 32, 111-149.

Peltier, W. R., R. Drummond, and K. Roy (2012), Comment on “Ocean mass from GRACE and glacial isostatic
adjustment” by D. P. Chambers et al., J. Geophys. Res., 117, B11403, doi:10.1029/2011JB008967.

Tamisiea, ME; Mitrovica, JX; Davis, JL , 2007. GRACE gravity data constrain ancient ice geometries and continental dynamics over Laurentia . SCIENCE 316 881 - 883 .

Velicogna, I., and J. Wahr (2006), Measurements of Time-Variable Gravity Show Mass Loss in Antarctica. Science vol 311, pp 1754-1756