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-Tellus mass grids described elsewhere in this website have had a reasonable GIA model of secular trends removed, in terms of mass changes expressed as cm of equivalent water thickness per year. Grids of that correction are provided here for users who wish to undo the correction and apply their own GIA 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 GIA model. We currently provide estimates based on the ICE5-G ice load history (Peltier, 2004), and the forward-model to estimate the contemporary GIA correction is that of A, G., J. Wahr, and S. Zhong, 2013. See also Chambers et al, 2010.

What is GIA?

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 far away from the centres of previous glaciation, the rates of relative sea level change as a consequence of ongoing glacial isostatic adjustment are not negligible. (e.g., Peltier, 1999).

How does GIA affect the Earth's Gravitational Fields?

The redistribution of lithospheric masses, adjusting from the glacial loading of the last ice age, produces long term ('secular') trends in the Earth's gravity field.

Is GIA an error in GRACE observations?

No, it is not an error. It is a signal of great scientific interest in itself. GRACE observations, in particular when combined with GPS measurements of vertical surface deformation, have provided new and more accurate estimates of GIA models, and have led to refinements of ice-load histories. For studies of contemporary surface mass changes, the GIA signal must be removed from the GRACE observations. This is particularly important for estimates of Antarctic ice mass changes. The GIA corrections add some uncertainty for surface mass trends over the GRACE period; a canonical (and rather heuristic) uncertainty range of 20% is often assumed for GIA models.

Which GIA Solution should be used to correct the GRACE data?

If you download the GRACE-Tellus gridded data, no additional GIA correction is needed. We have already removed a GIA correction from the data. We offer the GIA water equivalent grids for those who would like to add back the GIA model in order to subtract their preferred model.

Why are there different types of GIA grids?

GIA 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 GIA causes a physical deformation of the lithosphere, it can be expressed as trends in lithospheric height change (also in mm/yr). While the units are the same, the physical quantities they represent are quite different.

Is this the 'best' GIA model?

GIA is an area of active research. In fact, GRACE is providing additional constraints to estimate current GIA rates. The two main ingredients in any GIA model are (1) the ice (deglaciation) history, and (2) the viscosity profile of the mantle. The Geruo A et al (2013) model used here features a compressible Earth, uses the ICE-5G deglaciation history (Peltier, 2004) 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 versions (i.e., Paulson et al, 2007, which was available here until Jan 15, 2013), is that (1) the new results are for a compressible Earth, and (2) they use an elastic structure and a viscosity profile that varies continuously with radius throughout the mantle (they use exactly the same radial dependency that Peltier (2004) uses), rather than just a few homogeneous layers. As newer versions of the ice deglaciation history become available, especially for Antarctica, we plan to update these GIA model outputs.

What is the uncertainty of GIA?

The uncertainty is about +/- 20%. This 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 uncertainty.

Why are there different smoothing radii?

The results were smoothed using Gaussian smoothers with the same radii as our ocean and our land GRACE-Tellus grids, as well as an unfiltered version. These mass estimates are provided on a 1 x 1 degree grid. These GIA 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 GIA 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 reference the following two papers:

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.

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.


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.

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