GraceTellus Monthly Mass Grids

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 relatively closely related to 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).This deglaciation started 21-22 kybp (thousand years before present), just before the Milankovitch cycle, as evidenced by records of the Fennoscandian Ice Sheet in the North Sea. It took about 12ky to complete, as evidenced by the last large pieces of the Laurentide Ice sheet (Canada and northern U.S.) but even by 6 kybp residual ice loss continued (E. Ivins, 2007, pers. comm.).

By the end of this last ice age, the extensive ice loads over Canada and Scandinavia (the ice was up to three kilometers thick) had caused deep depressions in the Earth’s surface (the crust sunk into the viscous mantle). When the glaciers retreated, the removal of the weight from the depressed land led to an uplift due to the buoyancy of crustal material relative to the mantle. The rate of this uplift is related to the viscosity profile of the mantle and the history of the ice retreat.The Earth’s surface continues to rise as a result of horizontal inflow of mass from the surrounding regions, because over long periods of time, the Earth behaves mores as a viscous fluid than an elastic solid. This process of readjustment is referred to as Post-Glacial Rebound (PGR) or Glacial Isostatic Adjustment (GIA). Due to the extreme viscosity of the mantle, it will take many thousands of years for the land to reach an equilibrium level.

A primary goal of PGR studies is to provide constraints on the viscosity profile of the mantle. The community that models PGR, however, has yet to reach a consensus on the results, particularly on how much the viscosity of the lower mantle (i.e., at depths below 670 km) increases.

HOW DOES PGR AFFECT SEA LEVEL RELATIVE TO NEARBY LAND?

“Beginning at LGM (Last Glacial Maximum) approximately 21,000 years ago, sea level rose on average over the ocean basins by an amount near 120 m due to the collapse of the large continental ice sheets that existed at that time (e.g., Peltier, 1994). Although this deglaciation event was essentially complete by 6000 years ago, sea level has continued to change, essentially everywhere on the earth’s surface, due to this cause. This continuing variation of sea level 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 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 Velicogna and Wahr (2005) had to do to estimate trends of Greenland ice loss.

WHICH PGR SOLUTION SHOULD I REMOVE FROM THE DATA?

PGR is an area of active research. In fact, GRACE will provide 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 "best" model we recommend is now based on Paulson et al (2007), with an uncertainty of +/- 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 uncertainty.

Our best model uses the global ICE-5G deglaciation model of Peltier (2004). It assumes an incompressible, self-gravitating Earth. The mantle is a Maxwell solid, and overlies an inviscid core. The viscosity and all other rheological parameters depend on radius, but they are independent of latitude and longitude (i.e. we are assuming a spherically symmetric Earth). We include the effects of a dynamic ocean response through the sea level equation, and we use the formulation of polar wander described by Mitrovica et al (2005). We include the effects of center-of-mass motion; although those effects contribute to our mass results only through the sea level equation, because we omit degree-one terms when computing the mass anomalies included here (see below). The mantle viscosity model is a 4-layered approximation to Peltier's (2004)
VM2 viscosity profile:
    - lithospheric thickness: 90 km
    - upper mantle viscosity: 0.9E21 Pa-sec
    - lower mantle viscosity: 3.6E21 Pa-sec
    - upper mantle/lower mantle boundary radius: 1170 km

The PGR Stokes coefficients were converted into estimates of the rate of change of surface mass, expressed in mm/yr of equivalent water thickness. Degree-one terms were omitted
when computing the mass, because they are not included in the GRACE solutions. The results were smoothed using a Gaussian averaging function of 300 km radius. The mass estimates are provided on a 1 x 1 degree grid, spaced a half-degree apart.

The following two figures illustrate the results (different color scale only); the third one illustrates the uncertainty. All panels are expressed in mm/yr of equivalent water thickness (click on the figures to display them with a larger size).

These PGR rates in mm/yr of equivalent water should be ADDED to mass rates in rates in mm/yr of equivalent water retrieved from GRACE to obtain corrected trends.

The data can be downloaded here

REFERENCES:

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, 2007. Inference of mantle viscosity from GRACE and relative sea level data, Geophys. J. Int. (in press).

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.

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 (2005), Greenland mass balance from GRACE, Geophys. Res. Lett., 32, L18505, doi:10.1029/2005GL023955.