Editor's commentsThe mass balance for the Antarctica and Greenland ice-sheets is critical for our understanding of the impact of global warming because of the impact they have on sea level. If the Antarctica and Greenland ice-sheets melted, sea level would rise 61.1 and 7.2 m, respectively. Calculating mass balance requires a combination of direct observation typically form satellites, and modeling physical processes, for example, the rebound of bedrock as the ice layer becomes thinner, and the migration of the grounding line as ice shelves become thicker or thinner. In this review, the authors discuss how different types of observation (altimetric, gravimetric, and mass budget) require different corrections and estimate the magnitude of the errors introduced by the uncertainties in the modeling.


Mass balance of ice-sheets

Mass balance is the net result of mass gains from snow accumulation and mass losses from melt water runoff and ice movement across the grounding line. Surface mass balance (SMB) is the net balance of mass gains and losses at the ice-sheet surface. It does not include ice loss by glaciers across the grounding line.

Interaction of an ice-sheet with the ocean
Interaction of an ice-sheet with the ocean

Marine ice sheets rest on bedrock that lies below sea level. These grounded ice sheets are fringed by floating ice shelves. The grounding line is where the ice mass starts to float by buoyancy. Accurate knowledge of the grounding line is important for a correct calculation of the mass budget of the ice sheets because ice from the grounded ice sheet is discharged across the grounding line into the floating ice shelves.

The grounding line migrates as a result of the local balance between the masses of ice and displaced ocean water. The grounding line advances if previously floating ice becomes thick enough to ground, or retreats if previously grounded ice becomes thin enough to float.

Techniques for measuring the mass balance of ice sheets

There are three satellite geodetic techniques altimetry, interferometry and gravimetry that are used to measure the mass balance of the Antarctic ice sheet (AIS) and the Greenland ice sheet (GIS).

  • Altimetry - volume change is measured with repeated altimetry observations and converting to mass (using estimates of the density of snow or ice lost or gained) and corrected for the glacial isostatic adjustment (GIA).

  • Gravimetry - mass change is directly estimated from very accurate measurements of changes in the Earth's gravity from the Gravity Recovery and Climate Experiment (GRACE) satellite system corrected for corrected for the glacial isostatic adjustment (GIA)

  • Mass budget - flux imbalance is calculated by using measurements of glacier flow and knowledge of glacier thickness and surface mass balance.

Modeling physical effects

Effects that need to be taken into account through physical modeling include

Glacial isostatic adjustment (GIA)

GIA is the response of the solid Earth, including associated changes in planetary gravity and rotation, to past redistributions of ice and ocean mass. The clearest observable effect of GIA is vertical rebound of the Earth’s surface. Models of GIA are necessary for correcting measurements of present-day ice-mass change.

Migration of the grounding line

The grounding line advances if previously floating ice becomes thick enough to ground, or retreats if previously grounded ice becomes thin enough to float. To simulate grounding-line migration, it is necessary to include (horizontal) stress gradients across the grounding zone.

Mass balance observations using these techniques have been sharpened recently by comparing the measurements from all three techniques for common spatial and temporal domains.

New GIA models have been tested and evaluated against Global Positioning System (GPS) data. The new models have led to a significant downwards revision in GIA, and hence downwards revisions of gravimetric and altimetric satellite estimates of Antarctic mass loss.

Modelled snowfall

Mass budget studies use modelled snowfall fields from atmospheric reanalysis data to estimate the mass input into glacier basins.

Comparison of mass-balance estimates

Estimates of ice mass change for Antarctica and Greenland
Estimates of ice mass change for Antarctica and Greenland

Each estimate of a temporally averaged rate of mass change is represented by a box whose width indicates the time period studied, and whose height indicates the error estimate. Single-epoch (snapshot) estimates of mass balance are represented by vertical error bars when error estimates are available, and are otherwise represented by asterisks. Line colour indicates mass assessment technique . Line type indicates data source. 2012 studies in b comprise IMBIE combined estimates (solid lines), and estimates by Sasgen and others and King and others11 (dashed lines), Zwally and others (dot-dashed lines), Harig and Simons and Ewert and others (dotted lines).

Recent mass-change estimates have been derived from three categories of techniques.

  • Volumetric techniques - These determine changes in the volume of the ice sheet via measurements of the height of the ice-sheet surface. They are based on radar altimetry or laser altimetry.

  • Space gravimetric - The Gravity Recovery and Climate Experiment (GRACE) satellite system measures changes in the Earth's gravity field very accurately, spatially and temporally.

  • Mass budget technique - Estimates the net ice accumulation on the ice sheets and the discharge of ice across the grounding line into the sea.

None of these provide a direct observation of the mass or change of mass of an ice-sheet. Each requires additional data, often involving modeling a physical process, to augment the primary observation. For example, GRACE and radar and laser altimetry studies require the effects of GIA-related vertical bedrock motion to be calculated accurately other wise this effect would be included in the estimated ice-thickness change. The GIA correction is only ~5% of the total elevation change measured by altimeters, so these altimetry measurements are not very sensitive to errors in the estimated GIA. GRACE data, however, is much more sensitive to GIA, which is related to the relative densities of bedrock and ice. This is not as large a problem for Greenland where the GIA correction is a much smaller fraction of the total mass change.

Mass budget estimates have a first-order sensitivity to errors in the modelled mean accumulation rate, while radar and laser altimetry estimates have only limited sensitivity to errors in fluctuations in the accumulation rate, because mass budget studies use modelled snowfall fields from atmospheric reanalysis data to estimate the mass input into glacier basins, whereas radar and laser altimetry studies use the same fields to estimate the effective density of measured volume changes.

Published estimates of rates of Greenland and Antarctic ice-sheet mass change obtained using the above methods show a large spread of values for the past two decades. Some of this spread is due to technical differences and some is due to different measurement periods. However, in the past year, estimates have begun to give a more coherent picture for both Antarctica and Greenland. For Greenland, the trend of increasing mass loss (due to both SMB decrease and ice-to-ocean discharge increase) is clear, while some of the large mass loss estimates for Antarctica have been discarded.

The Figure shows that the disparity of recent mass-balance results among different techniques is considerably reduced from that seen before. There tend to be systematic differences between the results from different techniques, with the mass budget method giving the most negative estimate for both ice sheets, laser altimetry the most positive, and GRACE in between.

An unweighted average of the estimates indicates that Antarctica, which was in a state of weakly negative balance in the 1990s, is now losing mass at a rate between −45 and −120 gigatonnes (Gt) per year, with large losses due to ice-to-ocean discharge in West Antarctica partially offset by SMB gains in East Antarctica.

For Greenland, an independent group of researchers compared laser altimetry, mass budget and GRACE estimates over the 2003–09 ICESat (Ice, Cloud, and land Elevation Satellite) period: the mass budget estimate gave the maximum loss rates at −260 ± 53  Gt  per year and GRACE the minimum, at −238 ± 29  Gt per year.

The new, reconciled GRACE estimates of whole Antarctic mass balance are now largely in agreement with one another, with spreads of 30–50  Gt per year between the largest and smallest 2003–08 rates. Previously published GRACE values show spreads around twice as large for similar time periods.

In the Antarctic Peninsula and West Antarctica, the estimates from laser altimetry and GRACE are in good agreement. For East Antarctica, a mass gain of +101 Gt  per year for 2003–08 has been proposed recently on the basis of laser altimetry, which is larger than the GRACE estimate of +35 Gt per year and near the upper end of the laser altimetry estimates.

Sea level rise

The table below summarizes the most recent estimates of contributions from different sources including AIS and GIS as reported in this article to SLR and compares their sum with the observed SLR from tide gauges and satellite altimetry.

Sea Level Rise (mm  per year)
Source of contributions1992/93 to 2008/112000/03 to 2009/11
GIS + AIS0.59 ± 0.200.82 ± 0.16
Glaciers and ice caps1.40 ± 0.16 0.71 ± 0.08
Ocean thermal expansion1.10 ± 0.431.11 ± 0.80
Terrestrial water storage (1993–2008)0.02 ± 0.26-
Sum of contributions3.11 ± 0.562.66 ± 0.86
Observed (1993–2008)3.22 ± 0.41-


Notes:
  • ‘Terrestrial water storage’ and ‘Observed’, only the values for the longer time span are given.
  • ‘Observed’ means observed SLR from tide gauges and satellite altimetry.
  • The two periods given here need to accommodate data from a variety of sources, and so flexible start and finish dates are given. For example, ‘1992/93 to 2008/11’ means that the data in the column below start in 1992 or 1993, and end somewhere between 2008 and 2011.
  • The apparent decrease in the contribution from the GICs between the two periods is mostly a result of the different methods used, rather than a result of a lower SMB observed during 2005.

Hanna et al, Nature, 498, 51–59 (06 June 2013)doi:10.1038/nature12238