Thwaites Glacier

Thwaites Glacier, Antarctica, is of particular concern to scientists. Here, warm water is pushed up onto the continental shelf, where it flows along the bottom until it reaches the floating ice shelf in front of Thwaites Glacier.

Thwaites Glacier today is rapidly losing mass in response to changing atmospheric and oceanic conditions.

Thwaites Glacier
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What is the global volume of land ice and how is it changing?

How much land ice is there in the World?

Most (99.5%) of the permanent ice volume in the world is locked up in ice sheets and glaciers. The Antarctic Ice Sheet is the largest store of frozen freshwater; it would raise sea levels by 57.9 m (its “sea level equivalent”, or SLE) on full melting (BedMachine). The Antarctic Ice Sheet covers 8.3% of the Earth’s land surface.

The Greenland Ice Sheet has a sea level equivalent ice volume of 7.42 m, and covers 1.2% of the global land surface (BedMachine).

Finally, glaciers and ice caps have a sea level equivalent ice volume of 0.32 m, covering just 0.5% of the global land surface (Figure 1). There is a nice illustration of this here.

Global glaciers (in yellow) and ice sheets (white). From IPCC AR5

Figure 1. Global land ice. Glaciers are highlighted in yellow, ice shelves in green, ice sheets in white.

Other sources of global ice

There are also small amounts of ice stored in the ground in permafrost regions, frozen lakes and rivers, seasonal snow cover, and so on.

Sea ice (frozen sea water) and ice shelves (frozen floating extensions of land ice; green on Figure 1 above) do not have a “sea level equivalent” of ice volume as they are already floating, so would not raise sea levels on full melting.

Measuring changes in global ice volume

Changes in global ice volume are often expressed in gigatonnes per year (yr-1). A gigatonne is 1,000,000,000 tonnes. 1 kmwater = 1 Gt water; 361.8 Gt of ice will raise global sea levels by 1 mm.

Greenland Ice Sheet

Mass balance of the Greenland Ice Sheet

The Greenland Ice Sheet has been losing mass for over 20 years. The most recent estimates suggest that the Greenland Ice Sheet from 2012 to 2016 had a negative mass balance, losing 247 ± 15 Gigatonnes (Gt) per year of ice volume, contributing 0.69 ± 0.04 mm per year to sea level rise[2]. The mass balance of Greenland has been increasingly negative since 1995, and it is now equivalent to the global contribution to sea level rise from glaciers and ice caps (Figure 2).

Figure 2. Cumulative ice mass loss from Greenland ice sheet 1992–2012[1] (from IPCC AR5).

Driven by changes in surface mass balance

These changes have largely been driven by changes in surface mass balance. While in Greenland 60% of mass loss is through ice discharge across the grounding line to the ocean (as icebergs or melting in the ocean), 40% of mass loss is from surface melt. Increases in surface melt (ablation) are largely responsible for the increasing melting of Greenland [3].

On June 15, 2016, the Advanced Land Imager (ALI) on NASA’s Earth Observing-1 satellite acquired a natural-color image of an area just inland from the coast of southwestern Greenland (120 kilometers southeast of Ilulisat and 500 kilometers north-northeast of Nuuk). From Wikimedia Commons

Figure 3. Surface meltwater on the Greenland Ice Sheet.

The estimates of Greenland Ice Sheet mass balance above include the peripheral glaciers surrounding the larger ice sheet. These peripheral glaciers account for around 15-20% of the total mass imbalance of the ice sheet[2, 4].

These increases in surface melt and mass losses from Greenland are due to recent increases in winter and summer air temperatures, with increases in the size of the ice sheet ablation area (the area with net melting over one year). This is associated with changes in the surface albedo, as ice has a lower albedo than white snow, exacerbating melt. Overall, this is leading to a lowering of the Greenland Ice Sheet surface elevation (Figure 4), and a decrease in ice volume.

Acceleration in outlet glaciers

Ice discharge from the major outlet glaciers of the Greenland Ice Sheet has also increased, with glaciers accelerating in western Greenland (e.g. Jakobshavn Isbrae, JI) (Figure 4). This faster ice flow leads to these outlet glaciers discharging more ice volume to the ocean as icebergs than is replaced by snow, so the outlet glaciers are also thinning, as can be seen by the red on the figure below.

Figure 4. Average rates of surface elevation change (dh/dt) through time (2010-2017) for the Greenland and Antarctic Ice Sheets[2].

Antarctic Ice Sheet

Antarctic Ice Sheet ice volume

The best estimates of Antarctic volume come from BEDMAP2 [5]. BEDMAP2 provides us with a detailed map of the base of the ice sheet, derived mostly from radar data. There are three ice sheets in Antarctica, each with their own unique characteristics. They are the larger East Antarctic Ice Sheet (EAIS), with an SLE of 53.3 m, the West Antarctic Ice Sheet (WAIS), with an SLE of 4.3 m, and the Antarctic Peninsula Ice Sheet (APIS) with an SLE of 0.2 m.

Surface elevation of the Greenland and Antarctic ice sheets (IPCC AR5)

Figure 5. BEDMAP2 (Fretwell et al., 2013; IPCC AR5).

Antarctica surface mass balance

It is very cold in Antarctica, with very limited surface melt [6]. There is abundant accumulation in the coastal parts of Antarctica, especially western West Antarctica and on the APIS.  The figure below shows where surface mass balance is highest; reds and yellows indicate far more snowfall than is lost through surface melting. It is cold and dry in the centre of the East Antarctic Ice Sheet, with very little snowfall or surface melt.

The average ice-sheet integrated surface mass balance of Antarctica is +2418 ± 181 Gt yr-1 [6].

Figure 6. Mean (1979–2010) surface mass balance [mm w.e. y−1]. [6]

Changes in Antarctic mass balance

Most mass loss in Antarctica is driven through ocean melting and iceberg calving[7, 8]. This ice discharge to the ocean through the grounding line is increasing as outlet ice streams are accelerating and grounding lines are retreating (see here). Thus increased ice flow in Antarctica accounts for almost all recent increases in mass losses.

The sea level rise contribution from Antarctica was 0.49 – 0.73 mm yr-1 from 2012-2017, mostly from the APIS and WAIS and due to acceleration of outlet glaciers in Amundsen Sea Embayment (e.g. Pine Island Glacier/Thwaites Glacier) (Figure 4; 7)[2].

Ice streams of Antarctica with Pine Island Glacier and Thwaites glacier highlighted.

Figure 7. Location of Pine Island and Thwaites Glacier in Antarctica, with ice velocity from Rignot et al. 2011

Including ice gained and lost through all mechanisms, the current mass balance of Antarctica from 1992 to 2017 was:

  • EAIS: +5 ± 46 Gt yr-1
  • WAIS: –94 ± 27 Gt yr-1
  • APIS: –20 ± 15 Gt yr-1
  • Total Antarctic Ice Sheet: -109 ± 56 Gt yr-1

Antarctic Ice Sheet mass balance changed from 2012 to 2017 to -219 ± 43 Gt yr-1 [8] . Mass losses from West Antarctica are driving most of the total mass losses from Antarctica, with the mass balance of East Antarctica showing negligible changes [8].

Shepherd et al. 2018

Figure 8. Mass changes in Antarctica (Shepherd et al. 2018).

Glaciers and Ice caps

Glacier extent

The amount of ice contained in global glaciers and ice caps is mapped by the Randolph Glacier Inventory[9, 10]. This inventory uses satellite imagery and a formalised methodology to organise researchers working on mapping glaciers and glacier change. The Randolph Glacier inventory estimates that there are 198,000 glaciers worldwide (Figure 9); however, this is an arbitrary number as it depends on:

  • Subdivision of glaciers and mapping of ice divides
  • Accuracy of the digital elevation model used
  • Minimum area threshold; it is hard to map glaciers smaller than 0.2 km2 and so this is usually set as a minimum area threshold. There could be up to 400,000 glaciers if small glacierettes are included (but they only account for 1.4% of glacierised area).

Bamber et al. 2018

Figure 9. Global glaciers (yellow) and their area (pie charts) [2, 10].

The RGI estimates a total glacierised area of: 726,000 km2

  • Subantarctic and Antarctic: 132,900 km2
  • Arctic Canada North: 104,900 km2
  • Asia: 62,606 km2
  • Low latitudes: 2346km2
  • 44 % is in Arctic regions, 18% in Antarctic & Subantarctic.

Global glacier ice volume

An estimate of global ice volume in glaciers and ice caps remains a “grand challenge” in glaciology; there are few glaciers with direct measurement by radar [11]. Bed topography and thus ice thickness is usually then estimated, either by volume-area scaling [12, 13], inversions of ice surface slope and velocity [14, 15], or from numerical modelling of ice flow [16].

Our best current estimate of global glacier ice volume is[16]:

  • 170 x 103 ± 21 x 103 km3 (moutain glaciers & ice caps outside Greenland & Antarctica)
  • = 0.43 ± 0.06 m SLE.

Glacier recession

Glaciers worldwide are receding. The key methods for mapping glacier change include:

  • Satellite images (1970s-present)[17]
  • Topographic maps (~1900 to present)
  • Geomorphological evidence of glacier extent (LIA/sig. advances)
  • Automated and manual mapping from satellite imagery
  • Limit realistically of mapping glaciers min. 0.2 km2

Mass loss can also be quantified from analysis of glacier surface elevation change (dh/dt)[18, 19] using digital elevation model differencing, satellite gravimetry or altimetry, and in-situ surface mass balance measurements [20].

The figure below shows the current best estimates of ice volumes lost from Antarctica and Greenland from 2012-2016 (taken from Bamber et al. 2018) and from glaciers around the world. Bamber et al. 2018 do not provide an individual assessment of ice volume lost from each area, so here I have plotted ice volumes lost from 2003-2009 from Gardner et al. 2013. Each region corresponds to those mapped out in Figure 9 and glacier outlines are from GLIMS and the Randalph Glacier Inventory.

Note that peripheral glaciers around Greenland and Antarctica are included in the assessment for the ice sheets (cf. Bamber et al. 2018). These glaciers are however changing rapidly, and indeed account for a large portion of the overall change.

World glaciers and ice sheets mass balance

Figure 10. Global glacier mass budgets from 2012-2016 by Bamber et al. 2018 (ice sheets) and 2003-2009 (glaciers; Garder et al. 2013).

These data, recently compiled by Bamber et al. 2018, give a global estimate of mass loss from glaciers of -227 ± 31 Gt yr-1 (2012-2016). This does not include losses from peripheral glaciers around Greenland and Antarctica, which are included in the ice sheet mass balance assessments.


Figure 11. Global glacier melt (IPCC AR5)[1]

This has led the World Glacier Monitoring Service (WGMS) to state: “rates of early 21st-century mass loss are without precedent on a global scale, at least for the time period observed and probably also for recorded history” [21].

This global melt is a challenge for society. While the sea level rise from glaciers is ultimately constrained by their small ice volume globally, they remain important as sources of freshwater [22]; their melting poses new hazards to mountain communities[23-25], and they remain important for local economies [26].


Global changes in land ice volume were recently summarised by Bamber et al. (2018):

Ice mass Total ice volume % Global land surface Volume change 2012-2016 Sea level contribution 2012-2016
EAIS 53.3 m SLE 8.3% -19 ± 20 Gt yr-1 0.05 ± 0.06 mm yr-1
WAIS & APIS 4.5 m SLE -172 ± 27 Gt yr-1 0.48 ± 0.08 mm yr-1
Greenland 7.36 m SLE 1.2% -247 ± 15 Gt yr-1 0.69 ± 0.04 mm yr-1
Global glaciers and ice caps* 0.43 m SLE

(113,915 to 191,879 Gt)

0.5% -227 ± 31 Gt yr-1 0.63 ± 0.08 mm yr-1
Total 12.5% -665 ± 48 Gt yr-1 1.85 ± 0.13 mm yr-1

*excl. glaciers peripheral to ice sheets

Accelerating mass loss from land ice

Mass loss is accelerating (Figure 12), with changes in ocean melt driving recession in Antarctica, increased ice discharge and surface melt driving changes in Greenland, and negative surface mass balances largely driving glacier recession worldwide. Losses from Greenland are now the most significant contributor to global sea level rise (this includes the peripheral glaciers around the ice sheet), recently overtaking glaciers as the largest contributor.

Bamber et al. 2018

Figure 12. Mass losses from glaciers and ice sheets, annually (Bamber et al. 2018)

Below is a nice summary of the key changes and processes from the IPCC AR4:

Figure 13. Summary of global changes in land ice, IPCC AR5 (2013).

Further reading


  1. Vaughan, D.G., et al., Observations: Cryosphere, in Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, T.F. Stocker, et al., Editors. 2013, Cambridge University Press: Cambridge, UK. p. 317-382.
  2. Bamber, J.L., et al., 2018, Environmental Research Letters.
  3. van den Broeke, M., et al., 2017, Current Climate Change Reports. 3, 345-356.
  4. Bolch T, et al., 2013, Geophys. Res. Lett. . 40, 875-881.
  5. Fretwell, L.O., et al., 2013, The Cryosphere. 7, 375-393.
  6. Lenaerts, J.T.M., et al., 2012, Geophysical Research Letters. 39, L04501.
  7. Pattyn, F., et al., 2018, Nature Climate Change.
  8. Shepherd, A., et al., 2018, Nature. 558, 219-222.
  9. Arendt, A., et al., Randolph Glacier Inventory [v2.0]: A Dataset of Global Glacier Outlines. 2012, Global Land Ice Measurements from Space: Boulder Colorado, USA.
  10. Pfeffer, W.T., et al., 2014, Journal of Glaciology. 60, 537.
  11. Gärtner-Roer, I., et al., 2014, Global and Planetary Change. 122, 330-344.
  12. Bahr, D.B., Estimation of glacier volume and volume change by scaling methods, in Encyclopedia of Snow, Ice and Glaciers. 2014, Springer. p. 278-280.
  13. Bahr, D.B., W.T. Pfeffer, and G. Kaser, 2014, Reviews of Geophysics.
  14. Carrivick, J.L., et al., 2018, Geografiska Annaler: Series A, Physical Geography, 1-23.
  15. Carrivick, J.L., et al., 2016, Global and Planetary Change. 146, 122-132.
  16. Huss, M. and D. Farinotti, 2012, Journal of Geophysical Research: Earth Surface. 117, F04010.
  17. Davies, B.J. and N.F. Glasser, 2012, Journal of Glaciology. 58, 1063-1084.
  18. Willis, M.J., et al., 2011, Remote Sensing of Environment. 117, 184-198.
  19. Willis, M.J., et al., 2012, Geophys. Res. Lett. 39, L17501.
  20. Gardner, A.S., et al., 2013, Science. 340, 852-857.
  21. Zemp, M., et al., 2015, Journal of Glaciology. 61, 745-762.
  22. Immerzeel WW, van Beek L P H, and B.M.F. P, 2010, Science. 328, 1382–85.
  23. Emmer, A., 2017, Quaternary Science Reviews. 177, 220-234.
  24. Emmer, A., Glacier Retreat and Glacial Lake Outburst Floods (GLOFs), in Oxford research Encyclopedias–Natural Hazard Science. 2017, Oxford University Press. p. 1-38.
  25. Harrison, S., et al., 2017.
  26. al, H.M.e., 2017 Earth’s Future 5 418-35.

Choosing the future of Antarctica

In a new article in the journal Nature, Stephen Rintoul and colleagues present two very different visions of Antarctica’s future, from the perspective of an observer looking back from 2070. In one vision, humanity continues to exploit Earth’s natural resources (such as fossils fuels) and does little to protect the environment, and in the other, there is a global movement towards conservation. The article shows how Antarctica will change over the next 50 years, should either of these two situations occur.

Post by Jacob Bendle. Continue reading

Calculating glacier ice volumes and sea level equivalents

How do we estimate the global volume of ice?

Sea level equivalents

The IPCC and other outlets frequently indicate how much sea levels will rise under given climate change scenarios (mm sea level rise) [1]. Other times, you might see that such and such volume of ice (km3) is equivalent to so many millimetres of sea level rise (sea level equivalent (SLE); the amount of sea level rise on full melting of the ice). But how are these calculations made?

Table 1. Sea level equivalent (SLE) from various land ice sources. From Morligheim et al. (2017; 2019) and Farinotti et al. 2019.

Ice on landSea level equivalent (m)
Antarctic Ice Sheet57.9
Greenland Ice Sheet7.42
Glaciers and ice caps0.32

Calculating the volume of ice


The first complexity is in calculating the volume of ice in the world. This is complex, as we often do not have a complete picture of the bed of the ice sheet or glacier. For Antarctica, BEDMAP2 and Bedmachine provides the most complete and up-to-date estimate of ice volume, and it is derived by combining thousands of radar and seismic measurements of ice thickness [2,3].

In fact, BEDMAP 2 is derived from 25 million measurements. Fretwell et al. 2013 estimated that the Antarctic Ice Sheet comprised 27 million km3 of ice, with a sea level equivalent of ~58 m. BedMachine estimates the sea level equivalent of Antarctica to be 57.9 ± 0.9 m [3].

BEDMAP 2, showing that the bedrock on which the West Antarctic Ice Sheet rests is well below sea level.
BEDMAP 2, showing that the bedrock on which the West Antarctic Ice Sheet rests is well below sea level. The Antarctic Ice Sheet has a sea level equivalent of 58.3 m (i.e., if all the ice in Antarctica melted, this is how much global sea levels would rise).


BedMachine V3 provides a recent estimate of ice volume for the Greenland Ice Sheet [4].

In Greenland, the bed topography is a primary control on ice flow, grounding line migration and calving, and subglacial drainage. Deep fjords allow penetration of warm Atlantic Water that undercuts Greenland’s tidewater glaciers that terminate in the ocean. This means that sectors of the Greeland Ice Sheet, like the Antarctic Ice Sheet, are also vulnerable to oceanic forcing.

The BedMachine V3 is a 150 m horizontal resolution bed topography and bathymetric map, which shows that the sea level potential of the Greenland Ice Sheet is 7.42 ± 0.05 m [4].

(a) BedMachine V3 bed topography, with areas below sea level in blue. (b) regions below sea level (light pink) that are connected to the ocean and maintain a depth below 200 m (dark pink). Morligheim et al., 2017

Global glaciers

For glaciers, ice thickness datasets are sparse [5].  While we have a good estimate of global glacier ice surface area [6] from satellite measurements, direct observations of glacier ice thickness are available for only around 3000 glaciers [5, 7, 8; Welty et al.]. These include radar measurements (both airbourne and from the ice surface) and seismic measurements. Unfortunately, these methods are time consuming and costly, and glaciers are often remote and difficult to access.

This figure shows the global distribution of glaciers. The diameter of the circle shows the area covered. The area covered by tidewater glaciers is shown in blue. The number refers to the RGI region. From the IPCC AR5 Working Group 113.
This figure shows the global distribution of glaciers. The diameter of the circle shows the area covered. The area covered by tidewater glaciers is shown in blue. The number refers to the RGI region. From the IPCC AR5 Working Group 113. The sea level equivalent of glaciers is important because glaciers are responding rapidly to climate change and are likely to be a large contributor to global sea level rise over the next century.

Yet glacier volume and ice thickness data are essential parameters required for understanding sea level rise, water resource management and assessment of future glacier changes [9]. Glaciers and small ice caps are also contributing rapidly to present-day sea level rise [9, 10]. Ice thickness data and bed topography are essential data required for numerical modelling of glaciers [11]. 

Other methods employed to calculate glacier volume include volume-area scaling [12-16], and calculations of ice thickness based on ice surface slope [16, 17] that assume a given basal shear stress, and numerical models based on principles of ice physics and mass conservation [18]. These methods, when correctly applied, do well against direct observations of ice thickness [11, 13, 18].

Farinotti et al. (2019) provided an updated estimate for ice thickness for all glaciers on Earth. They used an ensemble of five models to provide a consensus esimate for 215,000 glaciers outside of the Greenland and Antarctic ice sheets. They find a total volume of 158 ± 41 x103 km3.

Taking into account and discounting the ice below present-day sea level, this is equivalent to 0.32 ± 0.08 m of sea-level equivalent [19]. Roughly 15% of glacier ice is below sea level.

These data have been compiled and can be explored in the “World Glacier Explorer” app in OGGM-Edu.

World Glaciers Explorer, OGGM-edu

Calculating the mass of ice


The mass of ice is usually given in metric gigatonnes (Gt). 1 Gt = 109 tonnes (where 1 tonne = 1000 kg); a gigatonne is 1 billion tonnes.

A tonne of water occupies one cubic metre (a cube 1m x 1 m x 1m). A gigatonne (Gt) occupies one cubic kilometre of water (1km x 1km x 1km).

Densities of ice and water

Calculating the sea level equivalent for a given volume of ice requires some simple maths and a knowledge of the densities and properties of ice and sea water.  Ice volumes are usually given in km3.

Table 2. Densities of ice and water (at 1 atmospheric pressure and 4.3°C)

Density of glacier ice916.7 kg/m3or 0.9167 Gt/km3
Density of pure water1000 kg/m3or 1.000 Gt/km3
Density of sea water1027 kg/m3or 1.027 Gt/km3

We can calculate the mass of something if we know the volume and the density:

Density = Mass / Volume

Mass = Volume x Density

Volume = Mass / Density

See this website for more information on these equations.

Because ice and water are different densities, 1 km3 results in different masses. However, remember that 1 Gt of ice = 1 Gt of water! They take up different volumes but have the same mass. So, 1 Gt (whether ice or water) is equal to:

  • 1.091 km3 ice
  • 1.000 km3 pure water
  • 0.9737 km3 sea water

Converting a volume (km3 ) to a mass of ice (Gt)

We can convert a given volume of ice (in km3) to a mass of ice (in Gt) by using the following equation:

Mass of ice (Gt) = Volume of ice (km3) x Density of ice (Gt/km3)

If we have a calculated ice volume of 500 km3, then:

Mass of ice = 500 x 0.9167

The mass of ice here is 458.30 Gt. If it all melted, you would have 458.30 Gt of water.

Calculating sea level equivalent

Removing ice below sea level and floating ice

Calculating the sea level equivalent from a mass of ice involves firstly, removing all ice below sea level. This ice is already displacing water, and will not raise sea levels upon melting. This is explained in excellent detail here.

Floating ice (ice shelves, sea ice, floating ice tongues) are already floating and displacing water, and so these ice masses do not raise sea levels upon melting.

However, increased ice discharge, which delivers more icebergs to the ocean, will raise sea levels as ice that was not floating is delivered into the ocean.

The ice that is excluded from sea-level equivalent calculations is shown in the figure below. Firstly, the ice volume, ice thickness and bed topogrpahy must be known. Then, ice below sea level is excluded (it already displaces water) (2).

In (3) below, ice that is below hydrostatic equilibrium is excluded as it will not contribute to sea level rise (only ice that is above freeboard will contribute to sea level rise).

Finally, in (4) a firn air correction is applied; the snow and firn near the upper surface includes a lot of air. If you remove all the air, the surface of the ice sheet would be slightly lower.

Calculating the amount of ice that contributes to sea level rise. Only ice above hydrostatic equilibrium can contribute to sea level rise. Ice below sea level and ice that is floating is excluded from sea level equivalent calculations. The amount of air in firn and ice is also excluded.

Converting ice volume to sea level rise

To convert a mass of ice into the total amount global sea levels would rise if the ice all melted (i.e., the sea level equivalent), we need to know how much area the oceans cover. This is usually given as 3.618 x 108 km2. A 1 mm increase in global sea level requires 10-3 m3 (10-12 km3) of water for each square metre of the ocean surface, or 10-12 Gt of water.

We can calculate the volume of water required to raise global sea levels by 1 mm:

Volume = area x height

Area = 3.618 x 108 km2

Height = 10-6 km (1 mm)

Volume (km3) = (3.618 x 108 km2 ) x (10-6 km) = 3.618 x 102 km3 = 361.8 kmwater.

We can convert km3 of water to Gt of water as we did above; 1 kmwater = 1 Gt water.  In the same way, 1 Gt of ice = 1 kmwater. So, 361.8 Gt of ice will raise global sea levels by 1 mm. 361.8 Gt of ice is equivalent to 394.67 km3 ice.

Calculating sea-level equivalent

If we took our 458.30 Gt of ice (as calculated above), then we could calculate the global sea level equivalent by:

SLE (mm) = mass of ice (Gt) x (1 / 361.8)

SLE = 458.30 x (1 / 361.8)

SLE = 1.27 mm

However, we should note that some of the world’s glaciers have parts that are below sea level. This ice will not affect sea level if it melted. The volume of glacier ice below the surface of the ocean should therefore be subtracted from the total volume of glaciers and ice caps when calculating sea level equivalents [20].

Also remember that ice that is floating (like ice shelves, sea ice and icebergs) does not contribute to sea level rise upon melting. Only land ice above sea level will contribute to sea level rise.

Useful websites


  1. Vaughan, D.G., et al., Observations: cryosphere. Climate change, 2013: p. 317-382.
  2. Fretwell, L.O., et al., Bedmap2: improved ice bed, surface and thickness datasets for Antarctica. The Cryosphere, 2013. 7: p. 375-393.
  3. Morlighem, M., Rignot, E., Binder, T., Blankenship, D., Drews, R., Eagles, G., … Young, D. A. (2019). Deep glacial troughs and stabilizing ridges unveiled beneath the margins of the Antarctic ice sheet. Nature Geoscience.
  4. Morlighem, M., Williams, C. N., Rignot, E., An, L., Arndt, J. E., Bamber, J. L., … Zinglersen, K. B. (2017). BedMachine v3: Complete Bed Topography and Ocean Bathymetry Mapping of Greenland From Multibeam Echo Sounding Combined With Mass Conservation. Geophysical Research Letters, 44(21), 11,11-51,61.
  5. Gärtner-Roer, I., et al., A database of worldwide glacier thickness observations. Global and Planetary Change, 2014. 122(0): p. 330-344.
  6. Pfeffer, W.T., et al., The Randolph Glacier Inventory: a globally complete inventory of glaciers. Journal of Glaciology, 2014. 60(221): p. 537.
  7. Welty, E., Zemp, M., Navarro, F., Huss, M., Fürst, J. J., Gärtner-Roer, I., … Li, H. (2020). Worldwide version-controlled database of glacier thickness observations. Earth Syst. Sci. Data Discuss., 2020, 1–27.
  8. Andreassen, L., et al., Ice thickness measurements and volume estimates for glaciers in Norway. Journal of Glaciology, 2015. 61(228): p. 763-775.
  9. Hock, R., et al., Mountain glaciers and ice caps around Antarctica make a large sea-level rise contribution. Geophysical Research Letters, 2009. 36: p. L07501.
  10. Radic, V. and R. Hock, Regionally differentiated contribution of mountain glaciers and ice caps to future sea-level rise. Nature Geosci, 2011. 4(2): p. 91-94.
  11. Grinsted, A., An estimate of global glacier volume. The Cryosphere, 2013. 7(1): p. 141-151.
  12. Bahr, D.B., Estimation of glacier volume and volume change by scaling methods, in Encyclopedia of Snow, Ice and Glaciers. 2014, Springer. p. 278-280.
  13. Bahr, D.B., W.T. Pfeffer, and G. Kaser, A Review of Volume‐Area Scaling of Glaciers. Reviews of Geophysics, 2014.
  14. Bahr, D.B., W.T. Pfeffer, and G. Kaser, Glacier volume estimation as an ill-posed inversion. Journal of Glaciology, 2014. 60(223): p. 922-934.
  15. Radić, V. and R. Hock, Regional and global volumes of glaciers derived from statistical upscaling of glacier inventory data. Journal of Geophysical Research: Earth Surface, 2010. 115(F1): p. F01010.
  16. Marshall, S.J., et al., Glacier Water Resources on the Eastern Slopes of the Canadian Rocky Mountains. Canadian Water Resources Journal / Revue canadienne des ressources hydriques, 2011. 36(2): p. 109-134.
  17. Cook, A.J., et al., Glacier retreat on South Georgia and implications for the spread of rats. Antarctic Science, 2010. 22(03): p. 255-263.
  18. Farinotti, D., Brinkerhoff, D. J., Clarke, G. K. C., Fürst, J. J., Frey, H., Gantayat, P., … Andreassen, L. M. (2017). How accurate are estimates of glacier ice thickness? Results from ITMIX, the Ice Thickness Models Intercomparison eXperiment. The Cryosphere, 11(2), 949–970.
  19. Farinotti, D., Huss, M., Fürst, J. J., Landmann, J., Machguth, H., Maussion, F., & Pandit, A. (2019). A consensus estimate for the ice thickness distribution of all glaciers on Earth. Nature Geoscience.
  20. Haeberli, W. and A. Linsbauer, Brief communication” Global glacier volumes and sea level–small but systematic effects of ice below the surface of the ocean and of new local lakes on land”. The Cryosphere, 2013. 7(3): p. 817-821.

Antarctic Ice Sheet mass balance

How does mass balance vary over Antarctica? | Surface mass balance in the past | Surface mass balance in the future | References | Comments |

How does mass balance vary over Antarctica?

Is Antarctica currently losing or gaining mass? Will this massive ice sheet grow or shrink in the future? And what effect will increased snowfall have over coming centuries? In order to answer these questions, we must analyse the surface mass balance of the Antarctic Ice Sheet.

First, let’s introduce some definitions.

  • Mass balance is the sum of all processes of accumulation and ablation, including those at the ice surface and at the bed, but does not include mass changes due to ice flow1. See this page (Introduction to Glacier Mass Balance) for more information.
  • Surface mass balance is the net balance between the processes of accumulation and ablation on a glacier’s surface (it does not include dynamic mass loss and basal melting)1.
  • Climatic mass balance includes surface mass balance and internal accumulation1.
  • Ice dynamical changes may include changes to ice discharge and acceleration or deceleration of flow, which can lead to dynamic thinning or thickening, ice-shelf collapse, marine ice sheet instability, and other factors resulting in changes in the glacier beyond surface mass balance.

Surface mass balance

Surface mass balance varies extensively over Antarctica. The Antarctic Peninsula has the highest accumulation rates (up to 1500 mm per year), followed by coastal West Antarctica, which has around 1000 mm accumulation per year2. Compare this with the interior of the Antarctic Ice Sheet, where it is dry and cold; here accumulation can be less than 25 mm per year.

Surface mass balance of the Antarctic and Greenland ice sheets. From Van den Broeke et al., 2011.

Surface mass balance of the Antarctic and Greenland ice sheets. From Van den Broeke et al., 2011.

Surface mass balance estimates are constantly improving as scientists gain better understandings of glacio-isostatic adjustment, improve glacier modelling techniques and gain access to higher resolution satellite datasets over longer timescales3. Surface mass balance estimates therefore tend to improve over time, but are subject to large uncertainties4. For this reason, there tends to be differences between the results of different techniques used to measure surface mass balance. Surface mass balance of the grounded Antarctic Ice Sheet is currently estimated at ~2000 gigatonnes per year2, 5, 6, and it is subject to large variability across the ice sheet and through time.

Total mass balance

The figure below shows some recent estimates for total mass balance (including basal processes) over Antarctica7. Each box is bounded by the time interval studied and the uncertainties identified.

Summary of estimates of rates of ice mass change for Antarctica and Greenland. Reprinted by permission from Macmillan Publishers Ltd: [Nature] (Hanna et al., 2013) copyright (2013)

Summary of estimates of rates of ice mass change for Antarctica and Greenland. Reprinted by permission from Macmillan Publishers Ltd: [Nature] (Hanna et al., 2013) copyright (2013)

Overall, a recent estimate puts Antarctic net mass balance at -71 ± 53 gigatonnes per year8, so just negative over the 19 year survey. Mass losses are increasing in West Antarctica and the Antarctic Peninsula. The mass balance of West Antarctica is dominated by dynamic losses from the Amundsen Sea sector, and dynamic gains from the Kamb Ice Stream8. From the period 2005-2010, Shepherd et al. (2012) estimate the mass balance of the entire Antarctic Ice Sheet to be -81 ± 37 gigatonnes per year8.

An unweighted average of recent estimates suggests that Antarctica moved from a weakly negative mass balance in the 1990s to a faster rate of mass loss at a rate of between -45 and -120 gigatonnes per year7. Larger dynamic losses in West Antarctica are being partially offset by increases in accumulation over East Antarctica.

The total mass balance of Antarctica was recently updated here.

Accelerating total mass losses from Antarctica

The GRACE (Gravity Recovery and Climate Experiment) satellite gravity mission shows that total mass loss in Antarctica is accelerating over time. They found that total mass loss increased by 26 ± 14 gigatonnes per year from 2002 to 20099. Rignot et al. (2011) found a smaller acceleration of 14.5±2 gigatonnes per year from 1993-20115, but this change is still three times larger than that found for mountain glaciers and ice caps.

Surface mass balance of Antarctica in the past

How has the surface mass balance of Antarctica changed in the past? Firn and ice-core records can hold the key to providing a longer perspective on surface mass balance than is currently available from satellite records. Frezzotti et al. used 67  of these cores to reconstruct surface mass balance over the last 800 years. They found that current surface mass balance is not exceptionally high compared with the last 800 years10. Periods of high accumulation occurred in the past, in the 1370s and 1610s AD, but there has been an increase of 10% in snow accumulation in some coastal regions since 1850 – a fact that agrees with independent work on the Antarctic Peninsula11.

Surface mass balance of Antarctica in the future

Climate models predict that, for a generally warmer climate, snowfall will increase over Antarctica7. Surface melt will increase around the more northerly Antarctic Peninsula, and dynamic changes such as increased ice discharge12, ice-shelf collapse and grounding line recession13, and marine ice-sheet instability are likely to offset any increases in precipitation7. However, if no dynamical ice response is assumed, then increases in snowfall over the entire continent of 6-16% to 2100 AD and 8-25% to 2200 AD are likely to result in a drop in sea level of 20-43 mm in 2100 and 73-163 in 2200, compared with today14. However, it is more likely that the Greenland and Antarctic ice sheets will lose mass over the next century, with rapid coastal changes, increases in ice flow and ice-shelf collapse all likely4. As a result of these complex expected changes, there are a number of uncertainties in past, present and future ice sheet mass balance.

Further reading


1.            Cogley, J.G., Hock, R., Rasmussen, B., Arendt, A., Bauder, A., Braithwaite, R.J., Jansson, P., Kaser, G., Moller, M., Nicholson, L., & Zemp, M. Glossary of Glacier Mass Balance and related terms. Paris: IHP-VII Technical Documents in Hydrology No. 86, IACS Contribution No. 2, UNESCO-IHP. 124 (2011).

2.            Lenaerts, J.T.M., van den Broeke, M.R., van de Berg, W.J., van Meijgaard, E., & Kuipers Munneke, P. A new, high-resolution surface mass balance map of Antarctica (1979–2010) based on regional atmospheric climate modeling. Geophysical Research Letters. 39, L04501 (2012).

3.            Van den Broeke, M., Bamber, J., Lenaerts, J., & Rignot, E. Ice Sheets and Sea Level: Thinking Outside the Box. Surveys in Geophysics. 32, 495-505 (2011).

4.            Alley, R.B., Spencer, M.K., & Anandakrishnan, S. Ice-sheet mass balance: assessment, attribution and prognosis. Annals of Glaciology. 46, 1-7 (2007).

5.            Rignot, E., Velicogna, I., Van den Broeke, M., Monaghan, A., & Lenaerts, J. Acceleration of the contribution of the Greenland and Antarctic ice sheets to sea level rise. Geophysical Research Letters. 38, (2011).

6.    Agosta, C., Favier, V., Krinner, G., Gallée, H., Fettweis, X., & Genthon, C. High-resolution modelling of the Antarctic surface mass balance, application for the twentieth, twenty first and twenty second centuries. Climate Dynamics. 41, 3247-3260 (2013).

7.            Hanna, E., Navarro, F.J., Pattyn, F., Domingues, C.M., Fettweis, X., Ivins, E.R., Nicholls, R.J., Ritz, C., Smith, B., Tulaczyk, S., Whitehouse, P.L., & Zwally, H.J. Ice-sheet mass balance and climate change. Nature. 498, 51-59 (2013).

8.            Shepherd, A., Ivins, E.R., A, G., Barletta, V.R., Bentley, M.J., Bettadpur, S., Briggs, K.H., Bromwich, D.H., Forsberg, R., Galin, N., Horwath, M., Jacobs, S., Joughin, I., King, M.A., Lenaerts, J.T.M., Li, J., Ligtenberg, S.R.M., Luckman, A., Luthcke, S.B., McMillan, M., Meister, R., Milne, G., Mouginot, J., Muir, A., Nicolas, J.P., Paden, J., Payne, A.J., Pritchard, H., Rignot, E., Rott, H., Sørensen, L.S., Scambos, T.A., Scheuchl, B., Schrama, E.J.O., Smith, B., Sundal, A.V., van Angelen, J.H., van de Berg, W.J., van den Broeke, M.R., Vaughan, D.G., Velicogna, I., Wahr, J., Whitehouse, P.L., Wingham, D.J., Yi, D., Young, D., & Zwally, H.J. A Reconciled Estimate of Ice-Sheet Mass Balance. Science. 338, 1183-1189 (2012).

9.            Velicogna, I. Increasing rates of ice mass loss from the Greenland and Antarctic ice sheets revealed by GRACE. Geophysical Research Letters. 36, (2009).

10.            Frezzotti, M., Scarchilli, C., Becagli, S., Proposito, M., & Urbini, S. A synthesis of the Antarctic surface mass balance during the last 800 yr. The Cryosphere. 7, 303-319 (2013).

11.            Thomas, E.R., Marshall, G.J., & McConnell, J.R. A doubling in snow accumulation in the western Antarctic Peninsula since 1850. Geophysical Research Letters. 35, L01706 (2008).

12.          Winkelmann, R., Levermann, A., Martin, M.A., & Frieler, K. Increased future ice discharge from Antarctica owing to higher snowfall. Nature. 492, 239-243 (2012).

13.          Barrand, N.E., Hindmarsh, R.C.A., Arthern, R., Williams, C.R., Mouginot, J., Scheuchl, B., Rignot, E., Ligtenberg, S.R.M., van den Broeke, M.R., Edwards, T.L., Cook, A.J., & Simonsen, S.B. Computing the volume response of the Antarctic Peninsula Ice Sheet to warming scenarios to 2200. Journal of Glaciology. 59, 397-409 (2013).

14.          Ligtenberg, S.R.M., Berg, W.J., Broeke, M.R., Rae, J.G.L., & Meijgaard, E. Future surface mass balance of the Antarctic ice sheet and its influence on sea level change, simulated by a regional atmospheric climate model. Climate Dynamics. 41, 867-884 (2013).

Sea level rise

Sea level rise is probably one of the biggest threats imposed on us by climate change. Sea level rise is the reason why we study glacier recession. Our current best estimates suggest that we should expect around 60 cm of sea level rise by 2100 AD. Just a small increase in sea level is enough to severely increase the damage done by storm surges. It will worsen coastal erosion, particularly in eastern England, flood low-lying areas in Britain and mean that the Thames Barrier will need to be replaced.

This small increase in sea level rise will come mainly from thermal expansion of the ocean and from contributions from small glaciers and ice caps. There is likely to be only a small contribution from the Antarctic and Greenland ice sheets over the coming century. However, the collapse of the West Antarctic Ice Sheet could rapidly increase sea levels by around three metres.

We need to be able to understand how much sea level will rise over coming centuries. If we know how much sea levels will rise, we will be able to put in place adaptation and mitigation strategies that will avoid the worst of the impacts. This is the focus of most of our research; understanding the relationship between glaciers and climate, and investigating past rates and magnitudes of change. We want to understand the processes by which glaciers, ice caps and ice sheets melt and contribute to sea level rise, and we are always trying to reduce uncertainty in future projections.

This section contains many articles about sea level rise. For more information and for recently published papers, see the blog:

Dealing with uncertainty: predicting future sea level rise

How much sea level rise? | Climate change and rising sea levels | The West Antarctic Ice Sheet | How much sea level rise from Antarctica? | Comments |

How much sea level rise?

A 5 m sea level rise would inundate many coastal cities in Europe. Source: CReSIS

A 5 m sea level rise would inundate many coastal cities in Europe. Source: CReSIS

How much will global sea levels rise in our lifetime, or in the lifetime of our children? We need to know the answer to this question if we are to mitigate effectively against sea level rise, particularly when it’s associated with storm surges, hurricanes and extreme weather events, which test our already strained flood defence schemes. However, uncertainty in the response of polar ice sheets to climate change limits our ability to project sea level rise into the future.

Climate change and rising sea levels

Figure 5. Climate change over the last 11,500 years from multiple proxies. From Marcott et al., 2013

Figure 5. Climate change over the last 11,500 years from multiple proxies. From Marcott et al., 2013. Used with permission from the author.

During the Twentieth Century, the Earth warmed by 0.6 ± 0.2°C. Since 1900 AD, a long-term cooling trend that began around 5000 years ago and culminated in the Little Ice Age in the 1750s (with its ice fairs on the frozen River Thames) has been reversed. Global sea level is now rising at a rate of 3.1 mm per year, which will lead to a total rise of 18-59 cm by 2100 AD. Most of this rise is caused by thermal expansion of the ocean and the melting of small ice caps and glaciers. However, the large polar ice sheets have the potential to contribute to sea level rise above and beyond this modest rate. The West Antarctic Ice Sheet alone could raise global sea levels by 3.3 m if it all melted. But how likely is this to happen, and how quickly?

The West Antarctic Ice Sheet

An unstable marine ice sheet

BEDMAP 2, showing that the bedrock on which the West Antarctic Ice Sheet rests is well below sea level.

BEDMAP 2, showing that the bedrock on which the West Antarctic Ice Sheet rests is well below sea level.

The West Antarctic Ice Sheet is currently warming particularly rapidly, and this warming is associated with increased ocean temperatures and changes to atmospheric circulation, which drives increased upwelling of deep, relatively warm oceanic water onto the continental shelf.

The West Antarctic Ice Sheet is drained by fast-flowing, marine-terminating ice streams and it is surrounded by floating ice shelves. Much of the rock on which the ice sheet rests is below current sea level, and the bedrock slopes downwards towards the centre of the ice sheet. Because of this, the ice sheet is unstable, because as water gets deeper, more icebergs are calved, increasing ice discharge.

Ice streams in West Antarctica are also melted rapidly at their base by those warming ocean waters, leading to melting, recession into deeper water and more melting again. The West Antarctic Ice Sheet may therefore be inherently susceptible to ever faster glacier recession, and could pass tipping points that mean rapid sea level rise irrevocably occurs. Pine Island Glacier, one of the fastest ice streams in the world, is already thinning and receding, making it susceptible to rapid recession in ever deeper water.

Ice streams of Antarctica with Pine Island Glacier and Thwaites glacier highlighted.

Ice streams of Antarctica with Pine Island Glacier and Thwaites glacier highlighted.

Thinning and retreating ice shelves

Warm ocean waters are melting a cavity beneath Pine Island Glacier

Warm ocean waters are melting a cavity beneath Pine Island Glacier

Ice shelves around the West Antarctic Ice Sheet are thinning as they are melted from below by upwelling warm ocean currents. Ice shelves have been known to disintegrate rapidly over the course of just one summer.

Ice shelves ‘buttress’ or hold back glaciers on the interior of the continent. Rapid removal of bounding ice shelves, such as those around Pine Island Glacier, could therefore result in increased thinning and recession of grounded glaciers, initiating a positive-feedback loop that could be catastrophic.

Increased snowfall

It doesn’t end there. Although there may be more snow over the Antarctic Ice Sheet under a warmer climate, this too could lead to changes in glacier dynamics. Increased snow will steepen surface gradients near the edge of the Antarctic Ice Sheet. Glaciers will flow faster, discharging more icebergs into the ocean, negating any impact the increased snowfall would have in mitigating sea level rise.

Increased meltwater from melting ice shelves also produces a layer of cold, fresh water on the ocean’s surface, which easily freezes, increasing winter sea ice extent. Sea surface temperatures are directly related to snowfall, so cooler sea surface temperatures and more sea ice may actually decrease snowfall over Antarctica.

How much sea level rise from Antarctica?

Sea level rise to 2100. Modified from the IPCC sea level rise estimates (from Wikimedia Commons) and using estimates from Bamber and Aspinall 2013, assuming a uniform rate of sea level rise.

Sea level rise to 2100. Modified from the IPCC sea level rise estimates (from Wikimedia Commons) and using estimates from Bamber and Aspinall 2013, assuming a uniform rate of sea level rise.

Because of these factors, the West Antarctic Ice Sheet could rapidly and catastrophically melt, resulting in as much as 3.3 m of sea level rise within 500 years.

Rates such as these are common in the geological record, but these dynamic behaviours are too difficult for even our most complex computer models to solve.

A new paper in the journal Nature Climate Change by Bamber and Aspinall has attempted to untangle this thorny problem. They pooled different assessments by numerous experts in order to reach a consensus on likely sea level rise by AD 2100.

Bamber and Aspinall used a mid-range carbon emissions scenario, with an increase of 3.5°C above pre-industrial temperatures. They found that the average rate of sea level rise from just the Greenland and Antarctic ice sheets agreed upon by these experts was 5.4 mm per year by 2100 AD.

Combined with melting glaciers and ice caps and thermal expansion of the ocean, Bamber and Aspinall gave a range of 33-132 cm, with 62 cm the average estimate, for sea level rise by 2100. It’s still uncertain, but it’s the best estimate we have for now.

Sea level rise over the next 2000 years

A new paper by Levermann et al. in PNAS uses the record of past rates of sea level rise from palaeo archives and numerical computer models to understand how much sea level rise we can expect per degree of warming in the future. These data suggest that we can expect a global sea level rise of 2.3 m per 1°C of warming within the next 2000 years: well within societal timeframes. A 2°C of warming would result in a global sea level rise of 4.8 m within 2000 years. This would inundate many coastal cities in Europe alone, and cause untold economic and societal damage.

Continue reading

Postglacial rebound

This page was kindly contributed by Dr Pippa Whitehouse from Durham University.

How does the Earth recover after an Ice Age? | Ice sheet deglaciation | Sea level change | Solid Earth Shape | Modern ice sheet melt | Further reading | References | Comments |

How does the Earth recover after an Ice Age?

Around 20,000 years ago vast tracts of the Earth’s surface, including much of northern Europe and North America, were covered in ice. In fact, due to the volume of water that was tied up in the ice sheets, the sea level at the time was, on average, around 125m lower than it is today [1]; the UK was joined to Europe by dry land, and you could walk from Alaska to Russia across the Bering Straits.

Figure 1a. Solid Earth subsidence and rebound due to ice loading. Courtesy of Tom James at Natural Resources Canada

But it wasn’t just sea level that was different; the enormous mass of ice that was sitting on the continents, over 3 km thick in places [2], squashed the land downwards so that the whole shape of the Earth was altered. The land beneath the thickest ice was pushed down by up to half a kilometre, while the land outside the ice sheets bulged upwards by several hundred metres (Figure1a). The reason for this is that the Earth’s mantle – the 2900 km-thick layer within the Earth which lies beneath the rocky layer that we stand on – behaves like a viscous fluid. Imagine what would happen if you managed to fill a lilo with really thick honey and then stood on it: For a while nothing would happen, then, slowly, you’d start sinking as the honey beneath your feet flowed outwards because it couldn’t support your weight. However, since you’ve closed the valve on the lilo, that honey can’t escape completely, and instead it forms a bulge around your feet. This is exactly what happens when a large ice sheet grows on the surface of the Earth.

Ice sheet deglaciation

Figure 1b. Solid Earth subsidence and rebound due to ice loading. Courtesy of Tom James at Natural Resources Canada

Around 19,000 years ago, the ice sheets of North America and northern Europe began to melt, and the processes described above were reversed (Figure 1b). The meltwater from the ice sheets flowed into the oceans, raising the sea level once again, and the land which had been beneath the ice began to rebound upwards, a process known as ‘postglacial rebound’. And, just as the lilo wouldn’t immediately return to its original shape once you stepped off it, the Earth also returns to its original shape very slowly. In fact, postglacial rebound continues today, albeit at an exponentially-decaying rate. The land beneath the former ice sheets, e.g. around Hudson Bay and central Scandinavia, is still rising by over a centimetre a year [3, 4], while those regions which had bulged upwards around the ice sheet are subsiding – regions such as the Baltic states and much of the eastern seaboard of North America (Figure 2).

Sea level change

Figure 2: Rates of present-day postglacial rebound. Courtesy of Glenn Milne. From the Encyclopedia of Quaternary Science (2nd Edition).

Due to this ongoing ‘relaxation’ of the Earth, when we try to measure how quickly sea-level is changing, the answer we get depends not only on how much meltwater is being added to the ocean, but also whether the land we are standing on to measure sea-level change is rising or falling (Figure 3). The rate of rebound or subsidence has to be added to or subtracted from the raw observations made by, for example, tide gauges (see the Permanent Service for Mean Sea Level website for more information).

Figure 3: Sea-level measurements will be affected by rebound or subsidence of the solid Earth.

But the rebound of the Earth is not the only complicating factor when we try to measure how much sea level is rising. When meltwater is added to the oceans, sea level doesn’t rise by the same amount everywhere; in some places it rises by more than the average amount, and in others it rises by less. The reason for this variation is gravity.

Gravity is the force which pulls two masses towards each other; the larger the mass, the greater the attraction. This is why the ocean stays stuck to the Earth – because the Earth is a very large mass. Since the ocean is a liquid, its surface must track a surface of equal gravity (this is also why water in a glass placed on a table forms a flat surface), and we call this surface the ‘geoid’. Now, the distribution of mass throughout the Earth is not uniform, so the pull of gravity is not the same everywhere. Therefore, the geoid, or sea surface, doesn’t follow the outline of a perfect sphere; it bulges downwards where the interior of the Earth is very dense, and it bulges upwards where there is a large mass on the surface of the Earth, such as an ice sheet (Figure 4).

Figure 4: The geoid; the surface that defines the shape of the ocean’s surface.
Courtesy of the European Space Agency. (See here for a video)

Solid Earth Shape

Figure 5: Cartoon showing how the change in the shape of the geoid and the rebound of the solid Earth following the melting of an ice sheet results in non-uniform sea-level change. Red dashed lines in the lower plot indicate the original land/ocean configuration of the upper plot. From Tamisiea et al., Space Science Reviews, 2003.

Figure 5: Cartoon showing how the change in the shape of the geoid and the rebound of the solid Earth following the melting of an ice sheet results in non-uniform sea-level change. Red dashed lines in the lower plot indicate the original land/ocean configuration of the upper plot. From Tamisiea et al., Space Science Reviews, 2003.

The reason that this complicates our measurements of sea-level change is because when an ice sheet melts it alters the distribution of mass on the surface of the Earth, and this alters the shape of the geoid. In addition, the rebound of the solid Earth beneath the former ice sheet alters the distribution of mass within the Earth, also altering the shape of the geoid. As the meltwater enters the ocean, it follows the new geoid shape, and since this shape differs from the shape before the ice sheet melted, the sea-level rise is not uniform [5]. In some locations, far from the melting ice sheet, sea-level rise will be larger than the average value. While close to the melting ice sheet, sea level will actually fall because there is no longer a strong gravitational attraction towards the former ice sheet, and this cancels out the increase in sea level due to the addition of meltwater (Figure 5).

In an ideal world we would have a record of sea-level change over the whole of the Earth’s surface for the last 20,000 years, and this would enable us to work out how much ice has melted during that time, and from where. In reality, the sea-level records that we have are sparse in both space and time, and therefore we need to use mathematical models to work out the possible melting scenarios which fit the sea-level records that we do have [6]. Using this method we are gradually building up a picture of how the ice sheets have changed over the last 20,000 years.

Modern ice sheet melt

Figure 6: The average spatially-variable change in sea level between 1993 and 2009, as measured derived from satellite data. From Willis et al., Oceanography, 2010.

We have to be similarly devious to work out how quickly our remaining ice sheets are melting. Satellites measure changes in the height of the sea surface, pinpointing areas where it is rising the fastest (Figure 6). This information relating to the spatial pattern of sea-level rise could potentially enable us to work out the source of the meltwater [7], but the signal is complicated because some of that sea-level rise is due to the water in the ocean becoming hotter and expanding, rather than due to the addition of meltwater [8]. Therefore, we must turn to the ice sheets themselves to try to measure how quickly they are melting. As they melt, the land beneath them rebounds rapidly upwards, just as it did when the ancient ice sheets began to melt. By placing GPS receivers on mountains poking through the ice sheets (Figure 7) we are slowly building up a picture of this modern-day rebound, and hence a picture of the mass of ice which is being lost to the oceans today.

Figure 7: GPS receiver in Antarctica. Photo courtesy of Matt King.

Further reading


1.            Milne, G.A., J.X. Mitrovica, and D.P. Schrag, 2002. Estimating past continental ice volume from sea-level data. Quaternary Science Reviews, 21(1-3): 361-376.

2.            Tarasov, L. and W.R. Peltier, 2004. A geophysically constrained large ensemble analysis of the deglacial history of the North American ice-sheet complex. Quaternary Science Reviews, 23(3-4): 359-388.

3.            Sella, G.F., S. Stein, T.H. Dixon, M. Craymer, T.S. James, S. Mazzotti, and R.K. Dokka, 2007. Observation of glacial isostatic adjustment in “stable” North America with GPS. Geophysical Research Letters, 34(2): -.

4.            Lidberg, M., J.M. Johansson, H.G. Scherneck, and G.A. Milne, 2010. Recent results based on continuous GPS observations of the GIA process in Fennoscandia from BIFROST. Journal of Geodynamics, 50(1): 8-18.

5.            Farrell, W.E. and J.A. Clark, 1976. On postglacial sea level. Geophysical Journal of the Royal Astronomical Society, 46(3): 647-667.

6.            Lambeck, K., Y. Yokoyama, P. Johnston, and A. Purcell, 2000. Global ice volumes at the Last Glacial Maximum and early Lateglacial. Earth and Planetary Science Letters, 181(4): 513-527.

7.            Mitrovica, J.X., M.E. Tamisiea, J.L. Davis, and G.A. Milne, 2001. Recent mass balance of polar ice sheets inferred from patterns of global sea-level change. Nature, 409(6823): 1026-1029.

8.            Ishii, M., M. Kimoto, K. Sakamoto, and S.I. Iwasaki, 2006. Steric sea level changes estimated from historical ocean subsurface temperature and salinity analyses. Journal of Oceanography, 62(2): 155-170.