Planes travelling from Europe to the west coast of the US usually fly directly over Greenland. Most passengers miss it, but if you have a window seat and keep watch at about the time that the dinner trays are being cleared away, then you may be lucky enough to catch a glimpse of a truly majestic landscape in which massive glaciers, fed from a vast and featureless ice sheet, spill into iceberg-choked fjords. Although your plane will be thousands of metres overhead, these remote glaciers are nonetheless feeling the impact of human activities like air travel. As the temperatures over Greenland rise as a result of climate change, the speed at which many of these glaciers are moving is increasing so rapidly that more ice is being lost from the ice sheet than is being replaced by new snowfall. In other words, the ice sheet is giving up its mass to the oceans, and, as a result, sea levels are rising.

The rate of sea-level rise has startled both scientists and policy-makers enough to make headlines and become embedded in government and international reports. It is easy to see why they are concerned – even a half-metre rise would cause flooding that would affect hundreds of millions of people in low-lying areas. Suddenly, "glacier dynamics" – the physics that controls how fast glaciers flow – has become a subject of international importance.

The 2007 report from the Intergovernmental Panel on Climate Change (IPCC) cites retreating glaciers and rising sea levels as evidence that warming of the climate system is unequivocal. And with enough water stored in the Greenland and Antarctic ice sheets to raise global sea levels by approximately 7 m and 57 m, respectively, being able to predict how these large ice sheets will behave in a warming climate is critical if we are fully to understand the consequences of climate change.

We know from satellite measurements and an international network of tide gauges that sea levels are currently rising at a rate of slightly more than 3mm per year. About half of this increase is due to the loss of ice from glaciers and ice sheets, with the remainder being caused by thermal expansion as the oceans warm. This rate is higher now than at any point in the past century and continued climate warming means that it is highly likely to increase further in the future. Using a linear extrapolation of data from the past 100 years, Stefan Rahmstorf at the Potsdam Institute for Climate Research in Germany last year showed that sea levels will rise by 0.5–1.4m over the next 100 years. But, as NASA climate scientist James Hansen has pointed out, the data from the last 100 years do not include much contribution from the ice sheets. The impact of these ice sheets melting is sure to be felt more and more over the next century.

Ice in motion

Glacier flow was first measured scientifically in the early 19th century by Franz Josef Hugi, who was a physicist and natural historian at Solothurn University of Applied Sciences in Switzerland. Using simple visual methods to study the position of a rock on the surface of a glacier in the Alps, Hugi found that it moved by a total of about 1300 m over a nine-year period between 1827 and 1836. By the early 1840s, the Swiss–American geologist Louis Agassiz and the Scottish physicist James Forbes were also studying alpine glaciers. One of Forbes’s most significant findings came in 1842 when he reported results from theodolite surveys that showed that the flow rate of glaciers is not constant but varies from day to day and from week to week. Measurement techniques have continued to improve since then and, thanks to the advent of satellites and the Global Positioning System (GPS), we have now discovered a vast richness of glacier behaviour.

On a typical mountain glacier, snow is added to the surface during the winter, while the snow and exposed ice on the lower part of the glacier (known as the ablation zone) melts during the summer. However, further up the glacier, in the region known as the accumulation zone, the snow remains year round and is converted into ice as the load from the snow above it increases. For a glacier to stay in equilibrium (i.e. for the amount of water it contains to stay constant), the accumulation zone needs to comprise about 70% of the total area of the glacier.

If a glacier in equilibrium were not flowing, the ablation zone would get thinner and the accumulation zone would thicken, so overall the glacier would become steeper. A certain amount of flow, therefore, is required to maintain the geometry of a glacier in equilibrium. Recognizing these concepts allows us to calculate any glacier or ice sheet’s "balance velocity" – a theoretical concept that defines how fast any glacier needs to flow in order to retain the same shape and volume. If a glacier is flowing faster than the balance velocity, then it will thin; whereas if the glacier is flowing more slowly, then it will thicken.

We now know that there are three processes by which glaciers can flow. The first is viscous deformation of the ice itself, which depends on many factors, particularly temperature. A glacier can also slide over the rock or sediment bed beneath it. Finally, the sediment beneath a glacier can deform, thus carrying forward the ice resting on it. The rates of both sliding and sediment deformation are affected most by the presence of pressurized water at the glacier bed, since this reduces friction. This water can reach the glacier bed when surface meltwater enters the glacier through vertical shafts known as moulins, which form when water flows down into and so enlarges cracks or crevasses in the ice. Once water is flowing inside the glacier, it often reaches the glacier bed, where it flows in channels.

Sometimes the amount of water reaching the glacier bed can increase significantly – for example when melting begins at the start of summer, or when a surface lake drains. (Sudden drainage is a feature of icedammed lakes, since the ice can deform, be melted, be cut by flowing water or overtopped by rising lake levels.) When this occurs, the pressure of the water at the glacier bed can get quite high and so make the glacier flow significantly faster. This process explains the short-term variations in glacier speed that Forbes saw in the Alps.

Space-age measures

These days we can measure glacier flow rates much more widely than in Forbes’s time by using satellites such as the US Landsat series and the European Space Agency’s Envisat and ERS satellites. Indeed, such measurements are vital for monitoring the remote parts of ice sheets that have never, or only very rarely, been visited. Features such as crevasses on the ice surface can be automatically tracked over a period of time with either optical imagery from satellites that passively detect reflected solar radiation, or via synthetic aperture radar (SAR) microwave radiation that is actively transmitted by the satellite. As SAR provides its own illumination, it has the advantage of not being affected by clouds and can be used during the polar night.

By comparing two SAR images of the same surface obtained at different times, we can also map the topography and dynamics of a glacier or ice sheet using interferometry. This technique exploits the phase shift between the transmitted and backscattered SAR signals. If the same viewing location is used and the surface characteristics have not altered, then the phase difference depends only on the displacement of the surface. If, however, the viewing location changes, which is usually the case between two satellite passes, then the phase difference also depends on the local topography. Using interferometry we can therefore estimate not only flow rates but changes in ice thickness, too.

Satellite measurements could, in principle, be used to monitor almost all of the Earth’s ice masses. However, they are limited in temporal resolution because a satellite takes time to orbit the Earth and may only pass over the same point every few weeks at best. The shorter-term variations in ice flow, such as those reported by Forbes, are now usually measured by attaching GPS receivers to glaciers, which allows position to be measured to better than a few centimetres (see Physics World October :2007 pp34–38).

These techniques have revealed that glacier flow rates vary by several orders of magnitude: from a sluggish few metres per year, as seen in glaciers with cold bases such as Austre Brøggerbreen on Svalbard in the Arctic Ocean, to sustained flow rates of about 8-10 km per year. Jakobshavn Isbrae in Greenland used to be considered the fastest flowing glacier with a flow rate of about 8.3 km per year, but researchers now routinely measure velocities of 7-10 km per year for most Greenland outlet glaciers. Furthermore, recent observations by many different research groups show dramatic variations both spatially and temporally, which suggest that flow rates are very sensitive to local glaciologic, geologic and climatic conditions.

Particularly large spatial variations in flow rates occur within ice sheets. Most parts of the Antarctic ice sheet, for example, flow relatively slowly at only a few metres per year, but some areas move much faster at about 400 m per year or more. These variations are caused by changes in the resistive stresses at the bed of the ice, which occur due to changes in the temperature and the water system at the base, and the presence of wet sediments beneath the ice. Changes in the driving stress – primarily the surface slope – also play a part. These fast flow features, known as ice streams, constitute only about 10% of the Antarctic coastline but discharge about 90% of the snow that accumulates and so act to regulate the storage of water in the ice sheet.

Large temporal variations in flow have been observed both on ice sheets and on mountain glaciers. In Antarctica, ice streams have both sped up (discharging more ice to the oceans) and slowed down or stopped (reducing the discharge of ice), while an even more dramatic temporal variation is seen in "surge-type" glaciers. These glaciers lie quiescent for decades or longer before their flow rates suddenly increase by up to three orders of magnitude, allowing them to advance very rapidly. During its surges in 1982 and 1983, the Variegated Glacier in Alaska, for example, flowed up to 2.6 m per hour for a few hours, while the Hispar Glacier in the Karakoram Himalayas advanced 3.2 km in eight days during a surge event.

What is most intriguing about these surge-type glaciers is that they alternate between fast and slow flow in cycles that are thought to be largely independent of climate. During the slow phase of flow, the upper part of a surge-type glacier accumulates more snow than is lost and the glacier thickens and steepens, which increases the shear stress at the glacier bed. Eventually this increase in stress crosses a threshold and a surge is triggered. There are a number of competing theories as to what changes at the bed between the quiescent and fast-flow states, but all of these models involve the entrapment of high-pressure water at the bed, which reduces basal friction.

Breaking the ice

Other types of glacier, however, have been significantly affected by climate warming. In 2002 in the Antarctic, during the space of just a few weeks, the Larsen B Ice Shelf, which spanned an area of 1600 km2, collapsed. Before it broke up, air temperatures had reached record levels and satellite images showed lakes of meltwater on the ice shelf. This event did have one useful consequence, however. An ice shelf forms where a glacier or ice sheet flows down to a coastline and onto the ocean surface, and glaciologists had long debated how much back-stress the floating ice shelf provides to the glaciers that feed it and how much those glaciers would therefore be affected by removal of the ice shelf. The loss of Larsen B allowed them to find out.

Satellite feature tracking showed that the glaciers that had fed Larsen B started flowing twice to six times as fast after the ice shelf collapsed, whereas nearby glaciers that fed an intact region of the ice shelf did not change their speed. So, while the ice-shelf collapse itself did not raise sea levels because it was already floating, the increased flow rates of the glaciers that fed it led to greater discharge into the oceans, causing sea levels to rise.

In Greenland, temperatures are generally warmer than those in Antarctica and substantial areas of the ice sheet melt each summer – indeed melting accounts for half of the loss in the mass of the ice sheet. Most of the Greenland ice sheet terminates on land and measurements obtained using GPS receivers have shown that flow at the land-based margin of the ice sheet speeds up between 5-25% in periods of strong surface melting – just like the glaciers Forbes studied in the Alps. This makes it clear that the meltwater is efficiently transported to the ice-sheet bed even through thick ice.

The other half of the mass lost breaks off as icebergs from fast-flowing outlet glaciers, which discharge into deep fjords. Observations made in 2004 by a team led by NASA glaciologist Bill Krabill using airborne altimetry – a technique for mapping the topography of the ground using a laser flown on a plane – have shown significant thinning of some of these outlet glaciers at rates of more than 10m per year. Satellite observations have shown that many have also greatly increased their flow rates, especially in south-east Greenland. This acceleration in flow increases the glacier’s mass loss to the oceans and hence contributes to rises in sea levels.

Two of these outlet glaciers, the Helheim and Kangerdlugssuaq glaciers on the south-east coast of Greenland, simultaneously retreated by more than 5 km in spring 2004 while approximately doubling their flow rates and the volume of ice calved. A third glacier, Jakobshavn Isbrae, had similarly sped up a few years previously, after many years of stable flow.

These large changes in flow rates were a surprise to glaciologists and cannot be reproduced by current theories of glacier dynamics. They are almost certainly the result of increased air or ocean temperatures, although "tidewater glaciers" (which terminate in a fjord or the sea) do have a known cycle of advance and retreat. It is possible, therefore, that the changes observed in Greenland are part of a natural cycle. But it would certainly be surprising that so many glaciers are accelerating and retreating simultaneously if no external forcing were occurring. Without such forcing, one would expect some glaciers to advance while others retreat.

Model behaviour

Predicting the future contribution of glaciers and ice sheets to sea-level rises has become one of the most important goals of glacier studies, since such information is essential for planning sea-defences and adapting to sea-level rises. This is far from easy, however. We have too few records of the glacial response to climate change to build a statistical approach to prediction, and even the smallest glacier is too large on which to conduct a controlled experiment. Glaciologists therefore have to base their predictions on the results of numerical models.

Such models must balance increasing complexity against increasing computational cost. More complex models should be more accurate because the physics included in them is more advanced and because they have many more data points to improve the model’s spatial and temporal resolution. However, complex models can take a long time to run, which means that they are only used for short-term simulations of smaller glaciers. Where we are interested in the longer-term evolution of a large ice sheet, a lower-resolution model, including only a few key parameters, has to be used.

The simplest models represent 2D vertical slices though the ice, aligned along lines of flow, and consider the ice to be the same temperature throughout. The modelled quantities are ice-surface elevation and flow speed, while the ice temperature (which affects the softness of the ice), the properties of the bed (such as its elevation and the presence or absence of sliding), and the surface-mass balance (i.e. melting or accumulation) are the controlling parameters. The ice flow is assumed to be laminar so that only vertical gradients in the horizontal shear stresses need to be included – this is the shallow-ice approximation, which is based on the assumption that the horizontal extent of an ice mass is much larger than its thickness. This approximation is good for most parts of a large ice sheet, but is inappropriate for fast-flowing ice streams or for valley glaciers.

At the other end of the spectrum, the most complex models include representations of the additional stress gradients (termed higher-order stresses) and are also able to compute the 3D temperature field. Both of these aspects are essential for the representation of ice streams and outlet glaciers, and so are critical to an understanding of the Greenland and Antarctic ice sheets.

In recent years, a number of such higher-order models have been developed, by, among others, Frank Pattyn at Vrije Universiteit in Brussels, and Fuyuki Saito and co-workers at the University of Tokyo. These models are opening up exciting possibilities in the study of smaller-scale motion in ice sheets, but they do have their limitations. In particular, the bed of the ice sheet or glacier is of critical importance but current models make simple assumptions about this basal sliding rather than attempting to represent the full range of processes involved. In order to improve the numerical models, therefore, our understanding of the physics of basal sliding and the water systems that form at the beds of glaciers needs to be improved and generalized. To this end, much more information is needed about the basal conditions of particular ice masses.

This presents a difficult challenge, since the bed of an ice sheet or glacier is the hardest part to observe. A few access holes have been drilled through ice more than a kilometre thick using jets of high-pressure hot water, and Barclay Kamb and Herman Englelhardt’s group at the California Institute of Technology in the US has measured the pressure of basal water and the rates of sliding and sediment deformation through these holes. Borehole cameras have also revealed cavities full of water beneath an ice stream. Even when access can be achieved, however, spatial sampling is very small since the boreholes are typically less than 15 cm in diameter.

Geophysical techniques allow much greater areas to be covered, and indeed seismic and radar surveys, which were both originally used simply to measure the thickness of glaciers, have been highly successful in determining basal conditions. Seismic-reflection surveys use acoustic energy to map the impedance contrast across the basal interface. Rock and sediments that are not deforming are acoustically harder than ice, whereas deforming sediments are acoustically softer, so the reflection coefficient of the acoustic waves changes depending on whether the ice is sliding over hard sediments or moving with deforming soft sediments.

Radar, on the other hand, uses pulses of highfrequency electromagnetic radiation (at about 10-200 MHz). Since radar reflections from water are short in duration and high in amplitude, whereas soft sediments or rough bedrock produce longer and lower amplitude pulses, radar can be used to map the occurrence of water at the glacier bed, including the presence of sub-ice lakes. Radar systems can be mounted on an aircraft allowing very large areas of the bed to be surveyed, which is critical if ice-sheet models are to incorporate more basal physics. Used together, borehole and geophysical techniques have enormous potential to map the topography, basal environments and water systems of the major ice masses.

On thin ice

As observation technology improves, it is revealing an amazing richness of glacial behaviours. At present, however, most of this dynamic richness cannot be reproduced by models. An unfortunate result of this situation is that in its report last year, the IPCC said that its predictions of future sea-level rise have excluded future rapid dynamical changes in ice flow because "a basis in published literature is lacking". This limits our confidence in the predictions and hampers the ability of governments to draw up plans for dealing with the future consequences of climate change. Furthermore, the report’s predictions of 0.18-0.59 m rises are as a result most likely lower-limit scenarios. In the worst-case scenario, in which all of the world’s ice melts, sea levels would rise by over 65 m. Some 57 m would come from Antarctica, 7 m from Greenland and between 0.15 and 0.37 m from small glaciers. While this extreme case is unlikely, even a small rise in sea levels would have a devastating effect on millions of people, and could see large areas of land disappearing under water. To provide better confidence in calculated rates of future sea-level rises and begin preparing for them, significant further research is needed in the form of both improved modelling efforts and continued field and satellite observation.

More about: Glacier physics
De Angelis H and Skvarca P 2003 Glacier surge after ice shelf collapse Science 299 1560.

Krabill W et al. 2004 Greenland ice sheet: increased coastal thinning Geophys. Res. Lett. 31 L24402.

Luckman A and Murray T 2005 Seasonal variation in velocity before retreat of Jakobshavn Isbrae, Greenland Geophys. Res. Lett. 32 L08501.

Luckman A et al. 2006 Rapid and synchronous ice-dynamic changes in East Greenland Geophys. Res. Lett. 33 L03503 Rignot E and Kanagaratnam P 2006 Changes in the velocity structure of the Greenland ice sheet Science 311 986 www.ipcc.ch/index.htm