Introduction:
Of great interest to Earth system scientists is the mass balance of glaciers, ice sheets, and ice caps because these water stores contribute directly to sea level and ocean circulation, and potentially to climate change. For example, it is estimated that the Greenland and
Antarctic ice sheets together contain enough water to raise sea level by almost 70 m.
Clearly, quantifying ice sheet mass balance processes is of great interest globally.
Physical Characteristics:
Antarctica comprises the area of the Earth south of 60 o
S and includes the ice-covered continent, isolated islands and a large part of the Southern Ocean. The continent itself makes up about 10% of the land surface of the Earth with the combined area of the ice sheets and ice shelves covering 14 × 10 6
km
2
. It lies entirely within the Antarctic Circle, except for the northern part of the Antarctic Peninsula and the region south of the Indian
Ocean. The ice sheet has 3 distinct morphological zones: East Antarctica, West Antarctic, and the Antarctic Peninsula. The highest point in Antarctica is Vinson Massif (at 5440 m), located in the Ellsworth Mountains.
The vast majority of the surface of Antarctica is covered with ice, with the continent as a whole containing around 30 × 10
6
km
3
or 90% of the world’s freshwater. The ice thickness varies across the continent, with its maximum being 4776 m about 400 km south of Dumont d’Urville. The mass of ice conceals the details of the land below, which is made up of sub-glacial mountains and lower elevation topographic features. The ice that builds up in the interior of the Antarctic flows down to the edge of the continent in ice streams that move at speeds of up to 500 m per year. Some of the most rapidly moving ice streams are in West Antarctica and feed into the Ross and Ronne Ice Shelves.
When the ice streams reach the edge of the continent, they form floating ice shelves or the ice breaks into blocks, which become tabular icebergs. Ice Shelves are a permanent feature of certain parts of the Antarctic, making up about 11% of its area.
Meteorology:
Air Temperature:
There is a strong correlation between surface air temperature (SAT) and elevation over
Antarctica. There is a “dipole” of cold air temperature on the East Antarctica plateau where mean annual SATs are < -55 o C, whereas the South Pole experiences an annual
SAT of -50 o
C.
The annual range of SATs varies considerably across the Antarctic continent. Only in the northern part of the Antarctic Peninsula in summer do monthly mean SATs exceed
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freezing; hence, over the greater part of the Antarctic ice sheets, there is little or no direct ablation of the snow surface.
In the Antarctic Peninsula and around the coast of East Antarctica, the annual cycle of temperature takes a familiar form with a broad summer maximum and a minimum in July or August. However, moving southward onto the polar plateau, the form of the cycle changes to a short, peaked summer season and a “coreless” winter during which the temperature varies relatively little. Contributing to this cycle are the abrupt changes in solar radiation at the beginning and end of winter darkness, whereas during the dark period, the surface radiation balance is determined only by net longwave radiation. In addition, warm air advection onto Antarctica has a strong semi-annual component, and the snowpack acts as a heat reservoir, smoothing out extremes of temperature variations.
Katabatic Winds:
As the surface of the Antarctic continent cools radiatively, the air close to the surface also cools relative to the air aloft. The near-surface air is thus negatively buoyant and, over a sloping surface, will accelerate down the slope in response to the buoyancy force. The resulting flow, known as a “katabatic wind”, will be turned by the Coriolis force and retarded by surface friction. Even on some of the modest slopes of Antarctica, the surface wind is primarily determined by katabatic forcing. Early explorers on the continent remarked on the persistence and directional consistency of winds blowing down from the high interior plateau, but it was only with the advent of radiosonde measurements that the mechanisms maintaining the winds were fully understood.
In Antarctica and Greenland, the combination of extensive sloping surfaces and uninterrupted surface cooling for much of the year allows a large-scale katabatic circulation to develop. This flow dominates the low-level circulation over the Antarctic continent.
Precipitation:
Knowledge of precipitation formation mechanisms, snowfall distribution over the
Antarctic continent, and the synoptic origins of the precipitating air masses is important for the investigation of whether the ice sheets are growing or shrinking (mass balance), how accumulation may change in an environment of higher mean SAT, etc. It has been estimated that about 2300 km
3
yr
-1
of snow falls on the continent each year, but it is extremely difficult to make measurements of precipitation in Antarctica, not least because of the difficulty in distinguishing blowing snow from snowfall. With the strong winds experienced over the continent, conventional snow gauges give poor results so that other means of assessing accumulation must be found. These have included the use of snow stakes, stratigraphy, a knowledge of snowdrift density, etc.
Net accumulation of snow at the surface is often taken as equivalent to precipitation in
Antarctica. The largest accumulations are found slightly inland of the coast, where the steepest slopes are found and where air masses are lifted and cooled as they move
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poleward. The largest accumulations are over 1000 mm yr
-1
, found near southeastern
Bellingshausen Sea. The lowest values of snowfall accumulation (< 50 mm yr
-1
) occur over the Antarctic Plateau; this minimum in precipitation is strongly correlated to air temperature. The saturation vapour pressure, through the Clausius-Clapeyron relation, is by far the most important parameter in determining the distribution of precipitation.
Mass Balance:
An ice sheet gains mass by accumulating snow that is transformed into ice by densification processes. It loses mass (ablation) mainly by melting at the surface or base with subsequent runoff or evaporation of the meltwater. Meltwater may refreeze within the snow instead of being lost, and some snow may sublimate from the surface back to the atmosphere. Ice may also be removed by flowing into a floating ice shelf, from which it is lost by basal melting and calving of icebergs. In general, net mass ablation at lower altitudes are balanced by the downhill flow of ice under internal deformation (since ice is a plastic material) and by the sliding and bed deformation at the base. This balance is expressed usually as the rate of change of the equivalent volume of liquid water, in cubic metres per year; for a steady state the mass balance is zero. Mass balances are computed for both the whole year and individual seasons (winter and summer) with the specific mass balance being the net summer and winter mass balances averaged over the surface area, in metres per year.
Ice-covered regions are dynamic environments that are characterized by forcing responses at variable timescales, which may not always be synchronous with external weather and climate forcing factors. While seasonal accumulation and ablation processes might balance in approximate terms, internal ice dynamical processes occurring at both shorter and longer timescales contribute to balance inequalities. For example, the average annual solid precipitation falling onto Greenland and Antarctica is equivalent to 6.5 mm of sea level, this input being approximately balanced by loss from melting and iceberg calving. However, the balance of these processes is not the same for the two ice sheets, on account of their different climatic regimes. Antarctic temperatures are so low that there is virtually no surface runoff; the ice sheet mainly loses mass by ice discharge into floating ice shelves, which experience melting and freezing at their underside and eventually break up to form icebergs. On the other hand, summer temperatures on the
Greenland Ice Sheet are high enough to cause widespread melting, which accounts for about half of the annual ice loss, the remainder being discharged as icebergs or into small ice-shelves. Understanding ice sheet dynamics in the context of global environmental change, therefore, requires us to characterize the present state of the ice sheets and glaciers and to establish the historical and prehistorical trends of ice masses in order that we can understand variations in global and regional mass balance behaviours.
Current state characterizations can be made through specific in situ measurements of ice mass balance processes. These measurements can be linked to cryospheric climate forcing variables derived from in situ measurements or from coupled atmospheric-ocean global climate models. For volume estimates, the best way is to calculate the change in
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volume with time through the construction of digital elevation models (DEMs). Direct measurements of elevation change have a long history of application on alpine glaciers through the use of field survey methods. In mountain terrain, electronic distance measurers survey marked locations on the ice surface from fixed, stable sites located off the ice on the surrounding valley walls. Precise measurements, to centimeter accuracy, are possible provided that the markers, usually in the form of embedded stakes, remain intact during the survey period. The outcome of this approach is that three-dimensional
DEMs can be produced enabling annual changes in glacier volume to be made. For large ice sheets however, it is generally not possible to survey from peripheral stable sites.
Instead repeat leveling along predetermined transects is performed. This gives the relative height of the level sites and can be calibrated to absolute benchmark heights. Leveling experiments, however, are subject to uncertainties which can prevent the detection of long-term trends. In addition, while the full three-dimensional survey may be spatially comprehensive for mountain glaciers, this will not apply for ice sheets; the challenge is to derive representative transect profiles that can be repeated from year to year.
Traditional cartographic surveys have also been undertaken to directly estimate mass balance changes from year to year. Elevation contours derived from surveys can be produced to provide an estimate of surface topography. Repeated from year to year, it is possible to compare changing glacial volume as an indicator of mass balance variation.
Maps can also be derived from aerial photography, and using stereo photography methods, DEMs can be constructed directly, assuming stable ground control points can be located from year to year. The accuracy of cartographic methods, however, is 1-2m on account of both repeated height inaccuracy and horizontal uncertainty of stable targets.
This precision might be good enough to estimate general trends but it is inadequate for direct measurements of ablation or accumulation variations on a year to year basis. A more recent approach to mapping is through the use of global positioning system (GPS) surveys. Very accurate measurements of the glacier surface in three dimensions are possible with this method and profiles of GPS receivers mounted on “fixed” stake have been used to characterize the changing mass balance of both small glaciers to large ice caps. This approach has the advantage of being automated and also measuring the ice surface velocity, thereby providing a measurement of the glacier kinematics.
The measurement of specific components of mass balance equations, particularly mass accumulation and ablation, is another method to obtain the mass balance of the Antarctic ice sheet. Measurements of accumulation and ablation rate can be achieved by repeatedly surveying stakes that have been partially drilled into the ice to determine the accumulation and ablation of snow and ice relative to the stake during the year. This is repeated for a series of stakes comprising the “stake network.” To ensure a comprehensive identification of the accumulation area, “snow probing” can be undertaken. Snow density measurements from snow pits or cores must also be measured and when coupled with the stake measurements, an estimate of net surface accumulation or ablation can be obtained. By undertaking a survey at the end of the winter and summer seasons, the maximum mass accumulation and maximum mass ablation can be determined respectively. If a distinct “summer surface” is present over the glacier, the
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winter and summer balances can be measured at the end of the spring provided that the previous year’s stakes are intact.
For long-term studies (up to 250 k years) and to reconstruct previous accumulation rates, snow pit studies and ice core measurements have been used widely. Snow pits are used to quantify vertical variations in snow density and to identify accumulation layers in the snow that can be used to calculate densification rates. This process controls the rate at which snow is converted to ice. Ice core studies are used to reconstruct past climate variations. O
18
/O
16
ratios from ice cores can be used to identify temperature variations over the past 250 k years. However, analysis of the oxygen isotopic record enables the identification of discrete layers in the profile at depth that can be used to assess the accumulation rate over the glacier or ice cap. It should be remembered, however, that these methods are in situ in scope and are spatially limited. To extend the areal coverage of these measurements, accumulation layers can also be obtained from sled-based ground penetrating radar (GPR) measurements. Such instruments resolve accurately the accumulation layers for areas that are accessible form sled-mounted systems. GPR penetration depths may be limited depending on the snow and ice stratigraphy but several surveys have been conducted in this way .
Ablation terms are less straightforward to measure directly. Successive ice height measurements against a graduated stake remains stable and fixed in the ice. This is the dominant measurement approach taken. For ice sheets/ice shelves that discharge ice into the ocean, ice calving is generally defined as the mass of ice loss per unit time. The dimensions of the calved ice can be estimated either from the ablation area ice velocity and thickness or by surveying over-turned recently calved icebergs.
The spatial scale of an ice sheet determines the need for accurate representation of spatial variability of ice mass. This problem was intractable until satellite-based remote sensing techniques became available. The form of the relevant mass balance equation is:
B n
= M a
– M m
– M c
± M b
Where B n
is the mass balance at the end of the balance year, M a
is annual surface accumulation; M m
is annual loss by glacial surface runoff, M c
is annual loss by calving of icebergs, and M b
is the annual balance at the bottom (melting or freezing-on of ice). This equation suggests that the mass balance can be inferred from two methods: a) by direct measurement of the change in volume by monitoring surface elevation change and b) by the budget method, determining each term on the right-hand side of the equation separately.
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Table 1: Estimates of the terms in the mass budget of the Antarctic Ice Sheets (Jacobs et al. 1992)
Term
Accumulation
Mass Rate (Gt/year) Uncertainty (%)
Grounded Ice
Ice Shelves
Total Accumulation (M a
)
Ablation
1528
616
2144
20
Calving (M c
)
Sub-ice Melting (M b
)
Surface Runoff (M m
)
-2016
-554
33
50
Total Ablation
Net Mass Balance (B n
)
-53
-2623
-479
50
Mass loss by iceberg calving is clearly the largest negative term in the budget, but subice-shelf melting cannot be neglected. Runoff of meltwater from the grounded ice makes only a small contribution to the mass budget. It is largely controlled by the small amount of melting which takes place in coastal regions during the summer, with a small additional contribution from subglacial melting.
If the terms in the mass balance are summed, we obtain an imbalance in the net mass budget of the Antarctic ice sheet. However, given the large uncertainties in some of the terms, particularly in the amount of calving, the significance of this imbalance is not very high.
Blowing snow also plays a role in the mass balance of Antarctic, both through the divergence/convergence of mass and through sublimation. However, it is a term that, on a continental scale, is considerably less than the others listed in Table 1.
Subglacial Lakes:
Lake Vostok lies in the heart of the Antarctic continent hidden beneath 4 kilometers of ice. As big as Lake Ontario in North America, Lake Vostok is one of the world's biggest freshwater lakes. Lake Vostok has been covered by the vast Antarctic ice sheet for up to
25 million years. The lake was named for the Russian research station that sits above its southern tip - a place where in 1983 the temperature fell to -89°C, the coldest ever recorded temperature on Earth. More than 145 lakes have been identified beneath the thick Antarctic ice sheet. Most of these lakes, covered between 3-4 kilometers of ice, are several kilometers long. One of these lakes, Lake Vostok, is an order of magnitude larger than all other known subglacial lakes. In fact, Lake Vostok is 14,000 km
2
in area, 900 m deep, and has a volume of approximately 5,400 km
3
of water.
In the February 2006 issue of Geophysical Research Letters , scientists from the Lamont-
Doherty Earth Observatory at Columbia University, described for the first time the size, depth and origin of Lake Vostok's two largest neighbors. The two ice-bound lakes are
6

referred to as 90 o
E and Sovetskaya for the longitude of one and the Russian research station coincidentally built above the other. The scientists' findings also indicate that, as suspected with Lake Vostok, an exotic ecosystem may still be thriving in the icy waters
35 million years after being sealed off from the surface.
Geophysicists Robin Bell and Michael Studinger of Lamont-Doherty combined data from ice-penetrating radar, gravity surveys, satellite images, laser altimetry and records of a
Soviet Antarctic Expedition that unknowingly traversed the lakes in 1958-1959. The shorelines of the lakes appeared in satellite images of the region as perturbations in the surface of the East Antarctic ice sheet. In addition, because the ice is effectively floating on the surface of the lakes, the ice sheet exhibits slight depressions over the lakes that appear in radar and laser elevations.
The combination of heat from below and a thick layer of insulating ice above keeps the water temperature at the top of 90ºE and Sovetskaya at a balmy -2 o
C, despite temperatures on the surface that can drop to -89 o C in winter. Since the lakes are bounded by faults, Bell said it is likely the lakes receive flows of nutrients that could support unique ecosystems. Moreover, laser mapping of the ice sheet surface by NASA's Ice
Cloud and Land Elevation Satellite (ICESat) revealed that this water-ice boundary, or ceiling, is tilted.
This, along with the tectonic origin of the lakes, supports the idea that despite climate changes on the surface over the last 10 million to 35 million years, the volume of the lakes have remained remarkably constant, providing a stable, if inhospitable, environment that may harbor an ancient and alien ecosystem adapted to life beneath the ice sheet. However, just how, when or even whether scientists will risk the possibility of contaminating the lakes to confirm their suspicions remains the subject of an ongoing international debate.
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