Formation and characteristics of glacier ice
- Key People:
- Louis Agassiz
- James David Forbes
- Related Topics:
- moulin
- crevasse
- firn
- ice shelf
- subpolar glacier
Transformation of snow to ice
Glacier ice is an aggregate of irregularly shaped, interlocking single crystals that range in size from a few millimetres to several tens of centimetres. Many processes are involved in the transformation of snowpacks to glacier ice, and they proceed at a rate that depends on wetness and temperature. Snow crystals in the atmosphere are tiny hexagonal plates, needles, stars, or other intricate shapes. In a deposited snowpack these intricate shapes are usually unstable, and molecules tend to evaporate off the sharp (high curvature) points of crystals and be condensed into hollows in the ice grains. This causes a general rounding of the tiny ice grains so that they fit more closely together. In addition, the wind may break off the points of the intricate crystals and thus pack them more tightly. Thus, the density of the snowpack generally increases with time from an initial low value of 50–250 kilograms per cubic metre (3–15 pounds per cubic foot). The process of evaporation and condensation may continue: touching grains may develop necks of ice that connect them (sintering) and that grow at the expense of other parts of the ice grain, or individual small grains may rotate to fit more tightly together. These processes proceed more rapidly at temperatures near the melting point and more slowly at colder temperatures, but they all result in a net densification of the snowpack. On the other hand, if a strong temperature gradient is present, water molecules may migrate from grain to grain, producing an array of intricate crystal shapes (known as depth hoar) of lowered density. If liquid water is present, the rate of change is many times more rapid because of the melting of ice from grain extremities with refreezing elsewhere, the compacting force of surface tension, refreezing after pressure melting (regulation), and the freezing of water between grains.
This densification of the snow proceeds more slowly after reaching a density of 500–600 kilograms per cubic metre, and many of the processes mentioned above become less and less effective. Recrystallization under stress caused by the weight of the overlying snow becomes predominant, and grains change in size and shape in order to minimize the stress on them. This change usually means that large or favourably oriented grains grow at the expense of others. Stresses due to glacier flow may cause further recrystallization. These processes thus cause an increase in the density of the mass and in the size of the average grain.
When the density of the aggregate reaches about 830 to 840 kilograms per cubic metre, the air spaces between grains are sealed off, and the material becomes impermeable to fluids. The time it takes for pores to be closed off is of critical importance for extracting climate-history information from ice cores. With time and the application of stress, the density rises further by the compression of air bubbles, and at great depths the air is absorbed into the ice crystal lattices, and the ice becomes clear. Only rarely in mountain glaciers does the density exceed 900 kilograms per cubic metre, but at great depths in ice sheets the density may approach that of pure ice (917 kilograms per cubic metre at 0 °C and atmospheric pressure).
Snow that has survived one melting season is called firn (or névé); its density usually is greater than 500 kilograms per cubic metre in temperate regions but can be as low as 300 kilograms per cubic metre in polar regions. The permeability change at a density of about 840 kilograms per cubic metre marks the transition from firn to glacier ice. The transformation may take only three or four years and less than 10 metres of burial in the warm and wet environment of Washington state in North America, but high on the plateau of Antarctica the same process takes several thousand years and burial to depths of about 150 metres.
A glacier may also accumulate mass through the refreezing of water that occurs at its base. Previously, water at the base of a glacier was thought to serve as a lubricating layer that assisted the movement of the glacier across the ground, and refrozen water occurred only in subglacial lakes. However, scientists have demonstrated that refrozen water may also increase the size of the glacier by adding mass to its base. In addition, the refreezing process tends to lift and alter the upper layers of the glacier. This lifting phenomenon has been observed in several Antarctic ice fields, including the vast Dome A plateau that forms the top of the East Antarctic ice sheet.
Mass balance
Glaciers are nourished mainly by snowfall, and they primarily waste away by melting and runoff or by the breaking off of icebergs (calving). In order for a glacier to remain at a constant size, there must be a balance between income (accumulation) and outgo (ablation). If this mass balance is positive (more gain than loss), the glacier will grow; if it is negative, the glacier will shrink.
Accumulation refers to all processes that contribute mass to a glacier. Snowfall is predominant, but additional contributions may be made by hoarfrost (direct condensation of ice from water vapour), rime (freezing of supercooled water droplets on striking a surface), hail, the freezing of rain or meltwater, or avalanching of snow from adjacent slopes. Ablation refers to all processes that remove mass from a glacier. In temperate regions, melting at the surface normally predominates. Melting at the base is usually very slight (1 centimetre [0.4 inch] per year or less). Calving is usually the most important process on large glaciers in polar regions and on some temperate glaciers as well. Evaporation and loss by ice avalanches are important in certain special environments; floating ice may lose mass by melting from below.
Because the processes of accumulation, ablation, and the transformation of snow to ice proceed so differently, depending on temperature and the presence or absence of liquid water, it is customary to classify glaciers in terms of their thermal condition. A polar glacier is defined as one that is below the freezing temperature throughout its mass for the entire year; a subpolar (or polythermal) glacier contains ice below the freezing temperature, except for surface melting in the summer and a basal layer of temperate ice; and a temperate glacier is at the melting temperature throughout its mass, but surface freezing occurs in winter. A polar or subpolar glacier may be frozen to its bed (cold-based), or it may be at the melting temperature at the bed (warm-based).
Another classification distinguishes the surface zones, or facies, on parts of a glacier. In the dry-snow zone no surface melting occurs, even in summer; in the percolation zone some surface melting may occur, but the meltwater refreezes at a shallow depth; in the soaked zone sufficient melting and refreezing take place to raise the whole winter snow layer to the melting temperature, permitting runoff; and in the superimposed-ice zone refrozen meltwater at the base of the snowpack (superimposed ice) forms a continuous layer that is exposed at the surface by the loss of overlying snow. These zones are all parts of the accumulation area, in which the mass balance is always positive. Below the superimposed-ice zone is the ablation zone, in which annual loss exceeds the gain by snowfall. The boundary between the accumulation and ablation zones is called the equilibrium line.
The value of the surface mass balance at any point on a glacier can be measured by means of stakes, snow pits, or cores. These values at points can then be averaged over the whole glacier for a whole year. The result is the net or annual mass balance. A positive value indicates growth, a negative value a decline.
Heat or energy balance
The mass balance and the temperature variations of a glacier are determined in part by the heat energy received from or lost to the external environment—an exchange that takes place almost entirely at the upper surface. Heat is received from short-wavelength solar radiation, long-wavelength radiation from clouds or water vapour, turbulent transfer from warm air, conduction upward from warmer lower layers, and the heat released by the condensation of dew or hoarfrost or by the freezing of liquid water. Heat is lost by outgoing long-wavelength radiation, turbulent transfer to colder air, the heat required for the evaporation, sublimation, or melting of ice, and conduction downward to lower layers.
In temperate regions, solar radiation is normally the greatest heat source (although much of the incoming radiation is reflected from a snow surface), and most of the heat loss goes to the melting of ice. It is incorrect to think of snow or ice melt as directly related to air temperature; it is the wind structure, the turbulent eddies near the surface, that determines most of the heat transfer from the atmosphere. In polar regions, heat is gained primarily from incoming solar radiation and lost by outgoing long-wavelength radiation, but heat conduction from lower layers and the turbulent transfer of heat to or from the air also are involved.
Glacier flow
In the accumulation area the mass balance is positive year after year. Here the glacier would become thicker and thicker were it not for the compensating flow of ice away from the area (see ). This flow supplies mass to the ablation zone, compensating for the continual loss of ice there.
Glacier flow is a simple consequence of the weight and creep properties of ice. Subjected to a shear stress over time, ice will undergo creep, or plastic deformation. The rate of plastic deformation under constant shear stress is initially high but tapers off to a steady value. If this steady value, the shear-strain rate, is plotted against the stress for many different values of applied stress, a curved graph will result. The curve illustrates what is known as the flow law or constitutive law of ice: the rate of shear strain is approximately proportional to the cube of the shear stress. Often called the Glen flow law by glaciologists, this constitutive law is the basis for all analyses of the flow of ice sheets and glaciers.
As ice tends to build up in the accumulation area of a glacier, a surface slope toward the ablation zone is developed. This slope and the weight of the ice induce a shear stress throughout the mass. In a case with simple geometry, the shear stress can be given by the following formula: 
where τ is the shear stress, ρ the ice density, h the ice thickness, and α the surface slope. Each element of ice deforms according to the magnitude of the shear stress, as determined by (4), at a rate determined by the Glen flow law, stated above. By adding up, or integrating, the shear deformation of each element throughout the glacier thickness, a velocity profile can be produced. It can be given numerical expression as: 
where u1 is the surface velocity caused by internal deformation and k1 a constant involving ice properties and geometry. In this simple case, velocity is approximately proportional to the fourth power of the depth (h4). Therefore, if the thickness of a glacier is only slightly altered by changes in the net mass balance, there will be great changes in the rate of flow.
Glaciers that are at the melting temperature at the base may also slide on the bed. Two mechanisms operate to permit sliding over a rough bed. First, small protuberances on the bed cause stress concentrations in the ice, an increased amount of plastic flow, and ice streams around the protuberances. Second, ice on the upstream side of protuberances is subjected to higher pressure, which lowers the melting temperature and causes some of the ice to melt; on the downstream side the converse is true, and meltwater freezes. This process, termed regelation, is controlled by the rate at which heat can be conducted through the bumps. The first process is most efficient with large knobs, and the second process is most efficient with small bumps. Together these two processes produce bed slip. Water-filled cavities may form in the lee of bedrock knobs, further complicating the process. In addition, studies have shown that sliding varies as the basal water pressure or amount changes. Although the process of glacier sliding over bedrock is understood in a general way, none of several detailed theories has been confirmed by field observation. This problem is largely unsolved.
A formula in common use for calculating the sliding speed is: 
where u2 is the sliding speed at the base, pi and pa are the ice pressure and water pressure at the base of the ice, and k2 is another constant involving a measure of the roughness of the bed. The total flow of a glacier can thus be given by the sum of equations (5) and (6), u1 and u2. The total sum would be an approximation, because the formulas ignore longitudinal changes in velocity and thickness and other complicating influences, but it has proved to be useful in analyzing situations ranging from small mountain glaciers to huge ice sheets.
Other studies have suggested that many glaciers and ice sheets do not slide on a rigid bed but “ride” on a deforming layer of water-charged sediment. This phenomenon is difficult to analyze because the sediment layer may thicken or thin, and thus its properties may change, depending on the history of deformation. In fact, the process may lead to an unsteady, almost chaotic, behaviour over time. Some ice streams in West Antarctica seem to have exhibited such unsteady behaviour.
Response of glaciers to climatic change
The relationship of glaciers and ice sheets to fluctuations in climate is sequential. The general climatic or meteorological environment determines the local mass and heat-exchange processes at the glacier surface, and these in turn determine the net mass balance of the glacier. Changes in the net mass balance produce a dynamic response—that is, changes in the rate of ice flow. The dynamic response causes an advance or retreat of the terminus, which may produce lasting evidence of the change in the glacier margin. If the local climate changes toward increased winter snowfall rates, the net mass balance becomes more positive, which is equivalent to an increase in ice thickness. The rate of glacier flow depends on thickness, so that a slight increase in thickness produces a larger increase in ice flow. This local increase in thickness and flow propagates down-glacier, taking some finite amount of time. When the change arrives at the terminus, it causes the margin of the glacier to extend farther downstream. The result is known as a glacier fluctuation—in this case an advance—and it incorporates the sum of all the changes that have taken place up-glacier during the time it took them to propagate to the terminus.
The process, however, cannot be traced backward with assurance. A glacier advance can, perhaps, be related to a period of positive mass balances, but to ascertain the meteorological cause is difficult because either increased snowfall or decreased melting can produce a positive mass balance.
The dynamic response of glaciers to changes in mass balance can be calculated several ways. Although the complete, three-dimensional equations for glacier flow are difficult to solve for changes in time, the effect of a small change or perturbation in climate can be analyzed readily. Such an analysis involves the theory of kinematic waves, which are akin to small pulses in one-dimensional flow systems such as floods in rivers or automobiles on a crowded roadway. The length of time it takes the glacier to respond in its full length to a change in the surface mass balance is approximately given as the ratio of ice thickness to (negative) mass balance at the terminus. The time scale for mountain glaciers is typically on the order of 10 to 100 years—although for thick glaciers or those with low ablation rates it can be much longer. Ice sheets normally have time scales several orders of magnitude longer.
Glaciers and sea level
Sea level is currently rising at about 1.8 millimetres (0.07 inch) per year. Between 0.3 and 0.7 millimetres (0.01 to 0.03 inch) per year has been attributed to thermal expansion of ocean water, and most of the remainder is thought to be caused by the melting of glaciers and ice sheets on land. There is concern that the rate in sea-level rise may increase markedly in the future owing to global warming. Unfortunately, the state of the mass balance of the ice on the Earth is poorly known, so the exact contributions of the different ice masses to rising sea level is difficult to analyze. The mountain (small) glaciers of the world are thought to be contributing 0.2 to 0.4 millimetres (0.01 to 0.02 inch) per year to the rise. Yet the Greenland Ice Sheet is thought to be close to balance, the status of the Antarctic Ice Sheet is uncertain, and, although the floating ice shelves and glaciers may be in a state of negative balance, the melting of floating ice should not cause sea level to rise, and the grounded portions of the ice sheets seem to be growing. Thus, the cause of sea-level rise is still not well understood.
With global warming, the melting of mountain glaciers will certainly increase, although this process is limited: the total volume of small glaciers is equivalent to only about 0.6 metre (2 feet) of sea-level rise. Melting of the marginal areas of the Greenland Ice Sheet will likely occur under global warming conditions, and this will be accompanied by the drawing down of the inland ice and increased calving of icebergs; yet these effects may be counterbalanced to some extent by increased snow precipitation on the inland ice. The Antarctic Ice Sheet, on the other hand, may actually serve as a buffer to rising sea level: increased melting of the marginal areas will probably be exceeded by increased snow accumulation due to the warmer air (which holds more moisture) and decreased sea ice (bringing moisture closer to the ice sheet). Modeling studies that predict sea-level rise up to the time of the doubling of greenhouse gas concentrations (i.e., concentrations of atmospheric carbon dioxide, methane, nitrous oxide, and certain other gases) about the year 2050 suggest a modest rise of about 0.3 metre (1 foot).
