Glaciers

moving natural accumulations of ice of atmospheric origin on the earth’s surface. Glaciers are formed from solid precipitation in areas in which more precipitation is deposited during the year than melts and evaporates: Thus, glaciers consist of an alimentation area and an ablation area, separated by the alimentation line (a line on the glacier at which the ice gain during the year equals the ice loss). In cold regions the ablation area may be represented by just the terminal scarp from which icebergs (the Antarctic Ice Sheet) or glacial avalanches (hanging glaciers) break off. The dimensions, shape, and structure of a glacier are determined by the topography of the area, the ratio between the ice gain and ice loss across the external surface, and the slow movement of the glacier under the effect of gravity.

Distribution, dimensions, and morphology. In tropical and temperate latitudes glaciers can be found in high mountains, and in sufficiently wet polar regions they can also be found in low-lands and shallow seas. Morphologically, glaciers are divided into three types: terrestrial ice sheets, ice shelves, and mountain glaciers. On ice sheets the ice flows from the ice divides toward the periphery regardless of the underlying relief; in ice shelves the ice flows from the shore to the sea in the form of slabs that float or partially rest on the bottom. In mountain glaciers the ice flows down through valleys or down slopes. The shape of mountain glaciers is diverse and depends on the underlying terrain. Among mountain glaciers the following types are distinguished: hanging (located on steep high slopes of mountains), cirque (located in depressions or cirques near the peaks of mountains), valley (simple, compound, and dendritic), reticular, and piedmont.

Glaciers cover areas from hundreds of meters to 5,600 X 2,900 km and are from 10–20 m to several kilometers thick. (In some places the thickness of the Antarctic Ice Sheet has been measured and found to be 4.3 km.) The largest mountain glacier is Bering Glacier in Alaska, with a length of 170 km. In the USSR the largest mountain glacier is the Fedchenko Glacier in the Pamirs, with a length of 77 km. The total area of modern glaciers is approximately 16.1 million sq km (11 percent of the land area), and the total volume is of the order of 30 million cu km. Of these figures, continental ice sheets account for 89.6 percent and 98 percent, respectively; ice shelves for 9.1 percent and about 2 percent, respectively; and mountain glaciers for 1.3

percent and approximately 0.1 percent, respectively. The area of glaciers in the USSR is 71,665 sq km (see Table 1). In accumulating an enormous quantity of pure fresh water, glaciers have a substantial effect on many aspects of human economic activity. The role of glaciers is particularly great in arid regions—for example, in Middle Asia, where a significant part of the supply of water for the rivers comes from glaciers. To adopt a scientific approach to the problem of rationally utilizing and replenishing the water resources contained in glaciers, it is necessary to understand the conditions that control gain and loss of glacial material, as well as the nature and regime of surface and internal processes.

Regime of surface processes. The distribution of ice gain and loss at the surface of a glacier changes over time depending on the state of the atmosphere and is a function of the albedo, altitude, gradient, the curvature of the particular section of the glacier’s surface, and the glacier’s orientation relative to the sun and the wind. A calculation of the alimentation and ablation rates, based on data on the state of the atmosphere and the surface, is a problem of glacio-meteorology that is common to all types of snow and ice cover.

Snow turns into névé and ice in the alimentation area as a result of settling under the pressure of the layers of snow accumulating above, accompanied by recrystallization, and as a result of the partial melting and freezing of water percolating into the pores. Depending on the relative participation of these processes, ice formation zones are distinguished on the surface of a glacier; the distribution of the zones is caused by the relationship between the amount of precipitation and summer melting (see Figure 1).

Figure 1. Ice formation zones and structure of surface layer of a standing glacier: (1) in dry cold regions, (2) in relatively warm wet regions. Ice formation zones: (I) recrystallization zone, (II) cold infiltration zone, (IIIl) ice alimentation zone, (IIIf) warm infiltration zone, (IV) ablation zone. Lines or boundaries: (a) alimentation line, (b) névé line, (c) 0° isotherm line at the depth of abatement of annual temperature fluctuations. Structure of surface layer: (A) snow and recrystallization névé and ice, (B) infiltration névé and ice, (C₁) superimposed ice, (C₂) deep ice. Boundaries of layers (thickness of the layers in diagram is given approximately; the vertical scale in zones I-IV differs): (1, 2, 3c) boundary of the accumulation of the last three years [dotted line gives boundary of melting] at the end of summer, (3a) boundary of the greatest height of last year’s snow surface, (3b) boundary of the greatest height of last year’s superimposed ice surface. (7) temperature.

In the interior of continental sheets and high in the mountains where melting does not take place, there lies a recrystallization or snow zone. The névé is turned into ice at a great depth, and the temperature of the névé at a depth of the abatement of annual temperature fluctuations equals the mean annual air temperature. (At the world pole of cold in the center of Antarctica, ice is found at a depth of more than 100 m, the mean temperature is — 61°C, and the absolute minimum is of the order of — 90°C.) Below that lies the cold infiltration or névé zone, where all the meltwater freezes in the pores of the névé without turning the névé into ice and without warming the entire layer to the melting point. Still further below that there is differentiation of the ice formation zones.

In dry cold regions there is an ice alimentation zone where the snow cover, in becoming saturated with water, turns into a layer of ice (superimposed ice) every year, and the temperature of the underlying ice remains below zero. In comparatively warm and wet regions the lower part of the alimentation area is part of the warm infiltration or névé zone in which the meltwater seeps through the névé layer, warming it to the melting point, and runs off the glacier along crevices inside the glacier and along subglacial channels. Owing to the differing mechanism of the penetration of warm and cold waves, the warm névé zone extends into regions with a mean air temperature of down to — 8°C; in zones where the air temperature is lower than — 8°C, in the ablation area, the ice temperature is below zero. Under the névé layer the density of the ice changes an insignificant amount owing to the compression of trapped air, increasing sharply only in the bottom layer owing to the moraine.

Regime of internal processes. Under the effect of gravity, a stress field is set up in a glacier, causing deformation of the ice. Under a slowly changing load the polycrystalline ice is deformed like a macroscopically isotropic nonlinearly viscous fluid, with a hyperbolic dependence of the steady-state creep rate on the stress deviator (the difference between the stress and the pressure) and with an exponential dependence on the absolute temperature (T). The flow is accompanied by recrystallization, and after recrystallization the rate of flow increases by an order of magnitude. Under sufficiently high stress, tension fractures occur in the upper layer, and shearing occurs in the interior. When the temperature is close to the melting point, movement along the thrust-fault planes is accompanied by melting and refreezing with the formation of a banded structure. Under the same conditions, the ice slips along the bottom as a result of melting brought on by the increased pressure in front of protrusions of the bottom and the freezing of extruded water behind them, as well as a consequence of the accelerated flow of the ice around the protrusions of the bottom owing to the concentration of stresses. In the process the bottom is scoured by rock fragments contained in the ice.

The interrelated stress, velocity, and temperature fields of glaciers are described by a system of 18 partial differential equations. The system includes equations expressing the laws of (1) mass conservation (equation of continuity), (2) energy conservation (equation of heat conductivity, heat transfer, and heat release under deformation), and (3) momentum conservation (owing to the low speed these equations reduce to equilibrium force equations); there are also rheological equations relating the rate of flow, the stress, and the temperature, and compatibility equations for the components of the deformation rate tensor, expressing the conditions of integrability of the vortex field of the velocity of the ice.

The stress, velocity, and temperature fields of glaciers are determined by the boundary conditions on the glacier’s external surface. The upper and underwater surfaces are under hydrostatic pressure (of the atmosphere or water) and are free of shearing stress; but the basal surface of ground glaciers experiences, in addition, shearing stresses caused by friction against the bottom. The temperature of the upper layer at the level of the abatement of annual fluctuations depends on the mean temperature of the air and the ice formation zone. The temperature of the underwater surface is at the melting point, while the temperature on the bottom depends on the ratio of the influx of geother-mal heat to its dissipation inside the glacier, that is, on the temperature gradient, as well as on the movement of the ice. If the influx of heat exceeds the outflow, then melting and slippage of ice occur on the bottom under the influence of the shearing stress; moreover, the heat from friction on the bottom is also expended on melting.

In the case of uniform isothermal (melting) ice, the stress and velocity fields are described by a system of elliptical equations, and changes in the fields over time are caused solely by changes in the boundary conditions. An analytical solution is obtained only for planar flow in a viscous (Newtonian) approximation, which leads to biharmonic equations for the components of the stress deviator and the rate of deformation. For three-dimensional glaciers that are thin in comparison with the horizontal dimensions and have no major irregularities on the bottom, a satisfactory approximate solution is obtained by disregarding the normal stress components that under such conditions are less than the tangential stress by one to two orders of magnitude.

Observations and calculations provide velocity fields of a glacier with special points (maxima and minima) and lines (races and ice divides) on the external surface. The points and lines are closely linked to morphology, since the velocity on the upper surface is proportional to the gradient of the surface and to the thickness of the ice by not less than the third to the fifth power. Thus, the velocity decreases with depth, and the closer to the bottom, the more rapidly it decreases. Accordingly, in a glacier, there is, as it were, a slipping of thin layers of ice against each other; the layers are roughly parallel to the bottom and extend lengthwise and taper off in the alimentation area and at the same time are compressed lengthwise and grow thicker in the ablation area. This deformation is accompanied by lateral compression or tension from changes in width in mountain glaciers and by tension during the radial flow of ice sheets. The flow lines enter the interior of the glacier in the alimentation area and emerge from the glacier in the ablation area and are parallel to the surface at the alimentation boundary.

In cold glaciers the velocity is equal to zero on the bottom, and the main shear deformation occurs in the relatively warmer bottom layer where heat of deformation is released, while the rigid upper ice moves almost without being deformed at all. The temperature field is significantly affected by the transfer of cold by ice that descends into the glacier in the alimentation area and moves into the warmer lower parts of the glacier. Consequently the temperature here initially decreases with depth and then rises in the bottom layers from internal heat release and geothermal heat. In an isothermal glacier all the heat of deformation is expended on the internal melting of the ice. The higher the shear stress, the greater the rate of slipping along the bottom, so that the thin layers of ice that slip over each other in an isothermal glacier are not parallel to the bottom but are rather, as it were, sheared off by it. Some of the flow lines terminate at the bottom and inside the glacier, where bottom and internal melting occurs.

In the steady state the flow lines coincide with the trajectories of the ice particles, which makes it possible to calculate the age field of the ice that corresponds to this state (the positions of isochronous surfaces and of the annual ice layers). In plan view the flow lines deviate from the surface gradient lines (in mountain glaciers up to 45°) in a direction opposite to the midstream line under the effect of the torque created by the drag of the slower moving lateral masses of ice. The maximum speed of mountain glaciers is usually from several meters per year in small glaciers to several hundred meters in large ones. For ice shelves it is 1.9 km per year and up to 7.3–13.8 km per year for certain finger glaciers on the western edge of the Greenland Ice Sheet.

Fluctuations. If a glacier is in a steady state, the position of its surface does not change, since the resultant rate of movement of the surface along a perpendicular to the surface itself due to alimentation or ablation and to the movement of the ice equals zero. However, this condition is never fulfilled owing primarily to the alternation of the weather and the seasons. Thus, at best only a quasi-steady state is possible, with a return to the initial position after the annual cycle of changes.

If a glacier is in a nonsteady state, the external alimentation line does not coincide with the kinematic boundary at which the velocity vector is parallel to the surface and the velocity component perpendicular to the surface equals zero. The position of the kinematic alimentation boundary is much more stable than the external alimentation boundary; it moves slowly, and for this reason is simultaneously the structural boundary between the area of annual layers that are parallel to the surface above and the area of the exposure of inner structures and moraines below.

In the process of glacier fluctuations, there is a change in the magnitude of the flow rate as well as slow changes in the configuration of the velocity field—that is, in the direction of the flow lines and the position of special points and lines.

The nature of glacier fluctuations is determined by the glaciers’ physical peculiarities. Among these peculiarities are their nonautonomous, dissipative, and aperiodic nature (the absence of restoring forces and the resistance to disturbing forces only by quasi-viscous dissipation), their activity (the presence of internal sources of gravitational energy), the nonlinearity of kinematic relationships and boundary conditions, and their nonuniformity in time owing to the nonsteady nature of the relationships.

Similar physical systems can be subject to fluctuations of two types: induced fluctuations and relaxation autofluctuations. The former are transformations of fluctuations of the external load —that is, the rate of alimentation or ablation caused by random and cyclic (due to astronomical factors) fluctuations in the state of the atmosphere; the latter are processes of periodic relaxation caused by the nonsteady nature of the glacier’s conditions, that is, by changes in the frictional force against the bottom and by the crushing of the ice.

All glaciers are constantly subjected to induced fluctuations, while self-triggered fluctuations are inherent only to certain glaciers as active nonlinear systems. With induced fluctuations, the flow of mass between the glacier and the environment receives a positive or negative acceleration, and there is a relationship between the frequencies and phases of the fluctuations of the external flow and the velocity of the ice. With self-triggered fluctuations, there is an acceleration of the movement of the ice that is independent of external influences, and there is no relationship between the frequencies and phases of the fluctuations of the external and internal flows of the mass. Here the characteristics of the movement are interrupted in time owing to a periodic rupture of some of the relationships and the subsequent slow reestablishing of the relationships with a recurrence cycle of from ten to 100 years. In this category are kinematic waves, which can cause glacier termini to surge forward for up to 10–20 km at a speed of up to hundreds of meters per day.

Such surges are known in the Alps, the Caucasus, Tien-Shan, the Pamirs, the Karakoram, Kamchatka, Spitsbergen, Iceland, North America, South America, and New Zealand. On the territory of the USSR, more than 70 cases of surges have been established. In 1963, as a result of the catastrophic surge of the Medvezh’ii Glacier into the headwaters of the Vanch River in the Pamirs, it descended 1.6 km down the valley. The surge was accompanied by the formation of a dammed lake and the destruction of a geologists’ camp. This glacier moved again in 1973, but owing to the measures that were taken, it was possible to avoid catastrophic consequences. In 1969 the Kolka Glacier, which is 3 km long and lies in Severnaia Osetiia, advanced 4.6 km, covering up the wells drilled for mineral water. (The preceding catastrophic surges of the Kolka Glacier in 1835 and 1902 were practically ice avalanches.)

For induced fluctuations of glaciers, the local reaction of stress and velocity to the changes in the external load is instantaneous and steady—that is, it is directed toward restoring an equilibrium. But this process requires a more or less extended period of time for its completion, and for continental ice sheets it is evidently of the order of thousands of years.

Induced fluctuations of glaciers have a complex frequency spectrum, part of which corresponds to periods of time that are significantly shorter than those of the transient processes. Therefore, induced fluctuations of glaciers constantly occur under a nonsteady transitional state, or asynchronously: simultaneously, part of the glacier retreats, another part advances, and a third part is in a quasi-steady state. Only over a sufficiently long period of time can periods of a predominance of advances or retreats be established.

Until the 1940’s a retreat of glaciers predominated, and then this was replaced in places by an advance. In the geological past the largest glacier fluctuations have led to the alternation of glacial and interglacial ages, glacial and ice-free periods. An important role has also been played by feedback—that is, the effect of snow and ice cover on climate.