Mass balance

Glaciers exist because there are areas, generally at high elevations or in polar latitudes, where snow fall during the winter exceeds melt (and other losses) during the summer. This results in net accumulation, and this part of the glacier is thus called the accumulation area (Figure 3.1). As each snow layer is buried, the pressure of the overlying snow causes compaction, and movement of molecules in the liquid and vapor phases results in snow metamorphism. Snow that is more than a year old, and has thus been altered by these processes, is called firn. The end result of the firnification process, normally after several years, is solid ice.

Where there are lower elevations to which this ice can move, gravitational forces drive it toward these areas. This eventually brings the ice into places where the annual melt exceeds snow fall. Here, all of the winter snow and some of the underlying ice melts during the summer. This is called the ablation area. The line separating the accumulation and the ablation areas at the end of a melt season is called the equilibrium line. Along the equilibrium line, melt during the just-completed summer exactly equaled net snow accumulation during the previous winter.

In this chapter, we first discuss the transformation of snow to ice, and show how the processes involved result in a physical and chemical stratigraphy that, under the right circumstances, can be used to date ice that is thousands of years old. We then explore the climatic factors that result in changes in the altitude of the equilibrium line, and hence in advance and retreat of glaciers.

Glacier Mass Balance Processes
Figure 3.1. Cross sections of: (a) a typical polar ice cap or ice sheet, and (b) a typical valley glacier, showing the relation between equilibrium line and flow lines. Sketches are schematic, but relative proportions are realistic.

The transformation of snow to ice

The first phase of the transformation of snow into ice involves diffusion of water molecules from the points of snow flakes toward their centers; the flakes thus tend to become rounded, or spherical (Figure 3.2a), reducing their surface area and consequently their free energy. This is an example of an important thermodynamic principle, namely that the free energy of a system tends toward a minimum. Such rounding occurs more rapidly at higher temperatures.

Trapped air bubbles

Figure 3.2. Transformation of snow to ice. (a) Modification of snow flakes to a subspherical form. (b) Sintering. (c) Processes during sintering: 1 = sublimation, 2 = molecular diffusion within grains, 3 = nucleation and growth of new grains, and 4 = internal deformation of grains. (Based on Sommerfeld and LaChapelle, 1970, Figures 2, 16, and 17; and on Kinosita, 1962, as reported by Lliboutry, 1964, Figure 1.14.)

The closest possible packing of spherical particles would be one with a porosity of about 26%, the so-called rhombohedral packing. However, in natural aggregates of spheres of uniform diameter, the pore space is usually closer to 40%. In the case of firn, this corresponds to a density of ~550 kg m—3.

Further densification involves a process called sintering (Figure 3.2b), which involves transfer of material by sublimation and by molecular diffusion within grains, nucleation and growth of new grains, and internal deformation of the grains (Figure 3.2c). Sublimation is more important early in the transformation process when pore spaces are still large. Internal deformation increases in importance as the snow is buried deeper and pressures increase. In warm areas, the densification process is accelerated, both because grains may be drawn together by surface tension when water films form around them, and because percolating melt water may fill air spaces and refreeze.

An important transition in the transformation process occurs at a density of ~830 kg m—3. At about this density, pores become closed, preventing further air movement through the ice. Studies of the air thus trapped provide information on the composition of the atmosphere at the time of close off (see, for example, Raynaud etal., 1993). Measurements of the volume of such air per unit mass of ice yield estimates (albeit fairly crude, given present technology) of the altitude of the pores at the time

Accumulation area

Accumulation area

Ablation area

Maximum surface height in current year

Maximum height / of superimposed -X ice

-Surface at end of previous summer

Snow

Snow with ice layers and lenses Superimposed ice

Superimposed ice zone

Figure 3.3. Variation in snow facies with altitude. (After Benson, 1962.) Horizontal distance from equilibrium line to dry-snow line is tens to hundreds of kilometers.

Ablation area

-Surface at end of previous summer

Maximum surface height in current year

Maximum height / of superimposed -X ice nrm

Snow

Snow with ice layers and lenses Superimposed ice

Superimposed ice zone

Figure 3.3. Variation in snow facies with altitude. (After Benson, 1962.) Horizontal distance from equilibrium line to dry-snow line is tens to hundreds of kilometers.

of close off (Martinerie et al., 1992). Knowing the depth in the glacier at which this occurs then permits an estimate of the elevation of the ice surface at that time. Pore close off can occur at depths of tens to over a hundred meters, depending on temperature (Paterson, 1994, Table 2.2).

Snow stratigraphy

At high elevations on polar glaciers, such as the Antarctic or Greenland ice sheets, there are areas where no melting occurs during the summer. At somewhat lower elevations, some melting does occur, and the meltwater thus formed percolates downward into the cold snow where it refreezes, forming lenses or gland-like structures. The higher ofthese two zones is called the dry-snow zone and the lower is the percolation zone (Figure 3.3) (Benson, 1961;Muller, 1962). In keeping with stratigraphic terminology in geology, parts of the annual snow pack on an ice sheet that have distinctive properties are referred to as facies - in this case the dry-snow facies and the percolation facies, respectively. The boundary between these two zones or facies, the dry-snow line, lies approximately atthe elevation where the mean temperature ofthe warmestmonth is -6 °C (Benson, 1962, cited by Loewe, 1970, p. 263).

At lower elevations, summer melting is sufficient to wet the entire snowpack. This is called the wet-snow zone (Figure 3.3). When this snow refreezes, a firm porous layer is formed. In downglacier parts of this zone, the basal layers of the snow pack may become saturated with water. If the underlying ice is cold, this water-saturated snow may refreeze, forming ice that is called superimposed ice. As long as it is still undeformed, superimposed ice is readily recognized by its air bubbles, which are large and often highly irregular in shape.

At still lower elevations, only superimposed ice is present at the end of the melt season, and this is thus called the superimposed ice zone. The lower boundary of the superimposed ice zone at the end of the melt season is the equilibrium line.

On typical alpine glaciers, the first water percolating into cold snow at the beginning of the melt season may refreeze to form glands and lenses as on polar ice sheets. However, by the end of the melt season, the entire snow pack will have been warmed to the melting point. Thus, neither the dry-snow nor the percolation facies are present on these glaciers. Furthermore, on a temperate glacier, heat conduction downward into the glacier beneath the snow pack is minimal, so little superimposed ice is formed.

Most of the warming of alpine snow packs is a result of the release of latent heat during refreezing of the first water to infiltrate. Freezing of 1 kg of water can warm 160 kg of snow 1 °C. Conduction of heat from the surface is insignificant by comparison.

In addition to the zonation in snow stratigraphy with altitude (or temperature), particularly onpolar glaciers, there is also a distinct vertical zonation at any given point on a glacier. Because the autumn snow in an annual layer is warmer than the overlying winter snow, the former has a higher vapor pressure. Thus, a vapor-pressure gradient exists, resulting in diffusion of molecules from the autumn to the winter snow. The autumn snow thus becomes coarser, and its density may decrease. These layers of coarse autumn snow are called depth hoar. Tabular crystals are the norm in depth hoar, but in extreme cases, large prism-shaped, pyramidal, or hollow hexagonal crystals develop.

Dating ice using preserved snow stratigraphy

Depth hoar layers are important because they can be recognized at depth in snow pits and ice cores. Using such stratigraphic markers, glaciologists have been able to determine accumulation rates, averaged over several years or decades, in many areas of Antarctica and Greenland, and in some cases over millennia in deep cores from these ice sheets.

In one of the most remarkable examples of the use of such physical stratigraphy, Alley et al. (1993) found that the accumulation rate high on the Greenland Ice Sheet increased by approximately a factor of two at the end of the Pleistocene, and that the change took place in a time span of only three or four years! The increase in the accumulation rate

Depth along core segment, m

Figure 3.4. Variations of S18O in the Camp Century, Greenland, ice core. (a) Ice from 1963 to 1968. (b) Ice that is approximately 8300 years old, and in which seasonal variations can still be detected. (Adapted from Johnsen et al, 1972. Reproduced with permission of the authors and Nature.)

Depth along core segment, m

Figure 3.4. Variations of S18O in the Camp Century, Greenland, ice core. (a) Ice from 1963 to 1968. (b) Ice that is approximately 8300 years old, and in which seasonal variations can still be detected. (Adapted from Johnsen et al, 1972. Reproduced with permission of the authors and Nature.)

was attributed to a warming of the climate, and it was this warming that caused retreat of the ice sheets.

Dating of ice can also be accomplished by detailed laboratory studies of cores or of samples from pit walls. The most commonly used technique for this purpose involves measuring S18O variations. Because the air is colder during the winter, S18O values in winter snow are more negative (the snow contains less of the heavier isotope of oxygen, 18O) than in summer snow. Thus, a series of samples taken from a single annual layer will show a roughly sinusoidal variation in S18O (Figure 3.4). A prodigious number of samples must be analyzed when this technique is used to date very old ice. However, annual layers, much compressed but still recognizable by their isotopic variations, have been identified in ice more than 8000 years old (Figure 3.4). Thus, the potential is there, and techniques for making the analyses rapidly have been developed.

The electrical conductivity of ice and the concentration of micropar-ticles in ice also vary seasonally. The former is a consequence of seasonal variations in the aerosol content of the snow. The seasonality in micropar-ticle concentration is the result of entrainment of dust by wind during the summer when outwash plains and similar surfaces are free of snow (see, for example, Thompson etal., 1986). Both these variations are used for dating.

When such techniques are used to date relatively old ice, errors accumulate because some annual layers either lack a variation of the parameter being used, or on occasion have two cycles of variation. However, volcanic ash layers are frequently found in cores, and when ash chemistry permits attribution of a layer to an eruption of known age, an absolute date can be assigned to the ice containing the ash. In this way, the age of ice that is thousands of years old has been established quite accurately.

Mass balance principles

A number of terms are used to describe different aspects of the mass balance on a glacier. The winter balance is the amount of snow that accumulates during the winter months. Conversely, the summer balance, a negative quantity, is the amount of snow and ice lost by melt. Over the course of a balance year, which is commonly taken to extend from the end of one melt season to the end of the next, the sum of the winter and summer balances is the net balance. Normally, these balances are expressed in terms of the thickness of a layer of water, or in water equivalents. When referred to a specific place on the glacier, they are expressed in m a— \ or kg a—!m—2, and are called specific balances. Sometimes the word budget is used instead of balance, particularly when referring to the net balance.

Significant amounts of accumulation may occur during the summer in the accumulation areas of polar glaciers, and conversely melt may occur throughout the winter in the ablation areas of some temperate glaciers. The terms summer and winter balance are applied with some poetic license in these instances. The most extreme example of this is on tropical glaciers where accumulation and melt may alternate on a time scale of hours to days. Despite these complications, the basic principles are still applicable.

There are a number of ways of measuring mass balance, and we will not go into them all here. Perhaps the most common method, and the one that is easiest to visualize, is to measure the height of the snow or ice surface on stakes that are placed in the glacier in holes drilled for the purpose. The measurements are made first at the end of one melt season, then at the end of the following winter to obtain the winter balance, and finally at the end of the next melt season to obtain both the summer and the net balances. Snow density measurements must also be made in order to convert the winter accumulation and summer snow melt to water equivalents.

We define bs(x,y,z) as the specific summer balance, bw(x,y,z) as the specific winter balance, and bn(x,y,z) as the specific net balance. Clearly, bn = bs + bw (3.1)

and the overall state of health of the glacier can be evaluated from:

where A is the area of the glacier and Bn is the net balance. Bn is often normalized to the area of the glacier, thus: bn = Bn/A. When Bn or bn are positive, the glacier is said to have a positive mass balance; if this condition persists for some years, the glacier will advance, and conversely. Thus Bn is an important parameter to measure and to understand, and to this end we now consider meteorological factors influencing its components, bs and bw.

It is convenient to restrict our discussion to variations in bs and bw with elevation, z. This is not normally valid in practice because of the effects of drifting and shading, which result in lateral variations in both accumulation and melt.

It is common to plot bn(z) as a function of elevation; this is illustrated with data from a valley glacier in the Austrian Alps, Hintereisferner, in Figure 3.5a. The curve labeled "o" in this figure represents the situation during a year in which the mass budget is balanced, or Bn = 0. (Despite the low values of bn at higher elevations, JAbndA = 0 in this instance because, as is true of most valley glaciers, the width of Hintereisferner increases with elevation.) Curves labeled "+" and "-" represent years of exceptionally positive or negative mass balance, respectively. Note that melting normally increases nearly linearly with decreasing elevation, so the lower parts of the curves in Figure 3.5a are relatively straight. However, at higher elevations in this particular case, snow fall decreases with elevation, resulting in curvature in the upper parts of the plot.

The differences between the "o" curve and the "-" and "+" curves are shown in Figures 3.5b and c, respectively. These differences are referred to as the budget imbalance, bi (Meier, 1962). In years of exceptionally negative bn (Figure 3.5b), bi typically increases with decreasing elevation; this means that such years are normally a consequence of unusually high summer melt. Conversely, unusually positive budget years commonly result from exceptionally high winter accumulations

Specific net budget, Mg m 2

0 1000 0 1000 Imbalance and standard deviation, kg m-2

b = budget imbalance <r = standard deviation

Figure 3.5. (a) Specific net budget, bn, plotted against elevation for Hintereisferner. Curve "o" is for a year of balanced mass budget, while curves "—" and "+" are for years of exceptionally negative or positive budget, respectively. (b) and (c) Difference between curve "o" and curves "-" and "+", respectively. (After Kuhn, 1981, Figure 1. Reproduced with permission of the author and the International Association of Hydrological Sciences.)

(Figure 3.5c). Budget years that are only moderately positive or negative can result from deviations of either accumulation or melt from their values in years when the budget is balanced.

Programs of mass balance measurements normally continue for several years. Cumulative mass balances can then be calculated by summing the annual values of Bn. There are two ways of doing this, however. In the conventional approach, A in Equation (3.2) should be adjusted annually to reflect expansion or shrinkage of the glacier. (In practice, new maps of the glacier are not prepared every year, and as A varies slowly it is more common to use the same value of A for several years and then adjust it when a new map is made.) In the reference-surface approach (Elsberg et al., 2001), on the other hand, A is the area of the glacier surface at a particular time, such as the time of the first mass balance survey if a good map exists for that time, and is not changed during the course of the program. Furthermore, the annual measurements are then adjusted to the level of the reference surface with the use of measured or estimated values of dBn/dz. The conventional approach is better for hydrological forecasting and other applications when the actual change in glacier volume is desired. However, for studies of climate, the reference-surface approach is more useful because it provides a measure of climate change at a fixed reference elevation.

Climatic causes of mass balance fluctuations

Let us assume that bw is composed of precipitation and drifting alone, thus ignoring mass additions by condensation and avalanching. Likewise, we take bs to be a function only of surface melt, ignoring mass losses by evaporation, calving, bottom melting, and so forth. Although we assume that mass additions and losses by condensation and evaporation, respectively, are negligible, the energy involved in these phase change processes is taken into consideration in the following analysis. Surface melting is controlled by the available energy:

where Q is the energy in kJ m-2d-1; R is the net radiation; H is the sensible heat input; and V is the latent heat input due to condensation, or loss due to evaporation (Kuhn, 1981). Then, neglecting any summer snow fall:

where T is the length of the melt season and L is the latent heat of fusion, 334 kJ kg-1. (In the remainder of this discussion it will be convenient to use kg m-2a-1 for the units of mass balance.)

Assume further that the transfer of sensible and latent heat to the glacier surface is proportional to the temperature difference between the air and the glacier surface, thus:

where Ta and Ts are the temperatures of the air and the glacier surface, respectively, and y is a constant of proportionality. Kuhn (1989) suggests that y lies between 0.5 and 2.7 MJ m-2d-1K-1; a value frequently found for firn is 1.0 MJ m-2d-1 K-1, while a reasonable mean value for glacier ice is ~1.7 MJ m-2d-1K-1. The range of values reflects the fact that the actual heat transfer is strongly influenced by such factors as the wind speed and the roughness of the glacier surface.

Combining Equations (3.1), (3.3), (3.4), and (3.5), rearranging terms, and writing all of the parameters as functions of elevation, z, yields: T

bw(z) = L [R(z) + Y(Ta(z) - Ts)] + bn(z) (3.6)

As we are dealing with melting conditions, Ts = 0, and does not vary with z.

Climatic causes of mass balance fluctuations 27

Our objective now is to study quantitatively how changes in winter precipitation, summer temperature, and radiation balance affect a glacier's mass balance. Curves "—", "o", and "+" in Figure 3.5a are nearly parallel to one another, suggesting that one may be "derived" from another simply by a lateral translation. Such a translation, however, results in a change in the equilibrium line altitude (ELA), represented in Figure 3.5a by the point where the curves cross the 0 specific net balance line. This suggests that changes in equilibrium line altitude may be a fairly good measure of the impact of climate variations. The effects of changes in the principal measures of climate, namely precipitation and temperature, on the ELA are best studied with the use of perturbation theory, a technique used by Kuhn (1981), whose approach we adopt herein.

At the equilibrium line, bn(z) = 0 by definition. Thus if h is the elevation of the equilibrium line and ho is its elevation in a year of balanced mass budget, Equation (3.6) can be rewritten as:

The standard approach in perturbation theory is to rewrite Equation (3.7) for a situation in which the equilibrium line is at an elevation, h, which is slightly higher or lower than in the "o" state, and then to subtract this new relation from Equation (3.7), which we now proceed to do. Let primed values represent the perturbed state, thus:

Subtracting:

bw(h) — bw(h0) = l[R (h) — R(ho) + Y(Ta'(h) — Ta(h0))] (3.9)

Any of the primed parameters in Equation (3.9) that vary with z can be represented by perturbation equations of the form, using Ta as an example:

Here, Ah may be an observed change in altitude of the equilibrium line, so (9Ta/dz)Ah represents the change in temperature that would be expected simply because the ELA changed. However, a change in mean summer air temperature may have been partially responsible for the change in ELA, and this part of the change in Ta is represented by 5Ta. Figure 3.6 is a graphical representation of Equation (3.10). Writing equations similar to (3.10) for bw and R, rearranging them, and substituting

Table 3.1. Possible causes of a 100 m increase in ELA

Sbw = -400 kg m-2 if STa = SR = 0

SR = +1.35 MJm-2d-1 if Sbw = STa = 0

STa = + 0.8 °C if Sbw = SR = 0

Figure 3.6. Sketch illustrating parameters in Equation (3.10). Consider a year during which the equilibrium line is at elevation h, Ah m above its elevation, ho, in years when the mass budget is balanced. The lapse rate during a year of balanced mass budget and during the year in question are represented by the slopes of the slanting solid and dashed lines, respectively. To obtain the mean air temperature, ta', at elevation h during this warm summer, start with Ta(ho), add (dTa/dz)Ah keeping in mind that dTa/dz is negative so this is a negative number, and add 8Ta, following the arrows in the figure. Note that 8Ta is the amount by which the temperature at elevation h exceeds the temperature at this elevation during a year of balanced mass budget.

into Equation (3.9) yields:

'9 , , ..id Ta dbw Ah+sbw=t dz L

The significance of this relation can be elucidated with the use of a numerical example. Suppose dbw/dz = 1 kg m-2m-1, T = 100 d, Y = 1.7 MJ m-2d-1K-1, and the lapse rate, dTJdz, is -0.006 Km-1. Suppose further, for the purposes of this example, that d R/d z = 0, as the radiation input does not vary significantly with elevation. Now consider an increase in the ELA of 100 m (= Ah) in a particular year. Calculate the changes Sbw, SR, and STa that would be sufficient, if they occurred alone, to cause this change in ELA. The reader is encouraged to carry out this calculation in order to gain familiarity with the relation. The answers are given in Table 3.1.

To place the results of this calculation in perspective, at 3050 m on Hintereisferner in the Austrian Alps, an elevation that is slightly above the normal position of the equilibrium line, the mean winter snow fall is 1620 kg m-2 and its standard deviation is 540 kg m-2. Likewise, the mean summer temperature is +0.4 °C, and its standard deviation is 0.8 °C. Comparing these standard deviations with the values of Sbw and STa in Table 3.1, it is clear that a 100 m change in the ELA could result, with nearly equal likelihood, either from a change in bw or from a change in Ta. Similarly, the total radiation input is -46 MJ m-2d-1, while the loss is -40 MJ m-2d-1, leaving a mean radiation balance, R, of —6 MJ m-2d-1. Changes of 1.35 MJ m-2d-1, owing to changes in cloud cover for example, are small compared with the total radiation budget, and thus are not unreasonable.

For comparison, the mean winter balance on Barnes Ice Cap on Baffin Island is -400 kg m-2 (Hooke et al., 1987). Here, a Sbw of -400 kg m-2 is highly improbable, as this would mean virtually no accumulation. Thus in this case, a 100 m change in the ELA would most likely be a result of a change in Ta.

This comparison illustrates a fundamental difference between glaciers in relatively dry but cold areas, areas that we refer to as having a continental climate, and glaciers in warmer wetter maritime climates. Glaciers in continental settings owe their existence to low temperatures, and fluctuations in their mass budgets are strongly (inversely) correlated with mean summer temperature. Conversely, glaciers in maritime settings form in response to high winter snow fall; on such glaciers, the mass balance is less well correlated with Ta alone, and correlations can be improved significantly by adding winter precipitation to the regression. In fact, on some maritime glaciers the correlation of net balance with bw alone is quite good (Walters and Meier, 1989, p. 371).

In the above analysis, Ta and R have been treated as independent variables. This is not strictly correct because an increase in Ta of 1 °C increases R byabout0.3 MJm-2d-1 (Kuhn, 1981). This is a result of the increase in "black body" radiation, which varies as T 4. Incorporating this effect into the above calculation (Table 3.1) reduces STa to +0.7 °C.

The budget gradient

Recall that curve "o" in Figure 3.5a represents the distribution of bn in a year in which the mass budget is balanced. The slope of this curve at the elevation of the equilibrium line in a year of balanced budget, (9bno/dz)ho, is known as the budget gradient. High budget gradients represent situations in which there is a lot of accumulation above the equilibrium line and a lot of ablation below the equilibrium line, and

Figure 3.7. Sketch Z

illustrating difference between low and high budget gradients.

Low,

conversely (Figure 3.7). High budget gradients are thus indicative of high flow rates, as a lot of ice must be transferred from the accumulation area to the ablation area in order to maintain a steady state profile. For this reason, Shumskii (1964, p. 442) referred to dbno/dz as the energy of glaciation and Meier (1961) called it the activity index. (For simplicity we will omit the subscript ho in this discussion, but all derivatives should be understood as being evaluated at the elevation of the equilibrium line during a year of balanced budget.) High subglacial erosion rates are likely to be associated with high budget gradients.

The budget gradient tends to be high on glaciers in maritime settings and low in continental settings. Typical values might be 10 kg m—2m—1a—1 in the former and 3 kg m—2m—1a—1 in the latter (Haefeli, 1962).

To explore factors controlling (dbno/dz), rearrange Equation (3.6) and take its derivative, noting again that Ts = 0 on a melting glacier surface:

Thus dbno/dz depends upon dbw/dz, (T/L)(dR/dz), and (Ty/L) x (d Ta/d z).

On valley glaciers, the precipitation gradient, dbw/dz, is commonly almost negligible. It may become significant if snow drift is important at higher elevations, and is also larger in areas where a significant amount of the summer precipitation occurs as snow at high elevations and rain at low elevations. In the Alps, where this is commonly the case, Kuhn (1981) suggests that a value of 0.5 kg m—2m—!a—1 is reasonable.

The net radiation gradient, dR/dz, is small as long as snow covers the ablation area. However, once ice is exposed, particularly if it has a thin dirt cover, the albedo drops and there is a significant change in R across the firn edge, or boundary between firn and ice. The first ice to become exposed is normally near the snout of the glacier or the margin of an ice cap, and the firn edge rises as the melt season progresses. Taking this into consideration, (T/L)(dR/dz) may be as high as —7 kg m-2m-1 over a 120-d melt season (Kuhn, 1981).

The lapse rate, dTa/dz, is limited by the dry adiabatic rate, —0.010 °Cm-1, but a more realistic free air lapse rate along a glacier surface is -0.007 °Cm-1. Thus, for a 120-d melt season, (Ty /L) (d Ta/dz) is —4.3 kg m-2m-1.

So to explain the differences in dbno/dz between maritime and continental climates, the dominant terms are those involving the lapse rate and, below the equilibrium line, the radiation balance. As d Ta/dz is likely to be comparable in maritime and continental settings, we have to appeal largely to differences in the length of the melt season, T, and in dR/dz. Melt seasons in high arctic continental settings may be a half to a third as long as those in, say, the Alps. Similarly, glaciers in continental settings also tend to be cleaner, thus reducing the albedo contrast across the firn edge, and hence the effective dR/dz. Differences in dbw/dz may contribute some, as summer rain is less likely to be a factor in arctic continental areas.

During a year of balanced mass budget, the ratio of the area of the accumulation zone to that of the entire glacier, the accumulation-area ratio, is typically —0.7 (Glen, 1963). Using terminal and recessional moraines, one can use this ratio to estimate the change in size of an accumulation area, and hence the change in ELA, during a glacier retreat. Then it is clear that the imbalance in bn is:

(see Figure 3.5). Thus, if moraines suggest that an equilibrium line rose by an amount Ah, and if (dbno/dz)no can be estimated, bli(h) can be calculated. To a good approximation, bni(h) is equal to the average of bni(z) over the glacier. In this way, one can estimate the change in climate that produced an observed change in glacier area.

Other modes of ice loss from valley glaciers

Calving

Cliffs form at the snouts of tidewater glaciers and of valley glaciers that end in lakes. Blocks of ice, ranging in size from single ice crystals to hundreds of cubic meters, break off these cliffs and float away to melt in more distant places. This process is called calving. The cliffs typically

Table 3.2. Mass balance of the Greenland and Antarctic ice sheets and of smaller glaciers and ice capsa

Location

Accumulation, Gtb a-1

Runoff, Gt a-1

Galving, Gt a-1

Bottom melting, Gt a-1

Net balance, Gt a-1

Equivalent sea-level rise,c mm a-1

Greenland

520 i 26

297 i 32

235 i 33

32 i 3

-44 i 53

0.05 ± 0.05

Antarctica

2246 i 86

10 i 10

2072 i 304

540 i 26

-376 i 384

-0.1 ± 0.1

Glaciers and

688 i l09d

778 i ll4d

-91 i 36

0.3 ± 0.1

ice caps

a Data from Houghton et al. (2001, p. 648-651 and Table 11.10). b 1 Gt = 1012 kg or a billion metric tons.

c Values are for period 1910-1990, and are based, in part, on models and thus may not agree with figures in previous column.

d Values calculated from data given in Houghton et al. (2001, Tables 11.3 and 11.4).

a Data from Houghton et al. (2001, p. 648-651 and Table 11.10). b 1 Gt = 1012 kg or a billion metric tons.

c Values are for period 1910-1990, and are based, in part, on models and thus may not agree with figures in previous column.

d Values calculated from data given in Houghton et al. (2001, Tables 11.3 and 11.4).

stand 60-80 m above the water level, and may extend to depths of a few hundred meters below the water level (Brown etal., 1982). Mostofthese glaciers are grounded. The termini of some outlet glaciers in Greenland and Antarctica, however, are afloat.

For the most part, the following discussion applies equally to tidewater glaciers and to valley glaciers ending in freshwater lakes. Thus, we will use the term "tidewater" to refer to both, and will understand "submarine" to include sub-lacustrine. In addition, the reader should keep in mind that most tidewater glaciers are in valleys or, once they reach sea level, in fjords.

Although only a fraction of the world's glaciers end in water, calving is an important, if not the dominant, mode of mass loss on these glaciers. It is estimated, for example, that nearly 50% of the ice loss from Greenland is through calving from outlet glaciers that end in fjords (Table 3.2).

The characteristics of ice in the snouts of tidewater glaciers control the size of the ice blocks shed from them and the subaerial height of the faces. The ice is normally temperate; thus water is present along crystal boundaries and this weakens the ice. In addition, the snouts are typically heavily crevassed. These two factors limit the size of ice blocks discharged from such glaciers. The crushing strength of a free-standing column of temperate ice with appreciable intergranular water may be reached at depths as shallow as 60-80 m, and this may limit the height of the calving face.

Ice blocks also become detached below the water level and float upward to the surface, creating dramatic disturbances in the process.

Careful observations of calving events on San Rafael Glacier in Chile suggest, however, that the volume of ice released by these submarine events is not sufficient to account for the observed rate of retreat of the subaerial part of the terminus (Warren et al, 1995). This suggests that melting below the water surface may be an important part of the process we call calving. This suspicion is reinforced by the observation that calving rates are highest in October (Meier et al., 1985), when the water is warmest (Matthews, 1981; Walters et al., 1988).

The calving rate, uc, is usually determined by measuring the width-averaged rate of ice flow toward the calving face and the mean position of the calving face at two different times, usually a year apart, to obtain an annual average. If the glacier retreats during this time interval, uc is greater than the ice speed, and conversely. It turns out that uc is proportional to the mean water depth, hw, thus:

(Brown et al., 1982). The physics behind this relation are poorly understood and hotly disputed (Van der Veen, 1996, 2002), but the relation seems to be robust. In Alaskan marine environments, c « 27 a-1 ,whereas in freshwater c « 2 a-1 (Funk and Rothlisberger, 1989). This difference is probably a consequence of the greater density difference, in marine environments, between water immediately adjacent to the calving face and that further away. The water against any calving face is diluted by melting. In marine environments, the resulting density contrast is large, resulting in strong free convection and thus enhancing heat transfer to the face. Thus, the observation that c is larger in marine environments further supports the inference, above, that melting is an important part of the calving process.

The dependence of uc on water depth results in an unusual cycle of advance and retreat of tidewater glaciers. As is the case with normal valley glaciers, tidewater glaciers advance during periods when the climate is cool and accumulation exceeds surface melting. During the advance, however, they build a submerged moraine and slowly push it down the fjord (Figure 3.8). This process can take hundreds of years, so the climate may become warm again long before the terminus reaches a stable position. Once the mass balance finally turns sufficiently negative to halt the advance and initiate retreat, the terminus withdraws from its moraine bank, and backs into deeper water. The calving rate thus increases. This increases the budget imbalance, and the retreat accelerates. The retreat usually continues until the terminus reaches shallow water near the head of the fjord. Since the end of the Little Ice Age, all glaciers in coastal Alaska have retreated dramatically in this way. However, the retreats have not been synchronous and have not been in response to

Figure 3.8. Schematic diagram showing how calving tidewater glaciers advance by rolling over their moraines. Arrows show how sediment is washed and dragged up proximal slope of moraine and slumps down distal slope, resulting in migration of the moraine.

identifiable climatic changes. Some glaciers reached their maximum extent and began to retreat in the late 1700s, but Columbia Glacier, the last of these glaciers to begin retreating, did not back off its moraine until the mid 1980s.

Bottom melting

If the base of a glacier is at the pressure melting point and the glacier is sliding over its bed, frictional heating associated with the sliding and with deformation in the basal ice can melt significant quantities of ice. For example, on the lower part of Columbia Glacier, the specific net balance at an elevation of ~400 m is 4.5 m a—1 (Rasmussen and Meier, 1982). The glacier is ~600 m thick at this elevation, its surface slope is ~0.032, and the depth-averaged velocity is ~1.3 km a—1 (Meier et al, 1994). Thus, a column of ice of unit cross sectional area would drop ~40 m in a year, releasing ~2.2 x 108 J of potential energy, which is sufficient to melt ~0.7 m of ice. Some of this melting will be internal, but much of it will occur near or at the bed. Thus, bottom melting may be as much as ~ 14% of the total ice loss at this elevation. On most glaciers, however, the amount of such melting is a much smaller fraction of the total, and can be neglected in mass balance studies.

Mass balance of polar ice sheets

On polar ice sheets, owing to their scale, the accumulation pattern reflects elevation and degree of continentality. If there is significant melting near the margin of a continental ice sheet, as is the case in Greenland

0.05, 0.1,0.15, 0.2, 0.3, 0.4, 0.5, 0.6, 0.8, 1.0, and 1.2 m a—1 (water equivalent). (After Giovinetto and Zwally, 2000. Reproduced with permission of the authors and the International Glaciological Society.)

but not Antarctica, bn increases with elevation because the temperature decreases and the melt season becomes shorter. However, owing to oro-graphic effects storms also lose much of their moisture within a few hundred kilometers of the coast. Thus, in the interior of the Greenland and Antarctic ice sheets, bn decreases with distance from the moisture source (which also means that it decreases with increasing elevation). For example, in Antarctica accumulation rates are typically 0.3-0.6 m a—1 (water equivalent) around the perimeter of the continent, but decrease to <0.1 ma—1 at the South Pole (Figure 3.9) (Giovinetto andZwally, 2000).

Thus, along the margins of ice sheets, accumulation patterns resemble those of maritime glaciers while between the margins and the interiors the pattern reflects the change from a maritime to a continental environment.

Calving of ice shelves

Over 90% of the ice loss from Antarctica is through calving, and most of this is from ice shelves. The blocks of ice released by such calving are commonly much larger than those from tidewater glaciers. This is probably because ice shelves are stronger. Their colder temperatures and less-extensive crevassing would increase their strength. Reeh (1968) has shown that under such conditions the width of an iceberg, measured normal to the calving face, is likely to be comparable to the thickness of the shelf. Many icebergs, however, are much larger than this. Iceberg B-15, which broke off from the Ross Ice Shelf in Antarctica in April 2000, measured 37 x 290 km and was -430 m thick (WISC, 2003). Processes producing bergs of this size are still poorly understood.

We have recently found that polar ice shelves can break up exceedingly rapidly. The 1600 km2 Larsen A ice shelf disintegrated in 39 d in 1995, and then in February 2002, in only 41 d, the 3250 km2 Larsen B shelf collapsed. It appears that climate warming resulted in extensive melting on the shelf surface. Water percolated into crevasses, and because water is denser than ice, high stresses were generated at the tips of the crevasses (Weertman, 1973). As a result, the crevasses apparently propagated through the shelf, resulting in the collapse (Scambos et al., 2000).

During the Wisconsinan glaciation, calving periodically produced armadas of icebergs that spread out across the North Atlantic Ocean, dropping coarse sand as they drifted along. The resulting sand layers were first identified by Hartmut Heinrich, and now bear his name (Heinrich, 1988). These ice-age calving events are widely believed to have been associated with rapid discharges of ice through Hudson Strait and partial collapse of the Laurentide Ice Sheet over Hudson Bay. Whether they were initiated by collapse of a buttressing ice shelf in the Labrador Sea or were entirely a consequence of a tidewater-glacier type of retreat is a matter of speculation.

Bottom melting

Ocean currents penetrate beneath floating ice shelves, and the saline water mixes with fresh water draining subglacially from the interior of the ice sheet. At the base of the ice shelf, either melting or freezing can take place, depending on the temperature and salinity of the mixture, the pressure, and the temperature gradient in the basal ice. Indeed, melting can occur in one place and freezing in another. In Antarctica, bottom melting beneath ice shelves may account for as much as 20% of the mass loss (Table 3.2).

Effect of atmospheric circulation patterns on mass balance

There are at least two spatial scales of variation in coherence of glacier mass balance patterns. On the one hand, there are world-wide climatic changes such as those that resulted in the major ice advances of the Pleistocene and the minor advances of the Little Ice Age. These are both well-known and poorly understood, except that variations in the Earth's orbit that affected the timing and amount of solar radiation received at higher latitudes appear to have modulated the longer cycles (Hays et al., 1976).

On a smaller scale there are regional variations in weather that may cause glaciers only a few hundred kilometers apart to behave differently. Let us consider some examples of these regional-scale variations.

Between the mid 1960s and the late 1980s, the net balances of maritime glaciers in Alaska were generally out of phase with those of glaciers in southwestern Canada and adjacent areas in the United States. When glaciers in one area had a relatively good year, those in the other normally had a bad year (Walters and Meier, 1989; Hodge et al., 1998). Walters and Meier found that when the atmospheric low pressure region that lies off the Aleutian Islands, the Aleutian Low (Figure 3.10), is normal in the fall and winter, storms are deflected into Alaska, resulting in high winter balances there. However, when this low is not as deep as it usually is, storm tracks remain further south and accumulation rates are high in Washington and British Columbia. This pattern began to break down in the mid 1980s. Since then, winter balances on Wolverine and South Cascade glaciers have still been out of phase, but a dramatic increase in ablation has resulted in negative net balances on both, so net balances are in phase (Hodges et al., 1998).

Summer balances in western North America are likewise affected by the summer low along the west coast. When this low is relatively deep and there is a corresponding high over British Columbia, conditions tend to be hot and dry, leading to large negative summer balances.

Asynchroneity of mass balances can also result from the scale of pressure patterns. In the winter, small-scale low-pressure disturbances, identified by variations in the height of the 500 mbar surface (the surface

Glacier North America Map
Figure 3.10. Map of the west coast of North America showing the Aleutian Low and locations of some glaciers for which there are good mass balance records. (Based on Walters and Meier, 1989, Figures 1 and 9.)

on which the atmospheric pressure is 500 mbar or about half the pressure at Earth's surface), result in cyclonic storms characterized by counterclockwise winds. Such storms, related to migratory perturbations embedded in larger-scale air flows, increase the winter balance on Sentinel Glacier in British Columbia. Conversely, frequent high-pressure disturbances resulting in anticyclonic patterns and thus accompanied by clockwise winds, inhibit accumulation in winter and increase melt in summer. In contrast, Peyto Glacier, which lies about 500 km east of Sentinel Glacier (Figure 3.10), is affected only by larger disturbances related to long-wave patterns over the North Pacific. Storms from smaller disturbances do not penetrate that far inland (Yarnal, 1984).

ENSO and Decadal Oscillations

At a larger scale, we are beginning to find that patterns of the type just described are linked to hemispheric and even global patterns. One of the most important of these is the El Nino-Southern Oscillation, or ENSO. Under "normal" conditions winds blow westward in the equatorial Pacific. This drives a westerly surface current in the ocean, resulting in an increase in elevation of the sea surface in the western Pacific relative to that off Peru. This surface current and the resulting super-elevation propel an eastward return current at depth, leading to upwelling of cold water off Peru. At intervals of between 2 and 6 or 7 years, the westerly air flow weakens, the upwelling is damped, and the ocean and hence the air off Peru become warmer. This is an El Nino. The warmer air decreases the pressure gradient between Peru and the western Pacific, thus further weakening the westerly air flow. Consequently, a region of heavy rainfall that is normally located in the western Pacific shifts eastward. This, in turn, shifts the position ofthejet stream, andhence weakens the Aleutian Low, causing storms to enter North America hundreds of kilometers south of their normal entry points (Rasmussen, 1984). Eventually, El Nino conditions weaken and normal or even slightly cooler than normal (La Nina) conditions return.

We do not know how El Ninos are initiated, but the consequences are far reaching, affecting not only glaciers along the northwest coast but weather patterns around the Pacific, throughout North America, and even globally. Even in Antarctica, accumulation was consistently higher in parts of West Antarctica, and there is a hint that it was lower at the South Pole, during El Nino years (Kaspari et al., 2004). The pattern in West Antarctica persisted during much of the twentieth century; a low-pressure cell in the Admundsen Sea shifted clockwise during El Nino events, and this increased accumulation in the eastern part of West Antarctica and decreased it in the western part (Cullather et al., 1996). This pattern, however, appears to have broken down after 1990.

Although global in its effect, ENSO is generated by ocean-atmosphere interactions that are internal to the tropical Pacific and overlying atmosphere (Houghton et al., 2001, p. 454). Recently, we have become aware of other similar oscillations in the atmosphere and ocean. One is the Pacific Decadal Oscillation, or PDO. During the warm phase of the PDO, sea-surface temperatures in the eastern equatorial Pacific are somewhat warmer than normal, while in the northwest Pacific, they are significantly cooler. The PDO seems to have two dominant periodicities,

15-25 years and 50-70 years (Mantua and Hare, 2002). The transitions between the warm and cool phases are abrupt: a warm phase began in 1977, and appears to have ended in 1998. El Ninos tend to be strengthened during the warm phase of the PDO, and moderated during the cool phase (Maxwell, 2002).

Another recently discovered oscillation occurs in the north Atlantic. During the positive phase of this oscillation, there is a strong low-pressure region over southern Greenland and Iceland during the winter, and the jet stream is further north. Northern Europe is thus warmer and wetter than normal, while north Africa is drier (NOAA, 2003). This could affect glacier mass balance in Scandinavia and the Alps. Cook et al. (1998) have identified periodicities in the north Atlantic oscillation of 2, 8, 24, and 70 years.

On a still broader scale, temperature and accumulation patterns in Antarctica appear to reflect processes in the upper levels of the atmosphere. Warming of the troposphere, the layer of air between the Earth's surface and —11 000 m, prevents heat from reaching the higher stratosphere. Consequently, the stratosphere cools and becomes denser, strengthening downwelling over the South Pole. Thus, when the periphery of the continent is warmed by a warm troposphere, the interior is cooled by increased downwelling from the stratosphere, and conversely. As cool air contains less moisture, this results in a similar oscillation in accumulation (P. Mayewski, personal communication, 2003).

Clearly, atmospheric circulation patterns that we are just beginning to understand result in regional variations in mass balance on a variety of spatial and temporal scales. The data base necessary for identifying and studying these circulation patterns is expanding rapidly, and much will be learned as glaciologists and meteorologists begin to extend and exploit it. Particularly intriguing are the remarkable teleconnections between oceanic and atmospheric circulation that are beginning to appear. Beyond this, however, is the question of what controls variations in atmospheric and oceanic circulation on time scales of decades to centuries.

Global mass balance

Of considerable interest currently is the question of whether global warming is responsible for melting enough ice to account for the observed world-wide rise in sea level. The best estimates of this rise presently lie between 1 and 2 mm a-1 (Houghton et al., 2001, p. 665). Because any estimate of the change in mass of a glacier or ice sheet involves calculating a small difference between two large numbers, namely the total accumulation and total loss, uncertainties are large (Table 3.2). Indeed, even with the best figures available we are still unable to say whether the Greenland and Antarctic ice sheets are growing or shrinking. The uncertainties for smaller glaciers and ice caps are lower, however, and suggest that melting of these ice masses may be responsible for 15% to 25% of the sea-level rise. (In fact, Arendt et al. (2002) estimate that in the late 1990s the mass loss from Alaskan glaciers alone was —96 ± 35 km3 a— \ which is more than the estimate in Table 3.2 for all valley glaciers and ice caps.) Other contributions to sea level are thermal expansion of the oceans (0.5 ± 0.2mm a—1), melting ofpermafrost (0.025 ± 0.025 mma—l), sedimentation in the oceans (0.025 ± 0.025 mm a—1), and terrestrial storage in lakes and groundwater reservoirs (—0.35 ± 0.75 mm a—1).

Although the mass balance data for Greenland are ambiguous, yielding a net balance of—44 ± 53 Gt a— 1, the pattern is suggestive. The observational data show that the ice sheet is growing thicker in the interior, at least locally, as warmer air transports more moisture inland. However, it is thinning along the margins where the increased temperature results in more melting (Krabill et al., 2000; Thomas et al., 2000). As mentioned earlier, this is precisely the pattern inferred from Greenland ice cores for the end of the Younger Dryas (Alley et al., 1993).

Summary

In this chapter we discussed snow accumulation and the transformation of snow to ice. We found that in polar environments where there is little if any melting, the physical and chemical stratigraphy in an annual layer of snow persists for many thousands of years and can be used to date the ice.

We then defined some terms used to discuss mass balance, particularly summer, winter, and net balance, and used a perturbation approach to study the influence of winter balance, temperature, and radiation on net balance. By comparing observed variations in these parameters with calculated values, it became clear that the net balance of glaciers in continental environments was sensitive, primarily, to summer temperature, while that of glaciers in maritime areas was sensitive to both winter balance and summer temperature. Radiation balance, principally resulting from differences in cloud cover, could play a role in either environment. The lower budget gradient, and consequently the more sluggish behavior of polar glaciers compared with their temperate counterparts, turned out to be largely related to the shorter melt season in polar environments. On ice sheets, we also noted that accumulation decreases with distance from the moisture source.

We then discussed the importance of calving and bottom melting in mass balance, and discovered that on tidewater glaciers calving can lead to retreats that are, at best, only weakly related to climate. On ice sheets, calving turns out to be a dominant process of mass loss. Bottom melting is an important component of mass balance on some fast-moving valley glaciers and beneath ice shelves.

Finally, we found that variations in intermediate and large scale weather patterns that we are just beginning to understand can result in asynchronous mass balance patterns on glaciers only a few hundred kilometers apart.

Continue reading here: Crystal structure of ice

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