Mass balance

Glaciers and ice sheets are stores of water, exchanging mass with other components involved in the global hydrological system. Glaciers and ice sheets grow by snow and ice accumulation, and lose mass by different ablation processes. The difference between accumulation and ablation over a given time span is the mass balance, which can be either positive or negative. The mass balance reflects the climate of the region, together with glacier morphology and local topographic conditions. Mass balance measurements can therefore give information on the causes of retreat or advance of glaciers.

One of the first systematic analyses of the annual mass budget of a glacier was made by Ahlmann (1927). Statistical relationships between mass balance and meteorological parameters have been investigated on several glaciers (Letreguilly, 1988; Pelto, 1988), and the physical relationships studied by Holmgren (1971), Kuhn (1979) and Braithwaite (1995), amongst others.

Mass-balance variations can be associated with atmospheric circulation, linking them to atmospheric changes rather than single meteorological parameters. This approach was used by Hoinkes (1968) to show how glacier variations in Switzerland were related to cyclonic and anticyclonic conditions. Alt (1987) found that extreme mass balance years at the Queen Elisabeth Island ice caps, Canada, were related to the position of the Arctic front. In southwestern Canada, Yarnal (1984) found that two glaciers were sensitive to both large- and small-scale synoptic weather situations. Voloshina (1988) discussed why the position of the Siberian anticyclone forms an inverse relationship between the mass balance for glaciers in northern Scandinavia and in the northern Urals. The strength of the Aleutian low is important for the determination of the storm track and high mass balance in the Alaskan Range and the Cascades (Walters and Meier, 1989). McCabe and Fountain (1995) found that the winter balance of the South Cascade Glacier correlates to the pressure difference between the Gulf of Alaska and the west coast of Canada. Finally, Pohjola and Rogers (1997a,b) used atmospheric circulation and synoptic weather studies to explain variations in glacier mass balance on Scandinavian glaciers. They also demonstrated that a high net balance on Storglaciaren, the glacier with the longest mass-balance record in the world, is favoured by strong westerly maritime air flow which increases the winter accumulation. Holmlund and Schneider (1997) used a continentality index as a measure of the nature of climate, mass balance, and glacier-front response along a west-east transect in a region just north of the Arctic Circle in Scandinavia. These studies demonstrate the potential of the relationship between glacier mass balance and synoptic weather studies. This is important when using glacier-front or ice-core records to reconstruct past atmospheric circulation.

The most important accumulation factor on glaciers is snowfall. The amount and distribution may, however, vary considerably geographically and seasonally. The highest accumulation rates are observed in maritime, mountainous regions with frequent winds blowing in from the sea, for example, in western North America, the west coast of New Zealand, western Patagonia, southern Iceland and western Scandinavia. In contrast, snowfall is lowest far away from oceanic sources and in precipitation 'shadows' in downwind positions relative to high mountains. Locally, accumulation may be strongly influenced by wind transport of dry snow and by snow avalanches. Ice and snow crystals, or rime ice, can also form on glacier surfaces by freezing of wind-transported, supercooled vapour or water droplets. This process is most common on maritime glaciers.

The glacier accumulation zone has been divided according to melting and refreezing (Fig. 4.8). The dry snow zone is below 0°C and therefore no meltwater is present. The dry snowline separates the dry snow zone from the percolation zone. The percolation zone is characterized by some surface melting, and the water percolates through the snow where it refreezes. The percolation depth normally increases with decreasing altitude. The wet snowline marks the upper boundary of the wet snow zone, where the snow temperature is 0°C.

In some places, most commonly in the lower areas, the refrozen meltwater may form a continuous layer of superimposed ice, called the superimposed ice zone. The equilibrium line marks the zone where the annual accumulation at the end of the ablation zone is balanced by the total ablation.

Ablation refers to the processes causing mass loss from the glacier, including wind deflation, avalanching from the front, calving of icebergs, from runoff melting, evaporation and sublimation. Wind deflation is wind-scouring of snow resulting in the removal of snow and ice from the glacier surface. The process is most efficient in areas of strong katabatic winds and on narrow valley glaciers. Avalanching may be an important ablation factor, especially where the ice front terminates above steep rock cliffs. Ice that breaks off from the glacier front falls down, and if the avalanching rate is greater than the melting rate, regenerated glaciers may form below. Iceberg calving is the mass loss at the margins of glaciers and ice sheets terminating in water (lake or sea). Calving events may vary considerably in scale, from small blocks to enormous icebergs. In March 1990, for example, a 3.5 km long iceberg, weighing approximately 100 million tonnes, of the Erebus Glacier in Antarctica broke off. In January 1995, a portion of the Larsen ice shelf in the Antarctic Peninsula broke up, causing a marginal retreat of 2 km in five days. On a global scale, calving is an important ablation process since large portions of the Antarctic ice sheet terminate in the sea.

Runoff occurs

REGELATION

Accumulation area

MOST OF THE ANTARCTIC -ICE SHEET

Dry snow zone

Equilibrium line

Max. height of surface in current year Surface in summer

■ Ablation area

GLACIER ICE

Figure 4.8 Subdivision of glacier accumulation zones according to patterns of melting and refreezing. (Adapted from Menzies, 1995)

Runoff occurs

GLACIER ICE

REGELATION

Accumulation area

MOST OF THE ANTARCTIC -ICE SHEET

Dry snow zone

GREENLAND ICE SHEET

■MOST MOUNTAIN GLACIERS

Equilibrium line

Max. height of surface in current year Surface in summer

■ Ablation area

Figure 4.8 Subdivision of glacier accumulation zones according to patterns of melting and refreezing. (Adapted from Menzies, 1995)

Melting, evaporation and sublimation are processes causing transformation of ice to water, water to vapour, and ice to vapour, respectively. These processes take place if there is extra energy available at the glacier surface when the temperature has been raised to the melting point. A net deficit of energy, on the other hand, can lower the ice temperature or cause ice accumulation by condensation of vapour or freezing. The energy balance is the surplus or deficit of energy over time, and is an important factor for ablation rates (Paterson, 1994). Energy balance factors on a glacier surface are solar radiation, long-wave radiation, sensible and latent heat, freezing, condensation, evaporation and sublimation.

Solar radiation reaches the surface as direct sunshine or as diffuse radiation scattered through the atmosphere. Some of the radiation is reflected, and the percentage that is reflected from the surface is termed albedo. The albedo is high for new-fallen snow and low for dirty glacier surfaces (Table 4.3).

The short-wave radiation is dependent on its aspect. Radiation is highest when the sun's rays make an oblique angle with the surface. The low solar angle in the mid- and high latitudes during winter reduces incidence

Table 4.3 Albedo values (in per cent) for different tvoes of snow and ice (from Paterson, 1994)

Range

Mean

Dry snow

80-97

84

Melting snow

66-8B

74

Firn

43-69

53

Clean ice

34-51

40

Slightly dirty ice

26-33

29

Dirty icc

15-25

21

Debris-covered ice

10-15

12

SUBLIMATION

DEPOSITION

Figure 4.9 Phase changes between ice, water and vapour. The amount of latent heat energy consumed and released by the transformation is shown. (Modified from Benn and Evans, 1998)

DEPOSITION

Figure 4.9 Phase changes between ice, water and vapour. The amount of latent heat energy consumed and released by the transformation is shown. (Modified from Benn and Evans, 1998)

compared with the tropics. Locally the solar receipt pattern is modified by surface gradient, aspect, and mountain shading.

Long-wave energy is emitted from the atmosphere, bedrock surfaces and other heated surfaces. Long-wave radiation is an important energy budget component when the air is humid. Dry, clear air has a lower ability to trap long-wave radiation. Along the margins of valley glaciers, where radiation is emitted from dark rock surfaces, long-wave radiation may be an important ablation process.

Thermal energy exchanged at the interface between the atmosphere and the glacier surface is termed sensible heat transported by warm air masses, such as valley winds or fohn-winds on the lee sides of mountains, or winds accompanying cyclones. Transfer of sensible heat is most efficient when the air is much warmer than the ice and snow surfaces, and where strong, turbulent winds blow over a rough glacier surface (Paterson, 1994).

Changes between ice, water and vapour consume energy in the form of latent heat. Melting consumes 334 joules per gram of ice melted. Evaporation consumes over eight times as much (2500J g_1). Freezing and condensation release the same amount of energy (Fig. 4.9). Freezing of rainwater or condensation of water vapour on a glacier surface can transfer considerable amounts of energy.

The relative importance of each of the energy balance components varies both temporally and spatially. Commonly, the net radiation (both short- and long-wave) is the most important component, the highest proportions being associated with clear skies. In areas with a continental climate, net radiation has been calculated to amount to more than 60 per cent of the ablation energy. In more humid, maritime climates, this value may be reduced to 10-50 per cent.

Debris on the surface of snow and glacier ice influence ablation rates in two ways. Rock surfaces can heat up and re-emit long-wave radiation, causing melting of adjacent ice and snow. If the debris layer, on the other hand, is thicker than 1-2 cm, the debris will protect the ice and snow from ablation. On glaciers with a thick debris cover, the ablation may be negligible.

The amount of snow and ice stored in glaciers is subject to systematic changes during a year, due to cycles of accumulation and ablation. Several types of cycles occur, depending on the timing of warm and cold seasons, maximum precipitation, and variations in the proportion of precipitation falling

Figure 4.10 Terms used in mass-balance studies for one balance year, adapted from UNESCO (1970). See Glossary of terms used in mass balance studies in Box 4.2

as snow. The most common cycles are: (a) winter accumulation type, with a well-defined winter accumulation season and summer ablation season; (b) summer accumulation type, with maxima in accumulation and ablation taking place at the same time during the summer season; and (c) year-around ablation type, with one or more accumulation maxima coinciding with wet seasons.

The mass balance of a glacier is measured at representative points on its surface. The results of the mass balance measurements are integrated and reported as a value averaged for the whole glacier surface, so that comparisons may be made between different glaciers. The mass balance components are expressed in metres of water equivalents.

The methodologies and techniques used to measure glacier mass balance commonly follow guidelines from the Commission on Snow and Ice of the International Association of Scientific Hydrology (UNESCO, 1970). The different terms used are illustrated in Fig. 4.10.

The winter balance is commonly measured in April and May by sounding the snow depth at several points on the glacier surface. The soundings always refer to the last summer surface, which may consist either of glacier ice or firn, depending on where you are on the glacier. The density of the snow is measured at a few sites, preferably at different elevations. The water equivalents are thereafter calculated on the glacier. The points are plotted on a map and isolines of winter accumulation are drawn. Usually, some snow falls on the glacier after the measurements of the winter accumulation are finished. This additional accumulation may be measured, but the most common approach is to calculate it from precipitation and temperature measurements at meteorological stations close to the glacier.

The summer balance is calculated at several stakes drilled into the glacier surface by measuring the lowering of the snow/ice surface during the ablation season. The summer balance measured at the stakes is then transferred to a glacier map, and isolines of the summer balance can be drawn. The summer balance is commonly more evenly distributed than the winter balance, since in most cases it decreases with rising elevation. The net balance is calculated as the winter balance minus the summer balance (bn = bw — bs).

Box 4.2 Glossary of terms used in mass balance studies

Ablation: all processes that reduce the glacier mass, including calving.

Ablation zone: the part of the glacier where summer melt exceeds winter accumulation. Not only does this include the total melting of the snow cover of the last winter, but also a layer of glacier ice. A deficit of mass appears in that area. The zone lies at lower altitudes of the glacier surface. The ablation zone meets the accumulation zone at the equilibrium line.

Accumulation: all processes that increase the glacier mass. Winter snowfalls are the most important source of mass gain. Redeposition of snow by wind and avalanche are important factors on cirque glaciers and on glaciers surrounded by large mountain plateaux and steep valley sides.

Accumulation area ratio (AAR): the ratio of the accumulation zone to the entire glacier with respect to any particular year. The AAR is an indicator of the glacier balance state in the observation year. The ratio is expressed as a proportion of the total area of the glacier.

Accumulation zone: the part of the glacier where snow that has accumulated during the winter does not melt completely in the subsequent summer. An increase of mass is observed in this area. The zone lies normally in the upper part of the glacier. The accumulation zone meets the ablation zone at the equilibrium line.

Annual ablation: the mass loss during one measurement year in the fixed date system.

Annual accumulation: the mass gain to the glacier during one measurement year in the fixed date system.

Annual balance: the sum of the annual accumulation (positive) and the annual ablation (negative) at the end of the measurement year (balance year). This term is used in the fixed date system for measuring and reporting mass balance. Total values are averaged over the entire glacier surface and presented in terms of equivalent water layer (in metres).

Balance year: the time between dates of formation of two consecutive summer surfaces, commonly understood as the time between the beginning of the winter accumulation and the end of the ablation in the subsequent summer (the date of the minimum summer balance). The balance year is rarely exactly equal to one calendar year.

Calving: the process of mass loss in respect of tidewater glaciers (glaciers terminating in the sea or in a lake) and ice shelves (detachment of icebergs).

Climatic equilibrium line: the mean annual equilibrium line over a 30-year period.

Combined system: system of mass balance studies based on a combination of the fixed date system, stratigraphic systems and other direct data to obtain a measure of glacier summer balance, winter balance and net balance.

Cumulative mass balance: the mass balance summed from particular years of an observation period, which indicate the tendency of a glacier mass to have either grown or shrunk.

Equilibrium line: a line joining points on a glacier surface where winter balance equals summer balance. Normally this is a line or narrow zone where the summer melting entirely removes the winter snow cover but not any older ice or firn below this. The line separates the accumulation zone from the ablation zone.

Equilibrium line altitude (ELA): the altitude at which the equilibrium line is noted at the end of any particular balance year. Normally, it is an averaged value with respect to the whole glacier. ELA is used as an indicator of the glacier mass balance state; when it is higher, the net balance is lower and vice versa.

Firn: old, coarse-grained snow that has survived at least one summer melt season.

Fixed date system: a system of mass balance study, based on field measurements on the same date in consecutive years.

Glaciation threshold: the critical level where a glacier can form and is normally calculated by means of the 'summit method' (between the lowest mountain carrying a glacier and the highest mountain without a glacier).

Internal accumulation: the water melted out at times of ablation usually drains from the glacier and its mass is thereby reduced. However, in areas with snow or firn temperatures below zero, melt-water percolating through the summer surface can refreeze and thereby add mass to the lower layers of snow or firn.

Mass balance: the change in mass at any point on a glacier surface at any time (positive or negative mass balance). Normally it means a change in the mass of the entire glacier in a standard unit of time (the balance year or measurement year).

Measurement year: the unit of time used in the fixed date system of mass balance study, which is usually taken at the end of the summer or the beginning of winter and lasts 365 days.

Net balance (bn): the sum of the winter balance (positive) and the summer balance (negative) through the balance year (bn = bw + bs). The term is used in the stratigraphic system of measurement and reporting of mass balance. Total

The net balance is positive if the winter balance is greater than the summer balance, and negative if the summer balance is greater than the winter balance. The ELA is the zone on the glacier where the net balance is zero.

Figure 4.11 shows the exponential relationship between mean ablation-season temperature t (1 May-30 September) and winter accumulation A (1 0ctober-30 April) at the ELA of modern Norwegian glaciers (Liestol in Sissons, values are averaged over the entire glacier area and presented in terms of an equivalent water layer (thickness in metres).

Steady-state equilibrium line: the equilibrium line altitude (ELA) where the net balance (bn) is zero.

Stratigraphic system: a system of mass balance study based on recognition of the glacier summer surface and the maximum values of accumulation (winter balance) and ablation (summer balance) during the balance year.

Summer balance (bs): the change in mass (commonly negative) during the summer season. It is usually measured at the end of the summer season and at the time of formation of the summer surface (minimum balance). The term is often used synonymously with summer ablation.

Summer surface: the glacier surface formed as a result of the summer balance. This represents the surface of the minimum glacier volume during the balance year.

Temporary equilibrium line altitude: the equilibrium line at an arbitrarily chosen time of the year. During early spring the temporary ELA is in the lower glacier area, while it is higher up the glacier later in the ablation season.

Winter balance (bw): the maximum balance value (positive) during the balance year in the stratigraphic system (considered synonymous with winter accumulation). The time when the maximum balance is measured divides the balance year into the winter and summer seasons.

1979a; Sutherland, 1984), and expressed by the regression equation (Ballantyne, 1989):

where A is in metres water equivalent and t is in °C. The positive correlation between these two variables for different glaciers reflects the fact that higher levels of mass turnover at the

Continental

Climate

Oceanic

t = mean ablation-season temperature I May-30 Sept. (°C) at the ELA

Figure 4.11 Mean summer temperatures plotted against accumulation (in metres water equivalent) at the equilibrium line for ten Norwegian glaciers (1, Alfotbreen; 2, Engabreen; 3, Folgefonna; 4, Nigardsbreen; 5, Tunsbergdalsbreen; 6, Hardangerjokulen; 7, Storbreen; 8, Austre Memurubreen; 9, Heillstugubreen; 10, Grasubreen). (Modified from Sutherland, 1984; Dahl et al, 1997)

ELA require higher ablation and thus higher summer temperatures to balance the annual mass budget. This relationship, which is of global application, has also been demonstrated by Loewe (1971) and Ohmura et al. (1992). The scattering of the data points in these compilations are due to the fact that they include glaciers where non-climatic factors heavily influence the mass balance.

A similar approach was used to expand the range of summer temperature and winter precipitation of this glacier/climate relationship by using annual winter (1 0ctober-30 April) accumulation measurements and summer (1 May-30 October) temperature at the ELA in the corresponding years calculated from adjacent meteorological stations. The four glaciers used were Alfotbreen, Hardangerpku-len, Hellstugubreen (all three in southern Norway), and Broggerbreen (Svalbard) together with summer temperature data from the adjacent meteorological stations Sandane, Finse, 0vre Tessa, and Isfjord Radio, respectively (Fig. 4.12).

Mass balance data from 14 glaciers in different climatic regimes worldwide (Table 4.4, p. 71) were used to test whether there is a relationship between net mass balance variations and ELA variations. Regression analyses show that there is a fairly good correlation (R2 = 0.80) between these two parameters. An ELA depression of 100 m, taken as a typical Little Ice Age value, indicates a net mass balance increase of about 20 m water equivalents

1 25

rrp-r

■ il I ■■ ■ ■■ 1 ■» ■ I» ■ inn

Summer (I May-30 Oct) temperature (°C) at the ELA

Figure 4.12 Annual winter (1 0ctober-30 April) accumulation measurements and summer (1 May-30 October) temperature at the ELA in corresponding years calculated from adjacent meteorological stations. The ELAs at the four glaciers used were Alfotbreen, Hardangerjokulen, Hellstugubreen (all three in southern Norway), and Braggerbreen (Svalbard) were used, together with summer temperature data from the adjacent meteorological stations Sandane, Finse, 0vre Tessa and Isfjord Radio, respectively

(Fig. 4.13, p. 72, top panel). A depression of the ELA of 400 m (a typical value for the Younger Dryas ELA depression in western Norway) indicates a cumulative net mass balance of approximately 70 m water equivalents (Fig. 4.13, middle panel). A depression of the ELA of 1000m (suggested Late-glacial maximum ELA depression) indicates, according to this relationship, a net balance increase of about 170 m water equivalents (Fig. 4.13, bottom panel).

Glacier mass balance can also be calculated by measuring other parameters, such as precipitation and runoff. Thus, the net balance

(bn) of a glacier can be expressed as:

where P is precipitation, R is runoff and E is evaporation. This approach to calculating glacier mass balance is termed the hydrological method.

Where detailed mass balance data are not available, a statistical approach can be adopted to estimate ablation rates using mean annual or monthly temperatures or positive degree days, defined as the sum of the mean daily temperature for all days with temperatures above 0°C.

Box 4.3 How to calculate winter precipitation from the equilibrium line altitude on glaciers when summer temperature is known

Based on the regression equation 4.1, mean winter precipitation (A) can be quantified when mean ablation-season temperature (f) is known (see Dahl and Nesje, 1996, for further details). The procedure calculates what mean winter precipitation is or has been at the present ELA of a glacier in steady state. Variations in winter precipitation at other elevations can be calculated by using a precipitation gradient of 8 per cent per 100 m (Haakensen, 1989; Dahl and Nesje, 1992; Laumann and Reeh, 1993). As a first example, if we want to quantify the present mean winter precipitation at an ELA of 1640 m on a glacier, we apply the following procedure. Temperature is lowered by an adiabatic lapse rate of 0.6°C/100 m. If we use a climatic station at an altitude of 1224 m with a mean ablation-season temperature of 4.35°C, the present mean ablation season temperature (1961-90) at the ELA is 1.85°C. Substitution in equation 4.1 gives the following expression:

As a second approach we wish to quantify mean winter precipitation. For the time period we want to calculate, the mean ablation-season temperature was 1.35°C warmer (remember to adjust for isostatic movements if appropriate), while the contemporaneous ELA was 60 m lower (corresponding to 0.35°C) than at present. The mean ablation-season temperature at the ELA during the time interval in question is thus calculated to be 3.55°C (present mean ablation-season temperature at the ELA of 1.85°C + warmer mean ablation-season temperature during the specific time interval of 1.35°C + warmer mean ablation-season temperature due to a lower ELA of 0.35°C). Put into equation 4.1, this yields the following expression:

If the present mean winter precipitation of ca. 1710 mm corresponds to 100 per cent, this indicates a mean winter precipitation of approximately 175 per cent during the specific time interval used in this example.

For some Norwegian glaciers, Laumann and Reeh (1993) found melt rates of 3.5-5.6 mm of water per positive degree day for snow, and 5.5-7.5 mm of water per positive degree day for ice. The difference is due to the higher albedo of snow. Melt rates per degree day are higher for maritime glaciers, because higher wind speeds and humidity cause more melting due to transfer of sensible heat and the latent heat of condensation.

Glacier mass balance can also be calculated from aerial photographs and satellite images obtained from successive years or over longer periods. Changes in glacier volume can be measured by changes in the altitude of the glacier surface. This can be converted into mass of water by estimating or measuring the density of snow, firn and ice on different parts of the glacier. High-quality aerial photographs and satellite images are quite expensive to obtain, but they make it possible to study mass balance variations in very remote areas. So far, the radar altimetry used for studies of altitudinal variations of glacier surfaces has not been accurate enough for precise estimates. However, the use of laser altimetry gains sufficient precision for such investigations.

On most glaciers, the amounts of annual ablation and accumulation vary quite systematically with altitude. The rates of which annual accumulation and ablation change with altitude are termed the accumulation and ablation

Table 4.4 Mass balance data from 14 glaciers in different climatic regimes

Glacier

Cum bn

Steady-state ELA

Mean ELA

Difference

(m>

(m)

(m)

(m)

1 Place

-19.601

2080

2231

+ 151

2. White

-4.341

930

1018

+88

3. Al fot breen

4 14.90

1 180

1132

- 48

4 Nigardsbreen

+ 16 96

IS60

1494

-66

S. H ardange r ja k ul en

+7.S4

1680

1595

85

6. Grásubreen

-7 41

2060

2121

-61

7, A usere Broggerbreen

-12 58

265

403

- 138

8. Midtre Lovénbreen

-9.98

290

400

+ 110

9. Obruchev

-1.67

525

528

+3

10. Maliy Aktru

-1.24

3140

3149

+9

I 1. Ts Tuyuksyskiy

- 14 348

3740

3814

+ 74

12. Urumqihe S. No. 1

-5.196

4030

4047

+ 17

1 3. Hintere is ferner

- 17 466

2920

3002

+ 82

14 Sil vret ta

-0 163

2760

2765

+5

gradient, respectively. Together, they are defined as the mass balance gradient. Mass balance gradients for some North American glaciers are shown in Fig. 4.14 (p. 73). Steep mass balance gradients are the result of heavy snowfall in the accumulation area and high ablation rates near the front, characteristic of maritime glaciers. Low mass balance gradients, on the other hand, indicate small differences in mass balance with altitude, characteristic of slow-moving, low-gradient, continental glaciers.

On valley and cirque glaciers, the net annual accumulation usually increases with increasing altitude. In western Norway, the precipitation elevation gradient is in general ca. 8 per cent per 100 m (Haakensen, 1989; Dahl and Nesje, 1992; Laumann and Reeh, 1993). If, however, high mountains stand above snow-bearing weather systems, the accumulation may decrease with altitude. The accumulation gradient can also be influenced by topography and by snow avalanching from adjacent valley sides.

The amount of mass gained or lost by a glacier in response to a change in the ELA depends on the hypsometry of the glacier. If, for example, a glacier has a large part of its area close to the ELA, a rising or lowering of the ELA will cause significant variations in mass. If, on the other hand, a minor proportion of the glacier is close to the ELA, ELA variations will have little effect.

Due to the wet-adiabatic lapse rate (altitudinal temperature change) of ca. 0.65°C per 100 m, ablation generally varies linearly with altitude. Ablation gradients are generally steepest where the summer temperature frequently rises above 0°C near the terminus, while temperatures higher up the glacier are below 0°C. Non-linear ablation gradients may be caused by altitudinal variations in cloudiness and humidity, proximity to rock faces, the amount of shading, aspect, and perhaps the most important factor, presence of debris on the glacier surface.

Accumulation and ablation gradients usually have different values, because they are controlled by different climatic variables. The ablation gradient is normally steeper than the accumulation gradient, showing an inflection at the equilibrium line altitude. The ratio between the two gradients is termed the balance ratio, given as

where bnb and bnc are the mass balance gradients in the ablation and accumulation zones, respectively. The balance ratio ignores any non-linearity which may exist in the respective mass balance gradients, but it is a useful

S Net balance variations (m)
S Net balance variations (m)

S Net balance variations (m)

Figure 4.13 Relationship between net mass balance variations and ELA variations. The mass balance data are obtained from 14 glaciers in different climatic regimes worldwide (see Table 4.4)

S Net balance variations (m)

Figure 4.13 Relationship between net mass balance variations and ELA variations. The mass balance data are obtained from 14 glaciers in different climatic regimes worldwide (see Table 4.4)

Balance (m)

Figure 4.14. Annual mass balance gradients for glaciers in western North America. (Adapted from Benn and Evans, 1998)

Balance (m)

Figure 4.14. Annual mass balance gradients for glaciers in western North America. (Adapted from Benn and Evans, 1998)

parameter that summarizes the balance curve of a glacier. For 22 Alaskan glaciers, Furbish and Andrews (1984) found mean balance ratios of 1.8. A value of around 2 may be representative for mid-latitude maritime glaciers, while balance ratios for tropical glaciers may exceed 20 (Benn and Evans, 1998).

Several studies have tried to examine the complicated relationship between changes in glacier mass balance and climate variables. Chen and Funk (1990) correlated variations in mass balance of the Rhone Gletscher in Switzerland with climate records for the period 1882-1987. They found that most of the mass loss of the glacier was related to temperature increases, especially after 1940. Chen and Funk (1990) suggested that summer temperatures are in general more important than precipitation on mountain glaciers located in maritime climates. Nesje et al. (1995), however, demonstrated that both winter precipitation and summer temperature correlate with a 3-4 year lag in glacier front fluctuations of Briksdalsbreen, a western outlet of the semi-maritime Jostedalsbreen ice cap in western Norway. In the New Zealand Alps, Salinger et al. (1983) found that the retreat of the Stocking Glacier correlated with

monthly temperatures (two-year lag). On the opposite side of the water divide, however, variations of the Franz Josef Glacier were correlated by Hessell (1983) and Brazier et al. (1992) with precipitation changes. A similar effect was reported by Letreguilly (1988) and Pelto (1989) for glaciers in the coastal ranges of western North America. Negative cumulative mass balance of the South Cascade Glacier in the state of Washington, USA, is associated with reduced winter snowfall related to shifts in atmospheric circulation over the North Pacific Ocean and northern North America. Years of reduced mass balance on Peruvian and Bolivian

Year ad

Figure 4.IS Annual winter (bw), summer (bs) (1966-1995), net (bn) (1966-1997) (upper panel), and cumulative net balance (lower panel) at Gulkana Glacier. (Data from Jania and Hagen, 1996, and WGMS)

Year ad

Figure 4.IS Annual winter (bw), summer (bs) (1966-1995), net (bn) (1966-1997) (upper panel), and cumulative net balance (lower panel) at Gulkana Glacier. (Data from Jania and Hagen, 1996, and WGMS)

glaciers have been related to occurrences of the El Niño situation (Thompson et al, 1984; Francou et al, 1995). Most of the recent negative cumulative net balance of Lewis Glacier on Mount Kenya is related to air humidity effects on the energy balance on the glacier surface.

The formation of superimposed ice at the surface of high-Arctic glaciers is an important control on glacier mass balance (Woodward et al, 1997). Increased temperatures are likely to reduce the extent and thickness of the superimposed ice, having a negative effect on the mass balance.

4.8.1 Long-term regional mass balance variations

Annual accumulation and ablation rarely balance, causing net mass gains or losses over a mass balance year. Variations in the net mass balance may average out over several years. In this case there is no long-term variation in the net mass balance. However, if the net mass balance is either positive or negative over several years, this will result in significant thickening or thinning of the glacier, respectively. Long-term trends in glacier mass balance are demonstrated by the cumulative net balance, or the running total of annual net balance.

A compilation of published mass-balance records from all over the world indicates that small glaciers appear to have been at equilibrium or shrinking slightly during the period between 1961 and 1990 (Cogley and Adams, 1998). For details about the different glaciers from which the mass balance records are obtained, see the World Glacier Monitoring Service's web page (www.geo.unizh.ch/wgms/ index.html).

Gulkana Glacier, Alaska. Gulkana Glacier (63°15'N, 145°28'W) is a valley glacier in the south-facing eastern Alaska Range. The glacier covers an area of 19.3 km2, while the total drainage basin covers an area of 31.6 km2. In 1965, mass balance studies by the United States Geological Survey (USGS) began. Annual mass balance variations are shown in Figure 4.15 (upper panel). The cumulative net balance (Fig. 4.15, lower panel) shows that the glacier has decreased in thickness by 11.46 m water equivalents between 1965 and 1997. After 1988 the mass loss has accelerated. Regression analysis shows that the summer balance is the controlling factor for the net mass balance (R2 = 0.75), while the winter balance is of negligible importance (R2 — 0.19).

Wolverine Glacier, Alaska. Wolverine Glacier (60°24'N, 148°54'W) is a valley glacier in the Kenai Mountains, south central Alaska. The Kenai Mountains contain hundreds of smaller glaciers. The glacier and perennial snowfields cover about 72 per cent of the glacier catchment. From the 4 km wide accumulation basin, the glacier descends in a steep ice fall to an approximately 5 km long and 1.5 km wide valley glacier. The glacier has a maritime climate, despite being in the precipitation shadow of the Sargent Icefield, and the mass balance is considered to be quite representative of valley glaciers in the maritime part of Alaska. The annual mass balance variations are shown in Fig. 4.16 (upper panel). The cumulative net balance (Fig. 4.16, lower panel) shows that the glacier decreased in volume until 1979, when the glacier started to experience a positive net balance trend which lasted until 1988, after which the glacier has experienced significant mass loss. Between 1966 and 1997 the glacier volume was reduced by a layer corresponding to 7.68 m water equivalents. An evaluation of the mass balance factors influencing the net balance shows that the winter balance dominates (R2 = 0.69), while the correlation between summer balance and net balance during the observation period is 0.21.

South Cascade Glacier. The annual net mass balance variations of the South Cascade Glacier (48°22'N, 121°03'W) between 1953 and 1997 are shown in Fig 4.17, p. 77 (upper panel). The cumulative net balance (Fig. 4.17, lower panel) shows a decreasing trend, especially after 1976. During the observation period the glacier has lost a surface layer corresponding to 22.88 m water equivalents. The steady-state ELA (ELA when bn = 0) is close to 1910 m. The mean ELA for the periods 1971-1980 and 1986-1997 (22 years) was 1965 m, 55 m higher than the steady-state ELA.

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Figure 4.16 Annual winter (bw), summer (bs) (1966-1995), net (bn) (1966-1997) (upper panel) and cumulative net balance (lower panel) at Wolverine Glacier. (Data from Jania and Hagen, 1996, and WGMS)

4.8.1.2 Canada

Devon Ice Cap. Mass balance measurements have been carried out on the northwest side of the Devon Ice Cap (75°20'N, 82°30'W) since 1961. The annual mass balance until 1995 is shown in Fig. 4.18, p. 78 (upper panel). For two years during the observation period (1976 and 1986) the summer balance was positive. The winter balance has been remarkably stable in contrast to the summer balance, which has shown great interannual variations.

The cumulative net balance (Fig. 4.18, lower panel) shows a decreasing trend; during the observation period the glacier has lost a surface layer corresponding to 1.795 m water equivalents. Regression analyses show that summer balance is the most important factor for the net balance (R2 = 0.88), while there is no correlation between winter balance and net balance (R2 = 0.07) for the observation period.

Place Glacier. Variations in annual net balance of Place Glacier (50°26'N, 122°36'W) between

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Figure 4.17 Annual net (bn) (upper panel), and cumulative net mass balance (lower panel) on the South Cascade Glacier between 1953 and 1997. (Data from Jania and Hagen, 1996, and WGMS)

1965 and 1997 are shown in Fig 4.19, p. 79 (upper panel). The cumulative net balance (Fig. 4.19, lower panel) shows a decreasing trend, which accelerated after 1976. The steady-state ELA (ELA when bn = 0) is 2080 m, while the mean ELA during the observation period was 170 m higher at 2250 m.

Athabasca Glacier. Changes in areal extent, elevation and volume were calculated for Athabasca Glacier, Alberta, Canada, between 1919 and 1979 (Reynolds and Young, 1997).

During the study period, the glacier experienced a volume reduction of 2.344 x 108 m3.

4.8.1.3 Norway

Alfotbreen. The annual winter (bw), summer (bs), net (bn) and cumulative net mass balance for Alfotbreen (61°45'N, 5°39'E), a plateau glacier located close to the coast of western Norway, are shown in Fig. 4.20, p. 80, for the period 1963 to 1998. The steady-state ELA (ELA when bn = 0) is ca. 1180 m, while the ELA

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Figure 4.18 Annual winter (bw), summer (bs), net (bn) (upper panel) and cumulative (lower panel) net balance at the Devon Ice Cap between 1961 and 1995. (Data from Jania and Hagen, 1996)

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Figure 4.18 Annual winter (bw), summer (bs), net (bn) (upper panel) and cumulative (lower panel) net balance at the Devon Ice Cap between 1961 and 1995. (Data from Jania and Hagen, 1996)

mean for the observation period is 35 m lower at 1145 m. The AAR when bn = 0 is 0.52. Correlation analyses of the mass balance data show that winter precipitation is the main factor explaining the net balance variations (R = 0.76), while the R2 between bn and bs is 0.35.

Nigardsbreen. The annual winter (bw), summer (bs), net (bn) and cumulative net mass balance of Nigardsbreen (61°43'N, 7°08'E), an eastern outlet glacier from Jostedalsbreen, are shown in Fig. 4.21, p. 81, for the period 1962 to 1998.

The steady-state ELA (ELA when bn - 0) is 1560 m, while the mean ELA for the observation period is 65 m lower at 1495 m. Regression analyses of the mass balance data show that bn and bs are almost equally important for the net balance (R2 = 0.71 and 0.70, respectively).

Hardangerjekulen. The annual winter (bw), summer (bs), net (bn) and cumulative net mass balance of Hardangerjokulen (60°32'N, 7'22'E), a plateau glacier in central southern Norway, are shown in Fig. 4.22, p. 82, for the period 1963 to 1998. The steady-state ELA is

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Figure 4.19 Annual net (bn) (upper panel) and cumulative (lower panel) net balance at Place Glacier between 1965 and 1997. (Data from Jania and Hagen, 1996, and WGMS)

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Figure 4.19 Annual net (bn) (upper panel) and cumulative (lower panel) net balance at Place Glacier between 1965 and 1997. (Data from Jania and Hagen, 1996, and WGMS)

1680 m, while the mean ELA for the observation period is 75 m lower at 1605 m. Regression analysis of the mass balance data shows that the winter balance is the most significant factor explaining the net balance (R = 0.71), while the determination coefficient between net balance and summer balance is 0.48.

Storbreen. The annual winter (bw), summer (bs), net (bn) and cumulative net mass balance of Storbreen (61°34'N, 8°08'E), an east-facing glacier in western Jotunheimen (Liestol, 1967), are shown in Fig. 4.23, p. 83, for the period 1949 to

1998. The steady-state ELA is 1720 m, while the mean ELA for the observation period is 30 m higher at 1750 m. Regression analyses of the mass balance data show that the summer balance is the dominant factor for the net balance (R2 = 0.66), while the correlation coefficient between net balance and winter balance is 0.51.

Hellstugubreen. The annual winter (bw), summer (bs), net (bn) and cumulative net mass balance between 1962 and 1998 on Hellstugubreen (61°34'N, 8°26'E) in eastern

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Figure 4.20 The annual winter (bw), summer (bs), net (bn) (upper panel) and cumulative net mass balance (lower panel) on Alfotbreen between 1963 and 1998. (Data from Kjollmoen, 1998, and WGMS)

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Figure 4.20 The annual winter (bw), summer (bs), net (bn) (upper panel) and cumulative net mass balance (lower panel) on Alfotbreen between 1963 and 1998. (Data from Kjollmoen, 1998, and WGMS)

Jotunheimen are shown in Fig 4.24, p. 84. The mean ELA between 1963 and 1998 was 1900 m, which is 60 m higher than the steady-state ELA of 1840 m. Regression analyses of the mass balance data show that summer balance is the dominating factor (R2 — 0.80), while the determination coefficient between the net balance and the winter balance is 0.34.

Gràsubreen. The annual winter (bw), summer (bs), net (bn) and cumulative net mass balance between 1962 and 1998 for Grasubreen (61°39'N, 8°36'E), located in eastern Jotunheimen, central southern Norway, are shown in Fig. 4.25, p. 85. The steady-state ELA is 2060 m, while the mean ELA for the period 1962-1998 (except the year 1992) is 60 m higher at 2120 m. The AAR on the glacier at steady-state is 0.46. Regression analyses show that the summer balance is the main factor for the net balance variations (R2 = 0.80), while the correlation between the net balance and the winter balance is 0.28.

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Figure 4.21 The annual winter (bw), summer (bs), net (bn) (upper panel) and cumulative net mass balance (lower panel) on Nigardsbreen between 1962 and 1998. (Data from Kjollmoen, 1998)

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Figure 4.21 The annual winter (bw), summer (bs), net (bn) (upper panel) and cumulative net mass balance (lower panel) on Nigardsbreen between 1962 and 1998. (Data from Kjollmoen, 1998)

Engabreen. The annual winter (bw), summer (bs), net (bn) and cumulative net mass balance between 1970 and 1998 for Engabreen (66°39'N, 13°5l'E), a southwestern outlet glacier of Svartisen, are shown in Fig 4.26, p. 86. The mean ELA during the observation period was 1060 m, 100 m lower than the steady-state ELA of 1160 m. Regression analyses between winter balance and summer balance versus net balance shows correlation coefficients of 0.55 and 0.49, respectively.

4.8.1.4 Svalbard

Austre Breggerbreen. The annual winter (bw), summer (bs), net (bn) and cumulative net mass balance between 1967 and 1997 for Austre Braggerbreen (78°53'N, 11°50'E) are shown in Fig. 4.27, p. 87. Ablation values show greater interannual variations than winter balance values. Because the summer ablation has been larger than the winter accumulation in all but two years in the observation

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Figure 4.22 The annual winter (bw), summer (bs), net (bn) (upper panel) and cumulative net mass balance (lower panel) for Hardangerjakulen between 1963 and 1998. (Data from Kj0llmoen, 1998, and WGMS)

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Figure 4.22 The annual winter (bw), summer (bs), net (bn) (upper panel) and cumulative net mass balance (lower panel) for Hardangerjakulen between 1963 and 1998. (Data from Kj0llmoen, 1998, and WGMS)

period, the glacier has experienced a steady volume decrease, with a total loss of 13.56 m during the observation period (Fig. 4.27, lower panel). The steady-state ELA on Austre Broggerbreen is ca. 260 m, while the mean ELA during the observation period, except 1993, was 140 m higher at 400 m. The AAR on Austre Br0ggerbreen at steady state is about 0.52. Regression analyses for bw and bs versus bn show correlation coefficients of 0.08 and 0.76, respectively. Between the meteorological station at Ny-Alesund and the glaciers only

5-6 km away, the correlation coefficient between the measured winter precipitation (September-June) at Ny-Alesund and the measured snow accumulation from sounding profiles during the 14-year period from 1974/ 75 to 1987/88 was 0.63. The relatively poor correlation is mainly due to strong winds and snow-drifting (Hagen and Liest0l, 1990).

Midtre Lovenbreen. The annual winter (bw), summer (bs), net (bn) and cumulative net mass balance between 1968 and 1997 for

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Figure 4.23 The annual winter (bw), summer (bs), net (bn) (upper panel) and cumulative net mass balance (lower panel) on Storbreen between 1949 and 1998. (Data from Kjollmoen, 1998, and WGMS)

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Figure 4.23 The annual winter (bw), summer (bs), net (bn) (upper panel) and cumulative net mass balance (lower panel) on Storbreen between 1949 and 1998. (Data from Kjollmoen, 1998, and WGMS)

Midtre Lovenbreen (78°53'N, 12°04'E) are shown in Fig. 4.28, p. 88. The cumulative net balance shows a steady decrease, with a total loss of 10.39 m during the observation period. The steady-state ELA on Midtre Lovenbreen is ca. 290 m, while the mean ELA for the observation period is 110 m higher at 400 m. The AAR at steady state is ca. 0.6. Regression analyses between winter balance/summer balance and net balance show correlation coefficients of 0.15 and 0.68, respectively.

4.8.1.5 Sweden

Storglaciaren. The annual mass balance (upper panel) and cumulative net balance (lower panel) variations between 1946 and 1997 for Storglaciaren (67°54'N, 18°34'E), northern Sweden, are shown in Fig. 4.29, p. 89. The cumulative net balance shows that the glacier reduced in volume until 1974. From 1988 the glacier has increased in volume. The steady-state ELA on Storglaciaren is 13 m higher at

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Figure 4.24 The annual winter (bw), summer (bs), net (bn) (upper panel) and cumulative net mass balance (lower panel) for Hellstugubreen between 1962 and 1998. (Data from Kjollmoen, 1998, and WGMS)

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Figure 4.24 The annual winter (bw), summer (bs), net (bn) (upper panel) and cumulative net mass balance (lower panel) for Hellstugubreen between 1962 and 1998. (Data from Kjollmoen, 1998, and WGMS)

1460 m, while the mean ELA for the observation period (except the years from 1953 to 1959) was 1473 m. Regression analyses between winter balance/ summer balance and net balance show correlation coefficients of 0.51 and 0.68, respectively. This demonstrates that the winter balance contributes significantly to the net mass balance variations on Storglaciàren, as also pointed out by Raper et al. (1996).

Cumulative net mass balance variations for nine Norwegian (including Svalbard) glaciers and Storglaciären in northern Sweden (Fig. 4.30, p. 90) show that the maritime glaciers have increased their mass significantly, especially after 1988. The continental glaciers in southern Norway (Storbreen, Gräsubreen and Hellstugubreen), together with the Spitzbergen glaciers Austre Broggerbreen and Midtre Lovenbreen, have decreased in mass.

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Figure 4.25 The annual winter (bw), summer (bs), net (bn) (upper panel) and cumulative net mass balance (lower panel) for Grâsubreen between 1962 and 1998. (Data from Kj0llmoen, 1998, and WGMS)

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Figure 4.25 The annual winter (bw), summer (bs), net (bn) (upper panel) and cumulative net mass balance (lower panel) for Grâsubreen between 1962 and 1998. (Data from Kj0llmoen, 1998, and WGMS)

Analysis shows that the net balance on the maritime glaciers is more influenced by the winter balance than by the summer balance, while the opposite is the case for the continental glaciers (Fig. 4.31, p. 90).

One source of interannual variability in the atmospheric circulation of NW Europe is the North Atlantic Oscillation (NAO). This oscillation is associated with changes in the westerlies in the North Atlantic and NW Europe (Hurrell, 1995; Hurrell and van Loon, 1997). After 1980, and especially around 1990, the NAO tended to remain in an extreme phase and explained a substantial part of the observed temperature rise and increased precipitation during wintertime in NW Europe. Hurrell (1995) presented a NAO index for the period 1864-1995 based on air pressure gradients between Iceland and the Azores. The correlation between the NAO index and winter precipitation (Dec.-Mar.) in Bergen is 0.77. This is also reflected in the winter balance on glaciers in southern Norway

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Figure 4.26 The annual winter (bw), summer (bs), net (bn) (upper panel) and cumulative net mass balance (lower panel) for Engabreen between 1970 and 1998. (Data from Kj0llmoen, 1998, and WGMS)

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Figure 4.26 The annual winter (bw), summer (bs), net (bn) (upper panel) and cumulative net mass balance (lower panel) for Engabreen between 1970 and 1998. (Data from Kj0llmoen, 1998, and WGMS)

(Fig. 4.32, p. 91); years with a high NAO index correspond to years of large winter balance, and vice versa.

4.8.1.6 Russia

Obruchev Glacier. The summer (bs), net (bn)

annual winter (bw), and cumulative net mass balance between 1958 and 1981 for Obruchev Glacier in the Urals are shown in Fig. 4.33, p. 92. From 1958 to 1981, the net mass balance loss was 3.22 m. The steady-state ELA is

520 m, while the mean ELA between 1960 and 1981 was 530 m. The AAR when the net balance on Obruchev Glacier is zero (steady state) is 0.50.

Maliy Aktru. The annual and cumulative net mass balance variations between 1962 and 1997 for Maliy Aktru (50°05'N, 87°45'E) are shown in Fig. 4.34, p. 93. The cumulative net balance shows significant variations; during the observation period the glacier lost a mass of 1.42 m water equivalents. The steady-state

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Figure 4.27 The annual winter (bw), summer (bs), net (bn) (upper panel) and cumulative net mass balance (lower panel) for Austre Broggerbreen between 1967 and 1997. (Data from Jania and Hagen, 1996, and WGMS)

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Figure 4.27 The annual winter (bw), summer (bs), net (bn) (upper panel) and cumulative net mass balance (lower panel) for Austre Broggerbreen between 1967 and 1997. (Data from Jania and Hagen, 1996, and WGMS)

ELA is 3140 m, while the mean ELA for the observation period was 3150 m. Regression analysis shows that the AAR at steady-state is 0.70.

4.8.1.7 Kirghizstan

Kara-Batkak. The annual and cumulative net balance between 1957 and 1997 for Kara-Batkak (42°08'N, 78°16'E) are shown in Fig. 4.35, p. 94. During the observation period the glacier reduced its mass by 17.95 m water equivalents, most of which has occurred since 1972.

4.8.1.8 Kazakhstan

Ts. Tuyuksuyskiy. The annual and cumulative net mass balance variations between 1957 and 1997 for Ts. Tuyuksuyskiy (43°03'N, 77°05'E) are shown in Fig. 4.36, p. 95. The total mass loss during the observation period was 16.27 m water equivalents, most of which occurred after 1972. The steady-state ELA is

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Figure 4.28 The annual winter (bw), summer (bs

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