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FRAGILE ALPINE ENVIRONMENTS  
Snow and perennial ice

Energy balance | Mass balance

Energy and mass balance

 

Energy balance

Changes in mass, temperature and water content of glaciers are determined by the energy fluxes through the interface between glacier and atmosphere and in the glacier body itself. Mass changes are mainly dominated by the energy exchange between atmosphere and glacier surface. Energy fluxes

  • in the ice body itself (heat diffusion, convective heat transfer by water, internal friction by ice deformation) and
  • at the glacier bed (friction by basal sliding, geothermal heat flux, convective heat transfer by subglacial groundwater)

are orders of magnitude smaller.
If there is no horizontal transfer of heat, conservation of energy requires that, at any point on the surface at any instant the energy balance is equal to zero.

energy balance measurements

1 - Energy balance measurements (104K)

 

M = R + H – LvE + LfP` - ΔG

processes determining glacier energy flux

2 - The most important processes determining the energy flux at the glacier - atmosphere interface and the thermal structure in the upper layer of the glacier


The symbols have the following meaning:
M heat used to melt snow and ice. If melt water refreezes in the snow pack, this term represents a gain in heat; it is negative.
ΔG rate of gain of heat of a vertical column from the surface to the depth at which vertical heat transfer is negligible.
R net radiation: R = Q (1 - α) + Ii– I0.
Q rate of incoming solar radiation (direct and diffuse) at the surface
α surface albedo (ratio of reflected to incident solar radiation)
Ii rate of incoming long-wave radiation at the surface
I0 rate of emission of long-wave radiation by the surface
H rate of transfer of heat from the air to the surface by turbulence, when the air is warmer than the surface. If the surface is warmer than the air, H is negative.
Lv specific latent heat of vaporisation (2.8x106J/kg)
E rate of evaporation from the surface if water-vapour pressure decreases with height. If there is condensation on the surface, E is negative. Turbulence increases the rate of transfer of water vapour between the atmosphere and the surface.
Lf specific latent heat of fusion of ice (2.34x105J/kg)
P` precipitation rate of rain. The heat supplied by rain is negligible when the surface is melting but may be significant if the rain can freeze.

 

Mass balance

Mass balance studies are concerned with changes in the mass of a glacier and the distribution of these changes in space and time; more particularly, with measuring the change in mass in a given year. Such information is important in relating the chain of events leading to advances or retreats of glaciers to changes in climate.
A glacier acts as a natural reservoir that stores water during winter and releases it in summer. Conditions on glaciers in temperate regions form the basis of the definition for mass balance. Some difficulties arise in applying such definitions to cold or polythermal glaciers. On these glaciers, because of refreezing processes, the ablation caused by melting does not necessarily results in a mass loss for the glacier.

 

The income and expenditure terms in the budget of a glacier are represented by

accumulation and ablation
Accumulation includes all processes by which material is added to the glacier. Material is normally added as snow, which is slowly transformed to ice. Avalanches, rime formation, freezing of rain within the snow pack and refreezing of melt water are some other accumulation processes.   Ablation includes all processes by which snow and ice are lost from the glacier. Melting followed by run-off, evaporation, removal of snow by wind and the calving of icebergs are some examples.
measurement of snow accumulation   borehole in ablation area
3 - Measurement of snow accumulation at the Jungfraufirn, Grosser Aletschgletscher, Bernese Alps, Switzerland (64K)   4 - Drilling of a borehole for stake measurements in the ablation area of the Glacier de Corbassière, Valais, Switzerland (124K)

Mass balance measurements at individual points are normally expressed as equivalent volumes of water per unit area; thus they have the dimensions of length. Measurements are usually made at points that move with the ice, a stake set in the ice for example (see image 4). Such observations may have to be corrected with relation to fixed points before changes in volume or averages over areas are computed.

The thickness of a glacier at a given point reaches a maximum in late spring or early summer and a minimum in late summer or autumn. In accumulation areas the surface formed at the time of minimum thickness can normally be identified one year later by a layer of dirt. This layer is then called summer surface. If t1 and t2 are the times of two successive minima, and tm the time of the intervening maximum, the interval t1 and t2 is called the balance year. Its length is not exactly 365 days, but varies slightly from year to year. However, its average length should be close to 365 days. At a given point on a glacier at a given time the accumulation rate c is the rate of increase of water-equivalent thickness. Similarly the ablation rate a is the rate of decrease of thickness. Time integrals of these quantities are used (see equation).

mass change diagram

5 - Mass change diagram

The mass balance b at any time is the algebraic sum of accumulation and ablation and represents the change in mass per unit area relative to the previous summer surface. The mass balance at the end of the balance year is the net balance bn for the year. It can be subdivided into a winter balance bw, which is positive and a summer balance bs, which is negative.

See also Paterson (1994)


definitions mass balance terms

6 - Definitions of mass balance terms as measured at a point on a glacier

b = mass balance

c = accumulation rate

a = ablation rate


bn = net balance at the end of a balance year

bw = winter balance (positive)

bs = summer balance (negative)
 

The glacier can be divided into
  • an accumulation area where bn > 0 and
  • an ablation area where bn < 0

The boundary between the two is the equilibrium line.
Mass balance quantities, analogous to those defined for a point, can be defined for an area. These have the dimensions of volume and are denoted by capital letters.

In the mean specific net balance

S is the area of the glacier.

 

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29 August 2011
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