The melting of snow

A snow cover melts as the result of a combination of several processes:

• net incoming solar radiation: the older the snow cover, the lower its albedo, and the more solar radiation it absorbs;
• sensible heat from the air: at the same air temperature (above freezing), snow melts faster in windy conditions than under calm conditions;
• terrestrial radiation emitted by the clouds and sky (sky radiation): the emissivity of snow is very close to one, therefore it absorbs almost all incoming infrared radiation (in fact it is the infrared component in the solar radiation that explains why snow melts under bright sunlight when the air temperature is just below freezing);
• heat transfer from the ground below: the snowfall associated with a cold snap following a warm spell is less likely to last long;
• latent heat transfer: latent heat of evaporation is transferred to snow when moisture sublimes from the atmosphere;
• heat transfer by falling rain (1).

The factors are more or less ranked in order of importance, however, depending on the circumstances, any factor can be dominant, especially the first four (2).

Two studies were conducted at Resolute at 75°N in the north of Canada. Resolute, on Cornwallis Island, has the annual mean temperature of only -16.6°C.

In 1978, the albedo at Resolute was near 80% till mid June but fell to 20-30% within a week or so (3). Simultaneously the air temperature rose above 0° C. Serious snowmelt started around 25 July. The net-radiation intensity at seven other places on Cornwallis Island averaged about 150 W/m² during the first week after melt started, which would melt 38 mm/day in rainfall equivalent. In this case net radiation alone would melt a one meter snow layer in ten days (assuming a snow density a third that of water). That is roughly the time taken at Resolute in 1978 (3).

A second study documents hourly measurements at Resolute (4). Melting was compared at two sites 3 km apart, one with clean snow and the other coated with windblown dust. Snow at the latter site melted away 10 days sooner, on account of an albedo of only 40% instead of about 85. Snow of the order of 250 mm deep had an initial density of about 0.32, the water equivalents being 65 mm at the dirty-snow site and 145 mm at the other.

Net and global radiation (Q_n & Q*) to both sites fitted the following equation -

where a is the surface albedo. This equation resembles that for net radiation on grass (5). It implies that a change of albedo from 0.85 to 0.40 increases the net radiation available to melt snow by a factor of almost four. Melting occurred mainly during May and June, and the rate could be calculated from the energy-balance equation -

Q_m = Q_n + Q_h + Q_e + Q_r + Q_g,

representing heat used in melting Q_m, net radiation Q_n (visible and infrared), sensible heat transfer from the air Q_h, latent heat liberated by sublimation of atmospheric moisture onto the ice Q_e, heat from rain Q_r, and heat conducted up from the ground Q_g. The last two are usually negligible in Resolute.

Q_h is small if the air temperature is close to 0°C, and negative if temperatures are lower. In fact, monthly mean air temperatures rose from about -11°C in May to -1°C in June. The June daytime temperatures were about 3K higher and the wind speed averaged 5.9 m/s, which is strong, so Q_h might have been small but appreciable in June. It would the same for both clean and dirty snow, and therefore is not the explanation of the observed large difference in melting rates.

The different melting rates are more likely to be caused by the different Q_n, due to the different albedoes. The estimated Q_n to the dirty snow was of the order of 50 W/m², which is like the latent-heat requirement of the observed ablation rate of around 15 mm/day of water equivalent from the dirty snow, i.e. about 60 W/m² of energy. The similarity confirms that net radiation was indeed the factor mainly controlling melting.

A third study estimated the mid-summer energy balance over eight ice caps and glaciers in the Arctic region (3). The median values for net (visible plus infrared) radiation, sensible, and latent heat transfer were 32, 12 and 2 W/m², respectively, making a total input of 46 W/m². The median heat transfer into the snow layer (to bring to snow up to 0°C) was about 11 W/m², leaving 35 W/m² for melting. In fact, the median energy consumed in melting was 40 W/m², in fair agreement. These figures again show the dominant importance of net radiation in causing melting, in particular the significance of the albedo of the snow’s surface.

(1) Linacre, E.T. 1992. Climate Data & Resources (Routledge) p.308.

(2) ibid p 339.

(3) Woo, M.K. and A. Ohmura 1997. The Arctic Islands. In Bailey et al. (eds) The Surface Climates of Canada. (McGill-Queen’s University Press), 173-96.

(4) Yang, D., M-K. Woo and Z. Xia 1996. Snowmelt at the high Arctic sites, Resolute, N.W.T. Canada. Paper to 64th Western Snow Conference, Bend, Oregon, April 16-18.

(5) as (1), p 98.