Duration of the snow season

*R. W. Galloway, 68 Barada Crescent, Aranda, Canberra, Australia 2614.

The ‘Galloway snow model’ allows estimation with useful accuracy of the duration of snow cover at a place (1). The model requires only three kinds of data, which are commonly available:

• the monthly mean temperature of the surface air T_m (° C),
• the standard deviation s of daily mean temperatures within each month, and
• the monthly precipitation P_m (mm).

The procedure involves estimating separately for each month the deposition and ablation of snow. We express both in terms of the equivalent depth of water (mm). The fraction of P_m that falls as snow (rather than rain) depends on the ‘snow-day temperature’ T_snd, derived from a purely empirical formula:

The fraction is 100% when T_snd is less than or equal to -3° C, but 70% at -1° C and 6% at +1° C. For any given year, the deduced deposition of snow is added to what has fallen so far that year, to give the depth of water equivalent to the current snow cover (assuming no loss).

The loss by ablation is reckoned as governed chiefly by the temperature, i.e. by the number of degree-days above 0° C. The latter depends on T_m and the amplitude of the daily range, indicated by s. However, such an index of ablation needs correction to allow for the effect of radiation on melting. This in turn depends on the albedo of the snow, which changes with season as the initial fairly clean snow of autumn becomes the clean snow of winter and then the dirty snow of spring. So the model uses a semi-empirical albedo factor according to the month. The month’s ablation is obtained by multiplying together the number of degree-days, the albedo factor and a conversion term of 2.9 mm of water per degree-day. This increment of water loss is added to the values for previous months and plotted against the date, alongside that for snow accumulation.

Then the deposition graph is compared with the ablation graph. Snow cover begins when a month’s deposition exceeds the simultaneous ablation. Subsequently, the ground remains covered until the graphed curve of total ablation cuts that of snow accumulation, in spring. This procedure was used to calculate the effect of a change of T_m due to global warming, on the duration of the snow season in the Australian Alps (1). Galloway also used it to calculate snow seasons at 83 stations in Minnesota, where the results of the model agree well with measured values.

(1) Whetton, P.H., M.R. Haylock and R. Galloway 1996. Climate change and snow-cover duration in the Australian Alps. Climatic Change 32, 447-79.