In certain technical problems it is necessary to know the mass concentration of snow in the air ρ _s and the effective air density ρ _ea during periods of snow-fall. Defining ρ _s as ice mass per unit volume of snow-filled air (as is done for deposited snow):

(1)

where ρ _i is ice density (≈ 0.92 × 10³ kg/m³) and ρ _a is the density of clear air (≈ 1.3 kg/m³).

In calm weather, the vertical flux of snow q _v is easy to measure, e.g. by weighing the snow collected on a tray over a short time period. Representative fall velocities of snow particles u _t are also fairly easy to measure if the complications of fall velocity variation within the dispersion are ignored. In principle, it is easy to estimate ρ _s, since

(2)

However, while measurement of q _v is routine, corresponding measurements of u _t are seldom made.

At any given location. q _v can vary by two or three orders of magnitude during a winter season (say in the range 0.002 to 2.0 g/cm² h). By contrast, u _t is unlikely to change by more than a factor of four for the whole range of snow crystals and snow-flakes. Thus, variations in ρ _s must be controlled mainly by variations of q _v.

Reference MellorMellor (1966) sampled a range of snow-falls, recording q _v, u _t, ρ _s, and characteristics of the snow crystals. If the values of u _t(cm/s) are plotted against those of q _v(g/cm² h), there is a weak correlation (Fig. 1) which can be described by

(3)

Fig. 1. Fall velocity u _t plotted against accumulation rate q _v.

The coefficient of determination r ² for the power-relation regression is 0.3. Since u _t does not vary much, there must be a strong correlation between ρ _s and q _v (Fig. 2). The data can be described by

(4)

Fig. 2. Snow density ρ _s plotted against accumulation rate q _v.

where q _v is in g/cm² h (which is equivalent to the accumulation rate expressed in centimetres of water per hour). The coefficient of determination r ² is 0.969. A result that is essentially the same as Equation (4) is obtained by substituting Equation (3) into Equation (2) and adjusting the units.

The most basic quantitative description of a snow-fall is q _v. Knowing q _v, an estimate of ρ _s that is sufficiently accurate for many practical purposes can be obtained from a relation such as Equation (4).

This is very convenient, and so it would be useful to have more field observations of q _v, u _t, and ρ _s, especially for very heavy snow-falls.