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Snow Concentration and Effective Air Density During Snow-Falls

Published online by Cambridge University Press:  20 January 2017

Malcolm Mellor
Malcolm Mellor*
Affiliation:
U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire 03755, U.S.A.
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Abstract

The mass concentration of falling snow ρ s can be estimated from the snow-fall rate (accumulation rate) q v if there is no significant wind. Limited data show only a weak relation between fall velocity u t and q v (with q v in g/cm2 h). Consequently there is a strong correlation (r 2 = 0.97) between ρ s and q v (with q v in g/cm2 h). A simple relation of this kind is of practical value for certain technical purposes, and more data would be welcome.

Résumé

Résumé

On peut estimer la concentration de masse ρ s de la neige tombante à partir du taux de chute (vitesse d’accumulation) q v s’il n’y a pas un vent significatif. Des données peu nombreuses montrent seulement une relation faible entre la vitesse de chute u t et q v (avec q v en g/cm2 h). Par conséquent il y a une forte corrélation (r 2 = 0.97) entre ρ s et q v (avec q v et g/cm2 h). Une simple relation de ce type a une valeur pratique pour certains usages techniques et plus d’observations seraient les bienvenues.

Zusammenfassung

Zusammenfassung

Die Massenkonzentration ρ s fallenden Schnees kann aus der Schneefallrate (Akkumulation) q v geschätzt werden, wenn kein starker Wind weht. Begrenzte Daten zeigen eine nur schache Relation zwischen der.

Fallgeschwindigkeit u t und q v (mit q v in g/cm2h). Folglich besteht eine starke Korrelation (r 2 = 0.97) zwischen ρ s und q v (mit q v in g/cm2h). Eine einfache Beziehung dieser Art ist für gewisse technische Zwecke von praktischem Wert: mehr Datenmaterial wäre daher wünschenswert.

Information

Type
Short Notes
Information
Journal of Glaciology , Volume 29 , Issue 103 , 1983 , pp. 505 - 507
Copyright
Copyright © International Glaciological Society 1983

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.

References

Mellor, M. 1966. Light scattering and particle aggregation in snow-storms. Journal of Glaciology, Vol. 6, No. 44, p. 237–48.CrossRefGoogle Scholar
Figure 0

Fig. 1. Fall velocity ut plotted against accumulation rate qv.

Figure 1

Fig. 2. Snow density ρs plotted against accumulation rate qv.