Studies on depth hoar

Eizi Akitaya

Abstract. A series of experiments on growing depth hoar were carried out in a cold laboratory. Depth hoar crystals grew in snow when the snow was subjected to a consistent negative temperature gradient for a considerably long period. Depth hoar crystals were classified into the two types: skeleton type and solid type. The solid-type depth hoar (comprising short-column and thick-plate grains) grew predominantly under temperature gradients smaller than about -0.25°C/cm, and the skeleton-type depth hoar (cup, sheath or sector shapes) larger than that. Large crystals of skeleton-type depth hoar grew in snow having a large air space under large temperature gradient. Hardness of depth hoar decreased, changed scarcely, or increased, according to the magnitudes of temperature gradient and density of original snow. Finally, the occurrence of natural convection of air in snow subjected to negative temperature gradients was studied by using natural snow and artificially prepared snow samples and measuring the heat flow. Natural convection of air occurred only in artificial samples with very large air spaces.

Résumé. Une série d'expériences sur la croissance du givre interne ont été faites en laboratoire froid. Des cristaux de givre interne croissent dans la neige quand cette neige est soumise à un gradient de température négatif pendant une longue période. Les cristaux de givre interne sont classés en deux catégories: le type squelette, le type solide. Le givre interne de type solide (comprenant des grains en forme de colonne court ou des grains en forme de plaque) croît de façon prédominante avec un gradient de température plus faible que -0-25"C/cm alors que le givre de type squelette (enforme de coupe, fourreau ou lames en secteur) apparaît pour des gradients supérieurs. De gros cristaux de givre de type squelette se fourrent dans la neige ayant des creux d'air importants sous un fort gradient de température. La dureté du givre interne décroît, reste constant ou croît suivant l'importance du gradient de température et la densité de la neige de départ. Finalement, l'existence de courants naturels de convection d'air dans la neige soumise à un gradient négatif de température a été étudiée sur des neiges naturelles et artificielles par des mesures de conduction thermique. Les courants de convection d'air ne se produisent que dans le cas d'échantillons de neige artificielle avec des creux d'air importants.

INTRODUCTION A snow cover has a stratified structure, as a rule, according to the serial deposition of snowfalls. The original texture and properties of each layer are determined by snowfall conditions. Metamorphism of snow changes the texture and properties of the layer according to physical conditions (thermal and mechanical conditions caused by climatic and geographical factors) to which the layer has been subjected. Depth hoar is formed in the presence of a temperature gradient; fragile layers of depth hoar grow in deposited snow in Hokkaido and in alpine districts of Honshu, Japan. It is known that they play an important role in releasing ground avalanches in these districts. Experiments were carried out in the laboratory on the artificial growth of depth hoar, to clarify the growth condition of depth hoar in more detail.

GROWTH OF DEPTH HOAR Snow blocks of 26 x 26 x 26 cm with a fairly uniform texture were used as samples. These were placed in a thermally insulated box. A certain difference of temperature was Studies on depth hoar 43 brought about between the top and the bottom surface of the sample by applying electric heaters Ht and H2, each with a thermoregulator, respectively to the bottom and the top. This experimental device was set in a cold laboratory. A negative temperature gradient in a sub-freezing temperature range could be maintained in the snow sample, by keeping bottom heater Hj warmer than top heater H2. A temperature difference between the top and bottom, i.e. the magnitude of temperature gradient, was adjustable for an object of the experiment by the thermoregulators. Snow tempera­ tures were measured at five levels in the sample by five thermocouples, and four local temperature gradients were obtained in the sample from them. By this way a snow sample was subjected to a constant temperature gradient of a desired magnitude for a desired period. When the experiment was over, the sample was taken out so that a thin section was prepared for observations of the metamorphosed snow. All kinds of deposited snow with different textures were used in the experiment: new snow, fine grained compact snow and coarse grained granular snow. Depth hoar can be defined as a deposition of hoar crystals grown by internal sublimatic evaporation and condensation of water from/onto snow grains in a snow cover, the process which occurs when a snow layer is subjected to a consistent temperature gradient (generally a negative gradient). From a number of observations both in the laboratory and in the field, depth hoar crystals were classified into two types, 'solid-type depth hoar crystal' and 'skeleton-type depth hoar crystal'. A solid- type depth hoar crystal is generally a small solid crystal with sharp edges, corners and flat surfaces. It is a plate or a column in shape. A solid-type depth hoar layer is frequently misread as a fine grained compact snow layer, because a solid-type depth hoar layer is hard and sturdy like a fine grained compact snow layer. On the contrary, a skeleton-type depth hoar grain is very easily detected. It is a large skeleton crystal with rugged surfaces: cup, sheath, needle, plate or sector shaped. This type of crystal has a large crystal body and thin joints at the crystal base; a layer consisting of this type of depth hoar is extremely fragile against a dynamic force. The solid-type depth hoar comprising short-column and thick-plate grains grew predominantly under a negative temperature gradient smaller than about — 0.25°C/cm, regardless of snow temperature. The skeleton-type depth hoar grew predominantly under a negative temperature gradient larger than about —0.25°C/cm. Crystal habit had a dependence on snow temperature: skeleton cups 4 10°C forming in the snow temperature range, with malformed cups or plates being found at both sides of the cup area. A dependence of the crystal habit of depth hoar on snow tempera­ ture showed an agreement with those of snow crystals in Nakaya's diagram. In a large air space (hole, cavity and gap) in the natural snow cover, a fairly large hoar crystal grew under a large magnitude of negative temperature gradient. From the experiments and field observations, it became clear that a relation existed between the texture of the original snow and the crystal size of depth hoar. The controlling factor of the relation was 'the size of an air space' the original snow, namely, large crystals could grow in a large air space, and small crystals in a small air space. In an ordinary case of a natural snow cover, large crystals of depth hoar could grow in new snow, lightly compact snow, some of fine grained compact snow and coarse grained granular snow of low density, all with a large air space in them. Let us define this group of snow as A. On the contrary, in most of fine grained compact snow and coarse grained granular snow of medium and high density with a small air space, only minute crystals could grow. Let us define this group C. Group B consists of some fine grained compact snow and coarse grained granular snow of medium density, with air spaces of medium size. A qualitative graphical expression of this relation is given by Fig. 1(a). The grain size was measured by the diameter of an equi-areal circle for round-shaped grains, by the longest axis for bar-shaped grains, and by the diameter of an envelope circle for new snow crystals. The grain size can be an index indicating 44 Eizi Akitaya

t- . © © (a) Q © (b) - A \ loar N^ hard depth

•v

Skeleton-typA e depth hoar/\ A " ^^^^

Solid-type • \ + • 0 depth hoar n + i 1 0.5 1.0 1.5 2.0 2.5 A B C Grain size (mm) Snow texture FIGURE 1. Relation between the texture of original snow and metamorphism under a negative temperature gradient, (a) The types of metamorphosed snow A, B and C, and properties (grain size and density) of original snow. +, New snow; <, lightly compact snow; O, fine grained compact snow; ®, coarse grained granular snow, (b) Relations between the texture of original snow and temperature gradient, as regards the crystal shapes of depth hoar. the size of an air space in snow. A dependence of crystal shapes of the depth hoar metamorphosed from each group of snow (A, B and C) on the temperature gradient is also qualitatively given by a graphical expression in Fig. 1 (b). Observed in the upper right area of the diagram was a depth hoar with such an extremely complicated fine structure that it cannot be categorized in the two types mentioned earlier: it was tentatively named 'hard depth hoar' as it was very hard. 'Hard depth hoar' developed generally in a small pore space, under a fairly large magnitude of negative temperature gradient.

CHANGE OF HARDNESS OF SNOW BY DEVELOPMENT OF DEPTH HOAR Negative temperature gradients of — 0.33°C/cm at —7.1°C (mean value) and —0.90°C/cm at —6.5°C were applied to two snow samples A and B, prepared from the same block of fine grained compact snow, 0.36 g/cm3 in density and 2.3 kg/cm2 in hardness (Kinosita's hardness; Kinosita, 1960). Ten days after the start, the hardness of sample A was found to have decreased to 1.8 kg/cm2, while that of sample B to have increased to 6.9 kg/cm2, three times the original value. Such a remarkable differ­ ence in the mechanical properties of these two samples seems to be explained by the difference in their textures. Metamorphosed snow of sample A had a scanty connec­ tion among snow grains, mostly depth hoar crystals. On the contrary, skeleton-type depth hoar was well developed in sample B, a large number of minute crystals moreover having cemented them. A series of experiments were carried out to investigate the relations between hardness, density and temperature gradient. Thirty-six snow samples were subjected to individual negative temperature gradients for 1 — 10 days; to emphasize the effect of the development of depth hoar some of the samples were subjected to a temperature gradient for a long period (10 days) when the magnitude of temperature gradient was small. The hardnesses and densities of both the original and the metamorphosed snow were measured, whereby the mean value of hardness obtained from five measurements was taken as the hardness of each sample. The density of snow was hardly changed by metamorphism. The results were plotted in Fig. 2 in terms of density of the original snow versus magnitude of negative temperature gradient. The modes of changes in hardness subsequent to metamorphism of snow are distributed roughly in three divisions; A represents an increase in hardness, B indicates no change or a marginal change, and C represents a decrease. The modes of changes Studies on depth hoar 45

Temperature gradient (-°C/cm) -J I I I I I 0.2 0.4 0.6 0.8 FIGURE 2. Change of hardness of snow by metamorphism under negative temperature gradients. O, Hardness increased; ffi, hardness did not change (including a change less than 10 per cent of the original value); +, hardness decreased through metamorphism (development of depth hoar). in hardness of the metamorphosed snow are seen from the standpoint of the original snow as follows: (1) Hardness of snow with an original density less than 0.26 g/cm3 decreases by metamorphism, regardless of the magnitude of negative temperature gradient. (2) Hardness of snow with an original density more than 0.26 g/cm3 decreases, changes scarcely, or increases, according to the magnitude of negative temperature gradient. (3) As a special case, when snow was subjected to a magnitude of negative temperature gradient larger than — 0.5°C/cm (which is a fairly large value in natural conditions) hardness of snow with an original density more than 0.35 g/cm3 increases greatly. The results of the experiments with the foregoing samples can be summarized as follows: change (increase or decrease) of hardness of snow due to the development of depth hoar is controlled not only by the magnitude of negative temperature gradient applied but also by the density and texture of the original snow, as shown in Fig. 2 and Fig. 1(b).

TRANSFERENCE OF HEAT IN A SNOW COVER During the cold winter season, a snow cover on the ground is subjected to a negative temperature gradient, as a whole, and heat flows from the ground into the snow upward. Transference of heat in a snow cover can be divided into three mechanisms. (1) Thermal conduction through an ice network and an air space of a snow cover. (2) Diffusion of water vapour through an air space. Due to the existence of a negative temperature gradient in snow, water vapour migrates upward, from a lower and warmer grain to an upper and colder grain through a process of evaporation- diffusion—condensation. (3) Natural convection of air in an air space. When a temperature difference between the top and the bottom of a certain layer of snow reaches a critical value, referring to the thickness of the layer, natural convection of air occurs by the differ­ ence of density of air between the top and the bottom. Water vapour is also transferred upward by the convection current, carrying heat. A schematic diagram of a heat flow rate in snow as a function of temperature gradient is shown in Fig. 3. The heat flow rate in snow should increase proportionally to the temperature gradient in a region of small temperature gradients, where only thermal conduction through ice and diffusion of water vapour through the air space contribute to the transfer of heat. 46 Eizi Akitaya

1 + 2 j/1 + 2+3

J I I 1 L Temperature gradient FIGURE 3. Heat flow rate versus temperature gradient. 1, Thermal conduction; 2, diffusion of water vapour; 3, natural convection.

If natural convection occurs at critical point R, the heat flow rate in snow ought to increase abruptly with a further increase of temperature gradient, due to a contribution to heat transfer by a convection current in addition to thermal conduc­ tion and diffusion of water vapour mentioned above. A series of measurements was carried out on heat flow in snow to investigate the occurrence of natural convection of air in snow. A wooden box was divided into three sections: top, middle and bottom. Both in the top and bottom sections, an electric heater with a thermoregulator and an electric fan were installed, and the four lateral sides were thermally insulated by foam-stylene boards 10 cm in thickness. A snow sample (20 x 20 cm in area and 15 cm in thickness) was set in the central cabinet, namely the middle section, and was subjected to a temperature gradient, either positive or negative. By aid of a heat diffuser (a copper plate 1 cm in thickness), and an electric fan which stirs the hot air in the heat source section, temperature distribution could be maintained very uniformly at the top and the bottom surface of the sample at a proper temperature. Snow temperatures at five levels in the sample were measured by five sets of thermocouples, and steady-state heat flow rates were measured by a heat meter (a set of thermopiles, 20 x 20 x 1 cm) set immediately beneath the bottom of the sample. A series of negative temperature gradients down to —2.0°C/cm was applied to three different kinds of natural snow samples (20 x 20 cm in area and 15 cm in thickness): new snow, lightly compact snow and fine grained compact snow with densities of 0.12, 0.17 and 0.27 g/cm3, respectively. The resultant relations between the tempera­ ture gradient and heat flow rate were straight lines, which means that natural convec­ tion of air did not occur in the snow samples under these conditions. The second experiment was carried out using samples of sieved snow with large air permeabilities. A block of coarse grained granular snow was crushed, and two kinds of sieved snow were prepared: sample A (2—5 mm in diameter, 0.33 g/cm3 in density) and sample B (5—10mm, 0.28 g/cm3). The results were represented as before by straight lines down to a temperature gradient of —1.7°C/cm; natural convection of air still did not occur in the samples of sieved snow. The final experiment was carried out by samples of specially prepared snow, with a very large air space (accordingly large air permeability). A number of snow cubes (15 X 15 x 15 mm) were cut out of a block of fine grained compact snow. Three samples, C, D and E, were prepared by random packing of the snow cubes in a space of 20 x 20 cm with a height of 15 cm (a height of 13 cm only for sample E); bulk densities of samples C, D and E were 0.23, 0.15 and 0.16 g/cm3, respectively. The results were given in Fig. 4; finally, natural convection of air occurred in samples C, D and E at points C' (— 1.3°C/cm of temperature gradient), D' (-l.l°C/cm) and E' (— 0.7°C/cm), respectively. A series of positive temperature gradients were applied to sample D afterwards; the result was expressed by a straight line, the beginning half Studies on depth hoar 47

0 0.5 1.0 ( ±°c/cm)1.5 2.0

FIGURE 4. Temperature gradient and heat flow rate: convection occurred at points C, D' and E'. of which showed a complete agreement with that of the case of negative temperature gradients, as shown by OD* in Fig. 4. This fact is positive proof that natural convection of air actually occurred at points C', D' and E' when the magnitude of temperature gradient increased, because natural convection cannot occur under positive temperature gradients. Summarizing results of these experiments with samples of natural snow, sieved snow and snow cubes: (1) In natural snow and sieved snow, no natural convection of air occurred, even under a considerably large temperature gradient, —1.7 2.0°C/cm. (2) In the samples of snow cubes, with extraordinarily large pores, natural convection of air occurred under fairly large temperature gradient, —0.7 1.3°C/cm. The following tendency was confirmed: natural convection of air was apt to occur, (a) in a snow layer of smaller density (or higher porosity), if the thickness of the snow layer was constant, and (b) in a thicker snow layer, if the density (or porosity) was constant. Finally, the possibility of occurrence of natural convection of air in a snow cover in Hokkaido was investigated by use of meteorological data. Most of the estimated temperature gradients in snow were much smaller than the experimental values mentioned above. From consideration of the foregoing, it is concluded that natural convection of air does not occur in a snow cover even under the severest climatic conditions in Hokkaido, Japan.

Acknowledgements. This work was carried out at the Institute of Low Temperature Science, Hokkaido University, Sapporo, Japan, and on mountain slopes at the Snow Avalanche Research Station of the Institute of Low Temperature Science in the Teshio Experimental Forest of Hokkaido University. The author would like to express his sincere gratitude to Dr T. Huzioka, Dr H. Shimizu and Dr Z. Yosida for every encouragement and valuable advice accorded him for the preparation of this paper.

REFERENCES Akitaya, E. (1967) Some experiments on the growth of depth hoar. In Physics of Snow and Ice (edited by H. Ôura), International Conference on Low Temperature Science, 1966, Proceedings, vol. 1, pt II, pp. 713-723: Institute of Low Temperature Science, Hokkaido University. 48 Eizi Akitaya de Quervain, M. (1963) On the metamorphism of snow. In Ice and Snow; Properties, Processes and Applications (edited by W. D. Kingery), Proceedings of a Conference held at the Massachusetts Institute of Technology, 12-16 February, 1962, pp. 377-390: MIT Press, Cambridge, Mass. Kinosita, S. (1960) The hardness of snow. I (in Japanese). Low Temp. Sci. Series A, 19, 119-134. Yosida, Z. (1955) Physical Studies on Deposited Snow. I. Thermal Properties. Contributions from the Institute of Low Temperature Science, vol. 7, pp. 19-74: Institute of Low Temperature Science, Hokkaido University.

DISCUSSION (Dr Kuroiwa presented the paper on behalf of the author)

M. Kuhn: I would like to ask whether the temperature limits found for the transition from one shape to another (e.g. plate to needle) in depth hoar agree with those found by Nakaya for single crystals in air or surface hoar and if it is possible to arrive at any simple conversion from temperature gradients in depth hoar to values of supersaturation with respect to ice.

M. de Quervain: The experiments by Nakaya dealt with growth processes in the atmosphere where high supersaturations can prevail due to a negative radiation balance. On depth hoar formation, because only low supersaturations occur, no dendritic crystals form. However, there is an overlap in these two processes, for example in the formation of sector type crystals.

U. Radok: Convection tends to show different regimes even in the atmosphere. Moreover, in Fig. 4, the highest points of each of the curves E, C and D fall above the fitted line, suggesting a more precise relation would be curvilinear. Professor LaChapelle pointed out that the measurements shown in Fig. 4 were made on artificial snow samples.

D. Kuroiwa: In reply to the question from Dr Shoda, I can answer that in the experiments, the sign of the temperature gradient was reversed. However, I cannot comment on the effect of gravity on the results. My answer to the question by Dr Frolov is that the depth hoar crystals were monocrystalline rather than polycrystalline.

A. Frolov: It was unfortunate that there was no investigation'of the characteristics of the contacts between the depth hoar grains and that there were no quantitative data about the cohesive forces in these samples.