Grain growth in a wet arctic snow cover

CoMRegions Scienceand Technology, 14 ( 1987) 23-31 Elsevier SciencePublishers B.V., Amsterdam-- Printed in the Netherlands

23

GRAIN G R O W T H IN A W E T A R C T I C S N O W COVER t

Philip Marsh National Hydrology Research Institute, Environment Canada, 11 Innovation Blvd., Saskatoon, Saskatchewan, S7N 31-15 (Canada).

(ReceivedSeptember 26, 1986; accepted in revisedform October 17, 1986)

ABSTRACT Snow grain growth was measured in a natural, melting snow cover in the Canadian Arctic. Over a 12-day period the mean snow grain size increased, the range of grain sizes increased, and the smaller grains disappeared. This is in general agreement with previous laboratory studies of snow saturated with water. For snow with a water content similar to that found in melting snow covers, earlier studies assumed an initial rapid increase in mean grain size followed by a gradual decline in growth rate. In the present study however, data from a natural snow cover showed a nearly linear growth rate which declined slowly with time. Compared to earlier studies the growth rate was slower over the first few days and faster over the next 5 to 12 days. A power curve of the form d - do = 0.044 t 089 was successfully fitted to the data. It is hypothesized that grain growth in natural snow covers is controlled by a complicated sequence of metamorphic events. This includes grain growth under pendular and funicular water saturations, and during melting and freezing events. Further studies are required to improve our understanding of grain growth under these mixed processes which occur in natural melting snow covers.

INTRODUCTION As meltwater enters an initially cold, dry snow cover a number of physical changes occur in the snow. These include the refreezing of meltwater as ice layers and ice columns (Marsh and Woo, 1984a,

0165-232X/87/$03.50

b), the filling of liquid water storages (Colbeck, 1976; Ebaugh and DeWalle, 1977), and snow grain growth (Wakahama, 1968). These changes have important implications for the liquid permeability of snow (Shimizu, 1970), snow melt runoff (Colbeck, 1977, 1978), and for snow cover optical properties (Berger, 1979; Warren, 1982) which influence the surface energy balance and have applications to remote sensing of snow covers (e.g. Dozier et al., 1981; Stiles and Ulaby, 1982). The term "grain" generally refers to a particle comprised of a single crystal, but when referring to snow covers it is also used to describe polycrystalline particles (Sommerfeld and LaChapelle, 1970; Trowbridge, 1974). In this paper, snow grain refers to the smallest distinguishable unit, whether single or polycrystalline. When liquid water is added to dry snow, the snow grains undergo a rapid metamorphism. In general, the grains begin to round and the larger grains grow rapidly at the expense of smaller ones. Theoretical discussions of the grain growth phenomenon in wet snow were given by Colbeck (1973, 1974, 1979, 1982). In wet snow covers, three types of snow grains occur (Colbeck, 1982), each with different characteristics and, more importantly, different growth rates. At high liquid saturations (funicular regime) well rounded, cohesionless grains form. These grains are composed of single crystals. At lower liquid saturations (pendular regime) single crystal grains bond together to form distinct grain clusters. Under both funicular and pendular conditions the growth rate of individual grains is controlled by the degree of liquid saturation. If the wet snow experiences melting and freezing cycles, the

© 1987 ElsevierSciencePublishers B.V.

24 grains are frozen together to form larger irregular, polycrystalline grains. Laboratory studies of grain growth (Wakahama, 1968, 1974; Raymond and Tusima, 1979; Colbeck, 1986) have shown that (1) the rate o f grain growth declines with time, (2) grain size slowly approaches infinity, and (3) the growth rate is dependent on the water saturation. Using laboratory data for saturated snow, Colbeck (1986) fitted

d=do +0.42 t°36

(1)

where d is the grain diameter in mm, do is the initial grain size, and t is the time in days since the grain was first wetted. This is very similar to the change in grain size reported by Wakahama (1974) for saturated snow. In conjunction with data from Wakahama (1968) for snow at low liquid saturation, these laboratory data provide upper and lower limits for snow growth rates. At the intermediate pendular liquid saturations found in melting, freely draining snow covers however, very little data are available and the only estimate of growth rate was suggested by Colbeck (1976) as d=do +0.1 t °5

(2)

for "expected water saturations following a heavy rainfall on cold snow". Due to the paucity of data, this equation was based on a synthesis of Wakahama's (1968) data for saturated snow and that with a water content of only 3 to 5% by weight. There is little systematic data on grain growth for snow under natural conditions where the spatial and temporal variations in liquid water saturation, melt-freeze cycles, and solar radiation all affect grain growth. In view o f these deficiencies and problems, it is the purpose o f this note to provide information on grain growth in the natural snow cover under typical melt conditions.

METHODOLOGY Field observations were conducted in the Canadian High Arctic near Resolute Bay, Cornwallis Island ( 7 4 ° 4 5 ' N , 9 4 ° 5 0 ' W ) . Prior to the commencement of melt, a total of 29 snow pits were excavated on a range of terrain types. During the

snow melt period five snow pits located at sites on flat lying terrain and concave slopes (see Marsh and Woo (1984a) for the location of these sites) were monitored daily. At each pit, snow depth was measured as well as the thickness of individual stratigraphic layers. From each stratigraphic layer, samples were obtained to determine density and grain size. The existence of both uni- and polycrystalline grains and grain clusters complicates the measurement of "grain size" since it is not clear whether the crystal size, grain size, or some measure of cluster size is appropriate for use with relationships to determine, for example, the snow cover permeability or optical properties. In the present study, grain size is used since it is an easily measured, physical property of the snow cover. In addition, it is not clear what is the correct or most appropriate measure of grain size. Previous studies have used a simple measure of grain diameter (e.g. Wakahama, 1968, 1974; Shimizu, 1970), while others have used grain volume (Raymond and Tusima, 1979), or the diameter of a circle with the same area as the measured grain area (Colbeck, 1986). In this study a simple visual estimate of grain diameter was used. Snow grains from each stratigraphic layer were placed on a plexiglass plate with 1 m m grid markings, and a black and white photograph was taken using a transmitted illumination method (LaChapelle, 1969). In the laboratory, the photographs were projected onto a screen with a 12 X magnification. Square grids marked on the screen were picked randomly and all grains within it were measured to an accuracy of 0.1 mm. This procedure was repeated for 100 grains. Between measurements, the snow pits were protected with double layer mylar radiation shields to minimize melting of the pit wall. Immediately before sampling, half of the pit face was cleared back for approximately 0.2 m. Alternate sides of the pit were used on consecutive days to ensure undisturbed samples and to allow the continuity of the layers to be determined. The data from snow pit CC6 were the most detailed of the five snow pits studied. Since the other snow pits showed similar results, only those from pit CC6 will be presented in this paper.

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Fig. 1. Pre-melt snow cover properties for a typical snow pit. Layer structure was based on daily profiles from June 2 to June 26, 1981. All other data were observed in early June, 1981. Where x is the mean value, S.D. is the standard deviation, and n is the n u m b e r o f samples.

26

CHARACTERISTICS OF ARCTIC S N O W COVER

THE

PRE-MELT

Prior to the beginning of snow melt, all snow pits showed distinctive stratification along their vertical profiles (Fig. 1B). The number of strata ranged from 3 to 12, and the mean stratum thickness ranged from 0.05 to 0.16 m, depending on terrain type. Daily sampling of the snow pits during the melt period demonstrated that most strata were roughly parallel, although their boundaries showed small undulations (Fig. 1B), and they were continuous over a horizontal distance of 1.6 to 3.2 m. Within a stratum the snow had remarkably uniform properties and there were generally no visible laminations. Most strata at site CC6, for example, were characterized by a unimodal frequency distribution with a small range in density and grain size (Fig. 1C,D). The mean stratum density ranged from 270 to 450 kg/m 3 and the mean grain size from 0.15 to 1.78 mm. Before melt, the base of all snow pits showed a distinctive layer of depth hoar characterized by large cup shaped crystals (Fig. 1C), and low density (Fig. 1D), hardness and strength. Due to measurement difficulties caused by the low strength of the depth hoar layer, the growth characteristics of this layer will not be discussed in this paper. At the beginning of snow melt the snow and underlying soil were still below 0°C (Fig. 1A).

GRAIN GROWTH IN A W E T S N O W COVER The daily change in grain size after the snow was wetted is shown for two typical layers in snow pit CC6 (Fig. 2). These results show a general similarity to those provided by Wakahama (1968), with the mean grain size increasing, the range of grain sizes increasing, and the smaller grains disapppearing with time. The change in mean grain size, after the snow was first wetted, for all layers in snow pit CC6 are shown in Fig. 3. The best fit power curve for the data shown,

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(3)

has a correlation coefficient of 0.84. This curve is a better fit to the data than eqn. (2), which is also shown on Fig. 3. The growth rates in the present study are between the extreme values shown in Fig. 4 and are similar to the equation presented by Colbeck (1976) for pendular saturations. However, unlike eqn. (2), eqn. (3) shows a nearly linear growth rate over the 12-day study period. Initially the growth rate is significantly slower than that predicted by eqn. (2) and it does not decline as quickly over time. Equation (3) predicts that rapid grain growth continues over a longer period of time, with grain size gradually approaching that occurring under saturated conditions (Fig. 4). There are no available data to confirm the extrapolation of eqn. (3) beyond 12 days. In Fig. 5, eqn. (3) is applied to the original grain size data for each individual layer. This procedure will highlight depth dependent patterns of grain growth, and illustrate typical variations in grain size found in a melting snow cover. In Fig. 5 the wetting front advance was calculated by the method of Marsh and Woo (1984b). Grain growth was initiated when the background wetting front reached the mid-point of each layer and eqn. (3) was used to calculate grain size. Figure 5 suggests that the growth curve is applicable to each snow layer with few systematic variations with depth or time even though water content and radiation penetration are significantly different for each layer. The greatest difference between the curve and observed grain size occurs for layers 5 and 6 where the curve underpredicts grain size later in the melt period. Possible reasons for such variations are discussed in the following section. A second point of interest from Fig. 5 is that large differences in grain size develop within the melting snow cover. Before melt began, grain size was nearly uniform throughout the snow cover, with only the depth hoar layer having significantly larger snow grains (Fig. 1). However, during melt large differences in grain size developed. By June 13 for example, the top 4 layers had experienced considerable grain growth, with grain sizes up to 0.4 mm while layers 2 and 1 had not yet been wetted and had snow grains of 0.2 and 1.8 mm respectively. This demonstrates that for studies where grain size is impor-

27

tant (for example runoff modelling or remote sensing), melting snow covers cannot necessarily be considered uniform in terms of grain size.

DISCUSSION

The grain growth curve described above (eqn. (3)), differs from those given by previous studies for growth rates under either pendular or funicular conditions. This is~probably due to the large difference between conditions in the laboratory and those

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30 in the field. For example, unlike the laboratory situation where the snow is usually saturated with water, snow grains in a natural snow cover have a complex growth history due to water saturations which vary throughout the pendular and funicular regimes. In addition, the grains may experience a series of melting and freezing events. It is usually impossible to deduce the metamorphic history and therefore the processes responsible for producing a collection of snow grains. The following discussion illustrates typical conditions found in natural, melting snow covers and the implications to grain growth. At the study site, most of the snow cover experienced freely draining Conditions with measured liquid saturations ranging from the irreducible water saturation (approximately 7%) up to 14%, the commonly accepted upper limit of the pendular regime (Denoth, 1980). Variations within the pendular regime occurred due to diurnal variations in surface melt (0 to 4 mm/h), day-to-day variations in melt (5 to 65 mm/day), changes in grain size, and the concentration of water by flow fingers into small areas within the snow cover (Marsh and Woo, 1985a,b). Pendular water saturations dominated the snow cover and, as a result, clusters of round, unicrystal grains (identified under crossed polaroid filters) were most common. Although the melt rates were considerably larger later in the study period, the strata near the base of the snow cover experienced growth rates which were similar to those near the top of the snow (Fig. 5 ). These data suggest that the small range in water saturations found in freely draining snow has little effect on the growth rate and that eqn. (3) can be applied in general to snow within the pendular regime. Water saturations within the funicular regime occurred at boundaries separating snow strata, at the snow-soil interface and possibly within vertical flow fingers for brief periods. The faster growth rates under the funicular conditions would produce large individual unicrystal grains. However, when the liquid saturation decreased to the pendular regime, clusters of grains would reform. These clusters of larger grains would be indistinguishable from clusters formed entirely under pendular conditions. Melt-freeze grains formed in a thin frozen layer at the snow surface each morning, within the pack

as ice layers and ice columns (Marsh and Woo, 1985 a,b), and at wetting fronts penetrating sub-zero snow. Melt-freeze events can produce a rapid increase in grain size when grains are frozen together. When these melt-freeze grains undergo melting at a later date, either due to liquid water percolation or solar radiation penetration (Langham, 1974), they break down along crystal boundaries and revert to their original form. It would be expected that the occurrence of pendular and funicular water saturatons, and melt-freeze events would produce large variations in grain growth rates within a melting snow cover. This is difficult to document, but its importance is demonstrated by the presence of snow grains up to 3 mm in diameter at boundaries separating snow strata and at the snow-soil interface. Individual processes such as grain growth under funicular conditions can not account for grains of this size within a 10 to 15 day period (Fig. 4). Their development can be explained by postulating freezing of individual grains to form large polycrystalline grains, followed by rapid grain growth under funicular conditions. Extensive freezing, followed by high liquid saturations, occur at strata boundaries. Similar conditions occur for limited time periods at other locations in the snow cover. These processes may explain some of the variations found in the data on Fig. 3.

CONCLUSIONS Measurement of grain growth in natural, wet snow covers shows that with time the mean grain size increases, the range of grain sizes increases, and smaller grains disappear. Generally, this is in agreement with earlier laboratory studies, but the shape of the grain growth curve differs. In this study, the growth rate was nearly linear over a 12-day period, decreasing only slowly with time whereas previous studies showed an initial rapid increase followed by a more rapid decline in growth rate. Data from a number of layers within the snow cover suggest that grain growth under pendular conditions dominates and that the narrow range of pendular water saturations does not significantly affect the growth rate. However, the occurrence of funicular conditions and

31 m e l t - f r e e z e w i t h i n the snow cover, can p r o d u c e i m p o r t a n t v a r i a t i o n s i n grain size. F u r t h e r studies are r e q u i r e d to i m p r o v e o u r u n d e r s t a n d i n g o f grain growth u n d e r the c o m p l i c a t e d sequence of melt m e t a m o r p h i s m events which occur in n a t u r a l snow covers.

ACKNOWLEDGEMENTS T h e f i n a n c i a l s u p p o r t for this work was p r o v i d e d by the P r e s i d e n t i a l C o m m i t t e e o n N o r t h e r n Studies of M c M a s t e r U n i v e r s i t y a n d the Arctic I n s t i t u t e o f N o r t h America. T h e generous logistical s u p p o r t o f Polar C o n t i n e n t a l Shelf Project, D e p a r t m e n t o f Energy, Mines, a n d Resources is gratefully acknowledged. M a n y t h a n k s m u s t go to M.K. Woo for his help t h r o u g h o u t this project, a n d to P. Steer, R. Heron, M.A. Dubreuil, C. Rapheal, a n d R. Plinte for their assistance in the field. I w o u l d like to t h a n k Dr. S.C. Colbeck a n d Dr. R. Perla for reviewing a draft o f this paper.

REFERENCES Berger, R.H. (1979). Snowpack optical properties in the infrared. CRREL Report 79-11, 9 pp. Colbeck, S.C. ( 1973 ). Theory of metamorphism of wet snow. CRREL, Research Report 313, 11 pp. Colbeck, S.C. (1974). Grain and bond growth in wet snow. IASH-AISH, pub. 114, pp. 51-60. Colbeck, S.C. (1976). An analysis of water flow in dry snow. Water Resour. Res., 12: 523-527. Colbeck, S.C. ( 1977 ). Short-term forecasting of water runoff from snow and ice. J. Glaciol., 19: 571-588. Colbeck, S.C. (1978). The physical aspects of water flow through snow. Advances in Hydrosciences, 11:165-206. Colbeck, S.C. (1979). Grain clusters in wet snow. J. Colloid and Interface Sci., 72: 371-384. Colbeck, S.C. (1982). An overview of seasonal snow meta-

morphism. Reviews of Geophys. and Space Physics, 20: 45-61. Colbeck, S.C. (1986). Statistics of coarsening in water-saturated snow. Acta Metall., 34: 347-352. Denoth, A. (1980). The pendular-funicularliquid transition in snow. J. Glaciol., 25: 93-97. Dozier, J., Schneider, S.R. and McGinnis Jr., D.F. (1981). Effect of grain size and snowpack water equivalence on visible and near-infrared satellite observations of snow. Water Resour. Res., 17: 1213-1221. Ebaugh, W.P. and DeWalle, D.R. (1977). Retention and transmission of liquid water in fresh snow. Second Conf. on Hydrometeorology, American Met. Soc., Toronto, pp. 255-260. LaChapelle, E.R. (1969). Field Guide to Snow Crystals. J.J. Douglas Ltd., Vancouver, B.C., 101 pp. Langham, E.J. ( 1974). The mechanism of rotting of ice layers within a structured snow cover, IAHS Publ., 114, pp. 73-81. Marsh, P. and Woo, M.K. (1984a). Wetting front advance and freezing of meltwater within a snow cover 1. Observations in the Canadian Arctic. Water Resour. Res., 20: 1853-1864. Marsh, P. and Woo, M.K. (1984b). Wetting front advance and freezing of meltwater within a snow cover 2. A simulation model. Water Resour. Res., 20:1865-1874. Raymond, C.F. and Tusima, K. (1979). Grain coarsening of water saturated snow. J. Glaciol., 22: 83-105. Shimizu, H. (1970). Air permeability of deposited snow. Institute of Low Temp. Sci., 22: 1-32. Sommerfeld, R.A. and LaChapelle, E. (1970). The classification of snow metamorphism. J. Glaciol., 9: 3-17. Stiles, W.H. and Ulaby, F.T. (1982). Dielectric properties of snow. Proc. of a Workshop on the Properties of Snow. In: U.S. Army Cold Region Res. and Eng. Lab., Special Report 82-18, pp. 91-93. Trowbridge, A.C. (ed.) (1974). Dictionary of Geological Terms, American Geological Institute, Anchor Press/Doubleday, Garden City, N.Y., 545 pp. Wakahama, G. (1968). The metamorphism of wet snow. IASH-AISH, Pub. 79, pp. 370-379. Wakahama, G. (1974). The role of meltwater in densification processes of snow and tim. IASH-AISH, Pub. 114, pp. 66-72. Warren, S.G. (1982). Optical properties of snow. Reviews of Geophys. and Space Physics, 20: 67-89.