Distributions of crystals and gas bubbles in reservoir ice during growth period

Zhi-jun LI*, Wen-feng HUANG, Qing JIA, , Matti LEPP?RANTA

1. State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology,Dalian 116024, P. R. China

2. College of Water Conservancy and Hydropower, Heilongjiang University, Harbin 150086, P. R. China

3. Department of Physics, University of Helsinki, Helsinki FI-00014, Finland

1 Introduction

Ice crystals and gas bubbles control ice electronics (Li et al. 2010a), optics (Light et al.2003), and mechanics (Timco and Weeks 2010)to a large degree, and also play a key role in ice remote sensing (Shokr and Sinha 1994). The ice fabric determines the diffusion of light that have impacts on living conditions of under-ice creatures and sea ice ecology (Belzile et al.2001). A large number of studies and observations have been carried out on the relationship between ice properties and density or porosity that can shed light on gas bubbles in ice (Timco and Frederking 1996). Recent publications address the relationships between the density and porosity (Consolmagno et al. 2008), between the uniaxial compressive strength and porosity(Moslet 2007), between the coefficient of thermal properties of ice and porosity (Usowicz et al.2008; Shi et al. 2009), and between the thermal conductivity of snow-covering ice and density(Sturm et al. 2002). The history of inland fresh water ice studies in China began with river ice dams (Mao et al. 2002; Wang et al. 2005; Wang et al. 2007)and freeze-thaw of reservoir ice(Xiao et al. 2004), but a systemic study on the basic properties of fresh water ice has been lacking up to now.

Studies on ice fabrics and gas bubbles are important for understanding the basic properties of ice. Parameters of ice fabrics involve the type and size of crystals. Parameters of gas bubbles include the shape and size of bubbles as well as relative gas bubble content.

To study the basic physical properties of fresh water ice, field observations were conducted in the Hongqipao Reservoir in Heilongjiang Province, from December 18, 2008 to April 8, 2009. The growth of fresh water ice is mainly controlled by thermodynamic processes. Two ice pieces were taken from a site of the reservoir, which was about 150 m from the dam, on December 19, 2008 and February 9, 2009, corresponding to the fast growth and steady growth periods, respectively. Both pieces were typical reservoir ice and cut from the surface to bottom, and were used to analyze the type and size of ice crystals, the arrangement, shape, size and content of gas bubbles, and ice density. This paper provides the results of the investigations.

2 Ice sampling and preparation of ice sections

The thicknesses of the ice pieces taken on December 19, 2008 and February 9, 2009 were 50 cm and 85 cm, respectively. Complete ice pieces were cut out using ice augers and ice saws with a mark of the north direction. After the ice pieces were cut off from the reservoir ice sheet,they were transported to a cold room for observation. Because the air temperature was lower than -15℃, the ice fabric in ice pieces kept their original form. Four samples with a cross-section of 10 cm × 10 cm and thickness of 50 cm or 85 cm were vertically cut off from the intact ice piece directly, as shown in Fig. 1. Sample 1 was sectioned vertically for macro observations of ice stratigraphy and gas bubble distribution, and for micro observations of ice crystals. Sample 2 was sectioned horizontally for observations of crystals and fabrics as well as image analysis of gas bubbles in thin sections. Sample 3 was used to measure the ice density, and Sample 4 was stored as a backup.

Fig. 1 Sketch map of ice samples and sections from ice piece

The surface of Sample 1 was smoothened along the vertical direction and photographed with a dark background in order to obtain the macro features of the stratigraphy and gas bubbles in ice. It was then cut into vertical sections with intervals between 8 cm and 10 cm.Concurrently, Sample 2 was cut into horizontal sections with intervals between 8 cm and 10 cm.All of these horizontal sections were labeled with the north direction, and then smoothened and affixed to glass sheets with a temperature initially slightly above 0℃. After they were re-frozen, they were cut to about 1-mm thickness with planning knives. Six vertical and six horizontal sections were prepared from the piece from December 2008, and 11 vertical and ten horizontal sections were prepared from the piece from February 2009. According to Langway’s method of the analysis of ice crystals (Langway 1958; Iliescu and Baker 2007; Li et al. 2010b), these sections were placed on a Rigsby universal stage, photographed between crossed polarizers to measure the size and shape of crystals, and the C-axis orientations of crystals were determined. The result was processed by computer programs and presented in a Schmidt equal-area net, i.e., a fabric graph (Langway 1958). These sections were then photographed under normal light to measure the micro-arrangement and size of gas bubbles in ice. It was found that the section thickness had to be less than half of the smallest bubble diameter to get a clear image of gas bubbles.

3 Ice crystals and fabrics

Generally, with the decrease of air temperature, the water surface temperature first decreases to 0°C and undergoes a slight supercooling. Frazil ice then forms and progressively joins together to form an ice layer, corresponding to the fast-growing granular crystal. The ice growth rate slows down after the granular ice layer is formed. Ice crystals have enough time to grow, but are confined by ambient ones, so they have to grow downward, forming columnar crystals whose sizes increase with the decreasing growth rate and increasing thickness of ice.Figs. 2 and 3 are pictures of ice crystals in the vertical and horizontal sections from an ice piece from February 9, 2009. We can determine the number and total area of crystals from the horizontal thin sections and then calculate the mean area and equivalent diameter, which is considered the mean size of crystals in this section. Fig. 4 indicates that the mean crystal size increases with ice depth. Both ice pieces, having similar statistical features, were taken out during the ice growth period, when the ice crystal properties seldom change.

In addition, according to a spatial or planar directional distribution of C-axes on the fabric graphs, fresh water ice can be identified as isotropic, planar isotropic, or anisotropic material. According to the statistics of tilt directions of C-axes in the ice piece from February 9,2009, the C-axes of the upper layer of the ice piece were distributed randomly in the horizontal plane, and those of the deeper layer were oriented along the NNW-SSE direction(Fig. 5). If the number of grains in one horizontal section is less than 20, the adjacent section at the same depth should be analyzed to increase the observational data.

Fig. 2 Example photos of crystals of fresh water ice in vertical sections of ice piece from February 9, 2009

Fig. 3 Example photos of crystals of fresh water ice in horizontal sections of ice piece from February 9, 2009

Fig. 4 Variations of crystal size along depth in ice pieces

Fig. 5 Distribution of C-axes directions at different depths of ice piece from February 9, 2009

4 Gas bubbles and their relationship with density

Because of the random distribution of gas bubbles in ice, when the thickness of ice section is larger than the gas bubble size, the gas bubbles will be overlaid over each other and appear as a mess. Fig. 6 shows the bubble pictures of the ice piece from February 9, 2009. The gas bubbles in the layer between 0 and 18 cm are spherical, the bubbles in the 35-37 cm layer are arrow-shaped, which is abnormal, and the bubbles in the 70-80 cm layer are cylindrical. Results of the image processing reveal that the spherical bubble diameter varies between 0.3 mm and 5 mm, and the slenderness ratio varies within 10-70.

Fig. 6 Gas bubbles in ice piece from February 9, 2009

When an ice section was cut to a thickness less than the bubble diameter, there would be only one layer of bubbles in the section. Then the section was put onto the universal stage and photographed in the background of normal light (Fig. 7(a)). By image processing, the photos were converted into black and white images, where the white points are gas bubbles and the black background is ice (Fig. 7(b)). Then the pixel area and perimeter of every bubble were determined, and the true equivalent diameters as well as the areal fraction of gas bubbles in the section were calculated. The results are shown in Fig. 8.

Fig. 7 Photos of gas bubbles in horizontal section of ice

Fig. 8 Size distribution of gas bubbles in horizontal section

The equivalent diameter of gas bubbles first increased rapidly with depth and then remained at a stable level in the ice (Fig. 9(a)). Also, as shown in Fig. 9, the variation trend of bubble sizes in both pieces indicates that the bubble size decreased with time. Although the concentration of bubbles decreased with depth, the total content of bubbles increased with time (Fig. 9(b)), indicating that the gas bubble content varied in the growth period of ice. This provides a basis for understanding temporal variability in the thermodynamic, mechanical, and other kinds of properties of ice.

Sample 3 was cut into cubes based on the horizontal levels. The ice density was measured using the mass-volume method. Variations of density with depth are shown in Fig. 10. During the ice growth period from December 19, 2008 to February 9, 2009, two vertical profiles of ice density overlapped each other, indicating that the ice density did not change so much during the ice growth period. In fact, the ice density was inversely proportional to the content of bubbles. Fig. 11 presents the result of the ice piece from February 9, 2009. The measured curve (solid line)is very close to the curve (dash line)calculated by the two-phase method.

Fig. 9 Variations of gas bubble size and gas bubble content in ice pieces with depth

Fig. 10 Variation of ice density with depth

Fig. 11 Relationship between ice density and gas bubble content of ice piece from February 9, 2009

5 Conclusions

Field observations of ice conditions, including ice stratigraphy and crystals, the shape and size of gas bubbles, and the density of ice, were carried out in the Hongqipao Reservoir in Heilongjiang Province. The results are summarized as follows:

(1)The top layer of the ice piece is granular ice, and the middle and the bottom layers are columnar ice. The average crystal size increases linearly with depth. During the growth period,variations in ice stratigraphy were not detected. C-axes in the top layer are nearly horizontal with random orientation in the horizontal plane. C-axes in the middle and bottom layers are also nearly horizontal and have a preferential direction.

(2)The equivalent diameter of gas bubbles first increases rapidly with depth and then remains at a stable level. The concentration of gas bubbles decreases with depth, but the total content of gas bubbles increases with time, indicating that gas bubbles in ice vary during the growth period.

(3)Ice has an almost constant density during the growth period and is inversely proportional to the content of gas bubbles in ice.

Belzile, C., Vincent, W. F., Gibson, J. A. E., and van Hove, P. 2001. Bio-optical characteristics of the snow, ice,and water column of a perennially ice-covered lake in the High Arctic. Canadian Journal of Fisheries and Aquatic Sciences, 58(12), 2405-2418. [doi:10.1139/cjfas-58-12-2405]

Consolmagno, G. J., Britt, D. T., and Macke, R. J. 2008. The significance of meteorite density and porosity.Chemie der Erde-Geochemistry, 68(1), 1-29. [doi:10.1016/j.chemer.2008.01.003]

Iliescu, D. and Baker, I. 2007. The structure and mechanical properties of river and lake ice. Cold Regions Science and Technology, 48(3), 202-217. [doi:10.1016/j.coldregions.2006.11.002]

Langway, C. C., Jr. 1958. Ice Fabrics and the Universal Stage, Technical Report 62. Hanover: U.S. Army Cold Regions Research and Engineering Laboratory.

Li, Z. J., Jia, Q., Zhang, B. S., Lepp?ranta, M., Lu, P., and Huang, W. F. 2010a. Influences of gas bubble and ice density on ice thickness measurement by GPR. Applied Geophysics, 2010, 7(2), 105-113. [doi:10.1007/s11770-010-0234-4]

Li, Z. J., Nicolaus, M., Toyota, T., and Haas, C. 2010b. Analysis on the crystals of sea ice cores derived from Weddell Sea, Antarctica. Chinese Journal of Polar Science, 21(1), 1-10.

Light, B., Maykut, G. A., and Grenfell, T. C. 2003. Effects of temperature on the microstructure of first-year Arctic sea ice. Journal of Geophysical Research, 108(C2), 3051. [doi:10.1029/2001JC000887]

Mao, Z. Y., Wu, J. J., and She, Y. T. 2002. River ice processes. Journal of Hydroelectric Engineering, (s1),153-161. (in Chinese)

Moslet, P. O. 2007. Field testing of uniaxial compression strength of columnar sea ice. Cold Regions Science and Technology, 48(1), 1-14. [doi:10.1016/j.coldregions.2006.08.025]

Shi, L. Q., Bai, Y. L., Li, Z. J., Cheng, B., and Lepp?ranta, M. 2009. Preliminary results on the relationship between thermal diffusivity and porosity of sea ice in the Antarctic. Chinese Journal of Polar Science,20(1), 72-80.

Shokr, M. E., and Sinha, N. K. 1994. Arctic sea ice microstructure observations relevant to microwave scattering. Arctic, 47(3), 265-279

Sturm, M., Perovich, D. K., and Holmgren, J. 2002. Thermal conductivity and heat transfer through the snow on the ice of the Beaufort Sea. Journal of Geophysical Research (Oceans), 107(C10), 1-17. [doi:10.1029/2000JC000409]

Timco, G. W., and Frederking, R. M. W. 1996. A review of sea ice density. Cold Regions Science and Technology, 24(1), 1-6. [doi:10.1016/0165-232X(95)00007-X]

Timco, G. W., and Weeks, W. F. 2010. A review of the engineering properties of sea ice. Cold Regions Science and Technology, 60(2), 107-129. [doi:10.1016/j.coldregions.2009.10.003]

Usowicz, B., Lipiec, J., and Usowicz, J. B. 2008. Thermal conductivity in relation to porosity and hardness of terrestrial porous media. Planetary and Space Science, 56(3-4), 438-447. [doi:10.1016/j.pss.2007.11.009]

Wang, J., Chu, C. L., Fu, H., Gao, Y. X., and Yin, Y. J. 2007. Application of artificial neural networks to numerical simulation of ice jams thickness in a bend. Journal of Hydroelectric Engineering, 26(2),104-107. (in Chinese)

Wang, T., Yang, K. L., Guo, Y. X., and Huo, S. Q. 2005. Application of artificial neural networks to forecasting of river ice condition. Journal of Hydraulic Engineering, 36(10), 1204-1208. (in Chinese)

Xiao, J. M., Jin, L. H., Xie, Y. G., and Huo, Y. D. 2004. Study on mechanism of formation and melting of reservoir ice cover in cold area. Journal of Hydraulic Engineering, 35(6), 80-85. (in Chinese)