JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. C2, 3051, doi:10.1029/2001JC000887, 2003

4. Observations of Microstructure at -15°C

[16]   Structural observations to determine size distributions for brine inclusions and gas bubbles in cold ice were initially made at -15°C where changes in microstructure are not highly sensitive to changes in temperature. About 100 images were recorded from three different thin sections. Figure 4 shows photomicrographs of one sample illuminated in transmitted light. On the left is a mosaic composed of 30 individual images, each with a 1.9 × 1.4 mm field of view. After registering the 30 images, the dimensions of the composite scene are approximately 4.7 × 12.1 mm. Several types of features stand out distinctly: elongated brine tubes (arrow 1), smaller, isolated brine pockets (arrow 2), and gas bubbles within brine inclusions (arrow 3). Brine features that appear to have excessively high contrast may be inclusions that were cut open and drained during sample preparation (arrow 4). It is, however, possible that they may be gas bubbles directly in the ice. At this point, the classification of these inclusions is uncertain, so we assume them to be drained brine inclusions for this study. Gas bubbles within brine pockets have similarly high contrast but can usually be discerned by their nearly spherical shape. There are also areas where no inclusions exist in the ice, and the ice appears highly transparent (arrow 5). The horizontal stripes across the image are scratches produced by the microtome blade. Microtome cuts were intentionally made across the sample to avoid creating artifacts that might interfere with resolving the vertically oriented structure.

4.1. Brine Inclusions

[17]   Data were collected on the maximum horizontal and vertical dimensions of brine inclusions visible within the ten boxed areas shown in Figure 4. These areas were selected for sampling because they appeared to be representative of the overall structure. The sample volume within these boxes was 48.8 mm³ and more than 1600 inclusions were counted. The sizes of individual inclusions ranged from 0.01 mm to 8.0 mm in length (l), and 0.01 mm to 0.230 mm in diameter. Inclusions with l smaller than 0.50 mm were arbitrarily classified as brine pockets. Examples of these features are shown in the enlargement on the right-hand side of Figure 4. The large brine pocket (arrow A) has length 0.40 mm, diameter 0.11 mm, and a length-to-diameter aspect ratio () of 3.6. Numerous small pockets are also visible in this same image; for example, arrow B points to an area of concentrated pockets whose recorded length and diameter are 0.01 mm with = 1.0. Pockets frequently appeared in clusters (arrow B) or in vertical strings (arrow C), and were always oriented with their long dimension in the vertical. Inclusions with l 0.50 mm were classified as brine tubes. All observed tubes had near-vertical orientation. Since tubes were uncommon compared to pockets, the entire mosaic (sample volume 84.5 mm³) was used to estimate their number density.

[18]   The observed size distribution of the brine inclusions is shown in Figure 5. The data were binned by inclusion length and the number density, N(l), was adjusted to account for the width of each bin. The data are well represented (r² = 0.92) by the following power law

for 0.01 mm l 8 mm. Integrating (1) between these limits yields a total number density of 24 brine inclusions per mm³. This appears to be representative for the sample as a whole, although individual boxes in Figure 4 had number densities as large as 50 inclusions per mm³. There is also a clear dependence of the aspect ratio on l as shown in Figure 6. This relationship can also be approximated (r² = 0.77) by a power law:

for 1 70 and l > 0.03 mm. Nearly all the 1244 brine pockets observed to be less than 0.03 mm in diameter were recorded as spherical ( = 1) with l = 0.01 mm, and are indicated by a single point in Figure 6. Because inclusions this size were near the limit of our resolution, we assume that = 1 for all inclusions with l < 0.03 mm.

[19]   These results can be compared with the observations of Perovich and Gow [1996] and Cole and Shapiro [1998], both of whom studied ice extracted at the same time and location as the cores used here. Cole and Shapiro measured brine inclusion sizes in both vertical and horizontal thin sections taken from interior ice at a depth of 0.8 m. They observed inclusions with an average diameter of 0.27 mm in the horizontal plane and an average length of 2.4 mm in the vertical, values within the range we observed. However, they were not able to resolve individual inclusions smaller than 0.1 mm and did not estimate the size distribution or average number density. Perovich and Gow [1996] reported size distributions based on cumulative distributions of inclusion cross sections derived from horizontal thin sections. To compare our results with those of Perovich and Gow, we estimated horizontal cross-sectional areas of the inclusions in our images using the maximum observed diameter for each inclusion. Because Perovich and Gow observed mean horizontal axis ratios of 1:4 in their observations of inclusions with cross-sectional area greater than 0.002 mm², we examined imagery of a horizontal cross section cut adjacent to the vertical thin section shown in Figure 4. While this imagery was not examined for inclusion size and number distribution, it was scrutinized for information about the inclusion horizontal aspect ratio. While many of the inclusions did not have circular cross section, there was no clear indication that horizontal aspect ratios were elongated in a particular direction. As a result, brine inclusions were initially assumed to have average horizontal aspect ratios equal to unity. A comparison of the two data sets is shown in Figure 7. Our average number density of 24 per mm³ is 15 times larger than the value of 1.6 per mm³ observed by Perovich and Gow. This difference is due primarily to the detection of smaller inclusions in our images. It is likely that this population of small inclusions will have a significant impact on light scattering in the ice.

[20]   Besides the absence of small inclusions in the Perovich and Gow [1996] observations, there are other differences between the two size distributions. Perovich and Gow found cross-sectional areas up to 1 mm² which correspond to inclusion diameters of 1.1 mm. In our study, the largest diameter measured was 0.23 mm (corresponding to an area of 0.04 mm²). Figure 7 shows that number densities in our sample were as much as a factor of 2 smaller where the two distributions overlap (0.01–0.04 mm²). We suspect our sampling technique may have selectively avoided larger tubes and know that it avoided brine channels because vertical thin sections are difficult to keep intact when such features are present. Perovich and Gow sampled a volume of 282 mm³, more than three times greater than our sample volume. It is, therefore, reasonable to expect that their results may better represent the number density of larger brine tubes in first-year ice. But it should also be noted that the Perovich and Gow sample was imaged at -5.7°C and had a brine volume of 5.5%, while our samples were measured at -15°C and had a visible brine volume of only 1.2%. This visible brine volume was calculated by assuming that all the inclusions were isometric in the horizontal plane. Because the Perovich and Gow sample had such large brine volume, we might expect that their number density curve would shift to somewhat smaller cross-sectional areas if their measurements had been made at -15°C, bringing it into closer agreement with our observations. Despite the fact that the two samples were extracted from the same ice, the exact change is difficult to estimate without information about the vertical extent of the inclusions Perovich and Gow observed at -5.7°C.

[21]   Figure 8 shows the relative volume of visible brine in our sample for several inclusion size categories. The bin widths are arbitrary, however, the smallest bin represents brine pockets that were below the resolution of the Perovich and Gow [1996] study; the smallest three bins include all the pockets, while the largest three bins represent the tubes. While they are the most numerous (79% by number), inclusions in the smallest bin contain only a small fraction of the total brine volume. Although tubes contained about 90% of the brine seen in the thin section, there is reason to believe that they may account for an even larger percentage of brine volume in the ice as a whole. The ice from which the thin section was extracted had an average salinity of 4.7^o/_oo and a density of 0.915 Mg m^-3, resulting in a predicted brine volume of 1.9% at -15°C, significantly larger than the total visible brine volume of 1.2%.

[22]   It is likely that the missing brine was contained either in larger brine tubes that existed in the core sample but not in the thin section, or within visible inclusions whose volume was underestimated as a result of the assumption of horizontal isotropy. The supposition that larger tubes existed in the core sample is consistent with the Perovich and Gow [1996] size distribution (Figure 7) which shows inclusions with large cross-sectional areas that were not present in our thin sections. Extrapolating our size distribution to include tubes up to 15 mm in length would produce a total brine volume of 1.9%. In this case, 94% of the total brine volume would be in tubes and only 6% in pockets. If, instead of extending the distribution out to include longer tubes, existing tubes are taken to be anisometric in the horizontal plane, the missing brine can also be accounted for. If a horizontal aspect ratio of 1.64 and a maximum inclusion length of 8 mm are assumed, the observed brine volume would also be 1.9%. In all likelihood, both factors are probably involved, but it is difficult to assess their relative importance without further detailed study of additional sample material.

4.2. Equivalent Cross-Sectional Area

[23]   Basic objectives of the structural observations were: (1) to obtain data which could be used to develop more accurate predictions of light absorption and scattering in sea ice, and (2) to determine the optical importance of different elements in the microstructure. To make a quantitative comparison of the effects of various types of inclusions on radiative transfer, we represent all inclusions as equivalent spheres and calculate their equivalent cross-sectional area ():

where r_eq(l) is the equivalent spherical radius for inclusions of length l and N_eq(l) is the corresponding number of equivalent spheres per unit volume. The optical scattering coefficient is proportional to when inclusion sizes are much larger than the wavelength of the light. The scattering coefficient specifies how much light is scattered within a domain, but it does not specify the degree to which scattering is forward or backward directed. Redirection of light is tied to the scattering phase function and depends on the size, shape, and relative refraction of scatterers.

[24]   A variety of approaches has been applied to the calculation of equivalent spheres. When the total volume of all inclusions is conserved, absorption is accurately represented, however, scattering is generally underestimated because spheres of equal volume have less surface area than the original ellipsoids or cylinders. To accurately represent the scattering, the total surface area must also be conserved. According to Grenfell and Warren [1999], a collection of randomly oriented cylindrical inclusions can be represented by a collection of equivalent spheres with radius r_eq and number density N_eq whose total surface area and volume are the same as the original population. Figure 9a shows calculated r_eq values as a function of observed inclusion length and aspect ratio for the three different conservation schemes. All r_eq are about the same for small brine pockets since they are approximately spherical to begin with. As inclusion length increases, conservation of both total surface area and volume produces substantially smaller r_eq but larger N_eq values than are obtained by conserving surface area alone. The value of r_eq decreases as it becomes necessary to increase the number of equivalent spheres per inclusion to conserve both. The discontinuity in r_eq(l) arises because prolate ellipsoids with major axis l were used to calculate the volume and surface area for pockets (l < 0.5 mm), and cylinders with height l were used to represent the tubes. In Figure 9b, values of N_eq per inclusion show that when r_eq is approximately equal to l/2, which holds for l 0.03 mm, there is approximately one equivalent sphere per inclusion. As inclusions increase in size and aspect ratio, the number of equivalent spheres per inclusion increases to its maximum value of 18 for l = 8 mm. Values of reported below will always be calculated conserving both volume and surface area.

[25]   When integrated over all the brine pockets (l = 0.01–0.5 mm), (3) predicts that = 0.03 mm^-1; similarly, = 0.08 mm^-1 for brine tubes (l = 0.5–8 mm), giving a total = 0.11 mm^-1 for all brine inclusions. Contributions made to by various subcategories are shown in Figure 8. While due to the tubes is larger, the contribution from the pockets is significant. For example, even though only 10% of the brine volume is contained in pockets, it appears from this analysis that these pockets account for 25% of the light scattering due to the brine inclusions observed at -15°C. These estimates are sensitive to the assumption that brine inclusions are isometric in the horizontal plane. If the horizontal asymmetry parameter were increased to the value (1.64) needed to explain the brine volume of the bulk core sample, the estimated value of for brine tubes alone would increase 37% to 0.11 mm^-1.

4.3. Gas Bubbles

[26]   The boxed areas in Figure 4 were also used to estimate the size distribution of gas bubbles. All of the observed bubbles (about 60) were nearly spherical and all were contained within brine inclusions; none were observed in the ice itself. Gas bubble radius (r_gb) ranged from 0.004 to 0.07 mm at -15°C. Figure 10 shows the observed distribution as a function of r_gb; also shown are results from three other studies. As with the brine inclusions, a power law provides a good fit (r² = 0.94) to the observed distribution in this study:

When integrated over the observed size limits, the total number density was 1.3 per mm³. This number density is only 5% of the number density for brine inclusions, indicating that while all bubbles were observed to be within brine inclusions, such compound inclusions were relatively rare compared to brine inclusions with no bubble.

[27]   We also made field measurements of bubbles in warm, interior first-year ice using a sample collected at Ice Station SHEBA (Figure 11) in the Central Beaufort Sea during May 1998. The bubble size distribution for this sample is also shown in Figure 10. Although the total number density (1.2 per mm³) is close to that of the Barrow ice and follows the same power law trend, the bubbles are substantially larger because the sample was very close to its melting point (-2°C). Because of practical difficulties in sample preparation and lighting, the field image does not have the clarity of the laboratory images and it is difficult to be certain whether or not all the bubbles are actually contained in brine inclusions.

[28]   Earlier data from ice in a freezing lead [Grenfell, 1983] showed significantly larger bubbles, with r_gb ranging from 0.1 to 2 mm (see Figure 10). No bubbles this large were observed in our interior samples. The integrated number density resulting from a power law fit to Grenfell's data is 0.03 per mm³, forty times fewer bubbles per unit volume than in our observations. Similar data from Gavrilo and Gaitskhoki [1970] agree with the Grenfell observations. It appears, however, that these earlier observations were of bubbles entrained in rapidly growing, young ice during its initial formation.

[29]   Since the bubbles are mostly spherical, use of equivalent spheres is greatly simplified and the effective radius is equal to the observed radius. The value of _gb integrated between the observed bubble size limits was 0.002 mm^-1, only about 3% the integrated value for all brine inclusions. This value of _gb for interior ice is only 5% of the value predicted for the Grenfell [1983] observations (0.04 mm^-1) in rapidly growing young ice.

4.4. Mirabilite Crystals

[30]   Mirabilite crystals were frequently seen at temperatures below -8.2°C (e.g., Figure 12). Crystals were observed in piles at the bottom of brine tubes (arrow 1), in clusters strewn throughout the tubes (arrow 2), and stuck at narrow pinches in tubes (arrow 3). When piled at the bottom of brine tubes, the crystals often appeared to have tunneled downwards, extending the bottom of the tube. Mirabilite crystals were rarely observed in smaller brine pockets, presumably because the crystals were too small to resolve. The largest crystal in Figure 12b has a diameter of 0.14 mm while the smallest measured diameter was 0.015 mm. The crystals tended to have rounded edges and irregular shapes, and may have coarsened after initial precipitation. Light [1995] inferred an effective crystal size of 0.009 mm for mirabilite, and this supports the conclusion that crystals in most brine pockets were too small to resolve. The smallest brine inclusion that could grow a single 0.01 mm mirabilite crystal would necessarily have a volume corresponding to l 0.06 mm, based on our observations of (l). Because there were many brine inclusions with l < 0.06 mm, we believe there must be many crystals with edge length <0.01 mm. In addition, the refractive index contrast of mirabilite crystals relative to brine is smaller than that for brine inclusions in ice, so a brine inclusion with l = 0.01 mm may be visible in an image while a mirabilite crystal with the same size may not be.

[31]   To estimate an effective optical cross-sectional area for mirabilite, we followed Light [1995] and simply assumed an effective crystal edge length of 0.01 mm since a direct estimate of the size distribution was not feasible. We also assumed a sample salinity of 3‰, commensurate with the visible brine volume (1.2%) of the thin section at -15°C. For this salinity, the predicted mass fraction of precipitate at -15°C is 0.58 g/kg. Taking a density of 1.464 Mg m^-3 for mirabilite [Porter and Spiller, 1956], along with the monoclinic characteristics of the crystals as given by Light [1995], we estimated the total number density of crystals to be approximately 270 per mm³ at -15°C. Application of the equivalent spherical treatment to the mirabilite crystals at -15°C yielded = 0.05 mm^-1. This value is larger than that for brine pockets, about 60% of the value for brine tubes, and much larger than for gas bubbles.

Citation: Light, B., G. A. Maykut, and T. C. Grenfell, Effects of temperature on the microstructure of first-year Arctic sea ice, J. Geophys. Res., 108(C2), 3051, doi:10.1029/2001JC000887, 2003.

Copyright 2003 by the American Geophysical Union.