JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. C2, 3051, doi:10.1029/2001JC000887, 2003
[32] While microstructural data described in the previous sections should allow the calculation of equivalent cross-sectional areas and, ultimately, scattering coefficients for first-year sea ice at -15°C, a general treatment should also be able to describe how these properties evolve with temperature. When the ice cools, the laws of freezing equilibrium predict that brine pockets and gas bubbles will shrink, mirabilite crystals will begin to precipitate at -8.2°C and hydrohalite crystals at -22.9°C. When warmed, brine pockets and gas bubbles enlarge, and precipitated salts gradually dissolve. However, these laws do not predict how the size distributions of the various inclusions change or how these inclusions interact, factors which are likely to affect how the optical properties of the ice respond to changes in temperature. To obtain such information, ice samples were first cooled from -15° to -30°C, then warmed to -2°C. Changes in microstructure were monitored at 2°–5°C intervals. The samples were cooled first, then warmed, to prevent the irreversible changes that occur when the ice becomes very warm from affecting the observations. Mechanical limitations in temperature regulation of the cold room produced a ±1°C uncertainty in actual sample temperatures. While the size of brine and gas inclusions in thin sections was observed to adjust rapidly (on the order of minutes) to changes in temperature, it is not clear whether salt precipitation and dissolution occurred as quickly. Rapid warming experiments [Adams and Gibson, 1930; D. Erickson, personal communication, 1992] suggest that these processes may require a few hours to reach equilibrium. For this reason, samples were held at each temperature for a minimum of 24 hours before photographs were taken.
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[33] Figure 13 shows an example of structural changes observed in a 2.0 × 1.5 mm area of ice as it was cooled from (a) -15° to (b) -20° to (c) -25°C. The area contained three large brine tubes and numerous brine pockets. At -15°C, two of the tubes were observed to contain bubbles (arrows 1 and 2), as were several of the smaller pockets. The tube in the center of the image also contained several large crystals of mirabilite that had settled on top of the bubble (arrow 3). As the sample was cooled to -20°C, each of the brine and gas inclusions shrunk in size. In fact, some bubbles disappeared altogether. All the tubes decreased in diameter. Pockets generally shrank in size while maintaining an approximately constant 
. At -20°C, freezing equilibrium relationships predict that each brine inclusion should have about 82% of its volume at -15°C; at -25°C, this volume drops to 42%. If the tubes are assumed to be azimuthally symmetric and to have constant length, the observed decreases are to 81% at -20°C and 57% at -25°C; 57% is the volume predicted at -24°C and it is likely that the temperature of the ice was closer to this value at the time the bottom photograph was taken. Note that the ice brine refractive boundaries appear more distinct because the refractive index (n) of the brine increases from 1.370 at -15°C to 1.379 at -20°C [Maykut and Light, 1995]. This change increases the index contrast between brine and ice (nice = 1.30 to 1.32 at visible wavelengths), but decreases the contrast between mirabilite crystals (n = 1.396) and brine.
[34] The size and number of mirabilite crystals increased between -15° and -20°C. For example, a new group of mirabilite crystals is visible below the bubble in the center tube (arrow 4). Few sulfate ions remain in solution at -20°C and there was little additional change in the size or number of mirabilite crystals at -25°C. Further increases in n for the brine also mean less contrast for mirabilite crystals in brine, making them harder to see and reducing their effect on light scattering. No individual hydrohalite crystals were identified in our images. Nevertheless, the brine tube on the left side of Figure 13c became entirely opaque (arrow 5) and this is almost certainly due to the precipitation of hydrohalite crystals. Laboratory experiments [Maykut and Light, 1995] suggest that, on the macroscale, hydrohalite and ice frequently form a closely knit crystalline compound. Unlike mirabilite, which always appeared to remain separate from the ice, the formation of hydrohalite crystals was observed to be closely associated with ice crystal formation. It might be expected that this association would normally lead to brine inclusions being filled with an ice hydrohalite slush, as appears to be the case in Figure 13c. However, the formation of this slush was only occasionally observed in tubes and rarely in brine pockets, even at -30°C. Whether hydrohalite crystals tended to nucleate on pocket walls or whether they remained separate from the ice is unclear, but it appears that hydrohalite crystals do not generally exceed 0.01 mm in pockets or tubes.
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[35] Figure 14 shows how a group of brine pockets responded as temperature was increased from (a) -13° to (b) -8° to (c) -4°C, then decreased to (d) -13°C. Initially the four large inclusions were separate, having an average of 1.7 and sizes varying between 0.1 and 0.2 mm in length. Two of the inclusions contained bubbles, but no mirabilite crystals were visible. The predicted increase in brine volume between -13° and -8°C is 45%. The observed increases for the four pockets ranged between 32 and 57%, with the average being 48%. Volume estimates were made by assuming that the inclusions had horizontal aspect ratios of unity and grew the same amount in all horizontal directions. Both the horizontal and vertical dimensions of the pockets were observed to increase. The vertical dimension generally increased slightly faster, resulting in a small increase of . Examination of other pockets elsewhere in the same thin section showed similar results. It appears that a slight increase in was typical when the pockets became fairly warm. Although existing bubbles increased appropriately in size as the ice warmed, no new bubbles were observed to form in the pockets. Based on the observed increase in brine volume between -13° and -8°C and the difference in brine and ice densities, the pocket at the top of the image, if it were isometric in the horizontal plane, should have formed a bubble with a diameter of approximately 0.028 mm. Such a bubble would have been large enough to be easily resolved and would have been readily apparent. The failure of new bubbles to nucleate in enlarging brine pockets is surprising, but typical of all the scenes examined.
[36] Merging of inclusions was common at warmer temperatures. Note, for example, the third inclusion from the top in Figure 14b which combined with a small inclusion below it to produce a single inclusion of irregular shape (arrow 1). When the sample was then warmed to -4°C, three of the four prominent inclusions merged to form a single inclusion with = 6. Because these small inclusions typically form in vertical strings, it was common to observe strings of pockets being transformed to tubes as the ice warmed. This process tends to make the anisotropy of the structure more pronounced at higher temperatures. It is not immediately clear how this evolution affects the optical properties of the ice.
[37] When the sample was subsequently cooled from -4° to -13°C, the bubble in the newly merged inclusion disappeared, while the merged inclusion remained intact. No new mirabilite crystals were visible. The pocket at the bottom of the image (arrow 2) underwent changes that seem reversible, whereas the other three underwent changes that do not appear to be immediately reversible. Grenfell [1983] has suggested that inclusions of large aspect ratio may divide up into smaller inclusions when cooled, but this did not happen during the four days following these observations. Although many similar merged features were documented in other images, none were observed to break up into smaller inclusions when cooled. This does not rule out the possibility that irregular, high aspect ratio inclusions might evolve into strings of pockets, but such evolution would be controlled by diffusive processes in the pocket and the time constant would be greater than a few days. Cole and Shapiro [1998] have suggested that high-aspect ratio brine inclusions would require an entire annual cycle to evolve into smaller, more spherical inclusions.
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[38] Figure 15 presents a series of lower magnification images that show a broader range of structural changes as the ice was warmed from -15° to -5° to -2°C. At -15°C the inclusions were distinct and well-separated but, as the sample warmed, the inclusions became plump and rounded, and many began to merge. The net effect is that inclusions of brine and gas grew larger, yet decreased in number. These decreased numbers were a direct result of merging, as all inclusions were accounted for. Between -15° and -5°C, brine pocket density decreased from 51 per mm3 to 46 per mm3 and bubble density decreased from 5.4 per mm3 to 4.7 per mm3. Between -5° and -2°C, these values further decreased to 35 per mm3 (69% of the value at -15°C) and 2.7 per mm3 (50% of the value at -15°C) for brine pockets and bubbles respectively. Number densities in this particular scene are quite large and should not be taken to represent overall averages.
5.3. Temperature-Dependent Equivalent Cross-Sectional Area
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[39] The temperature dependence of 
for the various types of scatterers in sea ice was estimated using the freezing equilibrium parameterizations of Cox and Weeks [1983] and guidance from the warming and cooling image sequences. Although brine pockets were observed to become slightly more spherical upon cooling and slightly more elongated upon melting, the overall change in average aspect ratio was small. A model which specifies that melting and freezing take place equally on all inclusion surfaces would produce decreasing aspect ratios for melting and increasing aspect ratios for freezing, contrary to the observations. To estimate bp(T) for brine pockets, inclusion volumes were allowed to increase as specified by freezing equilibrium but was held constant at the value observed at -15°C. No merging between inclusions was considered. This has the effect of shifting the curve in Figure 6 to the right as the population warms. Values for req and Neq were then computed at various temperatures, treating all brine pockets as prolate ellipsoids. The resulting bp(T) is shown in Figure 16. It can be seen that, as brine pockets grow larger, the scattering cross-sectional area increases, the increase being most rapid above -5°C.
[40] Tubes showed a different behavior than pockets when the temperature was changed. In general, melting caused tube diameters to increase while tube lengths remained approximately constant. Freezing caused tube diameters to decrease while lengths again remained nearly unchanged. Based on these observations, bt(T) was calculated by representing the tubes as cylinders and requiring that cylinder length be conserved. The effect of this assumption is that the curve in Figure 6 would shift upwards with increasing temperature. The resulting bt(T) is also shown in Figure 16. The population of tubes visible in the sample clearly has a larger cross-sectional area than the pockets but the calculated values of bp and bt exhibit similar temperature dependence.
[41] To estimate gb(T) for the bubbles, we first assumed that all bubbles were spherical, that they were located within brine inclusions, and that no new bubbles formed during warming. The change in volume of an existing gas bubble depends on the volume of the brine inclusion in which it resides. Upon warming, more ice melts in a large pocket than in a small one. This means that the volume of a bubble in a large pocket can increase more than if the bubble were located in a smaller pocket. To simplify the problem of determining how req depends on temperature, the volume of bubbles observed at -15°C was specified to shrink or grow at the bulk rate specified by the freezing equilibrium relations with fixed bulk density. The resulting gb(T) is shown in Figure 16. The largest values occur at the highest temperatures but, even then, gb does not exceed 3% of the total for the brine inclusions.
[42] At this point it is not clear whether precipitated salt crystals tend to grow more in size or number as the ice cools. For the time being, let us assume that salt crystals have constant size (0.01 mm edge length) and that changes in temperature cause the crystal number to vary in proportion to changes in the total mass of precipitated mirabilite and hydrohalite. Predicted values of m(T) and h(T) for mirabilite and hydrohalite under these assumptions are shown in Figure 16. The maximum h is almost 6 times larger than m despite the fact that only 4 times more mass precipitates for the hydrohalite. The stronger effect on h is due to the fact that the hydrohalite crystal structure is closer to equidimensional than the mirabilite crystal [see Light, 1995]. The more equidimensional crystal has higher surface area relative to its volume, and this increases the magnitude of . Had we chosen a smaller crystal size, m and h would have been somewhat larger since the total crystal surface area would increase.
Citation: Effects of temperature on the microstructure of first-year Arctic sea ice, J. Geophys. Res., 108(C2), 3051, doi:10.1029/2001JC000887, 2003.
