Brine channels are formed in sea ice under certain constraints and represent a habitat of different microorganisms. The complex system depends on a number of various quantities as salinity, density, pH-value or temperature. Each quantity governs the process of brine channel formation. There exists a strong link between bulk salinity and the presence of brine drainage channels in growing ice with respect to both the horizontal and vertical planes. We develop a suitable phenomenological model for the formation of brine channels both referring to the Ginzburg-Landau-theory of phase transitions as well as to the chemical basis of morphogenesis according to Turing. It is possible to conclude from the critical wavenumber on the size of the structure and the critical parameters. The theoretically deduced transition rates have the same magnitude as the experimental values. The model creates channels of similar size as observed experimentally. An extension of the model towards channels with different sizes is possible. The microstructure of ice determines the albedo feedback and plays therefore an important role for large-scale global circulation models (GCMs).
Deep Dive into Modeling the morphogenesis of brine channels in sea ice.
Brine channels are formed in sea ice under certain constraints and represent a habitat of different microorganisms. The complex system depends on a number of various quantities as salinity, density, pH-value or temperature. Each quantity governs the process of brine channel formation. There exists a strong link between bulk salinity and the presence of brine drainage channels in growing ice with respect to both the horizontal and vertical planes. We develop a suitable phenomenological model for the formation of brine channels both referring to the Ginzburg-Landau-theory of phase transitions as well as to the chemical basis of morphogenesis according to Turing. It is possible to conclude from the critical wavenumber on the size of the structure and the critical parameters. The theoretically deduced transition rates have the same magnitude as the experimental values. The model creates channels of similar size as observed experimentally. An extension of the model towards channels with dif
Formation and decay of complex structures depend on changes in entropy. In the long run structures tend to decay since the entropy of universe leads to a maximum and evolves into a 'dead' steady state [1]. On the other hand not only living cells avoid the global thermodynamic equilibrium. A. M. Turing [2] showed in his paper about the chemical basis of morphogenesis which additional conditions are necessary to develop a pattern or structure. For instance, cells can be formed due to an instability of the homogeneous equilibrium which is triggered by random disturbances. In this sense it should be possible, that the habitat of microorganisms in polar areas, the brine channels in sea ice, can be described through a Turing structure.
The internal surface structure of ice changes dramatically when the ice cools below -23 o C or warms above -5 o C and has a crucial influence on the species composition and distribution within sea ice [3,4]. This observation correlates with the change of the coverage of organisms in brine channels between -2 o C and -6 o C [4]. Golden et al [5] found a critical brine volume fraction of 5 percent, or a temperature of -5 o C for salinity of 5 parts per thousand where the ice distinguishes between permeable and impermeable behavior concerning energy and nutrient transport. According to Perovich et al [6] the brine volume increases from 2 to 37 o / oo and the correlation length increases from 0.14 to 0.22 mm if the temperature rises from -20 o C to -1 o C. The permeabil-ity varies over more than six orders of magnitude [7]. Whereas Golden et al [5] used a percolation model we will demonstrate how the brine channel distribution can be modeled by a reaction-diffusion equation similar to the Ginzburg-Landau treatment of phase transitions. A molecular dynamics simulation shows the change between the hexagonal arranged ice structure and the more disordered liquid water structure [8].
After a short introduction into the key issue of the structure formation we describe the brine channel structure in sea ice and propose a phenomenological description. For the interpretation of the order parameter we discuss some microscopic properties of water using molecular dynamics simulation in the next chapter II. In chapter III we consider the phase transition and the conditions which allow a structure formation. We verify the model on the basis of measured values in chapter IV and give finally an outlook on further investigations in chapter V.
Various publications report on the life condition for different groups of organisms in the polar areas in brinefilled holes, which arise under certain boundary conditions in sea ice as base-or brine channels (lacuna) [9,10,11]. They are characterized by the simultaneous existence of different phases, water and ice in a saline en-FIG. 1: SEM-image of a cast of brine channels [9].
vironment. Because already marginal temperature variations can disturb this sensitive system, direct measurements of the salinity, temperature, pH-value or ice crystal are morphologically difficult [9]. Weissenberger et al [12] developed a cast technique in order to examine the channel structure. Freeze-drying eliminates the ice by sublimation, and the hardened casts illustrate the channels as negative pattern. Figure 1 shows a typical granular texture without prevalent orientation.
Sometimes, both columnar and mixed textures occur. Using an imaging system Light et al [3] found brine tubes, brine pockets, bubbles, drained inclusions, transparent areas, and poorly defined inclusions. Air bubbles are much larger than brine pockets. Bubbles possess a mean major axis length of some millimeters and brine pockets are hundred times smaller [13]. Cox et al [14,15,16] presented a quantitative model approach investigating the brine channel volume, salinity profile or heat expansion but without pattern formation. They also described the texture and genetic classification of the sea ice structure experimentally. A crucial factor for the brine channel structure formation is the spatial variability of salinity [17].
Different mechanisms are employing the mobility of brine channels which can be used to measure the salinity profile [17]. Advanced micro-scale photography has been developed to observe in situ the distribution of bottom ice algae [18] which allows to determine the variability of the brine channel diameter from bottom to top of the ice. By mesocosm studies the hypothesis was established that the vertical brine stability is the crucial factor for ice algae growth [19]. Therefore the channel formation during solidification and its dependence on the salinity is of great interest both experimentally and theoretically [20]. Experimentally Cottier et al [17] presented images, which show the linkages between salinity and brine channel distribution in an ice sample. To describe different phases in sea ice dependent on temperature and salinity one possible approach is based on the reaction diffu
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