Sea ice exhibits a marked transition in its fluid transport properties at a critical brine volume fraction p c of about 5 percent, or temperature T c of about -5°C for salinity of 5 parts per thousand. For temperatures warmer than T c , brine carrying heat and nutrients can move through the ice, whereas for colder temperatures the ice is impermeable. This transition plays a key role in the geophysics, biology, and remote sensing of sea ice. Percolation theory can be used to understand this critical behavior of transport in sea ice. The similarity of sea ice microstructure to compressed powders is used to theoretically predict p c of about 5 percent.Sea ice is a complex, composite material consisting of pure ice with brine and air inclusions, whose size and geometry depend on the ice crystal structure, as well as the temperature and bulk salinity. It is distinguished from many other porous composites, such as sandstones or bone, in that its microstructure and bulk material properties vary dramatically over a small temperature range. For brine volume fractions p below a critical value p c Ϸ 5%, columnar sea ice is effectively impermeable to fluid transport, whereas for p above p c (Ͼ5%), brine or sea water can move through the ice. The relation of brine volume to temperature T and salinity S (1) implies p c corresponds to a critical temperature T c Ϸ -5°C for S ϭ 5 ppt; we refer to this critical behavior as the "law of fives." Perhaps the most direct observations of this are that the time rate of change of sea ice salinity dS/dt due to gravity drainage vanishes for brine volumes below 5% (2, 3) and that the permeability of thin sea ice decreases by more than two orders of magnitude as the surface temperature is lowered, in a small critical region around -5°C (4).Brine transport is fundamental to such processes as sea ice production through freezing of flooded ice surfaces, sea ice heat fluxes, and nutrient replenishment for sea ice algal communities, as well as being an important factor for remote sensing. However, the basic transition controlling brine transport has received little attention. Percolation theory (5, 6) has been developed to analyze the properties of materials where connectedness of a given component determines the bulk behavior. We show that it provides a natural framework to understand the critical behavior of sea ice. In particular, we apply a compressed powder percolation model to sea ice microstructure that explains the law of fives, the observed behavior (4) of the fluid permeability in the critical temperature regime, as well as data on surface flooding collected recently on sea ice in the Weddell Sea and East Antarctic regions. It was observed in the Arctic (7) that a snow storm and its resultant loading on a sea ice layer can induce a complete upward flushing of the brine network. In the Antarctic, it was observed that the freezing of a surface slush layer, with resultant brine drainage, induced convection within the ice, whereby rejected dense brine is replaced by nutrient-rich sea water ...

[1] The fluid permeability k of sea ice constrains a broad range of processes, such as the growth and decay of seasonal ice, the evolution of summer ice albedo, and biomass build-up. Such processes are critical to how sea ice and associated ecosystems respond to climate change. However, studies of k and its dependence on brine porosity f and microstructure are sparse. Here we present a multifaceted theory for k(f) which closely captures laboratory and field data. X-ray computed tomography provides an unprecedented look at the brine phase and its connectivity. We find that sea ice displays universal transport properties remarkably similar to crustal rocks, yet over a much narrower temperature range. Our results yield simple parameterizations for fluid transport in terms of temperature and salinity, and permit more realistic representations of sea ice in global climate and biological models. Citation:

We give a mathematical formulation of a method for obtaining bounds on effective parameters developed by D. Bergman and G. W. Milton. This method, in contrast to others used before, does not rely on a variational principle, but exploits the properties of the effective parameter as an analytic function of the component parameters. The method is at present restricted to two-component media.

[1] We have imaged sea ice single crystals with X-ray computed tomography, and characterized the thermal evolution of the pore space with percolation theory. Between À18°C and À3°C the porosity ranged from 2 to 12% and we found arrays of near-parallel intracrystalline brine layers whose connectivity and complex morphology varied with temperature. We have computed key porosity-dependent functions of classical percolation theory directly from the thermally driven pore space evolution of an individual sample. This analysis is novel for a natural material and provides the first direct demonstration of a connectivity threshold in the brine microstructure of sea ice. In previous works this critical behavior has been inferred indirectly from bulk property measurements in polycrystalline samples. From a finite-size scaling analysis we find a vertical critical porosity p c,v = 4.6 ± 0.7%. We find lateral anisotropy with p c,pll = 9 ± 2% parallel to the layers and p c,perp = 14 ± 4% perpendicular to them. Lateral connectivity is established at higher brine volumes by the formation of thin necks between the brine layers. We relate these results to measured anisotropy in the bulk dc conductivity and fluid permeability using a dual porosity conceptual model. Our results shed new light on the complex microstructure of sea ice, highlighting single crystal anisotropy and a step toward a realistic transport property model for sea ice based on percolation theory. We present full experimental details of our imaging and segmentation methodology based on a phase relation formulation more widely applicable to ice-solute systems.

Bounds on the volume fraction of the constituents in a two-component mixture are derived from measurements of the effective complex permittivity of the mixture, using the analyticity of the effective property. First-order inverse bounds for general anisotropic materials, as well as second-order bounds for isotropic mixtures, are obtained. By exploiting an analytic representation of the effective complex permittivity, the problem of estimating the structural parameters is reduced to a problem of evaluating the moments and support of a measure containing information about the geometrical structure of the material. Rigorous bounds on the volume fraction are found by inverting first-and second-order (Hashin-Shtrikman) forward bounds on the complex permittivity. The inverse bounds are applied to measurements of the effective complex permittivity of sea ice, which is a three-component mixture of ice, brine and air. The sea ice is treated via the two-component theory applied to a mixture of brine and an ice/air composite. The bounds on the brine volume of sea ice derived from the effective permittivity measurements are in excellent agreement with data from experiments. The inversion of forward bounds on the complex permittivity of composite media provides a basis for a theory of inverse homogenization for recovering microstructural parameters from bulk property measurements. Such results are applicable to problems in remote sensing, medical imaging and non-destructive testing of materials.

Melt pond formation atop Arctic sea ice is a primary control of shortwave energy balance in the Arctic Ocean. During late spring and summer, the ponds determine sea ice albedo and how much solar radiation is transmitted into the upper ocean through the sea ice. The initial formation of ponds requires that melt water be retained above sea level on the ice surface. Both theory and observations, however, show that first year sea ice is so highly porous prior to the formation of melt ponds that multiday retention of water above hydraulic equilibrium should not be possible. Here we present results of percolation experiments that identify and directly demonstrate a mechanism allowing melt pond formation. The infiltration of fresh water into the pore structure of sea ice is responsible for blocking percolation pathways with ice, sealing the ice against water percolation, and allowing water to pool above sea level. We demonstrate that this mechanism is dependent on fresh water availability, known to be predominantly from snowmelt, and ice temperature at melt onset. We argue that the blockage process has the potential to exert significant control over interannual variability in ice albedo. Finally, we suggest that incorporating the mechanism into models would enhance their physical realism. Full treatment would be complex. We provide a simple temperature threshold‐based scheme that may be used to incorporate percolation blockage behavior into existing model frameworks.

Abstract. During the Arctic melt season, the sea ice surface undergoes a remarkable transformation from vast expanses of snow covered ice to complex mosaics of ice and melt ponds. Sea ice albedo, a key parameter in climate modeling, is determined by the complex evolution of melt pond configurations. In fact, ice-albedo feedback has played a major role in the recent declines of the summer Arctic sea ice pack. However, understanding melt pond evolution remains a significant challenge to improving climate projections. By analyzing area-perimeter data from hundreds of thousands of melt ponds, we find here an unexpected separation of scales, where pond fractal dimension D transitions from 1 to 2 around a critical length scale of 100 m 2 in area. Pond complexity increases rapidly through the transition as smaller ponds coalesce to form large connected regions, and reaches a maximum for ponds larger than 1000 m 2 , whose boundaries resemble space-filling curves, with D ≈ 2. These universal features of Arctic melt pond evolution are similar to phase transitions in statistical physics. The results impact sea ice albedo, the transmitted radiation fields under melting sea ice, the heat balance of sea ice and the upper ocean, and biological productivity such as under ice phytoplankton blooms.

Recent advances in forward modeling of the electromagnetic scattering properties of sea ice are presented. In particular, the principal results include the following: 1) approximate calculations of electromagnetic scattering from multilayer random media with rough interfaces, based on the distorted Born approximation and radiative transfer (RT) theory; 2) comprehensive theory of the effective complex permittivity of sea ice based on rigorous bounds in the quasi-static case and strong fluctuation theory in the weakly scattering regime; 3) rigorous analysis of the Helmholtz equation and its solutions for idealized sea ice models, which has led in the one dimensional (1-D) case to nonlinear generalizations of classical theorems in Fourier analysis. The forward models considered here incorporate many detailed features of the sea ice system and compare well with experimental data. The results have advanced the general theory of scattering of electromagnetic waves from complex media as well as homogenization theory, which relates bulk properties of composite media to their microstructural characteristics. Furthermore, the results have direct application to microwave remote sensing and serve as Manuscript