Sea ice is a dynamic porous medium due to the presence of brine inclusions whose volume fraction depends on temperature and bulk salinity. Brine is mostly incorporated during growth as intracrystalline layers and at grain boundaries [Weeks and Ackley, 1986; Eicken, 2003]. Inclusions shrink with cooling as brine salinity must increase to maintain thermohaline equilibrium with the surrounding ice, and vice versa for warming. Brine porosity can exceed 70% at the ice-ocean interface [Notz and Worster, 2008] and approach zero in cold, desalinated multiyear ice [Weeks and Ackley, 1986; Eicken, 2003]. Comparatively little is known, however, about associated changes in inclusion morphology and pore space connectivity. The present work is motivated by the dependence of sea ice properties on inclusion morphology and connectivity, and to gain insight into the processes governing pore space thermal evolution necessary to develop realistic predictive models of sea ice microstructure. Such questions are important since the microstructure controls bulk properties underpinning the large–scale behavior of sea ice, its role in earth's climate system, and as an important habitat for algal and bacterial communities [Thomas and Dieckmann, 2003].
 Bulk properties of sea ice are sensitive to the anisotropy, number density, connectedness, and temporal evolution of individual inclusions and secondary brine channel networks, each over a range of length scales. These properties and processes include remote sensing signatures [Hallikainen and Winebrenner, 1992; Golden et al., 1998b, 1998c], optical properties [Light et al., 2003], colonization of sea ice by microorganisms [Krembs et al., 2000] and pollutant transport [Pfirman et al., 1995]. Of special note is the fluid permeability which controls fluid flow in sea ice, affecting ice albedo through melt pond development [Eicken et al., 2004], nutrient delivery to microorganisms [Krembs et al., 2000] and salinity profile evolution [Cox and Weeks, 1975; Weeks and Ackley, 1986; Wettlaufer et al., 2000; Vancoppenolle et al., 2007].
 The widely held rule of thumb is that bulk sea ice is essentially impermeable for brine volume fractions below 5%, above which permeability increases rapidly [Cox and Weeks, 1975; Freitag, 1999; Freitag and Eicken, 2003; Eicken et al., 2004; Petrich et al., 2006]. This bulk behavior has been interpreted in terms of percolation theory [Golden et al., 1998a, 2007; Zhu et al., 2006]. Golden et al. [1998a] equated sea ice brine volume fraction with porosity and used an excluded volume model to explain the apparent critical porosity for fluid permeability, pc ≈ 5%. For a salinity of 5 ppt, typical for first year (FY) sea ice, this threshold corresponds to a critical temperature of approximately −5°C, dubbed the ‘rule of fives’ [Golden et al., 1998a]. We extend the application of percolation theory, applying it here to the much smaller scale of brine inclusions within sea ice single crystals.
 In doing so, we address the lack of a detailed description of the thermal evolution of brine inclusions. This lack reflects several measurement challenges. Sample microstructure should not be disturbed during preparation and measurement, requiring careful thermal control. Inclusions show length scales from submillimeter brine layers to meter long channels, requiring scale-specific methods which necessarily have optimal resolution over only some range of these length scales. Imaging methods should be free of stereological and resolution artifacts [Eicken et al., 2000; Jerram and Higgins, 2007].
 Average inclusion statistics have been derived in previous studies using thin section microscopy. Perovich and Gow  reported brine inclusion number densities of 1.0 to 4.5 per mm3. Light et al.  resolved 24 pockets per mm3, and a power law scaling of inclusion number density with length (highlighting the effect of imaging resolution). Cole and Shapiro  described inclusion shapes that ranged from spherical to vertically elongated ellipsoids. Nevertheless, the limitations of thin section microscopy motivated the use of nondestructive tomography. Our work builds on the low-resolution X-ray tomography of Kawamura  and later efforts by Lange . Eicken et al.  used magnetic resonance imaging (MRI) to measure inclusion dimensions from 2D horizontal and vertical images of polycrystalline natural and tank-grown sea ice with a resolution of 0.2 × 0.2 × 1 mm. They found an increase in inclusion length and elongation with warming, and good agreement with high-resolution thin section microscopy.
 In part due to the lack of pore evolution data, microstructural models of sea ice are highly simplified. The elongated brine channels and ice plate model of Assur  remains the standard descriptive and engineering model for mechanical properties. An ellipsoidal inclusion model was later developed by Tinga et al.  and applied by Vant et al.  to the dielectric permittivity of sea ice, with parameter fitting (vertical aspect ratio, and inclination angle) from measurements in the range 0.1–40 GHz. Effective medium models for thermal properties have used spherical brine and air inclusions [Yen, 1981; Pringle et al., 2007]. In a step toward the development of a more realistic model of sea ice microstructure, we characterize here the anisotropic brine connectivity using percolation theory.
 Percolation theory addresses transitions in disordered multicomponent systems whose properties depend on component connectivity [e.g., Stauffer and Aharony, 1994; Bunde and Havlin, 1995; Christensen and Moloney, 2005]. Below a critical volume fraction pc there are no percolating pathways spanning a sample, and properties near pc show power law scaling related to (p − pc). In numerical lattice simulations, the volume fraction corresponds to the probability a site is occupied or a bond exists; in tomographic images such as ours, it corresponds to porosity. Percolation theory has been applied to a broad range of materials including rocks [Broadbent and Hammersley, 1957; Bourbie and Zinszner, 1985; Fredrich et al., 2006], semiconductors [Shklovskii and Efros, 1984], thin films [Davis et al., 1991], glacial ice [Enting, 1985], compressed powder aggregates [Zhang et al., 1994], polycrystalline metals [Chen and Schuh, 2007], radar absorbing coatings [Kusy and Turner, 1971], and carbon nanotube composites [Kyrylyuk and van der Schoot, 2008].
 For these materials it is generally difficult to vary the volume fraction of the phase whose connectivity controls bulk properties. In rocks, for example, one must analyze different samples [Bourbie and Zinszner, 1985; Fredrich et al., 2006]. In contrast, it is precisely the strong variation of sea ice porosity over a narrow temperature range that motivates our work, and our results offer insight into the dynamic mechanisms by which the pores space changes with temperature.
 Despite more than 50 years of applying percolation theory to disordered materials, key variables such as the infinite cluster density, percolation probability, and correlation length have only been computed as functions of the occupation probability primarily for idealized lattice models. A novelty of our work is that we have computed key percolation variables directly from the microstructure of a natural material, indeed from thermally driven variations in the sample.
 We have grown sea ice single crystals, the building blocks of polycrystalline sea ice, and imaged the thermal evolution of their complex pore space with X-ray computed tomography. We have characterized the structure by computing key functions of classical percolation theory and applying finite-size scaling methods. The scope of this article is to present full details of our X-ray CT imaging, discuss our revealing new images of intracrystalline brine inclusions, and to characterize the brine pore space using percolation theory. We compare our findings with simple traditional models of sea ice microstructure and discuss them in the context of sea ice fluid transport and electrical properties. Although beyond the scope of this paper, a future end point of this groundwork is the development of a realistic, percolation theory based model of sea ice microstructure from which material properties can be derived.