Ice in .NET

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1 Ice
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development, growth conditions, and constituents of sea water, sea ice may contain varying amount of salinity, brine pockets, solid salts, air bubbles, and organic and inorganic inclusions. Sea ice is thus more like a multiphase, anisotropic composite material. Ice thickness, salinity, temperature, density, and the concentration of brine inclusions are important physical properties of sea ice. These properties are sensitive to the growth conditions and thermal history, which, in turn, affect the electromagnetic interaction with sea ice medium. According to its age and thickness, sea ice can be categorized into new ice (0-5 cm), young ice (5-30 cm), first-year ice (3D-180 cm), and multiyear ice (> 30 cm) [Onstott et al. 1982]. The ice temperature generally follows a linear profile, increasing linearly from the ice-atmosphere interface temperature to about -1.8 C at the ice-water interface. The salinity of sea ice, Si, is a measure of the salt content of sea ice and is defined by [Maykut, 1985]
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mass of salt x 103 mass of ice + mass of brine
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where Si is in 0/00 or ppt (part per thousand). The ice growth process also accompanies the bulk desalination. As the ice thickness increases, there is a decrease in the ice salinity by mechanisms such as brine migration and gravity drainage, resulting a brine loss to the ocean [Weeks and Ackley, 1982]. Salinity profiles in thinner ice have a C-shape indicating higher salinities at the upper and lower parts of the ice slab. The density of sea ice is a function of ice temperature and salinity; empirical relations can be found in [Cox and Weeks, 1983]. Brine pockets are entrapped brine rejections between ice platelets during the freezing process. The amount of brine entrapped depends on the salinity of sea water and the freezing rate. Brine pockets are typically long and narrow, being on the order of 0.05 mm in diameter. As the ice changes temperature, internal melting or freezing within the brine pockets influence the fractional volume of brine inclusions. Empirical relations for brine volume fraction as a function of ice temperature and ice salinity can be found in Frankenstein and Garner [1967] and Cox and Weeks [1983]. In addition to brine pockets, sea ice also contains a great number of air bubbles with dimensions between 0.1 and 2mm. Thus volume scattering effects of brine pockets and air bubbles are important for sea ice. The dielectric properties of ice can be found in Cumming [1952], Evans [1965], and Ray [1972]. At microwave frequencies, the real part of the relative permittivity of ice is about 3.2 and the imaginary part varies from 10-4 to 0.05. Thus ice is not an absorptive media. Depending on the frequency and the size of the particles in ice, it can be a strong scattering media. The dielec-
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4 CHARACTERISTICS OF DISCRETE SCATTERERS AND ROUGH SURFACES
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tric properties of ice also depends on its temperature [Ray, 1972]. Dielectric properties of sea ice are dependent on the properties of its constituents and temperature, and various expressions have been derived to express the sea ice effective permittivity [Weeks and Ackley, 1982]. The loss tangent of sea ice varies with the ice type, depending on whether it is pure ice, first-year sea ice, or multiyear sea ice.
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Snow
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Snow refers to ice particles that have fallen and deposited on the ground. As ice particles reach the ground, the snoW metamorphism process commences. Driven by the tendency of minimizing its surface free energy, snow grains reduce their surface area-to-volume ratio by forming larger and more rounded shape. The temperature profile and gradient of snow layer determine the rate and type of snow metamorphism. The freeze-thaw cycles of snow layer-ice grains melt during the daytime and the melt water refreezes at night-can yield clusters or aggregates of ice grains. Snow is classified as a dense medium because each of the constituents forming snow can occupy an appreciable fractional volume. Dry snow is a mixture of ice and air, and wet snow is a mixture of ice, air, and water. The amount of water in wet snow is given in terms of snow wetness, which is the fractional volume of water fw in snow. The amount of ice in snow can be calculated from snow density M (g/cm 3 ). Suppose that the specific density of ice is 10% less than that of water; then the fractional volume of ice in snow Ii in terms of M is approximately given by Ii = MIO.9. Typical values of fw run from 0% to 10%. The value of M usually falls between 0.10 g/cm3 and 0.30 g/cm3 . Particle diameters of ice and water are between 0.1 mm and 2 mm. For hydrological applications, it is desirable to infer the water equivalent from the remote sensing measurements. The water equivalent W (in em) is the amount of water that remains when the snow is melted. If the snow layer is of thickness d, then the water equivalent W is governed by the approximate relation W = Md. Particles do not scatter independently when they are densely distributed. To study the scattering from snow requires a theory of scattering from dense media. At very low frequencies, when the particle sizes are very much smaller than a wavelength and scattering can be ignored, the several constituents of snow contribute to an effective permittivity of snow which can be described by mixture formulas [Maxwell-Garnett, 1904; Polder and van Santern, 1946; Bottcher, 1952] and verified by experimental measurements [Cumming, 1952;
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