Dielectric Constant

Natural materials (e.g. snow, ice, soil, vegetation...) are generally a mixture of materials that exhibit different dielectric characteristics (Sihvola and Kong, 1988). The dielectric constant of snow (es) is comprised of an imaginary part, which is directly related to wetness (W), and a real part which is a function of the density (r) as well as the wetness. Wet snow can be treated as a three-component mixture of air, ice and water; the dielectric properties of these materials are well known (e.g. Hallikainen, 1977), see Table 1 below.

Table 1, Dielectric constant values, at 0 degrees C, for the three components of wet snow. The value for water is much greater than that for air and ice. Dry snow is considered as a mixture of ice and air. When liquid water is introduced, its high dielectric value drastically effects the dielectric properties of the mixture. This signal can be measured as an impedance of the wavelengths emitted by active dielectric sensors.

The dielectric constant of snow is a weighted average of the dielectric constants of its three components. This effective dielectric constant controls the rate of propagation and the degree of absorption of electromagnetic waves in wet snow. By using a dielecric constant that is relative to that in a real vacuum (the dielectric constant of air is not significantly different than that of a vacuum), a simple relationship between the complex refractive index and the complex dielectric constant can be assumed.

The dielectric constant of a water molecule is dominated by the reorientation of the molecule due to its large dipole moment. H2O is anisotropic and, because it crystallizes in a hexagonal system, it is considered uniaxial in that there is only one direction of single refraction, namely parallel to the principal crystal axis known as the optic axis. Refraction is the phenomenon which occurs when a wave crosses a boundary between two media (dry snow and liquid water) in which its phase velocity differs. This leads to a change in the direction of propagation of the wavefront in accordance with Snell's Law which relates the angles of incidence and refraction of waves at such a boundary as; n1 sinq1 = n2 sinq2 where n1 and n2 are the refractive indices on each side of the surface and q1 and q2 are the corresponding angles of incidence and refraction. The refractive index is the ratio of the phase velocity of electro-magnetic waves in free space (a vacuum) to that in another specific medium; in anisotropic, uniaxial minerals there are two refractive indices and the complex refractive index (m) is equal to the sum of these. The dielectric constant, e, is equal to the sum of the real (e') and imaginary (e'') permittivity of a material and is the square of the refractive index, or e = m2. e' is stable at approximately 3.2 with wavelength and is not significantly affected by temperature. No reliable data exist for e'', however; this loss term is positively correlated with both wavelength and temperature as well as solute concentration.

Back to Energy Balance