The formula for calculation of the complex dielectric constant of wet snow is determined on the basis of the following assumptions : 1) Wet snow is a mixture of ice spheres and water meniscuses packed in air. 2) The depolarization factor of a spheroid, (δ, δ, 1-2δ); 0≤δ≤1/2, is assumed to be that of a water meniscus, as an approximation. 3) Polder and van Santen's mixing formula (1946) is applicable. 4) The depolarization factor depends on the volume fraction of water,
Vw', in the sample. There is an adjusting parameter in the formula yielded from assumption 1-3). To determine the parameter, the dielectric constants of mixtures of glass beads and water, which were substitutes for wet snow samples, were measured at 8.83 GHz. Glass bead samples are suitable for many accurate measurements. The relation, δ=0.06+0.25
Vw is determined using the present data and the same data at 6 GHz measured by Sweeny and Colbeck (1974). This relation shows that the equivalent spheroid is flattened oblate (the axis ratio is 0.08-0.15 when
Vw≤0.15). The calculated dielectric constants agree well with the measured values.
The dielectric constants of natural snow samples were also measured at 8.83 GHz. Half of the measured values agree with the calculated values. Many of the remainder suggest water droplets in these samples to be spherical, and the rest suggest more flattened droplets than those in glass bead samples.
The frequency dependence of the calculated value is examined. Below 100 MHz, the present values are slightly less than those determined by Denoth and Schittelkoph (1978) at 18.5 MHz. Numerical analyses show that this difference is caused by the difference between the dielectric constants of ice calculated from dry snow data at 20 MHz and 9 GHz, and suggest the applicability of the present theoretical model in a wide frequency range.
View full abstract