Effective Dielectric Constants of Mixed-Phase Hydrometeors

Abstract Melting snow, graupel, and hail are often modeled as uniform mixtures of air–ice–water or ice–water. Two-layered models have also been proposed in which the particle consists of a dry snow or ice core surrounded by water or a wet snow mixture. For both types of particle models, the mixtures are characterized by effective dielectric constants. This information, along with particle shape, size, and orientation, provides the necessary data for calculating the scattering characteristics of the particles. The most commonly used formulas for the effective dielectric constant, eeff, are those of Maxwell Garnett and Bruggeman. To understand the applicability and limitations of these formulas, an expression for eeff is derived that depends on the mean internal electric fields within each component of the mixture. Using a conjugate gradient numerical method, the calculations are carried out for ice–water mixtures. Parameterization of the results in terms of the fractional water volume and the electromagnet...