Effective dielectric constants of melting hydrometeors and their use in radar bright-band models

Melting snow particles have been modeled either as uniform mixtures of air-ice-water or as concentric or confocal spheroids consisting of a dry snow core surrounded by water or a wet snow mixture. In the case of a uniform mixture, the effective dielectric constant, ε_eff is usually obtained by an application either of the Maxwell Garnett or the Bruggeman formula. In this paper an alternative formulation is investigated that expresses ε_eff in terms of the ratios of the mean fields in the air, ice and water. Although the mean field ratios can be computed numerically, the computational time needed to generate the results for different fractional contents and frequencies is prohibitive. To circumvent this problem the field ratios for water and ice are first parameterized in fractional melt water and frequency, next, the Debye formula is used to estimate the field ratio for ice and air. Although some accuracy is sacrificed, the formulation is relatively easy to compute for any air-ice-water uniform mixture for wavelengths between 3 mm to 30 mm. The formulas for ε_eff can be tested using dual-wavelength radar data. Using these radar data in the snow just above the melting layer a 2 parameter snow size distribution can be estimated if the snow density is assumed. Having obtained the size distribution, a melting layer model and ε_eff is used estimate the dual-wavelength profiles within the melting layer. To do these tests the Maxwell Garnett as well as the present formulas for ε_eff are used