Radar Backscattering of Microwaves by Spongy Ice Spheres

Craig F. Bohren Department of Meteorology, Pennsylvania State University, University Park 16802

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Louis J. Battan Institute of Atmospheric Physics, The University of Arizona, Tucson 85721

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Abstract

The radar backscattering cross section of a spongy ice hailstone—a mixture of ice and liquid water—depends on its size, shape and dielectric function. There are two types of theories of the effective dielectric function of two-component mixtures: Maxwell-Garnet and Bruggeman theories. In the latter, the two components are treated symmetrically, whereas in the former they are not. We have generalized the Maxwell-Garnet expression, originally derived for spherical inclusions in an otherwise homogeneous matrix, to ellipsoidal inclusions. When this expression, with all ellipsoidal shapes equally probable, is used in calculations of radar backscattering by ice spheres coated with spongy ice, the results are in generally good agreement with measured cross sections. Agreement is better if the inclusions are ellipsoidal rather than spherical, but only slightly so. Shape considerations are less important than taking ice to be the inclusions and liquid water to be the matrix.

Abstract

The radar backscattering cross section of a spongy ice hailstone—a mixture of ice and liquid water—depends on its size, shape and dielectric function. There are two types of theories of the effective dielectric function of two-component mixtures: Maxwell-Garnet and Bruggeman theories. In the latter, the two components are treated symmetrically, whereas in the former they are not. We have generalized the Maxwell-Garnet expression, originally derived for spherical inclusions in an otherwise homogeneous matrix, to ellipsoidal inclusions. When this expression, with all ellipsoidal shapes equally probable, is used in calculations of radar backscattering by ice spheres coated with spongy ice, the results are in generally good agreement with measured cross sections. Agreement is better if the inclusions are ellipsoidal rather than spherical, but only slightly so. Shape considerations are less important than taking ice to be the inclusions and liquid water to be the matrix.

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