Applicability of Effective-Medium Theories to problems of Scattering and Absorption by Nonhomogeneous Atmospheric Particles

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

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Abstract

Effective-medium theories yield effective dielectric functions (or, equivalently, refractive indices) of composite media. Such theories have been formulated that go beyond the Maxwell-Garnett and Bruggeman theories, which art restricted to media composed of grains much smaller than the wavelength. These extended effective-medium theories do not, however, yield effective dielectric functions that can be used for the same purposes for which we unhesitatingly use the dielectric functions of substances such as pure water and pure ice (e.g., reflection and transmission by smooth interfaces; absorption and scattering by particles). Extended dielectric functions can lead to unphysical results; for example, absorption in composite media with nonabsorbing components. Moreover, if the grains in composite media are large enough to give rise to magnetic dipole and higher-order multipole radiation, then the effective permeability of the composite medium cannot be taken to be that of free space even if the grains are nonmagnetic.

Recently, extended effective-medium theories have been applied to the problem of determining, the effective dielectric function of ice in which soot grains are embedded in order to explain a factor of 2 discrepancy between measurements of the albedo of soot-contaminated snow and calculations based on a snow albedo model. Setting aside questions about the applicability of these theories, reasonable alternative explanations for the discrepancy exist: (i) Soot is not an invariable substance; measured refractive indices of carbonaceous materials vary appreciably, especially the imaginary part (about a factor of 5). (ii) Absorption by a small soot particle depends on its shape, varying by as much as a factor of 2. (iii) Absorption by a soot particle may be enhanced by porosity; for a fixed particle volume, the enhancement is roughly proportional to the porosity. To predict exactly how much a given amount of soot reduces the visible albedo of snow requires, therefore, more detailed information about the soot than is likely to be readily obtainable.

Abstract

Effective-medium theories yield effective dielectric functions (or, equivalently, refractive indices) of composite media. Such theories have been formulated that go beyond the Maxwell-Garnett and Bruggeman theories, which art restricted to media composed of grains much smaller than the wavelength. These extended effective-medium theories do not, however, yield effective dielectric functions that can be used for the same purposes for which we unhesitatingly use the dielectric functions of substances such as pure water and pure ice (e.g., reflection and transmission by smooth interfaces; absorption and scattering by particles). Extended dielectric functions can lead to unphysical results; for example, absorption in composite media with nonabsorbing components. Moreover, if the grains in composite media are large enough to give rise to magnetic dipole and higher-order multipole radiation, then the effective permeability of the composite medium cannot be taken to be that of free space even if the grains are nonmagnetic.

Recently, extended effective-medium theories have been applied to the problem of determining, the effective dielectric function of ice in which soot grains are embedded in order to explain a factor of 2 discrepancy between measurements of the albedo of soot-contaminated snow and calculations based on a snow albedo model. Setting aside questions about the applicability of these theories, reasonable alternative explanations for the discrepancy exist: (i) Soot is not an invariable substance; measured refractive indices of carbonaceous materials vary appreciably, especially the imaginary part (about a factor of 5). (ii) Absorption by a small soot particle depends on its shape, varying by as much as a factor of 2. (iii) Absorption by a soot particle may be enhanced by porosity; for a fixed particle volume, the enhancement is roughly proportional to the porosity. To predict exactly how much a given amount of soot reduces the visible albedo of snow requires, therefore, more detailed information about the soot than is likely to be readily obtainable.

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