Theoretical Aspects of Modeling Backscattering by Cirrus Ice Particles at Millimeter Wavelengths

Timothy L. Schneider Department of atmospheric Science, Colorado State University, Fort Collins, Colorado

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Graeme L. Stephens Department of atmospheric Science, Colorado State University, Fort Collins, Colorado

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Abstract

This research attempts to understand how nonspherical ice particles backscatter electromagnetic radiation at millimetric wavelengths. The discrete dipole approximation (DDA) is employed to examine backscattering by single particles to (i) explore the limits of the Rayleigh approximation and (ii) test the use and validity of spheroidal models to model semirealistic cirrus particles. It is shown that spheroids are reasonable models of cirrus ice particles at wavelengths of 3 and 8 mm. Furthermore, with careful consideration of optical size it is possible to exploit the Rayleigh approximation for spheroids under many circumstances.

The sensitivity of backscattered radiation to variations in microphysical properties is examined, based on DDA calculations for ensembles of ice particles. The most important factor in the ice crystal size distribution is found to be the median diameter (Dm) of the ice crystal volume distribution. In particular, for values of Dm typical of cirrus, the contribution of crystals whose major dimension is D ≤ 100 µm is masked by the signal of larger crystals. Simulations of ice water content-effective radar reflectivity factor relations (IWC-Zi) are also presented. Comparison with available empirical relations indicates a functional dependence of the IWC on Dm (i.e., the relative number of large crystals) and also suggests upper and lower bounds on Dm. It is demonstrated that the effective radar reflectivity cannot be used in an unambiguous way to determine the IWC. The difference between reflectivities at 3.16 and 8.66 mm are found to be insignificant. Implications for the remote sensing of ice clouds at millimeter wavelengths are discussed.

Abstract

This research attempts to understand how nonspherical ice particles backscatter electromagnetic radiation at millimetric wavelengths. The discrete dipole approximation (DDA) is employed to examine backscattering by single particles to (i) explore the limits of the Rayleigh approximation and (ii) test the use and validity of spheroidal models to model semirealistic cirrus particles. It is shown that spheroids are reasonable models of cirrus ice particles at wavelengths of 3 and 8 mm. Furthermore, with careful consideration of optical size it is possible to exploit the Rayleigh approximation for spheroids under many circumstances.

The sensitivity of backscattered radiation to variations in microphysical properties is examined, based on DDA calculations for ensembles of ice particles. The most important factor in the ice crystal size distribution is found to be the median diameter (Dm) of the ice crystal volume distribution. In particular, for values of Dm typical of cirrus, the contribution of crystals whose major dimension is D ≤ 100 µm is masked by the signal of larger crystals. Simulations of ice water content-effective radar reflectivity factor relations (IWC-Zi) are also presented. Comparison with available empirical relations indicates a functional dependence of the IWC on Dm (i.e., the relative number of large crystals) and also suggests upper and lower bounds on Dm. It is demonstrated that the effective radar reflectivity cannot be used in an unambiguous way to determine the IWC. The difference between reflectivities at 3.16 and 8.66 mm are found to be insignificant. Implications for the remote sensing of ice clouds at millimeter wavelengths are discussed.

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