Multiple‐scattering effect on radiometric determination of rain attenuation at millimeter wavelengths

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Abstract
The multiple‐scattering effects in rain are negligibly small in comparison with the absorption effects when raindrop sizes are much smaller than a wavelength. This is often true for light to moderate rain below about 30 GHz, and the total atmospheric attenuation along the path may be estimated by the emission method using the usual radiometric formula. At higher frequencies and heavy rain the multiple‐scattering effects cannot be ignored. This paper describes a theoretical study of the correction due to the multiple‐scattering effect for the determination of the total atmospheric attenuation by the emission method. The observed temperatures at the ground both for vertical and horizontal polarizations and for various raindrop temperatures, precipitation rates, ground temperatures, ground albedos, and frequencies ranging from 30 GHz to 120 GHz are calculated on the basis of the equation of transfer, taking into account the polarizations and the Stokes parameters. The cross sections of rain droplets are calculated using the Mie solution with the Laws and Parsons drop size distribution and Saxton's formula for refractive index of water. These calculations show the differences between the total rain attenuation and the attenuation calculated from the sky temperature measurements and the assumed rain temperatures. The results are compared to some experimental data, showing a good agreement.