The theory of attenuation by hydrometeors is based on the exact results first obtained by Mie for scattering from large dielectric spheres. If the particle are small compared to wavelength, an assumption which is valid for wavelengths greater than 10 cm and all precipitation except hail, then the Rayleigh approxima tions can be used to simplify the expression for the total cross-section : Where and are the absorption and scattering cross-sections, respectively, a is the particle radius and m is the complex index of refraction of the hydrometeor, denotes the imaginary part of the complex quantity -K. The attenuation coefficient A is directly expressible in terms of and the drop size distribution per unit volume n(a). Where and a are in cgs units and n(a) is in mixed units cm /m . If the droplets are sufficiently small, then the attenuation can be re-expressed in terms of the water content. This is the usual practice in estimating decimeter attenuation due to water clouds. The drop distribution of rainfall is highly variable, contributing to a large spread in the estimate of A for a given surface rainfall rate. 6 Marshall and Palmer 7formulated an empirical distribution of the form with R, the rainfall rate, given in mm/hr. This distribution fits observations and nearly coincides with the classical Laws and Parsons distribution (which is based on three years of measurements near Washington, D. C. ) over the range of drop diameters that determine decimeter and centimeter attenuation. Substituting Equation (3-6) in (3-5) and carrying out the integration we obtain:
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