Integral equation approximation to microwave specific attenuation by distorted raindrops: the spheroidal model

An integral equation approximation together with a perturbation technique and the spherical vector eigenfunction expansion method is employed in this paper to investigate the microwave attenuation by arbitrarily-distorted raindrops. The electromagnetic fields outside the distorted raindrop scatterers are considered as the sum of the incident wave fields and the scattered fields due to the spheroids. Both direct and scattered waves are expressed in terms of integrals containing a volumetric current distribution located at infinity and the dyadic Green´s functions. A method of obtaining the volumetric current distribution of the assumed source that generates the plane waves, is developed in the paper and the current distribution of such a source is derived. Under the first-order approximation, the scattered fields expanded are represented analytically and compared with those published previously, although the derivation itself of the scattered fields does not require such an expansion. As an application, the spheroidal raindrops are investigated specifically and the expansion coefficients of the scattered fields are derived analytically to demonstrate the applicability of the method presented here. Numerical results of the extinction cross sections and the specific attenuations are obtained. The specific attenuations computed numerically are also compared with the updated specific attenuation data collected in Singapore