An efficient TCS formula for rainfall microwave attenuation: T-matrix approach and 3-D fitting for oblate spheroidal raindrops

The T-matrix approach to the computation of total cross sections of spheroidal raindrops due to electromagnetic scattering is considered numerically exact, and has therefore been used in this paper for the analysis of the total cross section (TCS) of the spheroidal raindrops. A more accurate computer programme based on the T-matrix method has been developed in MATHEMATICA^TM so as to evaluate the TCSs of the spheroidal raindrop scatterers. With the checked programme after comparison, a large amount of TCS data has been obtained and plotted in a three-dimensional (3-D) graphic in this paper. Utilizing these exact data points, a 3-D (or two-step) nonlinear least squares fitting procedure has been proposed and implemented successfully. As a result, an efficient formula of the TCS as a function of both raindrop mean radius and operating frequency has been obtained. In the analysis, four cases (both parallel and perpendicular polarizations, and outdoor temperatures of 10 and 20°C) are considered. Covering a very large validity range for practical useful problems, this formula is very compact, easy to use, and very much faster (by about two orders of magnitude) than the conventional algorithm