Scattering and depolarization of microwaves by spheroidal raindrops

Abstract

With a view to calculating depolarization and differential attenuation of microwaves by rain, with allowance for the variable shape and orientation of raindrops, the theory of P. C. Waterman is applied to the calculation of cross sections and depolarization ratios of spheroids, and drops of the shapes determined by H. R. Pruppacher and R. L. Pitter. Use of Waterman's extended boundary condition facilitates computation. The scattering characteristics of spheroids appear similar in nature to those of spheres, in the regimes considered. Marked singularities in the characteristics of backscattering depolarization appear at optical size 1.5. The Pruppacher and Pitter drops scatter similarly to equivalent oblate spheroids. Implications for weather radar measurements are briefly discussed.

Electromagnetic Modeling of the Propagation Characteristics of Satellite Communications Through Composite Precipitation Layers, Part II: Results of Computer Simulations

“…The results are given for LP (Laws and Parsons, 1948), MMP, JT, JD (Olsen, Rogers, and Hodge, 1978) and LN RSD (Ajaya and Olsen, 1985), drop temperatures of 0 0 C and 20 0 C and frequencies from 1 to 200 GHz with an increment of 1 GHz. With the exception of the limited data presented by Oguchi (1977), Fang andLee (1978), andLi et al (1995) previous results for ∆α and ∆φ were restricted to only oblate drops (Oguchi, 1964), (Morrison and Cross, 1974), (Warner and Hizal, 1976), (Holt, Uzunoglu, and Evans, 1978), (Seow et al 1998) at a single drop temperature and for frequencies less than 100 GHz using much wider frequency increments. It should be mentioned that the perturbation approximation utilized by Oguchi (1964) and Li et al (1995) yields less accurate results, particularly for ∆φ above 30 GHz.…”

“…An important aspect of the work reported in this paper is the implementation of the GMT for the EM scattering from realistically distorted raindrops at frequencies which have not been hitherto considered by any other numerical EM computational technique including the point-matching (Morrison and Cross, 1974), (Oguchi, 1977), perturbation (Oguchi, 1964) and (Li, et al, 1995), T-matrix (Warner andHizal, 1976), integral-equation (Holt, Uzunoglu, andEvans, 1978) and the finite element method (Ajase and Sadiku, 1995). The use of the GMT not only extends the solution to encompass frequencies well above 100 GHz, but also takes a step forward in improving the accuracy, particularly of ∆φ above 30 GHz.…”

“…This dearth of published data stemmed primarily from the formidable numerical difficulties encountered in computing the scattering properties of an arbitrarily-shaped, 3-D scattering object whose size is comparable to or larger than the wavelength of the incident radiation. This is probably why most of the early (Oguchi, 1964(Oguchi, , 1977, (Morrison and Cross, 1974), (Warner and Hizal, 1976), (Holt et al 1978) and more recent investigation (Ajase and Sadiku, 1995), (Li et al, 1995), (de Wolf and Zwiesler, 1996), (Seow et al 1998) focused their efforts on frequencies less than 100 GHz. In contrast, the dispersive characteristics of ∆α and ∆φ are provided herein for rain rates from 2.54 mm/h to 152.4 mm/h, raindrop temperatures of 0 o C and 20 o C, and frequencies from 1 to 200 GHz.…”

Microwave Specific Attenuation by Oblate Spheroidal Raindrops: an Exact Analysis of TCS's in Terms of Spheroidal Wave Functions

“…The most popular raindrop model for the analysis of rainfall attenuation in the published literature usually considers the raindrops as spheroidal raindrop scatterers. The methods and techniques employed for the analysis of specific rainfall attenuation are the boundary-perturbation and point-matching techniques by Oguchi [1,2], the leastsquares fitting process of boundary conditions by Morrison and Cross [3], the sphere-based Taylor expansion by Erma [4][5][6], the integral equation technique by Holt et al [7], the T-matrix method by Waterman [8][9][10] and the method of extended boundary conditions by Warner [11,12].…”

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

“…The methods that received most atitention over the past thirty years are: Rayleigh-Debye (R-D) approximation (or the Born approximation) [l], the perturbation theory [2], the least squares fitting technique [3], the Tmatrix method [4], the extended boundary condition method [5,6], the unimoment method [7,8], and some others given in [9,10]. Although each of them has its own shortcomings, nevertheless they have made significant contributions to the problem of microwave attenuation by rainfall.…”