B.S.T.J. Briefs: Perturbation Calculations of Rain-Induced Differential Attenuation and Differential Phase Shift at Microwave Frequencies

Vol. 52, No. 10, December, 1973 Printed in U.S.A. B.S.TJ. BRIEF Perturbation Calculations of Rain-Induced Differential Attenuation and Differential Phase Shift at Microwave Frequencies By J. A. MORRISON and T. S. CHU (Manuscript received August 24, 1973) In a recent note1 calculated results of differential attenuation and differential phase shift, as a function of rain rate, were given at frequencies of 4, 18.1, and 30 GHz. The calculations have since been done at 11 GHz also. These results are based on scattering of a plane electromagnetic wave by oblate spheroidal raindrops. The point matching procedure used to obtain nonperturbative solutions to the problem was briefly described, and full details will be presented later.2 Somewhat similar calculations have been carried out by Oguchi3 at 19.3 and 34.8 GHz. The purpose of this note is to point out that a modification of Oguchi's earlier first-order perturbation approximation,4 for spheroidal raindrops with small eccentricity, gives results which are quite close to those obtained by the point matching procedure. We also give these modified perturbation results at frequencies in the range up to 100 GHz, although they may be less reliable at the higher frequencies, particularly at the heavier rain rates.4 We remark that the perturbation results are obtained quite inexpensively, whereas the point matching procedure is very costly. The surface of an oblate spheroidal raindrop is given in spherical coordinates by r = R(d) = a{ - v sin2 0)"* = a[ 1 + v sin2 d + 0(j>2)], (1) for 0 ^ 6 ^ 7r, independently of the azimuthal angle It was assumed1 that the ratio of minor to major axis depends linearly on the radius 1907 1908 T H E B E L L SYSTEM T E C H N I C A L J O U R N A L , D E C E M B E R 1 9 7 3 a (in cm) of the equivolumic spherical drop; specifically a/b = (1 -- a).