150 



DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 









 

 















7 

 5 



3 

 Z 



,1 

 07 

 ,05 



,03 

 .02 



0.01 

 0.007 

 0.0 5 



0.00 3 

 0.002 



0.001 



150 90 50 



30 24 15 10 6.0 3.0 1.5 1.0 0.6 0.3 

 FREQUENCY IN IO'mC 



FicuRp; 2. Atmospheric attenuation im one-way tran.s- 

 mission. (1) Oxygen and water vapor (total p=76 cm 

 Hg, (=20 C, water vapor = 7..5 g per cu m). (Van 

 Vleck). (2) Moderate rain (6 mm per hr) of known droji 

 size distribution. (3) Heavy rain (22 mm ]ier hr). (4) 

 Rain of cloudburst jji-oiiortion (43 mm per hr). 



sorption is due to tlie paramagnetic character of this 

 gas. It is through the interaction of tlie magnetic field 

 strengtli with tlie magnetic dipole moment of the oxy- 

 gen molecule that microwaves are absorbed by this 

 gas. In tlie microwave region tlie oxj'gen molecule has 

 a resonance line at A = 0.25 cm and a band near 0.5 

 cm, while water vapor seems to have a resonance line 

 around 1.25 cm and interacts with the radiation field 

 through its electric dipole moment. The whole subject 

 has been discussed exhaustively.'-- 



The study of the scattering of microwaves by rain- 

 drops shows that the radar observations of rainclouds 

 can lie exphiined satisfactorily if the scattering is at- 

 tributed to spherical particles of dimensions similar 

 to those of raindrops, even tliougli no rain reaches the 

 grouiiil. liccent experimental work"'^'^ has lielped 

 considerably in clearing up the apparent inconsist- 

 ency which previouslj' existed in this subject. 



(Jn the whole, taking into consideration the irregu- 

 larities of the precipitation forms in space, it may be 

 said that theory pro\ides a fairly good picture of mi- 

 crowave propagation through a cloudy, foggy, or rainy 

 atmosphere. 



The major object of the present paper is to report 

 the theoretical and experimental work done on atten- 

 uation of microwaves by liquid or solid water particles 

 falling through the atmosphere, as well as clouds and 

 fog, which are water and ice particles in suspension. 



Theoretical work has thus far been concerned with 

 the problem of a plane electromagnetic wave scattered 

 and absorbed by a single spherical or spheroidal par- 

 ticle, first studied in detail by Mie^" for other purposes. 



The application of the results of Mie to very short 

 radio waves propagated through rain, clouds, and fog, 

 i.e., through a swarm of spherical water droplets, was 

 made by Eyde.^-'^'' The present report is, in part, an 

 extension of his work using more detailed meteorologi- 

 cal data on rains. 



A compact and elegant presentation of the problem 

 of absorption and scattering of a plane wave by a 

 s]ihere is given by Stratton.^*" The method followed 

 by him was first used by Lord Rayleigh.^^ In the follow- 

 ing section a lirief I'eview of this method will be given. 



""^ Scattering and Absorption of Radio 

 Waves by Spherical Particles 



Let the center of a sjihere of radius a be the origin 

 of a rectangular coordinate system and suppose a 

 jilaiie wave to be propagated along the positive z axis 

 and to fall on the sphere (Figure 3). The sphere of 

 ])crmeability /Xj (henrys per meter) and complex in- 

 ductive capacity ei (farads per meter) is em- 

 bedded in a medium of permeability /x, and inductive 

 capacity €,• The plane wave is supposed to be polarized 

 parallel to the .r axis. 



The electric and magnetic field strengths E;, Hj 

 of the incident wave (subscript %) are expanded into 

 sjiherical wave functions. '^^ The reason for this expan- 

 sion lies in the boundary conditions and will appear 

 clearly below. 



Ei = E^ = a:, £0 e -'V + '"' , 



1 



H. = H^ = - a^ £■„ e 



-jfc Z + }(jit 



where 



fc = (m« 



jlJL(To:)' 



(1) 



(2) 



is the complex wave number of the medium (here 

 I-., = 2ir/X, A being the w^aveleugth referred to air or 



