ATMOSPHERIC ABSORPTION AND SCATTERING 



171 



the assumption is made tliat the eclioiiig raiu layer is 

 1 km thick. This is clearly arbitrary but is likely to 

 give the right order of magnitude. 



There has been discussed in a rather unorthodox 

 way^^ the effect of the absorption on the back scatter- 

 ing of radiation taking into account also the tiuite 

 pulse length of the radiation source. 



These results seem to be consistent with the meager 

 quantitative information available in this field. This 

 fact would tend to classify the atmospheric radar 

 echoes as back scattering phenomena due to water 

 drops of precipitation size. It may further be re-em- 

 jjhasized that theory provides an adequate explanation 

 for scattering and al)sorption of electromagnetic waves 

 passing through different clouds or precipitation 

 forms. The limitations imposed on the theoretical re- 

 srdts are due essentially to irregularities inherent in 

 the meteorological elements. 



^"•^■' Summary 



The present report gives a detailed review of the 

 theoretical and experimental status of microwave at- 

 mospheric absorption. This absorption is due to the 

 gases of the atmosphere, oxygen, and water vapor, on 

 the one hand, and to the swarms of floating or falling 

 water drops, clouds, fog, rain, and snow, on the other. 



The status of the gaseous absorption of the atmos- 

 phere is reviewed briefly in Section 10.1.1. Figure 1 

 gives the oxygen and water vapor attenuation curves 

 in the 0.3 to 10-cm wavelength range. The water vapor 

 attenuation is given for a vapor content of 7.5 g/m^ 

 of air, or 6.2 g per kilogram of air. In the equatorial 

 belt, 15° S to 15° N, at sea level, the attenuation due 

 to the atmospheric gases is approximately constant. It 

 is about 0.18 and 0.008 db per kilometer for 1.25- and 

 3-cm waves respectively. In the tropical region the 

 seasonal variation of these attenuations is quite large. 



Figure 2 helps to give a clear picture of the atmos- 

 pheric absorption due to oxygen and water vapor 

 simultaneously with the absorption in rains of differ- 

 ent types. It is seen that in the wavelength range 1 to 

 5 cm the rain attenuation is more important than the 

 gaseous atmospheric attenuation. The latter predomi- 

 nates at waves shorter than 1 cm and longer than 

 about 5 cm, losing entirely its practical importance 

 at these longer waves. 



The theory of absorption and scattering of electro- 

 magnetic waves by dielectric spheres (see Section 

 10.1.2) is briefly presented following the Bayleigh 

 method as developed by Stratton. 



The contribution of a swarm of spherical water 

 drops of the same size, floating or falling in the atmos- 

 phere, to the average field strength attenuation factor 

 is given by 



a = i^^^Qt neper per unit length, 



where N is the average concentration of the drops, and 

 Qt their total cross section. This total cross section is 

 the ratio of the power removed from the incident beam 

 by one drop, through scattering and internal absorp- 

 tion to the power density of the incident beam. Similar 

 definitions hold for the scattering cross section, absorp- 

 tion cross section and differential cross section for 

 back scattering or radar cross section. The total cross 

 section Qt has the following form: 



Q< = — ( - Re) Z (2n+l) (a,.+5„), 

 2^^ « = i 



where A denotes the wavelengths in free space of the 

 incident radiation and a„ and b„, {n = 1,2,3, ■ • •) form 

 an infinite set of scattering amplitudes or coeflficients 

 associated with magnetic and electric poles of increas- 

 ing order induced in the water drop by the field 

 strengths of the radiation. Thus a■^ is associated with 

 a magnetic dipole, &i with an electric dipole, &, with 

 an electric quadrupole, etc. 



Section 10.1.3 is devoted to the study of the ampli- 

 tudes a„ and in- These are complicated functions of 

 the wavelength A, diameter D, or radius a of the drops, 

 as well as the complex refractive index N or dielectric 

 constant €c of water. Approximate expressions of the 

 amplitudes can be derived by expanding them in series 

 of ascending powers of the parameter p = ttD/X. for 

 p < 1. Eetaining only terms up to p''', we found the 

 following expressions of the first amplitudes. 



45 



■1) 



^ _^'^!:zi .3(^1,3^^ ,_?i^^^:zl 3^ 



b,= 



15 2iV2^3' 



where N is the comjjlex refractive index of water with 

 respect to free sjDace and N- = Cc = (e,- — jcj) is its 

 complex dielectric constant. The numerical computa- 

 tion of these amplitudes requires knowledge of the 

 dielectric constant of water in the desired wave- 

 length and temperature range. Whereas experimental 



