Chapter 10 



DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 



101 ABSORPTION AND SCATTERING OF 

 MICROWAVES BY THE ATMOSPHERE^ 



THE piiKtsEXT iiEPOitT (Ifiils witli the absorption of 

 microwaves in the 0.3- to 100-cm wavelength range, 

 by the atmospheric gases and by floating or falling 

 water drops like clouds, fog, and rain of maximum 

 drop diameter 0.55 cm. 



Tlie tlu'ory of absori>tion and scattering of waves 

 by spherical particles is In-iefly reviewed. The results 

 are applied to water drops. 



For small drops, the attenuation, wliich depends 

 only upon the amount of licjuid water per unit volume 

 and is independent of the drop size, is 0.38, 0.04!!. and 

 0.0045 db per kilometer for each gram of liquid water 

 per cubic meter of air for the K. X, and S bands, re- 

 spectively. Since the concentration of li(piid water in 

 clouds does not seem to exceed 1 g per cubic meter of 

 air, the above values represent upper limits. These 

 values refer to water droplets at temperatures around 

 IS C. The attenuation increases with decreasing tem- 

 perature of the water drops. 



AVliile the attenuation does not depend upon the 

 total rate of rainfall, it is possible to calculate the 

 maximum values to be expected for any precipitation 

 rate. These are 0.16, 0.45, 0.005, 0.001, and 0.0006 db 

 per kilometer for each millimeter precipitation per 

 hour at 1.35, 3, 5, 8, and 10 cm, respectively. These 

 theoretical maximum values of attenuation compare 

 fairly well with the values observed and are for water 

 drops at 18 C. 



In the wavelength j'ange mentioned it is shown that, 

 with the exception of the biggest drops and shortest 

 waves, the wave energy converted into heat inside the 

 drops is much larger than the scattered energy. 



The radar absorption coefficient, defined as the frac- 

 tion of the incident power scattered backward per unit 

 layer thickness of the echoing medium, has been com- 

 puted for different rains. This allows the estimation of 

 the power received in radar oljservations of storm clouds 

 and rains. The theoretical ])redictions seem to be con- 

 sistent here also with the results of the few recent radar 

 studies which tend to show that echoes are due mainly 

 to water drops of the dimensions occurring in rains. 



"By L. Goldstein, Columbia University W;ive Propagation 

 Group. 



In the introduction a resume is given of the status 

 of microwaxe absorption liy atmospheric oxygen and 

 water xapor. With the exception of the resonance re- 

 gion of oxygen (resonance wavelengtli around 0.5 cm), 

 this absorption turns out to be of only very limited 

 practical importance for waves longer than about 3 to 

 5 cm. 



^"■^•^ Introduction 



The present report is intended to review the status 

 of microwave ju-opagation through rain, clouds, and 

 fog. In order, however, to convey a precise idea of the 

 total atmospheric absorption, we shall include here 

 some of the most important numerical results recently 

 oljtained on the absorption of microwaves by atmos- 

 pheric gases, like oxygen and water vapor. ^'^ 



First of all. in medium- and low-altitude fair- 

 weather clouds and fogs, with the possible exception of 

 heavy sea fogs, the attenuation is of negligible impor- 

 tance for longer waves. It may become important at 

 .shorter waves. For instance, in the K band the atten- 

 uation'' is 0.38 db per kilometer for each gram of liquid 

 water per cubic meter of air. The X- and S-band 

 waves are attenuated, respectively, 0.049 and 0.0045 

 db/km/g/m^. Since in these cloitds and ordinary fogs 

 the liquid water concentration does not seem to exceed 

 1 g/m^, these values are very likely upper limits. Actu- 

 ally, by halving these numbers one would be nearer the 

 true values, inasmuch as liquid water contents reported 

 in clouds*'" varies between 0.15 and 0.50 g/m^. An in- 

 teresting and simplifying feature of cloud and fog 

 abisorption is the fact that the smallness of their 

 water drops, as compared with the wavelength, makes 

 the attenuation independent of the drop sizes. The 

 cloud and fog attenuation depends linearly on the 

 liquid water concentration of the atm'o,sphere, and in 

 the microwave region it decreases monotonically with 

 increasing wavelength. 



Ill laiiis or rain clouds the attenuation does not 

 depend directly on the total rate of rainfall, a variable 

 so familiar to meteorologists. It is, nevertheless, pos- 

 sible to give upper limits to the attenuation per unit 

 precipitation rate. These are as follows: 0.16, 0.45, 

 0.005. 0.001. and 0.0006 db per kilometer for each mil- 



••The attenuation values given in this report are always for 

 one-way transmission. 



148 



