THERMAL NOISE EMITTED BY ATMOSPHERE 305 



where the summation extends over all discrete noise sources which may 

 be present, I m{v) is the unattenuated flux density transmitted from the 

 mth discrete source located at position r^, s is the point of reception of 

 energy, and the other symbols have their previous meaning. It should 

 be recognized that the above integrals extend over a ray path determined 

 by the refractive properties of the medium and cannot be evaluated 

 unless these refractive properties are known. 



In analogy to the temperature dependence of the noise energy as by 

 the Rayleigh-Jeans law, we may, in the microwave region, relate the 

 intensity of radiation received from a particular direction, I{v), to an 

 equivalent temperature, T n{v), by the following relation 



/(^) = ?^ (7.12) 



or, from (7.8) 



TM = ^TnAv) exp(- / "'rfr) 



+ / T^expf-/ dr) dr. (7.13) 



This equivalent temperature is called the thermal noise temperature. 



It is apparent that the thermal noise temperature of the atmosphere, 

 as measured by an antenna, will depend explicitly upon the antenna angle 

 and the frequency, and implicitly upon the atmospheric conditions along 

 the ray path giving rise to attenuation and emission of energy. It seems 

 plausible, therefore, that one could exploit this dependence of thermal 

 noise on atmospheric conditions as a probe of atmospheric structure. 



Thermal noise is equally important in communications receiving, since 

 it represents the lowest possible noise level that can be attained by an 

 antenna immersed in the atmosphere. This minimum noise level will, 

 of course, vary, depending on atmospheric conditions, the frequency, and 

 the antenna orientation. For example, in the microwave region, the 

 antenna noise temperature at vertical orientation may be as low as 1 °K, 

 and in a horizontal position, where more of the lower layers are "seen" 

 the noise temperature may be of the same order as the actual tempera- 

 ture of the lower atmosphere; i.e., around 280 °K. Figure 7.27 shows 

 sky temperature as frequency for various anteinia angles for mean atmos- 

 pheric conditions at Bismarck, N. Dak., during February 1940-43. 



