230 REFLECTION AND TRANSMISSION OF RADIO WAVES 



In the presence of absorption, an additional factor is required in the radar 

 equation. This factor is 



lO-o.2adbR (4_81) 



where adt is the one-way attenuation in db per unit distance. 



4-16 ATTENUATION AND BACK-SCATTERING BY 

 PRECIPITATION 



Solid particles suspended in or falling through the air can affect radar 

 operation both by the attenuation to waves passing them, and by the 

 clutter due to back-scattering from them. The attenuation is a combination 

 of absorption by the particles and scattering out of the forward beam. The 

 particles which are most frequently encountered are those due to precipita- 

 tion — viz., water, snow, and ice (hail). Of these, only water absorbs 

 strongly, so that its attenuation is caused mainly by absorption. We shall 

 give here only some salient features of the attenuation and back-scattering 

 by precipitation, since rather complete summaries have been given in the 

 literature. ^^'^^ 



For liquid water drops, the attenuation caused by absorption is much 

 larger than that caused by scattering. For small drops (7rD/X<5C 1), the 

 absorption is proportional to D^ while the back-scattering is proportional 

 to D^. Hence the attenuation through small rain drops is proportional to 

 the total liquid water content, but the back-scattering is proportional to 

 SD^. Thus the larger drops are much more effective in back-scattering than 

 the smaller ones. 



Because of the dispersion of water in the microwave region (see Para- 

 graph 4-15) the attenuation varies in a complicated way with frequency, 

 and also with drop size. The total attenuation is the integrated effect of all 

 the drops in the beam between the radar and target, and thus depends on 

 the drop size distribution, the drop density (number of drops per unit 

 volume), and the length of the path through the precipitation. Drop size 

 distribution is known only imperfectly, since most measurements have been 

 made by catching rain drops af the ground. The distributions are then 

 usually related to the precipitation rate. These may not be the same as the 

 distribution and drop density encountered aloft. A further complication is 

 that the precipitation density usually is not uniform for any great distance 

 through the precipitation region. Hence the calculations made on the basis 

 of such measurements necessarily must be considered as only approximate 

 estimates of the actual effects which may be experienced. 



^The wartime research is summarized on pp. 671-692 of the reference of footnote 33 above. 

 ^^K. L. S. Gunn and T. W. R. East, "The Microwave Properties of Precipitation Particles," 

 ^uart. J. Roy. Meteorol. Soc. 80, 522-545 (1954). 



