ATMOSPHERIC ABSORPTION AND SCATTERING 



161 



It may be lueiitioiied. here that the earlier atlemiatioii 

 experiments on 1-cm waves by Eobertson and his col- 

 laborators-^ as well as those of Mueller^ on K/3 band 

 were made over a shorter path (about 400 meters) 

 and the rate of rainfall was measured only at one 

 place, roughly in the middle of the path. Since the 

 path length of the Oxford workers-^ was 2 km, there 

 was ample room for possible fluctuations in the rate 

 of precipitation. The K-band radar transmission 

 studies by the Bell Telejahone Laboratory workers 

 were made over longer paths,'^ and here, too, a situa- 

 tion somewhat similar to those reported by the Eadia- 

 tiou Laboi'atory workers might have existed, as the 

 authors duly noticed it. 



The meteorological irregularities which thus seem 

 to be inherent in precipitation data eliminate the pos- 

 sibility of a quantitative theory of attenuation and 

 back scattering of radiowaves hj rains or other pre- 

 cipitation forms. Although the data contained in 

 Table 7 are used extensively in this report, the re- 

 sults thus obtained should be regarded as semiquan- 

 titative indications rather than rigorous theoretical 

 predictions. 



Given the number of raindrops of known dimen- 

 sions falling over a certain area in a given time and 

 given also the terminal velocity of the drops, the 

 spatial concentration of raindrops can be derived at 

 once. In Figure 7 the terminal velocity curve is drawn 



9 



■ 



7. 



6 



S 



4 J 



3 -^- 



vL — 



0.0 5 aio ai5 ol2o 0.25 030 ojs 0.40 0.45 0.50 0.55 



DROP DIAMETER IN CM 



Figure 7. Terminal velocity of raindrops (experi- 

 mental). 



as a function of drop diameter. These velocities were 

 measured at Porton and are quoted in Best's paper." 

 From Table C we may obtain data for Table 7, 

 giving raindrop concentration iV^ of drops with diam- 

 eter l^B cm. These concentrations, as are the data in- 

 cluded in Table 6, may be regarded as characteristic 

 for rains of the indicated precipitation rate, but they 



are not necessarily typical for tiiose rains. Also given 

 is the liquid water content of the atmosphere as- 

 sociated with the rains of Table 6 and its graphical 

 representation in Figure 8. The curve drawn on this 

 graph should not, however, be considered as represent- 

 ing any functional relationship between the liquid 



10 20 30 40 



PRECIPITATION RATE IN MM PER HR 



50 



Figure 8. Computed liquid water distriljution (cm'/ 

 m^ or g/m^) based on experimental drop size distribu- 

 tions in different rains. The slope of the straight line 

 approximation is 0.038 g/mVmm/hr. 



water concentration of the rainy atmosphere and the 

 rate of rainfall. It can indeed easily be proved that 

 the liquid water concentration associated with a rain 

 depends only on the fractional precipitation rates of 

 the different drop groups. It does not depend directly 

 on the total rate of rainfall. Any rain of given total 

 precipitation rate can be built up by a number of drop 

 size distributions which determine different liquid 

 water concentrations in the atmosphere. This means 

 that it is tlieoretically incorrect to draw a graph entitled 

 "Liquid Water Concentration versus Rate of Rainfall", 

 as is frequently done. A curve so drawn can howe^'er be 

 of considerable practical value when rough concentra- 

 tions corresponding to given rates of rainfall are 

 desired. 



It can be seen that the resulting liquid water dis- 

 tributions are in fair agreement with those reported 

 by Humphreys in his table of precipitation values^" 

 already mentioned. It may be added here that aloft 

 and in certain parts of rain clouds, where considerable 

 updraft exists, the drop concentrations may be ex- 

 pected to be larger than those derived from Table 6. 



These data will now be used in the computation of 

 attenuation and back scattering by the different pre- 

 cipitation forms, assuming always ideal conditions 

 and lea\ing aside the alwve-mentioned irregularities 



