ATMOSPHERIC ABSORPTION AND SCATTERING 



173 



The iiieasLiremeiits cover i^ractically the whole range 

 of drops which reach the ground in rains, or from 0.05 

 to 0.55 cm. The terminal velocity of these drops varies 

 between 2 and 9 m per second approximately. Figure 

 8 represents another empirical relationship between 

 the liquid water concentration of the rainy atmos- 

 phere and the rate of rainfall. A rough linear approxi- 

 mation to the apparent empirical curve leads to a 

 water content 0.038 g/m^ for each millimeter per 

 hour precipitation rate. But, strictly speaking, there 

 cannot be an analytical connection between the liquid 

 water concentration and the rate of rainfall. Inasmuch 

 as the same rate of rainfall can be achieved by a num- 

 ber of different drop size distributions, therefore, to 

 a single value of the abscissa — the precipitation rate 

 — there may be associated a series of ordinate values 

 or liquid water concentrations. The curves of Figure 

 8 are, therefore, of interest only because they are 

 helpful in predicting very roughly liquid water con- 

 centrations in different rains. 



The subject of Section 10.1.6 is the computation of 

 the attenuation in different precipitation forms, no 

 account being taken of the inherent irregularities. 



Since the size of the drops in fogs and fair weather 

 clouds are small compared with even the shortest wave- 

 length (1.25 em) considered in this report, the one 

 term attenuation formula holds rigorously. Figure 9 

 represents the attenuation curve in decibels j)er kilo- 

 meter in clouds and fogs for a liquid water concentra- 

 tion of 1 g/m^ which, as mentioned above, is an up)per 

 limit. 



A few attenuation values may be given as follows : 



X, cm 

 a/m db/km/gm/m3 



1.25 

 0.28 



3 5 10 



0.049 O.OIS 0.0045 



Even for 1.35-cm waves the attenuation would be- 

 come important only at long ranges for radar observa- 

 tions. For waves of length A > 3 em the attenuation 

 in fair weather clouds and fogs is of no practical 

 importance. 



Table 3, on the critical diameter of water drops, 

 shows that the attenuation becomes p)ractically in- 

 dependent of the drop size distribution in rains for 

 wavelengths longer than about 15 or 20 cm, inasmuch 

 as raindrops whose diameter is larger than 0.55 cm 

 or 0.6 cm do not reach low altitudes. In the 5- to 20- 

 cm wavelength range the three-term attenuation 

 formula will represent fairly well the attenuation in 

 different rains. At wavelengths smaller than 5 cm 

 exact computations of the amplitudes a,„ &„ are nec- 

 essary. 



It is shown that in any rain the attenuation de- 

 pends linearly on the partial precif)itation rates of 

 the different drop groups making up this rain, but 

 it does not depend directly on the total rate of rain- 

 fall. 



Figure 10 purports to show the connection between 

 the drop size distribution in a given rain and the 

 partial or fractional attenuation values in the K and 

 X bands of the different drop groups making up this 

 rain. It is seen that the numerous small drops do not, 

 for practical purposes, contribute to the attenuation, 

 which is due mainly to the bigger drops. 



Table 9 contains attenuation values of different 

 rains of known drop size distribution and rate of rain- 

 fall. Figure 11 is a graphical representation of these 

 results. It will be seen that at the shorter waves the 

 attenuation may become important in heavy rains. 



Figures 12, 13, and 14 are graphical representa- 

 tions of certain results included in Table 9 at K-, 

 X-, and S-band wavelengths, respectively. The attenua- 

 tion values corresponding to the points in these graphs 

 have been computed for the rains of Table 9, and we 

 have drawn a curve through the computed points. 

 Accordingly, the plot of attenuation as a function of 

 total precip>itation is a mass plot. That is, for any 

 given total p)recipitation the attenuation will have 

 different values, depending upon the distribution of 

 the drop size for the rain in question. Figures 13, 

 13, and 14 represent mass plots of the meager data 

 available for K, X, and S bands, respectively, together 

 with the limiting curve that woidd result if all the 

 drops were of the size that gives maximum attenua- 

 tion. Tables 10 and 11 contain, respectively, the theo- 

 retically predicted upper limits of attenuation for 

 water drops around 1S°C and the experimental atten- 

 uation per unit rate of precipitation. In view of the 

 difficulties in the interpretation of the ex2Derimental 

 data, it may be said that there is fair agreement be- 

 tween the observed and predicted attenuation values 

 in rains. 



The attenuation due to hailstones and snow should 

 be considerably smaller than that caused by rain. The 

 reason for this difference is due to the small dielectric 

 absorption of ice as compared with the dielectric ab- 

 sorption of liquid water. 



Section 10.1.7 deals with the total scattering (in 

 the whole solid angle) of microwaves by spherical 

 water drops. The scattering cross-section fornmla is 

 given in a series of ascending powers of p = ttD/X, 

 the first term of the series being p*"'. For small 



