2.46 

 4.0 

 6.0 

 15.2 

 18.7 

 22.6 

 34.3 

 43.1 



2.94 10-5 

 5.06 10-5 

 1.4410-'' 

 6.12 10-4 

 6.67 lO-i 

 5.69 10-'' 

 1.2810-3 



4.21 10-6 



7.31 10-6 



2.32 10-5 

 1.73 10-'' 

 1.27 10-4 



1.01 10-4 



3.02 10-4 



7.01 10-' 

 1.1710-6 

 3.90 10-6 

 3.30 10-5 

 2.22 10-5 

 1.74 10-5 

 5.58 10-5 



2.86 10-' 

 4.81 10-' 

 1.61 10-6 

 1.41 10-5 

 9.25 10-6 

 7.24 10-6 

 2..36 10-5 



5.74 10- 

 9.63 10- 

 3.25 10- 

 2.94 10- 

 1.90 10-6 

 1.47 10-6 

 4.90 10-6 



1.82 10-s 

 3.03 10-s 

 1.17 10-' 



7.62 10-' 

 6.51 10-' 

 4.91 10-' 



1.63 10-6 



3.60 10-9 

 5.99 10-9 

 2.31 10-s 

 1.50 10-' 

 1.28 10-' 

 9.70 10-8 

 3.22 10-' 



4.66 10-i» 

 7.76 10-i» 

 2.99 10-9 

 1.94 10-s 

 1.06 10-s 

 1.26 10-s 

 4.17 10-s 



9.20 10-11 

 1.. 53 10-19 

 5.91 10-10 

 3.S3 10-9 

 3.28 10-9 

 2.49 10-9 

 8.24 10-9 



2.91 10-11 

 4.85 10-11 



1.87 10-19 

 1.21 10-9 

 1.04 10-9 



7.88 10-19 

 2.61 10-9 



A 

 C 

 D 

 E 

 F 

 G 

 H 



1.8310-3 4.8910-4 9.1610-5 3.9010-5 8.14 10-6 2.6610-6 5.26 10-' 6.82 IQ-s 1.35 10-s 4.2610- 



baek scattered per unit thickness of the scattering 

 medium, Tallies 14 and 15 allow the computation and 

 estimation of the echo power to be expected in radar 

 observations under given conditions. The difficulties 

 which seemed to exist earlier are cleared up Ijy assum- 

 ing that in those clouds which give rise to echoes pre- 

 cipitation actually' occurs, even though no rain reaches 

 the ground.^'' This is substantiated to some extent by 

 recent work^^ which succeeded in verifying Eayleigh's 

 law by observing cloud echoes simultaneously with 

 both S- and X-band radar sets. Further proof was 

 added by the Canadian group/* whose exhaustive 

 study in the S band clearly showed the role of rain- 

 drops in cloud echo phenomena. In fact, these workers 

 stated that there was no record of an echo without rain. 

 It is interesting to extract from Table 15 the frac- 

 tion of the incident power back-scattered from differ- 

 ent rains of 1-km depth expressed in decibels. As just 

 mentioned, the power back-scattered by a thickness 

 A.r is 



AP. = -2a, Pi Ax, (71) 



and the fraction of the incident power I'i scattered 

 backward by a layer A.r = 1 km is then 10 logm Af ^/ 

 Pi db or (10 logic, 2*^) 'lb (53(^) is given in Table L"). 

 The results are included in Table 16. 



With Tal)le 16 and the known sensitivity of a radar 

 set, the maximum free space distance from the set at 

 which these rains are observable can be computed at 



Table 16. Power scattered backward by a layer of 

 1 km of rain in different rains (decibels). 



once. The peak power received by 

 Volume 3. Cliapters 2 and 9, is 



a radar set from 



P2 — Pl(jlCr2 



4:TT(P Uirr// 



where P^ is the transmitted power (peak power), 



Gi and Go are respectively the transmitter and 

 receiver antenna gains relative to a doublet, 

 d is the distance of the set from the echoing 

 rain drops, and 

 S^ is the back scattering cross section. 

 The beam usually intersects the rain boundary and 

 therefore it can be assumed that 8^ is made up of the 

 combination of all the drops included in the echoing 

 volume. This volume may be taken as a spherical shell 

 of thickness Arf whose ba.se is a spherical segment of 

 area 



2«/2(l - cose), 

 26 being approximately the half-power beam width of 

 the set. 



The rain echo cross section is then 



,S, = 2tcP (1 



cos I 



Ar/2iV,<^:(T)] 



Here the summation extends over all the different drop 

 groups forming the rain and cri(7r) is the differential 

 cross section for back scattering in the direction tt with 

 the direction of propagation of the initial beam. It 

 should be remembered that ai{-n-) is the cross section per 

 unit solid angle. Hence, the received peak power, 



for small ^ (^ in radians ) . The quantity [X^V; (i") Ad] 

 is tabulated in Table 16 for Arf = 1 km and the 

 different rains of Table 7. It is thus clear that the 

 knowledge of the set characteristics permits at once the 

 computation of the received power echoed by a rain 

 falling at a certain distance r from the set provided 



