AHSOKPTIOft AM) SCA I TKHIiNC in CLOUDS. FOG, KAI1N. IIAII,, AND SNOW 



89 



rain front is usually wider than the irradiated area 

 SO that the radar beam intersects it. Under these 

 conditions, taking Al" approximately as a spherical 

 shell of thickness Ad, at a distance d from the radar 

 set, and denoting by 20 the half-power beam width 

 of the radar beam, one gets 



AV = 2ird- (1 - cos 6) Ad . (20) 



The rain echo cross section is then 



S(t) = 2ird- (1 - cos 6)(Ad ^ n t a t (w)\ . (21) 



Remembering that o-,(x) or S(ir) is precisely the cross 

 section per unit solid angle in the direction of the 

 radar set, one gets instead of equation (6) for the 

 ratio of received to transmitted power 



Pi 

 Pi 



CrjG'2 



3X 

 M 



e-[AdJ . nta, (x) (22) 



for small angles 6 which must be given in radians. 



Table 15. Fraction of incident power scattered back- 

 ward by a layer of 1 km of rain in different types of rain. 

 (Decibels) 



Drop size 

 distri- p, 

 bution*mm/hr 



Wavelength in centimeters 



5 8 10 15 20 30 50 



-45 -54 -61 -65 -72 -77 -84 -93 



-38 -46 -54 -58 -65 -69 -76 -85 



-32 -37 -45 -48 -55 -61 -68 -77 



-29 -35 -42 -46 -53 -58 -65 -74 



-27 -33 -40 -44 -51 -56 -63 -71 



*See Table 11 for drop size distributions. 



The quantity [AdL t n t c t {v)] or its value in decibels for 

 known drop size distributions has been tabulated in 

 Table 15. With this table and the known characteris- 

 tics of a radar set the ratio Pi/ Pi can be computed 

 at once. In the table Ad is taken as 1 km. Since the 

 maximum thickness Ad cannot exceed the pulse 

 length, the values found in the table can be adapted 

 immediately to any pulse length I by adding to it 

 (10 logio T), I being expressed in kilometers. Using 

 equation (22) for particular radar sets it is found 

 that the theoretically computed echo powers from 

 rains agree well with the observed values, if the 

 uncertainties of the meteorological knowledge of the 

 echoing elements, which are mostly rains and storm 

 clouds, is kept in mind. As expected, the echoing 

 power of snow is very much less than that of rain. 

 The systematic observations on S band by the 



Canadian group 4 " 2,122 and on X band by Bent 42 ' 

 clearly indicate that precipitation either in the form 

 of rain or snow is necessary to produce an echo on 

 the scope of the radar set. 



Absorption by the Atmospheric Gases 



It was predicted that oxygen and water vapor will 

 absorb electromagnetic waves in the microwave 

 range. 259,275 In particular, oxygen was predicted as 

 having a resonance band around 5 mm and one line 

 at 2.5 mm, while the water vapor absorption is caused 

 mainly by a single rotational line of relatively small 

 strength around 1 cm. Experiments have confirmed 

 both these absorption effects. 272,273 In Figure 5, the 



100.0 



20.0 



10.0 



5.0 



2.0 

 1.0 

 .5 





m 

 Q 



CE 

 O 

 CO 



III 



< 



.2 



.1 

 .05 



.02 

 .01 

 .005 



.002 



.00 



.0005 



.0002 

 .0001 



3.0 6.0 9.0 15 30 60 90 

 FREQUENCY IN I0 3 MC *■ 



150 



10 



1.5 



1— 

 0.8 



- 1 — i — i r 



0.5 0.4 03 0.2 



-X IN CM 



Figure 5.(1) Absorption due to water vapor in an atmos- 

 phere at 76-cm pressure containing 1 per cent water 

 molecules, or 7.5 g per cu m. The water resonance line is 

 assumed to be at 24,000 mc, and its half width at half 

 maximum (line breadth) is 3,000 mc. (2) Absorption 

 due to oxygen in an atmosphere at 76-cm pressure whose 

 resonance band at 60. 10 3 mc is supposed to have a line 

 breadth of 600 mc. 



