1268 
sponds to a frequency of 3000 mc sec. During the war, 
radar wave length of operation was highly confidential 
information, since radar countermeasure development 
by the enemy was considerably facilitated if this was 
known to him. Accordingly, wave lengths on which 
radars operated were designated by letters: S-band for 
10 cm; X-band for 3 em; and K-band for about 1 cm. 
Thus, a radar with an operating wave length of 10 cm 
was called an ‘‘S-band” radar. These designations have 
persisted since the war, and are utilized in this article 
to familiarize the reader with terms widely encountered 
in the literature. 
The radar energy back-scattered toward the receiver 
by a raindrop is inversely proportional to the fourth 
power of the wave length if Rayleigh scattermg [48] 
applies. However, absorption and attenuation of the 
scattered energy may become great enough at very 
short wave lengths to restrict maximum range seriously, 
and a compromise value of wave length must be used. 
Speaking im general terms, we may say that for use in 
areas of very heavy rainfall a wave length of about 10 
cm is best, while in regions where the average drop size 
is somewhat smaller, a wave length of about 3 cm is 
desirable [15,16]. From an analysis of this problem it 
seems that a storm-detection radar should be designed 
for the climate in which it is to be used [68]. Many 
authorities agree that the best “all-round” frequency 
for storm-detection radar equipment would probably 
be about 6000-7000 me sec™!, corresponding to a wave 
length near 5.5 em. 
Reflectivity Per Unit Volume of the Storm Region, 7. 
This is a measure of the energy back-scattered by 
particles in the storm. It is a function of the number of 
particles per unit volume, their size distribution, the 
frequency of the energy scattered [65, pp. 30-34], the 
composition of the particles, and their shape and aspect. 
The process of electromagnetic scattering by hydro- 
meteors is similar to that of the scattering of visible 
radiation by large molecules, by which the color of the 
sky is explained. Fundamental laws of scattering devel- 
oped by Rayleigh [48] and Mie [45] were applied by 
Ryde [50] to the special case of electromagnetic scat- 
tering and diffraction by raindrops. It was found that a 
spherical particle which is small relative to the wave 
length of radiation fallg upon it scatters the energy 
proportionally to the sixth power of its diameter [49, pp. 
33-66]. This mdicates that if the size of a drop is 
‘loubled, its scattering efficiency is increased by a factor 
of 64. Therefore it is evident that size is of much greater 
importance than number in the determination of re- 
flectivity. Reflectivity per unit volume turns out to be 
a function of N R® where N is the number of drops and 
R is their radius. However, when the drops become 
large compared to the wave length (2R > X/10), 
“Rayleigh scattering” no longer applies and the exact 
dependence of the scattering cross section upon 2 is 
a complex function. 
The composition of the particle affects its dielectric 
properties, and therefore its efficiency as a scatterer. 
For example, water has a greater dielectric constant 
than ice, hence for two spheres of equal diameter, one of 
RADIOMETEOROLOGY 
water and the other of ice, the water sphere will scatter 
about five times as much electromagnetic radiation of 
3- or 10-cm wave length. Shape and aspect are im- 
portant for nonspherical particles, therefore the prob- 
lem of evaluating the power of the echo from snow is 
difficult. 
If the rainfall intensity is known and one assumes a 
drop-size distribution in accordance with Laws and 
Parsons’ data [88], it is possible to compute the re- 
fleetivity per unit volume [6]. It is necessary, however, 
to assume that this reflectivity remains constant 
throughout the area covered by the radar beam (or 
fills a known fraction of it). The fact that reflectivity 
per unit volume is not a unique function of drop-size 
distribution greatly complicates the problem of de- 
termination of rainfall intensity by radar. At present, 
measurement of a given level of echo-signal power in- 
dicates only that the rainfall at that poimt lies within 
certain limits of intensity. This conclusion becomes evi- 
dent when one realizes that a few large drops can give 
an echo signal equal to that from many small drops. 
An additional factor which should be mentioned in 
connection with reflectivity is the variability of the 
back-scattered energy. This energy fluctuates rapidly 
with time because of interference between the electro- 
magnetic waves scattered by a large number of moving 
drops. The received power P, is the average power of a 
number of individual precipitation echo signals [49, 
pp. 81-85]. 
Attenuation Factor, k. During passage through the 
atmosphere between antenna and storm the electro- 
magnetic energy radiated by the transmitting antenna 
and scattered by the precipitation particles suffers at- 
tenuation due to several causes: (1) water-vapor and 
oxygen absorption, (2) molecular scattermg by atmos- 
pheric gases, and (3) hydrometeor scatterig and ab- 
sorption [51, 63, 65]. 
The problem of electromagnetic atmospheric attenu- 
ation, being a question not confined to the field of radar, 
has received the attention of a number of investigators 
[18]. Tables have been constructed giving attenuation 
in the free atmosphere and in rain in terms of decibels, 
as a function of path and wave length [49, pp. 58-62]. 
Precipitation attenuation is not a serious factor until 
drop sizes become appreciable in comparison to the 
wave length (about 140 or larger). Because large drops 
are frequently present in thunderstorms and tropical 
rain, X-band (3-cm) radar may sometimes not be the 
best for observation of storms of these types [13]. Rain 
attenuation and atmospheric absorption are seldom ob- 
served with S-band (10-em) radars. 
Fraction of the Beam Filled by the Storm, y. Determi- 
nation of the magnitude of this factor under certain 
conditions is difficult or impossible, but its significance 
cannot be minimized. The echo signal from a weak 
storm which fills the beam may equal that from a strong 
storm which only partially fills it, but at present it is 
‘not possible to tell from signal characteristics alone 
what the true condition is. The distances between half- 
power points at various ranges for beams of different 
angular widths are listed in Table I; it will be seen that 
