RADAR STORM OBSERVATION 
where f is a dimensionless factor which depends on the 
design and efficiency of the antenna and parabola 
(usually about 0.6 or 0.7). 
Fic. 1—Antenna parabolas of two of the radars used by 
the M.I.T. Weather Radar Research. The parabolic reflector 
to the left forms a conical beam of circular cross section. The 
one to the right (AN/TPS-10A) forms a “‘beaver-tail’’? beam 
of elliptical cross section 0.7° vertical and 2° horizontal. Both 
radars have an operating wave length of about 3 cm. (MI.T. 
Weather Radar Research.) 
The antenna gain is a term used to express the in- 
crease of power resultmg from the focusing of the 
radiated energy into a narrow beam, in contrast to 
isotropic radiation [49, pp. 18-21]. Microwave radar 
operates at such high frequencies in the radio spectrum 
that the radio energy may be focused by parabolic 
reflectors in a manner analogous to visible radiation 
focused by a searchlight. Directivity is desirable from 
the standpoint of target direction determination; energy 
conservation is necessary for maximum range of de- 
tection. The gain factor is dimensionless and may be 
loosely regarded as the ratio between the power density 
in the beam, resultmg from focusing, and the power 
density which would exist at the same range if the trans- 
mitter radiated isotropically. 
Beam Width, ¢ and @. The beam width is usually 
defined as the angle subtended at the antenna between 
points across the beam where the power density is one- 
half that along the axis. When using this term it must 
be understood that an appreciable amount of power is 
actually present beyond this angle. However, the power 
beyond the half-power point decreases rapidly with 
increasing angle, so for most purposes this definition is 
probably sufficient. If the beam is circular in cross 
section, it may be depicted as a cone with the apex at 
the radar antenna. 
Cross-section figures of radar beams may be in a 
variety of shapes, depending upon the use for which 
the radar is designed [49, pp. 22-28]. Most common 
shapes are circular and elliptical, especially for radars 
useful for storm detection purposes. Elliptical sections 
are employed when high directional accuracy or resolu- 
tion is desired in one dimension and good coverage in 
the other. For example, a radar used for height deter- 
mination would require excellent elevation angle dis- 
1267 
crimination, but only fair azimuthal resolution. It is 
neither easy nor desirable to have a beam with no 
angular spread. It is not easy because the long wave 
lengths (compared to light) would require prohibitively 
large parabolas to bring them into exact focus. It is not 
desirable because the beam would have to be precisely 
pointed at a target in order for the radar to detect it, if 
the target were small in size. For storm detection this 
would be no particular drawback because of the extent 
of most storm cells. However, the difficulty and expense 
of construction and control of large-size parabolas rules 
out beam widths much less than about 1° for radars 
with wave length of operation of about 3 cm. For a 
10-cem wave length radar this angle is at least doubled. 
The subjects of beam width and pulse length (which 
follows) are worthy of careful study by radar meteorolo- 
gists, for these two factors define the volume of space 
which is analyzed and strongly influence interpretation 
of the scope presentations of precipitation. There are 
distortions resulting from the finite beam width in the 
nature of azimuth and elevation angle errors, and from 
the pulse length in the nature of a range error [65, 
pp. 20-22]. 
Pulse Length, h. As beam width affects azimuthal and 
elevation angle resolution, so pulse length affects range 
resolution. Pulse length may be defined either in terms 
of time or length; a pulse one microsecond in duration 
has a wave-train of energy about 300 m long. Two 
targets in the beam of the radar will be resolved if—and 
only if—their range separation exceeds one-half the 
pulse length [65, pp. 17-20]. Extension of the analysis 
to storm detection results in the corollary that energy 
from the particles in only one-half the volume illumi- 
nated by the pulse can reach the receiver at the same 
time. 
The volume illuminated by the pulse is determined 
by the pulse length and the linear distance across the 
beam. The greater the number of scattering particles 
lying within this volume the stronger will be the echo. 
By increasing this volume the signal power of the echo 
may be strengthened, provided this increase in volume 
does not result in a decrease in the transmitted power 
density per unit area normal to the beam. However, loss 
of resolution results both from widening the beam and 
from lengthening the pulse. Therefore, a designer of 
radar equipment for storm-detection purposes must 
balance these factors in order to achieve the best possible 
presentation of the storm. 
Wave Length, \. The evaluation of a radar as a storm 
detector depends to a major extent upon the operating 
wave length. Wave length and frequency are used 
interchangeably in radar discussion, one being related 
to the other by the simple formula: 
c 
where f = frequency (cycles sec”), 
ce = velocity of light (em sec™), 
X = electromagnetic wave length (cm). 
Roughly speaking, a wave length of 10 cm corre- 
