RADAR STORM DETECTION 
bright band is then due to this discontinuous increase 
of the dielectric constant as a film of water develops on 
the exterior of the snowflake. The decrease of signal on 
the bottom portion of the bright band is due to the 
rapid increase of fall velocity as the snowflake approaches 
complete melting. It isnot necessary, however, to assume 
(as Ryde did) a nearly constant fall velocity of the 
snowflake until complete melting, but rather an in- 
crease, rapid with respect to one-half the pulse length; 
this is no serious limitation since the observed width 
of the bright band is of the same order as one-half 
the pulse length. 
Bowen‘ has recently reported the presence of an up- 
per band observed in Australia on about half the occa- 
sions on which the bright band was noted. This upper 
band, first located at temperatures between —12 and 
—17C, was observed to fall slowly towards the bright 
band, merge and intensify, after which the bright band 
and the precipitation below became more intense. There 
was a tendency for the process to repeat itself. Bowen 
ascribed this phenomenon to the freezing of large water 
droplets of about 400- diameter at about —16C and 
their subsequent rapid growth and fall toward the 
surface. If this were true the signal strength should 
first decrease by a factor of 5 and then slowly increase 
as the ice grew by diffusion. 
It is more probable that the upper band is a layer of 
graupel developed in a region of high liquid-water con- 
tent in the upper portion of the cloud. It may be shown 
that there is a critical water content below which crys- 
tals maintain their tabular shape and above which 
crystals convert into graupel of approximately spherical 
shape. Because of their increased fall velocity and effi- 
ciency of catch, graupel, once formed, will grow rapidly, 
by coagulation with the water droplets. A layer of 
graupel will deplete the water in its path rather rapidly 
and a succeeding layer will fall through air of smaller 
water content and will not acquire as great a mass in 
the same distance of fall. As an example, a layer of 
graupel initially of mass 0.001 mg and 150 m in depth 
(and of reasonable concentration) will grow in a cloud 
of 0.5 g m™ liquid-water content to a mass of 0.20 mg 
in a 600-m fall distance. In so doing it will have deple- 
ted the water in its path to an average value of about 
0.38 gm. The next 150-m layer of graupel will grow to 
a mean mass of about 0.1 mg in the same 600-m fall 
distance. Simce the resolving power of a radar with a 
lu sec pulse is only 150 m, the first layer will be ob- 
served to descend as a band of about four times the 
intensity of the second. Subsequently, the formation of 
graupel will cease due to depletion of the water below 
the critical value and will begin again only when the 
liquid water, replenished by the updraft, rises above 
that value. 
Of meteorological interest is the increase in signal 
strength from above, as the bright band is approached, 
as shown in Fig. 3. The ultimate effect of the mcrease 
in dielectric constant and fall velocity is an approximate 
4. Bowen, Ei. G., ‘‘Radar Observations of Rain and Their 
Relation to Mechanisms of Rain Formation.’’ J. atmos. terr. 
Phys., 1:125-140 (1951). 
1287 
equalization of signal. However, A-scope photographs 
generally show a rapid increase of signal strength 
through the bright band, sometimes apparently begin- 
ning at the upper edge as in Fig. 3, but often starting 
from slightly below the OC level. There is generally a 
gradual increase from several thousand feet above, 
where the signal is indistinguishable from the noise 
level of the radar, to almost the OC level. Observations 
made by Austin and Bemis [2] show that the ratios of 
the signal strength from below the bright band to that 
above it vary from 1 to 17, with a median near 5. In 
some cases the signal from above the bright band is 
vanishingly small. Ryde ascribed the increase in signal 
strength from above the bright band as due to the 
aggregation of numerous snow crystals at temperatures 
of about —4C to OC, and Austin and Bemis explain the 
increase in signal strength through the bright band 
(from above) as due to continued aggregation of snow- 
flakes. 
Radar observations of three warm-front rains by 
Browne in Cambridge, England, give the rate of de- 
crease of signal strength with altitude from the 0C level. 
In comparing these observations with the rate of growth 
of ice crystals by diffusion in a supercooled water cloud, 
calculated according to the methods of Houghton [4], 
it was found that the calculated growth rates above 
about the —6C level are not compatible with the ob- 
servations. The observations were found to be com- 
patible with a growth in an ice cloud such that the 
erystals consume within a layer the water produced by 
the updraft and make use of little or no “stored” water 
from below. This result holds for a rate of mass transfer 
of air by the updraft that is constant with height. From 
—6C to —8C the observations are compatible with 
growth in a water cloud. Between —3C and OC the ob- 
served increase in signal strength is greater than could 
be obtained by growth of ice crystals at water satura- 
tion at those temperatures. This discrepancy is ex- 
plained by coalescence of some of the ice crystals as they 
approach the OC level. 
If x crystals of equal mass coalesce, the resultant 
signal strength is x times the original value. To arrive 
at an exponential law of drop-size distribution [6], a 
similar law for coalescence is required. Let the number 
of coalescences of # crystals of equal mass be given by 
nm = noe, then the number of crystals before coales- 
cence is 2 we~** and the ratio of the radar echo from 
the coagulated crystals to that from the individual 
crystals is Dx?e—/Dae—*. For any ratio of signal 
strength from two levels between which coalescence 
is taking place, the constant a can be computed and 
the resultant size distribution calculated. 
The observations and calculations indicate that coa- 
lescence of the particles begins at about the —3C level, 
possibly because of the cohesive effect of the thin 
film of water forming on the crystal at these higher 
temperatures. Below the OC level, coalescence must 
continue in order to account for the increased signal 
below the bright band and the observed drop-size 
distribution at the ground. These conclusions also agree 
with snow observations which indicate individual erys- 
