364 DONALDSON, CHMELA, AND SHACKFORD 
the tornado storm are depicted in Figure 14. The 
areas covered by this well-developed storm are 
much larger than those found in the previous 
ease. During the development of the storm the 
maximum equivalent Z aloft increased, while the 
areas covering the lesser values of equivalent Z 
increased markedly near the surface but de- 
creased somewhat in the upper part of the storm. 
The areas were used to estimate the precipi- 
tated water of hailstone size as a function of 
height in the storm. For the purpose of this com- 
putation, all the precipitated water that contrib- 
utes appreciably to the radar echo was assumed 
to consist of ice spheres of unit density and diam- 
eter 1 em. From Ryde’s [1946] scattering curve 
for ice, a concentration of 1/m* of 1-em ice would 
give an equivalent Z of 10° mm*/m* for a radar 
wavelength of 3.2 em. (An equal concentration of 
7-mm water drops would have a slightly larger 
equivalent Z.) An integration of area by Z at 
various altitudes in the storm was interpreted in 
terms of grams of ice per meter thickness of the 
storm. The results are plotted in Figure 15 for the 
five times during which areas were obtained dur- 
ing the life cycle of the tornado-producing hail- 
storm of July 11, 1958. (The areas of two of these 
times were shown in the previous figure.) The 
early echo (but not first echo) case of July 30, 
1957 is included for comparison; the areas of this 
storm were the solid lines of Figure 13. 
Figure 15 shows a large development at all al- 
titudes in the mass content of large particles 
during the half hour preceding the first tornado, 
which touched down at about 15h30m. During the 
next two hours there is little further development 
except a redistribution of some mass from high 
altitudes to medium altitudes. 
50) 
40 
“3 — EARLY ECHO 
JULY 30, 1957 
The mean concentration of large particles in 
this storm, averaged over the total area of the 
radar echo at the altitude containing the greatest 
mass, ranged from about 0.3 to 1.3 @/m*. (In the 
‘early echo’ storm, July 30, 1957, 15h45m-+, the 
highest mean concentration was only 0.017 g/m’.) 
These values, somewhat lower than those men- 
tioned by Weickmann [1953], suggest that the 
large (1 em) particles, which give the strongest 
radar echo, contribute only a small fraction of 
the total water substance. On the other hand, the 
extremely high values of radar reflectivity in the 
small echo cores aloft indicate mass concentra- 
tions of 9, 19, 35, 170, and 125 g/m‘* in the five 
measurements. Thus, the distribution of large 
particles is extremely spotty, with a surprisingly 
large concentration in the echo core, falling off to 
low concentrations and probably smaller maxi- 
mum sizes as the storm periphery is approached. 
A word of caution is advised in interpretation 
of these water-content estimates. First, all cali- 
brations of weather radars reveal a systematic 
departure of the echo intensity by a factor of 2 to 
5, approximately, below the value expected on 
theoretical grounds. Corrections have been made 
for this factor. If the factor is somehow related 
to the calibration scheme but is not operative in 
meteorological observations, then the water con- 
centrations have been considerably overesti- 
mated. Secondly, attenuation by thunderstorm 
rain and water-coated hail, which is not accounted 
for here, leads to an underestimate of the water 
concentrations by an unknown amount. Finally, 
the assumption adopted regarding particle size 
and state has a marked effect on the water con- 
centration capable of giving the same intensity of 
radar echo. For example, the same radar echo 
15.2 
TOTAL MASS/UNIT HEIGHT ASSUMING | CM. HAIL (GRAMS/ METER ) 
Fria. 15—The relationship of total precipitated water mass per unit height 
to height, during five measurements in the tornado storm of July 11, 1958 
and one in the growing hailstorm of July 30, 1957 
