356 
near an echo top measurement thought to be in 
the ‘no hail’ category. 
Another error is inherent in the timing of the 
ground events relative to the echo-top determina- 
tion. Douglas [1959] associated echo tops with the 
appearance of hail or rain 20 min later at the 
ground, allowing time for the precipitation to 
0.9 
0.8 
0.7 
3 
20.6 
w 
> 
Ss 
w 
« 
u | 
w 
ce 
< 
iy) mol 
> 
= 
> 
° 
a 
Sei 
++. NO HAIL,450 OBSERVATIONS 
———— HAIL SMALLER THAN 3/4" 
0.1 r 92 OBSERVATIONS 
HAIL 3/4" AND LARGER 
* 39 OBSERVATIONS 
= / 
° [ee 6 ee os ee ee ————— —}} 
-20 -10 ° 10 20 
HEIGHT (THOUSANDS OF FEET ABOVE TROPOPAUSE) 
Fic. 3—Cumulative frequency distribution of 
thunderstorm echo top penetrations above and be- 
low the tropopause 
CUMULATIVE FREQUENCY 
12 
DONALDSON, CHMELA, AND SHACKFORD 
fall. The timing used in the present study is a 
rough attempt to relate hail production to con- 
vective forces that result in the increase or main- 
tenance of echo-top height. The optimum timing 
relationship probably lies somewhere between 
those adopted by the two investigations. 
Other errors are randomly distributed. They 
include echo-top height measurement, with a 
mean error estimated to be about +2000 ft; un- 
certainties in a few of the tropopause height de- 
terminations; and deviations in time and space 
(up to six hours and 150 mi) of the Albany radio- 
sonde from conditions at an echo-top measure- 
ment. Hopefully, the sum of these random errors 
should tend to zero in a distribution of many 
cases. 
The few special cases of extreme penetration 
are interesting. Echo tops pushed 10,000 to 15,000 
ft above the tropopause on five days during the 
three years studied (two complete years and part 
of a third). Tornadoes oceurred on four of these 
five days. The maximum penetrations of the par- 
ticular tornado storms were 8, 10, 13, and 15 k ft. 
On the fifth day widespread hail occurred with 
extremely severe electrical storms (45 houses 
were struck by lightning in one town alone) ; the 
maximum penetration on this day, 12 k ft, was 
related with the fall of one-inch hailstones. The 
negative energies overcome by the tornado storms 
ranged from 1.6 * 10% to 3.0 x 10° ergs/gm, or 
2 to 5 times the median value for hailstorms 
with %4-inch or larger hail. The severe lightning 
storm with one-inch hail had to overcome the 
greatest negative energy found during the entire 
study, 34 x 10° ergs/gm. These extreme cases 
NO HAIL, 450 OBSERVATIONS 
HAIL SMALLER THAN 3/47, 92 OBSERVATIONS 
HAIL 3/4” AND LARGER, 39 OBSERVATIONS 
20 24 
ERGS/ GRAM OF AIR xX 10° 
Fic. 4—Cumulative frequency distribution of negative energy required 
for thunderstorm echo top penetration above the tropopause 
