PLUME FORMATION IN THUNDERSTORMS 97 
formed. Such a comparison is attempted in the 
subsequent sections. 
Derivation of plume patterns from the winds 
—The trail followed by particles of given fall 
speed continuously released into the atmosphere 
can conveniently be constructed by the simple 
graphical method developed by Douglas, Gunn, 
and Marshall [1957] for the derivation of the 
pattern formed by snow trails from generating 
cells. Figure 5a shows such a trail, derived from 
the wind hodograph of Figure 4. Each straight- 
line segment represents the pattern swept out by 
particles falling through successive 1000-ft layers. 
The lengths and directions of these segments of 
the trail are calculated according to 
AS = (W — W,.)AZ/v 
Here W is the wind representative of the layer, 
and W, is the wind of the point of origin of the 
particles (the wind at 35 kft in this example) ; 
AZ, the thickness of the layer, was taken to be 
1000 ft, and v represents the fall speeds of the 
echo velocity: 45mph 
particles in that layer. A proportional variation 
in the fall speed at all heights leaves the shape 
of the trail unchanged, but affects the scale. For 
v = 1 ft sec‘, the over-all length of the trail as 
pictured here (from its origin at 35 kft to the 
point where it reaches 10 kft) is in excess of 
200 mi. For v = 2, or 4 ft sec”, this length would 
be just over 100 or 50 mi respectively. The time 
corresponding to each segment is 1000 see (16.7 
min) for 1-ft sec” particles, and 500, and 250 
sec respectively for particles falling twice and 
four times as fast. The trail pattern as a whole 
must be imagined to move eastwards at 45 mph 
(the velocity of its origin) so that as long as the 
parent storm is robbed of material at 35 kft, the 
trail will appear to remain in contact with the 
storm echo. The pattern of a trail originating 
at any level below 35 kft, say at 30 kft, is given 
by the part of the trail below the point marked 
30 kft. 
The length and direction of plumes at given 
heights (as they might appear on ideal CAPPI 
AY 
Np ve2ft sec-! 
ee 
AS 
\ 
N 
Plume ot 3Okft 
\ 
\ 
x \ 
\ 
#t (from 35kft) 
NN 
NG 
NOS, vel, 25000 
XN 
Plume ot 25kft \ 
(from 35kft) Zak 
\ \ ina 
echo  velocity=45mph 
30 
XS « Nees 4 
! 
Plume at 25kft | 
(from cated / 
Ms 
Fie. 5—Derivation of plume patterns from the wind hodograph; (a) the trajectory of a particle de- 
scending at v = 1 ft sec”! from 35 kft through the wind field of Figure 4; trajectories of faster particles 
are identical, but scaled down in size proportional to 1/v; (b) heavy dashed line joining 35 and 30 kft rep- 
resents locus of positions of particles originating in storm at 35 kft, reached after descent to 30 kft; 
this line suggests the plume pattern at 30 kft formed by particles of fall speed 1 ft sec! and up (part 
of the plume pattern formed by the same particles at 25 kft is also shown); (c) dashed line here suggests 
plume at 25 kft formed by particles released at 30 kft 
