WMOD00434

• Title: The Generation of Secondary Ice Particles in Clouds by Crystal-Crystal Collision
• Date: 11/11/1978
• Weather Modification - Doc Type: Report

2176

JOURNAL OF THE ATMOSPHERIC SCIENCES

VOLUME 3S

60

50

- Unrimed Plane Dendrites
-- LGT-MDT Rimed Plane Dendrites
........... HVY Rimed Plane Dendrites
-..- LGT- MDT Rimed Spatial Crystals
-.- Graupel

I

../;././
/....,/
/.:........../

/.. ......./.. ---

../ ././ ~.;...-~
~ ......... ...--;::;.---"'-
....,.,......- ~'l'::"-----_"-
.--" ....

40

z 30

20

10

o
10-5 10-4 10-3 1()2 10-' 100
l:.M (gm-cm/sec)

FIG. 6. Composite fragment generation functions for all five crystal types studied showing
the number N of fragments produced per collision as a function of the change of momentum
!!.M in the collision.

depending on the initial crystal type and size distribu-
tions, on the size distributions of the fragments which
are produced in the cloud and on the rate of accre-
tion and diffusion which takes place on the original
crystals and fragments. Since these factors change in
a time-dependent manner, a general analytic fnnction
for K (t) is not obtainable. Therefore, a numerical
model was constructed to approximate the change
in K (t) and integrate (17) in time.
The model was used in two modes: 1) to determine
the best crystal combinations and size distributions
for generating secondary particles and 2) to determine
the magnitude of secondary particle generation for
a specific time-dependent case. In the first mode the
model was run for one time step for each of 252 dif-
ferent crystal types and size distributions combina-
tions. Ko was determined for each combination. The
largest Ko's indicated the best crystal types and size
distributions for generating secondary particles. In the
second mode the model was run for fifteen time steps
for special cases. In these computations K (t) varied
with time and, consequently, C(t) had a different form
from that when K (t) was' equal to a constant K o.
The magnitude of secondary particle generation was
found to be less than the case for K(t)=Ko with some
assumptions and greater for other assumptions.

b. Determination of optimum rate const(Jnts

The numerical model was run with combinations
of the five crystal types. Including the combinations
of each crystal type with itself, fifteen possible com-
binations existed. Within a given combination of two
crystals, four size distributions for each type of crystals

were studied giving sixteen values of K 0 for each of
the fifteen combinations or a total of 240 values of Ko.
The following features of crystal-crystal collisions were
found from the distributions of K 0:

1) The broader the size distribution the larger the
value of K o. Reviewing from Section 2 we recall that
the larger Ko, the greater the generation of secondary
particles for a given crystal concentration. Thus, we
can say, the broader the crystal distribution the
greater the secondary particle generation. This effect
is most likely due to the greater concentration of
crystals at the larger sizes for broad distributions.
The larger the crystal size the larger the relative
velocity and the more fragments produced in a col-
lision. The collision frequency increases as the square
of the concentration so that more crystals at large
sizes rapidly increases the secondary particle generation.
2) Unrimed plane dendrites should not generate
secondary particles among themselves. Ko was equal
to zero for all sizes distributions studied. Since den-
drites appear to be the most fragile unrimed type of
crystal, this finding would seem to imply that no
unrimed crystals may produce secondary particles by
mechanical fracturing. However, plane dendrites also
have the lowest terminal velocity for a given crystal
size and other crystals which appear less fragile may
still produce fragments because of their greater fall
velocities. We find; however, that the magnitude of Ko
for even rimed crystals' is so small that a statement
to the effect that unrimed crystals' cannot generate
secondary particles is probably correct.
3) The greater the amount of rime the larger Ko
and consequently, the greater the secondary particle
generation. This finding is similar to that obtained