WMOD00434

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

2178

JOURNAL OF THE ATMOSPHERIC SCIENCES

VOLUME 35

2 3
DIAMETER (mm)

FIG. 8. Change in the size distribution of heavily rimed plane dendrites
due to collision with graupel.

E
::I.
g 0.10
I
~
....
""
z
o
fi
'0::
!z 0.05
ILl
u
Z
o
u

::"i:-:r-i:.J --~
,i Ji ~::d=;:,.......:
~ r- - 1_-t:J........ :r.o

o .
o

efficiency. The rates assumed in this model were
1 ,um S-I for moderate growth and 4 ,um S-I for heavy
growth on crystals> 300 ,um.
The model was run for 15 time steps of 60 s each
for several different' conditions. Fig. 7 shows the
results of these computations. The solid line is the
case of K(/) equal to a constant Ko=0.00081. For an
initial concentration of 1 crystal litecI it would take
over 20 min to increase the concentration by a factor
of 10 but only 6 min for an initial concentration of
3 crystals liter-I. If one looks at the curve for no
additional accretion and diffusion one notices that
after a short period of time, it levels off, and never
reaches a factor 'of 10 greater than the initial con-
centration. This was found to be true for all crystal
types and size distributions studied. The result should
not be surprising when one considers the fact that
without additional growth by accretion and diffusion
a single crystal will only produce so many fragments.
The calculations show that an average crystal will
produce less than 10 fragments unless additional
growth occurs. In many cases fewer fragments will be
produced because the fragments are too small to
produce additional fragments at their reduced fall-
speed. In a real cloud this is probably even more valid
because a fragile crystal is less likely to produce frag-
ments in a second collision of the same magnitude as the
first. All or most of the fragile protrusions are broken off
in the first collision.
The other curves show an increase in C greater
than that for K (I) = K 0 depending on the rate of
accretional and diffusional growth. This effect seems
physically valid because accretional and diffusional
growth can maintain the size distributions and the
fragility of the crystals such that K (I) may actually
increase. K (t) was found to increase slightly at first
with accretion and diffusion and then decrease but

--- TIME = Ominutes
........... TIME = 5 minutes
- TIME = 10minutes

(0)

4

5

at a much slower rate than without accretion and
diffusion. Depending on the rate of growth by accre-
tion and diffusion, then, the generation of secondary
particles may be more or less than that estimated hy
assuming K (I) = K o. For the largest growth rate likely
the generation rate was found to be greater by a factor
of about 10 over that previou~ly estimated. In the
case of no accretion or diffusion the multiplication
ratio is limited in all cases to less than a factor of 10.
It is quite informative to observe the change in
crystal distribution with time as the fracturing and
growth by accretion and diffusion occur. Figs. 8 and 9
show the size distributions for the heavily-rimed plane
dendrites and graupel respectively at 0, 5 and 10 min
after fragmentation is assumed to begin. This example
is the case for moderate accretion and diffusion with
an initial concentration of 1 crystal litecI in Fig. 7.
Notice the accelerating change in concentration of
crystals at the small sizes and the regular progression
of crystal concentration to larger sizes by accretion
and diffusion. Apparently, the accretion and diffusion
were able to cause an increase in K (I) at first but
the explosion of small particles eventually overwhelmed
the accretion and diffusion effects by changing the
shape of the distribution drastically. In a real cloud
this effect could be even more dominant because of
the effect on the vapor pressure and liquid water as
many small particles begin to grow. This model did
not attempt to maintai~ a water balance. Another
important restriction on the model results is the as-
sumed diffusional growth rate at -150C. If the air
parcel containing the ice crystals rises or falls to
another level the growth rate will fall and the secondary
particle generation will be less effective. If accretional
growth remains high, however, the effect of change
levels could be small.