WMOD00434

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

N.OVEMBER 1978

2177

LARRY VARDIMAN

1000

. .

directly from the fixed-plate experiment. However,
the result here is much more impressive. In the fixed-
plate experiment the effect of greater riming was to
increase the fragment genera.tion by a factor of 2 or 3.
Here, the generation of secondary particles may be
increased by orders of magnitude. The reason is that
riming not only increases the fragility of a crystal
but also increases the fall velocity whereby the col-
lision frequency is increased. Therefore, the model
calculations take both effects into account and the
influence of accretion is quite strong.
4) The magnitude of Ko for the combination of
crystal types and size distributions which are likely
to occur in smooth winter orographic clouds or other
cold stratification clouds, is not large enough to cause
secondary particle generation of great significance.
Only convective cells which can generate heavily
rimed crystals with broad distributions can have large
Ko's and thus generate secondary particles in large
quantities. Even here the initial concentration of
crystals must be greater than 0.1 crystal per liter in
rather extreme instances for secondary particle gen-
eration to occur. These findings are based on the
assumption that K (t) remains constant and equal
to Ko. However, this assumption is not true in gen-
eral and the effect of a change in K(t) will be explored
in the next section.

The best cases found in the earlier set of crystal
combinations and size distributions were those in-
volving graupel and heavily rimed plane dendrites.
The crystal combination which had the greatest
relative velocity was graupel and unrimed plane
dendrites. However, neither graupel nor unrimed plane
dendrites generate a large number of fragments.
A greater effect was found between graupel and
heavily rimed dendrites, although there was little
difference from that between moderately rimed plane
dendrites and graupel or lightly rimed plane dendrites
and graupel. Apparently, the reduction in relative
velocity is more than compensated for by the ability
of more heavily rimed crystals to produce fragments.
What will happen then, when a fairly broad distribu-
tion of plane dendrites is bombarded by a shower of
fairly large graupel?
To answer this question the model was run again
for one time step with unrimed, moderately rimed
and heavily rimed plane dendrites and spatial crystals
bombarded by graupel. Under these extreme condi-
tions Ko reached the maximum value observed. With
this value of Ko it would take about 3 min to increase
the initial crystal concentra.tion by a factor of 10 if
the initial concentration were 0.1 crystallitec1. If the
initial concentration were 0.01 crystal litec1 the time
would be about 30 min. We see, therefore, that under
extreme conditions, mechanical fracturing of fragile
crystals can be important.

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TIME (minutes)

NO ACCRETION OR DIFFUSION
K(t)=Ko
MODERATE ACCRETION AND DIFFUSiON
HEAVY ACCRETION AND DIFFUSION

FIG. 7. Change of concentration of all crystals as a function
of time for two different initial crystal concentrations and several
different rates of accretion and diffusion.

i5

c. Time-dependent computations

To go beyond the calculation of K 0 and find K (t)
as, a function of time requires knowledge of the frag-
ment distributions and diffusion and accretion rates.
As discussed earlier, the distributions for graupel
fragments and heavily rimed plane dendrite fragments
were of sufficient quality to allow modeling of this
crystal combination. Since this combination gave the
highest values of Ko it is appropriate that these
crystals should be studied in greater detail. Unfortu-
nately, the initial crystal distributions were not of
the most favorable shape to give high values of Ko.
Nevertheless, these distributions are actual observed
distributions and lend credence to the findings.
The effects of diffusion were modeled as linearly
dependent on size as shown by ~allett (1965), Marwitz
and Auer (1968), Koenig (1971), Fukuta (1969) and
Jayaweera (1971). Accretion on graupel was assumed
linearly dependent on size as Juisto (1968), Takeda
(1968) and Hindman (1968) indicate in a crude
manner. The rates of diffusional growth depend
strongly on the temperature with the maximum rate
of diffusional growth occurring at -150C. The esti-
mates of. the rate of growth at this temperature range
over an order of magnitude so no growth, moderate
growth and high growth rates were assumed. The
moderate rate was assumed to be 1 !Lm S-1 and the
high rate to be 4 !Lm S-I. Growth by accretion in the
model is even more crude. It depends on liquid water
content, drop size distributions and the collection