WMOD00434

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

2168

JOURNAL OF THE ATMOSPHERIC SCIENCES

VOLUME 35

The Generation of Secondary Ice Particles in Clouds
by Crystal-Crystal Collision

LARRY VARDIMAN1

Colorado State University, Fort Collins, CO 80521 .
(Manuscript received 6 June 1977, in final form 7 August 1978)

ABSTRACT

The number of fragments generated by crystal collisions in a cloud is a product of the number of fragments
produced per collision and the collision frequency. The first term, called the fragment generation function,
was obtained experimentally by taking high-speed photographs of collisions of natural ice crystals with a
fixed plate. The number of fragments in a collision was found as a function of the change in momentum on
impact with a fixed plate and as a function of crystal type and degree of rime. The difference in the change in
momentum for collisions in a cloud compared to the fixed plate is treated theoretically and developed into
a mathematical model. The collision frequency is incorporated into the model and rates of fragment genera-
tion studied for different crystal combinations, sizes and concentrations.
The generation of secondary particles by mechanical fracturing does not explain the presence of large
concentrations of ice crystals in relatively warm clouds. The additional crystals generated in smooth strati-
form clouds may reach a maximum of 10 times the expected natural crystal concentration at or near cloud
base. Isolated convective clouds do not appear to contain the proper conditions to produce significant addi-
tional crystals by mechanical fracturing. Stratiform clouds with embedded convection appear to provide
the greatest opportunity for secondary particle generation. Here the secondary crystal concentrations
could reach 100 to 1000 times the expected natural concentrations.

1. Introduction

Evidence has accumulated over the last 20 years
that in some clouds the concentration of ice crystals
may be a factor of four or five orders of magnitude
greater than the concentration of observed ice nuclei
apparently available to the cloud. One of the earliest
and most persistently proposed mechanisms to explain
this disparity has been the mechanical fracturing of
fragile ice crystals (Findeisen, 1943; Langmuir, 1948;
Mason, 1955; Grant, 1968; Koenig, 1968; Vardiman,
1972; Hobbs and Farber, 1972). However, only very
rough approximations have been used to determine
if collisions between crystals can generate sufficient
numbers of fragments to explain "ice multiplication."
This paper will describe the formulation of a model
to predict generation rates of fragments by crystal-
crystal collision, experimental data obtained to initiate
the model, results of the model calculations and ap-
plications of these results.

2. Theory

a. Mathematical formulation of secondary particle gen-
eration for clouds

1) RANDOM AND ORDERED COLLISIONS

In a cloud of particles varying in size, two basic
types of collision processes are possible-random col-

I Present affiliation: U.S. Bureau of Reclamation, Denver, CO
80225.

lisions and ordered collisions. Random collisions are
associated with turbulent motions in the air caused
by vertical and horizontal wind shear. Ordered col-
lisions are caused by the difference in terminal velocity
between particles. The component to the total col-
lision frequency in a cloud due to ordered collisions
can be visualized as the total collision frequency
between particles in a quiescent environment where
the particles fall without fluttering or being deflected
in the wake of other particles. If wake effects are to
be considered, a factor called the collision efficiency
must be multiplied by the computed collision frequency.
Although it is possible that random collisions may
outnumber ordered collisions in highly turbulent clouds
al,ld the collisions could be more "forceful," only
ordered collisions will be treated in this study due
to the inability to formulate random collisions in an
analytic manner. This assumption should ,not be too
restrictive as the number of random collisions should
be of the same order as the number of ordered col-
lisions in nonsevere cloud situations. For smooth
orographic clouds, the number of ordered collisions
should outnumber the random collisions.
The ordered collision frequency between crystals
has been shown by Lougher (1966) to be

Fijkl=ECijCklAiikl! Vij-Vkll,

(1)

where Fijkl is the collision frequency per unit volume