WMOD00291

• Title: Bulk Parameterization of the Snow Field in a Cloud Model
• Date: 6/6/1983
• Weather Modification - Doc Type: Report

JUNE 1983

UN, FARLEY AND ORVILLE

1071

teractions possible between liquid and solid water
forms in the subfreezing regions. For the process of
snow accreting cloud water, PSACW, the interaction
between the liquid (cloud: water) and solid (snow)
particles results in an incr~ase in the original solid
class (snow) and a loss in the accreted quantity (cloud
water). We refer to this ty~e of interaction as a two-
component freezing process.
A more complicated situation is that typified by
the interaction of rain and cloud ice. In this case, the
interaction of small ice cry&tals (cloud ice) with large
water drops (rain) produce~ a large ice particle (snow
or hail). This situation in 'Yhich the mutual interac-
tion ~f two separate water iclasses (in this case, rain
and cloud ice) results in a third, distinct water form
(snow or hail in this case), I is referred to as a three-
component freezing proces~. For a three-component
freezing process, two separate accretion rates must be
calculated to determine th~ appropriate sink terms
for each of the mutually in~eracting forms of water,
and the sum of these two rates determines the source
term for the distinct water form which results.
Having dispensed with these preliminary consid-
erations, we now return to !the microphysical devel-
opment. In the temperatu~e region T < To, super-
cooled water drops will freeze due to contact with
solid particles. Accordingly, ~e assume that raindrops
accreting cloud ice will free:ze and the resultant solid
particles contribute to the solid precipitation (snow
or hail). Two production rates must be considered in
this three-component freezIng process; namely, the
accretional rate of rain for Cloud ice (PRACI) and the
freezing of raindrops which collide with cloud ice
(PIACR). The first rate is a sink for the cloud ice con-
tent, and the second is a sink for the rainwater con-
tent. Both terms are source~ for either snow or hail
depending on the mass thteshold criterion defined
later in this section. . ,
First, we consider the accretion of cloud ice by rain,
a sink term for cloud ice and a source term for snow
or hail. Applying the geometric sweep-out concept
and integrating over all rain sizes for the assumed
distribution given by (1), we obtain
,

. ~ ( )IP
P _ 1fERIn()Raldr(3 + b) Po
RACI - 4~3-tlb -.
^R: P

The collection efficiency ot rain for cloud ice, E RI,
is assumed to be I in this model.
Now we shall consider tile sink term for rain due
to the presence of cloud ice, PIACR, which i& also a
source term for snow or hail. Due to the lack of an
individual prognostic value (or cloud ice number con-
centration in the present mqdel, we shall assume the
small ice crystal size distribu.tion to be monodisperse
with each ice crystal being of constant mass M; = 4.19
X 10-10 g. With raindrops and cloud ice particles as-

l '
'~;. I I
_.~~"".~'/;'i"i;;;' l

.~

(25)

sumed to be distributed evenly in the volume, and
integrating over all raindrop sizes, we obtain the ac-
cretion rate of rain by cloud ice particles, PIACR, which
'may be written as

P = 1f2ER1rloRaIClPWr(6 + b) (pO)1.2 (26)
IACR 24M; A~+b p'

Since the cloud ice is small compared to raindrops,
the density of the new product will be determined
mainly by the amount of rain. In other words, the
interaction of rain and cloud ice is likely to result in
the formation of hailstones as long as the raindrops
are fairly large. However, it is difficult to determine
the result of each collision in this bulk water simu-
lation; therefore, we will assign a threshold for the
rainwater content to determine whether the interac-
tion ofrain and cloud ice results in snow or hail (see
Fig. I). Based on preliminary calculations, we con-
cluded that if the mixing ratio of rain is IR < 10-4 g
g-l, then all the raindrops will be small enough to
become low-density particles (snow). If IR > 10-4 g
g-l, then the PIACR and PRACI contribute to the for-
mation of hail and provide an important collisional-
freezing mechanism for the generation of frozen drop
hailstone embryos. This collisional-freezing mecha-
nism (three-component freezing) usually dominates
over the probabilistic (Bigg, 1953) freezing of rain
which had formerly been the sole avenue for the gen-
eration of frozen drop hailstone embryos.
We now consider the interaction between snow-
flakes and raindrops. The accretion rate of rain for
snow, PRACS, and the accretion rate of snow for rain,
PSACR, are as follows:

PRACS = 1f2EsRnORrIosIUR - Us{;)

( 5 2 0.5 )
X A~AR + A~A1 + A}Ak ' (27)

PSACR = 1f2EsRrIosnORIUs - UR{p;)

( 5 2 0.5 )
X ^~AS + AkA~ + AkA1' (28)

where the collection efficiency of snow (rain) for rain
(snow), ESR, is assumed to be 1. Derivation of (27)
and (28) requires that we assume that all raindrops
and snow particles are falling at their appropriate
mass-weighted mean terminal velocities. The as-
sumption is required due to the fact that the differ-
ence in fallspeeds of interacting particles must always
be treated as a positive quantity to properly define
the sweepout volume. This requirement is further
complicated by the fact that the derivation of (27)
and (28) requires a double integration over all rain-
drop and snow particle sizes.