WMOD00291

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

1070

JOURNAL OF CLIMATE AND APPLIED METEOROLOGY

VOLUME 22

c. Production term for snow

We have noted earlier that ice crystals originally
grow by deposition until reaching a size where ag-
gregation and riming become important, leading to
the formation of snow crystals and snowflakes. Within
the model, the processes considered to generate snow
are the collision and aggregation of the smaller cloud
ice particles, contact freezing of small raindrops, and
depositional growth and riming of ice crystals. Once
generated, the snow continu~s to grow by accretion
and deposition. Sublimation and melting reduce the
snow content.
The total production teI11;l for snow may be written
for two temperature. regimes.
(i) If the temperature is below OOC (T <: To)

Ps = PSAUT'+ PSAC1 + PSACW + PSFW + PSFI
,

+ PRACI(li3) + P1ACR(lh) - PGACS - PGAUT
- PRACS(I - 152) + PSAcR(b2)
+ PSSUR(I - 151) + PSDEP(bl)' (18)
(ii) If the temperature is above OOC (T ~ To)

Ps = PSMLT - PGACS,

where 151, 152 and 153 are defined as
T< To
{I,
151 =
0,

{I,
152 =
0,
{I,
153 =
0,

for lcw + ICI > 0
otherwise

for IR and Is < 10-4 g g-I
otherwise

. for IR < 10-4 g g-I
otherwise

T~ To

15 I = 152 = 153 = 0

Each production tenri will be discussed in detail be-
low and typical values for most given later in Fig. 3.

I) ICE CRYSTAL AGGREGATION

The aggregation rate of ice crystals to form snow
is assumed to follow parameterization concepts orig-
inally proposed by Kessler (1969), to simulate the
collision-coalescence process for cloud droplets. It
may be written as

PSAUT = al(lcI - ho), (21)

where al is a rate coefficient (S'-I), which is temper-
ature dependent, and ho is a threshold amount for
aggregation to occur. In this study, we set ho to be
10-3 g g-I. The relationship used for the rate coeffi-
cient is

al = 10-3 exp[0.025(T - To)],

which is a crude parameterization of the dependence
of aggregation efficiency on crystal structure which,
in turn, is temperature dependent.
The physically similar mechanism of aggregation
of snow to form graupel, PGAUT, will be described in
subsection 3d, along with the other hail production
terms.

2) ACCRETION

(19)

A variety of accretional growth mechanisms in-
volving the interaction of snow with the other classes
of hydrometeors are allowed in the model. There are
also accretional processes involving the other classes
of hydrometeors which may generate snow. The
mathematical formulation for these accretional pro-
cesses which produce or involve the snow content will
now be described.
The accretion of cloud ice by snow is an aggre-
gation process which occurs if the temperature is less
than To (273 K). The rate of accretional growth,
PSACh is based on the geometric sweep-out concept
integrated over all snow sizes for the assumed snoW
size distribution (2) which yields

_ 1fEsIYI{)sclC/r(3 + d) (pO)I/2
PSAC1 - 4A}+d p'

(22)

(20)

where ESI is the collection efficiency of the snow for
cloud ice. Similar to the rate coefficient for ice crystal
aggregation noted for (21), the collection efficiency
of snow for cloud ice, ESI, is assumed to be temper-
ature dependent and can be expressed as

ESI = exp[0.025(T - To)]. (23)

The accretion of cloud water by snow, PSACW, is
similar to (22), and is expressed as

_ 1fEswnosclcwr(3 + d) (pO)I/2
PSACW - 4A}+d p' (24)

where Esw is the collection efficiency of snow for
cloud water, which is assumed to be 1 in this model.
PSACW will increase the snow content by accreting the
cloud water and subsequently freezing it if the tem-
perature is lower than ooc. If the temperature is
warmer than OOC, PSACW will contribute to the rain
content via the assumption that unfrozen water will
be shed from the snow particles. This will be described
later in subsection 3e. The sensible heat associated
with the accreted cloud water will also enhance the
melting of snow [see Eq. (32)].
In the following discussion, terminology which is
largely an artifact of the hydro meteor classification
scheme adapted for this study will be developed and
applied. This artificiality is related to the various in-