WMOD00291

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

JUNE 1983

LIN, FARLEY AND ORVILLE

1067

b. The properties of hail ,

. In clouds with sufficiently strong updrafts, the rim-
mg of snow crystals, snowflakes and graupel particles
may continue until hailstones are produced. Accord-
ing to the Glossary of Met~orology, hail is "precipi-
tation in the form of balls 6r irregular lumps of ice."
An individual unit of hail is called a hailstone which
by convention, has a diameter of 5 mm or more:
Smaller ice particles of similar character are called
graupel, ice pellets or frozen rain. In this study we
I '
shall use the term hail rather loosely to represent high-
density graupe1, ice pellets, frozen rain and hailstones.
The bulk density of hailstones tends to vary radially
from surface to core, with ~lternating concentric lay-
ers of lower and higher defl.sity. The density of such
hailstone shells has been (ound to vary usually be-
tween 0.8 and 0.9 g cm-3 (Pruppacher and Klett,
1978). The terminal veloc;ities of hailstones range
from about 10 to 40 m S-l pr more. Auer (1972) has
summarized measurements on the size distribution
of hailstones and graupel paIticles. The concentration
for graupel particles with diameters between 0.5 and
5 mm rang~ between 103 a~d 1 m-3, while large hail-
stones of dIameters between 2.5 and 8 cm range in
concentration from 10-6 to: 10-2 m-3. Auer proposed
an inverse power law to describe the hail size distri-
butions while others, such as Douglas (1960) and
Federer and Waldvogel (19~5), have proposed inverse
exponential distributions.
Pre~ent studies indicate ,hat hailstones may origi-
nat~ eIther as graupel or frozen drops (Knight and
Kmght, 1979). For warrn-pased clouds with cloud
base temperature 150C or : higher, the frozen drops
predominate in the formation of hailstones while for
cold-based clouds with cloud base temper~ture 50C
or lower, hailstones usually originate as graupel par-
!icles. List (1960) and Knight and Knight (1979)
Identified graupel particles as embryos for about 80%
of the sampled hailstones which fell in Switzerland
and Colorado, where the vast majority of cloud base
temperatures are lOoC or colder. The graupel em-
bryos, in turn, may have originated as snow crystals
or on small frozen drops. "Iherefore, snow is an im-
portant factor in hailstorms, especially for continen-
tal, cold-based clouds. Recent in situ observations
support this point of view (Dye et al., 1974; Gagin
1971 )', '

3. The cloud model

'a. General description

This model is mainly ba~ed on Chang (1977) and
Orville and Kopp (1977). It is a two-dimensional
time-dependent cloud model with bulk water micro~
physics. The domain of the model is 19.2 km in both
the X and Z dimensions with a 200 m grid interval.
The model contains five classes of hydrometeors:
,

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,t., .. \ .1
iIi~'J:..,i;..~";i'i.i.:J.""".,,,,,,,,,J,~~,,,.. .,

";,h..;", ;_\V':<>~~w;i;~:;:., ~ '", -~I, ~~<

cloud water, cloud ice, rain, snow and hail. Inclusion
of the snow content field allows for an intermediate
and distinct entity between the two forms of ice pre-
viously modeled, namely, the non-precipitating cloud
ice field and the hail veld, resulting in a more phys-
ically sound representation of ice in general and, in
particular, in the production of hail. Previous versions
of the model (e.g., Orville and Kopp, 1977) generated
precipitating ice (hail) via either raindrop freezing or
through a crude representation of the Bergeron pro-
cess. The new treatment allows for more realistic hail
generation mechanisms via the ice phase since the
Bergeron process now produces snow which must
undergo further growth before transforming to hail.
In addition to the Bergeron process, snow may also
be generated by contact freezing and aggregation of
cloud ice. Hail may be produced by a variety of con-
tact freezing mechanisms and via aggregation of
snow. For the model warrri-based clouds, the prob-
ability based freezing ofraindrops (Bigg, 1953) is no
longer the primary mechanism for producing hail
embryos, since raindrop capture of cloud ice or snow
can now be major hail generation mechanisms.
The microphysical equations for snow, as sum- .
marized below, generally follow the development of
Chang (1977), although the two-dimensional, time-
dependent (2DTD) version presented here differs
from Chang's original treatment in some respects.
The terminal velocity of rain now includes height
dependency, and different values of parameters for
the terminal velocity and density of snow are used.
Chang's treatment did not include a Bergeron pro-
cess, while previous versions of the 2DTD cloud
model have simulated this process (e.g., Orville and
Kopp, 1977). The 2DTD snow model includes the
Bergeron process, but as a generation mechanism for
snow instead of hail as originally developed. The ap-
proximation to the Bergeron process was also mod-
ified to conform to the more realistic scheme deVel-
oped by Hsie et al. (1980), who also developed a
modified form of the scheme to allow for coexistence
of cloud water and cloud ice in the temperature region
of -40 to ooc. This scheme allows cloud ice to grow
via deposition at the expense of cloud water which
evaporates to water vapor (Bergeron process).

b. Cloud microphysics

The model contains five classes of hydrometeors,
all treated in a highly parameterized fashion. The
cloud water and cloud ice particles are assumed to
be small enough that their terminal velocities can be
neglected co~pared with the velocity of air, rain,
snow and had. The rain, snow and hail possess ap-
preciable terminal velocities. The microphysical pro-
cesses simulated in the model are demonstrated in
Fig. 1 and explained in Table 1.