WMOD00291

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

1076

IOU R N A L OF CLI M ATE A ND A PPLI ED METEOROLOGY

VOLUME 22

4) SUBLIMATION

If hail falls out of a cloudy environment, then sub-
limation will occur in a subsaturated region. Similar
to (31), we obtain the equation

21f(S; - 1) [-2 1/3
PGSUB = p(A" + B") nOG 0.78AG + 0.31Se r(2.75)

X (;~:r4v-1/2Aa2.75J. (46)

The (S; - 1) in (46) is negative in the subsaturated
region and thus PGSUB is a sink term for hail content.

. 5) MELTING

The melting of hail is based on heat balance con-
siderations as described in Mason (1971) and Wisner
et al. (\972). The melting rate PGMLT is given by

21f
PGMLT = -=- - (KaTe - Lv1/;pflrs)nOG
pLf

X [0.78Aa2 + 0.31S~/3r(2.75)

X (:~:r4v-1/2Aa2.75J

CwTe
- - (PGACW + PGACR)' (47)
Lf

The discussion of the physics involved in this rate has
already been provided in the development of the
melting rate for snow, PSMLT [(32)]. The findings of
Rasmussen and Pruppacher (1982) noted in the dis-
cussion of (32), are especially relevant to (47). In the
current formulation, the accreted cloud water is shed
as rainwater and represents another source of rain
from cloud water.

e. Production term for rain

Similar to the previous sections, we consider the
total production rate first. The total production term
for rain can be written as:

(i) If the temperature is below OOC (T < To):

PR = PRAUT + PRACW - P1ACR - PSARC

- PGACR (or POACR) - PGFR + PREvp(1 - 151), (48)
(ii) If the temperature is above OOC (T;?; To):
PR = PRAUT + PRACW + PSACW + PGACW

- PGMLT - PSMLT + PREvP(1 - 151), (49)
The terms are described below.

I) AUTOCONVERSION

The collision and coalescence of cloud droplets to
form raindrops is parameterized using a modified
form of the relation suggested by Berry (1968). It may
be written as

PRAUT = p(/cw - IwO)2[1.2 X 10-4

+ {1.569 X 1O-12Nd[Do(lc~ - IWO)]}]-I, (50)

where Nl is the number concentration of cloud drop-
lets and Do the dispersion, with I WO, a threshold for
autoconversion, set equal to 2 X 10-3 g g-l. When
the amount of cloud water exceeds Iwo, there is a
probability of forming raindrops. The introduction
of the threshold in (50) is an empirical modification
to Berry's original form made to better simulate ob-
servations of first echoes. For cold-based clouds typ-
ical of the northern High Plains region, we normally
turn off PRAUT consistent with observations which in-
dicate the collision-coalescence process is rarely active
(Dye et al., 1974). The value of Nl and Do used in
this study are consistent with the continental nature
of the clouds but, even with the modification, do not
provide adequate suppression of the process. There-
fore we regard Case 3, which does not allow this pro-
cess, to be more realistic, especially with regard to
precipitation initiation.

2) ACCRETION

Raindrops, once formed, continue to grow by ac-
cretion of cloud water. By applying the geometric
sweep-out concept and integrating over all raindrop
sizes, this rate is given as

_ 1fERWnORalcwr(3 + b) (pO)1/2
PRACW - 4Ak+b p' (51)

where the collection efficiency ERW is assumed to be
1. This rate is the same as that used by Wisner et
.af. (1972) and Orville and Kopp (1977), except for
a height correction applied to the fallspeed relation-
ship. PRACW always serves as a source term of rain
content, independent of temperature regime.
In the temperature region T < ooe, there are three
additional accretion terms which provide negative
contributions to the rain field; they are P1ACR, PSACR
and PGACR (or POACR) given respectively by (26), (28)
and (42). Two other accretion processes [PSACW (24)
and PGACW (40)] provide positive contributions to
rain if the temperature is above ooc. This is another
example of shedding in the model.

3) FREEZING AND MELTING

The freezing of raindrops PGFR is a source term of
hail content and is a sink term for rain content