WMOD00291

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

1072

JOURN AL OF CLIMATE AND APPLIED METEOROLOGY

VOLUME 22

A similar assumption is required in deriving other
rates involving the collection of one class of precip-
itating particle by another class of precipitating par-
ticle, i.e., (29) and (42). Compared to detailed cal-
culations in which the interacting species are discre-
tized into many size categories, these four bulk rates
may all provide erroneous estimates. The nature of
the errors varies considerably over the full range of
likely equivalent water content values and also is gen-
erally different for each rate. We have investigated
various formulations of these bulk rates but have been
unable as of yet to find satisfactory alternatives. We
remain concerned with this problem, and efforts to
remedy the erroneous estimates are continuing.
In the temperature region T < To, if IR ~ 10-4 g
g-I or Is ~ 10-4 g g-I, we assume a three-component
freezing process with both rates PSACR and PRACS con-
tributing to the formation of hail. If the mass thresh-
old criterion is not met, i.e., both IR and Is are less
than 10-4 g g-I, the physical interpretation changes
to a two-component freezing Process. In this case, the
snow grows at the expense of the rain and only the
rate PSACR [Eq. (28)] need be calculated. In the tem-
perature region T'~ To, PSACR will not be active ex-
cept to enhance the melting of the snow due to the
sensible heat associated with the accreted rainwater
[see Eq. (32)].
The accretion of snow by hail, PGACS, always con-
tributes to hail content whether the temperature is
less than To or not. The equation for the production
rate is

PGACS = 7f2EGsfIQsnoGIUG ~ Us{:s)

( 5 2 0.5 )
X A~AG + A~A~ + A~Ab '

where EGs, the collection efficiency of hail particles
for snow particles, is assumed to be a function of
temperature given by

{eXp[o.09(T - To)],
EGs=
1.0,

T< To
T~ To.

Note that the collection efficiency of hail for snow is
considerably less than that of snow for ice crystals
given by (23).

3) DEPOSITION (SUBLIMATION)

The depositional growth rate of snow, PSDEP, is
mainly dependent on the supersaturation with respect
to ice. Based on the depositional growth of snow crys-
tals given by Byers (1965) with a modified ventilation
effect, the equation for PSDEP is given as

27f(S; - I) [ -2
PSDEP (or PSSUB) = p(A" + B") nos 0.78As

+ 0.3IS~!3r( d ; 5)CI/2(:0 YI4p-1/2AS(d+Sl/2] ,

where

A"= Li
KaRwT2 '

B"=~
prs;1/; ,

(31)

and we have assumed that the ventilation of heat is
equal to that of mass, and that the ventilation coef-
ficient for snow takes the same form as that deter-
mined by Beard and Pruppacher (I971) for small
raindrops. From (31), sublimation (a negative con-
tribution) occurs if the air is subsaturated with respect
to ice, i.e., S; < 1. An indicator 01 as defined in (20)
is applied such that PSDEP and PSSUB will not occur
simultaneously. Deposition occurs inside a cloud
only when the temperature is lower than ooc. From
(20), PSSUB is a sink term for snow when T < OOC and
the snow is outside the cloudy region. Although these
two terms PSDEP and PSSUB can be combined as a
single term and thereby eliminate the need for 01, we
chose to keep them separate to provide a'more thor-
ough accounting of these terms.

(29)

4 ) MELTING

The melting of snow is treated in a fashion anal-
ogous to that used for melting of hail by Mason (1971)
and Wisner et al. (1972). The melting rate is based
on heat balance considerations with the cooling as-
sociated with the melting being balanced by the com-
bined effects of conduction and convection of heat
to the particle surface, the latent heat of condensation
and evaporation of water to or from the particle sur-
face, and the sensible heat associated with the ac-
creted water. The rate of melting of snow to form
rain can be expressed as

(30)

27f [ .
PSMLT = - pLf (KaTe - Lv1/;pflrs)nos 0.78Ai

+ 0.31S~!3r( d; 5)Cl/2(;) 1/4p-1/2AS(d+S)/2]

CwTe
- ~ (PSACW + PSACR). (32)

In (32) we have employed the same assumptions re-
garding the ventilation coefficient noted for (31) and
have assumed that the collected and melted water is
at the air temperature Te rather than the wet bulb
temperature, which is more physically appropriate
(Kinzer and Gunn, 1951). Rasmussen and Prup-
pacher (1982) have investigated the melting of small
frozen drops experimentally and theoretically and
have shown that theory underpredicts the melting