WMOD00291

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

1068

JOU RN A L OF CLI MATE AND A PPLI E D METEOROLOGY

VOLUME 22

CLOUD
WATER

PlOW , P1HOM

CLOUD
ICE

lL
>
w
tE-

lL
W
o
(LU)

~
o
(L~

"
lD
:>
U)
(LU)

~ "
tE- 'I

-
~
(La::

SI
cf:?

f-
:>
..:
(La::

RAIN

FIG. I. Cloud physics processes simulated in the model with the
snow field included. See Table 1 for an explanation of the symbols.

I) P ARAMETERIZA nON

Exponential size distributions are hypothesized for
the precipitation particles:

nR(D) = floR exp(-ARDR), (I)

ns(D) = nos exp(-AsDs), (2)

nG(D) = floG exp(-A~G), (3)

where nOR, nos and nOG are the intercept parameters
of the rain, snow and hail size distributions, respec-
tively. The nOR is given by Marshall-Palmer (I 948)
as 8 X 10-2 cm-4. According to the measurements
of Gunn and Marshall (1958), nOs is given as 3 X 10-2
cm-4, Observations by Federer and Waldvogel (I975)
of hail distributions lead to a value of -4 X 10-4
cm-4 for nOG. DR, Ds and DG are diameters of the
rain, snow and hail particles, respectively. The slope
parameters of the rain, snow and hail size distribu-
tions O'R, AS and ^G, respectively) are determined by
multiplying (I), (2) and (3) by particle mass and in-
tegrating over all diameters and equating the resulting
quantities to the appropriate water contents; they
may be written as

( )0.25
A = 7fPWnOR
R I '
PR

(4)

( )0.25
A = 7fpsnos
s I '
Ps

(5)

( )0.25
A = 7fPGnOG
G I '
PG

where Iw, Is and IG are densities of water, snow and
hail, respectively. The density of snow is assumed to
be O. I g cm-3 in this study. The symbols IR, Is and
IG are mixing ratios of rain, snow and hail, respec-
tively.
The terminal velocities for a precipitating particle
of diameter DR, Ds or DG are

lD
:>
U)
~

(6)

TABLE 1. Key to Fig. I

Symbol

Meaning

P1MLT
PIDW

PIHOM

P1ACR

PRAC1

PRAUT
PRACW
PREVP
PRACS

PSACW

PSACR

PSACI
PSAUT

PSFW

.PSF1

PSDEP
PSSUB
PSMLT
POAUT
POFR
P OACW
POAC1
POACR
POACS
POSUB
POMLT

POWET

Melting of cloud ice to form cloud water, T;;. To.
Depositional growth of cloud ice at expense of cloud
water.
Homogeneous freezing of cloud water to form cloud
ice.
Accretion of rain by cloud ice; produces snow or
graupel depending on the amount of rain.
Accretion of cloud ice by rain; produces snow or
graupel depending on the amount of rain.
Autoconversion of cloud water to form rain.
Accretion of cloud water by rain.
Evaporation of rain.
Accretion of snow by rain; produces graupel if rain or
snow exceeds threshold and T < To.
Accretion of cloud water by snow; produces snow if
T < To or rain if T;;. To. Also enhances snow
melting for T;;. To.
Accretion of rain by snow. For T < To, produces
graupel if rain or snow exceeds threshold; if not,
produces snow. For T;;. To, the accreted water
enhances snow melting.
Accretion of cloud ice by snow.
Autoconversion (aggregation) of cloud ice to form
snow.
Bergeron process (deposition and riming)-transfer of
cloud water to form snow.
Transfer rate of cloud ice to snow through growth of
Bergeron process embryos.
Depositional growth of snow.
Sublimation of snow.
Melting of snow to form rain, T;;. To.
Autoconversion (aggregation) of snow to form graupel.
Probabilistic freezing of rain to form graupel.
Accretion of cloud water by graupel.
Accretion of cloud ice by graupel.
Accretion of rain by graupel.
Accretion of snow by graupel.
Sublimation of graupel.
Melting of graupel to form rain, T;;. To. (In this
regime, POACW is assumed to be shed as rain.)
Wet growth of graupel; may involve POACS and POAC1
and must include POACW or POACR, or both. The
amount of POACW which is not able to freeze is shed
to rain.