WMOD00291

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

1066

JOU R N A L OF eLl MATE AND A PPLI ED MET EO RO LOGY

VOLUME 22

pacher, 1979). An additional complicating factor in-
volving ice processes is the possibility of ice particle
multiplication within certain size and temperature
regions (Mossop, 1978) which can greatly enhance
the normally low ice concentrations at relatively
warm subfreezing temperatures indicated by ice nu-
clei measurements (as in Fletcher, 1962).
The theoretical studies of Danielsen et at. (1972)
and Nelson (1979) have demonstrated the impor-
tance of ice particles in the development of precipi-
tation. They used one-dimensional, detailed micro-
physical cloud models, including ice processes, and
obtained results consistent with observations. Nel-
son's model appeared to be capable of detecting the
dominant precipitation initiating mechanism and the
dominant hailstone embryo type for various atmo-
spheric situations. In a somewhat different approach,
Koenig and Murray (1976) developed a two-dimen-
sional, axisymmetric numerical cloud model with
parameterized microphysics for water drops and ice
particles. Interesting features of their approach in-
clude the calculation of the ice particle number con-
centration without specifying the form of the size
distribution function, although the ice particles were
. assumed to be monodisperse for many of the physical
processes and the use of variable ice particle density
assumptions and, hence, different fallspeed relations,
based on the mean particle mass and temperature.
In that study, the general comparison of model sim-
ulation against observations was satisfactory, and the
microphysical parameterizations seemed capable of
capturing many of the observed properties of gla-
ciating clouds with regard to the locations and sizes
of the liquid and solid hydrometeors.
This study builds on a thesis by Chang (1977) and
a paper by Orville and Kopp (\ 977). We modify the
two-dimensional, slab-symmetric cloud model with
bulk water microphysics described by Orville and
Kopp (1977) by incorporating equations for snow
originally developed and tested in a one-dimensional
cloud model by Chang (1977). The primary results
of Chang's study indicated the ability of the param-
eterized model to capture the dominant precipitation
initiation mechanism and dominant hailstone em-
bryo type for different soundings, similar to the results
of Nelson's detailed model.
The following sections describe various aspects of
the current study in greater detail. Section 2.examines
the basic characteristics of snow and hail and provides
some basic definitions used in this study. A general
description of the cloud model and the parameter-
ization scheme are given in Section 3, along with the
various production terms, with particular attention
devoted to the snow equations. Section 4 describes
the initial and boundary conditions and the numer-
ical techniques. The results of three comparative ex-
periments to assess the influence of the inclusion of

snow in the model are presented in Section 5. Section
6 provides further discussion of several points and
presents conclusions from this study.

2. The properties of snow and hail

a. The properties of snow

We shall use the term snow rather loosely in this
study to represent snow crystals, snowflakes and low-
density graupel particles. According to the Glossary
of Meteorology, snow is "precipitation composed of
white or translucent ice crystals, chiefly in complex
branched hexagonal form and often agglomerated
into snowflakes." Snow particles typically range in
size from 2 to 5 mm diameter with bulk densities
ranging from 0.05 to 0.89 g cm-3 (Pruppacher and
Klett, 1978). The major habits that snow crystals may
assume are needles, plates, columns, dendrites and
stellar crystals, with the particular habits being de-
pendent on the temperature and supersaturation with
respect to ice (Nakaya, 1954; Kobayashi, 1957; Ma-
gono and Lee, 1966; Mason, 1971).
Usually, ice crystals in a cloud grow by the diffu-
sion of water vapor to their surface due to the Ber-
geron process (Byers, 1965) and can, under suitable
conditions, increase in size to form snow crystals.
Snow crystals may grow by deposition and also collect
supercooled droplets that freeze on impact and endow
the crystal with a rimed appearance (Mason, 1971).
Snow crystals may also collide and aggregate to form
snowflakes, this being more pronounced in ice su-
persaturation conditions (Hosler et al., 1957; Hosler
and Hallgren, 1961; Hobbs, 1965). By continued de-
positional growth, aggregation, and the collection and
freezing of supercooled droplets, the snow crystals
and snowflakes may become embryos for graupel and
hail. The growth rate of these snow crystals and ag-
gregates is governed by the terminal velocities, col-
lision and aggregation efficiencies, while the terminal
velocity is a function of the mass and the dimension
of the particle itself(Locatelli and Hobbs, 1974; Prup-
pacher and Klett, 1978). Generally, the terminal ve-
locity of snow is between 0.5 and 3 m S-I.
Measurements in clouds over the Cascade Moun-
tains, Washington reported by Hobbs (1975) show
that at temperatures between -4 and -250C, the
range of number concentration of ice and snow crys-
tals varies little with temperature on the average, and
that the concentration may reach values as high as
107 m-3. This may be a reflection of the possibility
that ice crystal multiplication similar to that proposed
by Mossop (1978) is important in the clouds studied
by Hobbs. The studies of Gunn and Marshall (\958)
and Passarelli (1978) have indicated the size distri-
bution of snowflakes is similar in form to the well
known Marshall and Palmer (1948) raindrop size
distribution (i.e., inverse exponential). I