WMOD00430

• Title: A Diagnostic Technique for Targeting During Airborne Seeding Experiments in Wintertime Storms over the Sierra Nevada
• Date: 7/7/1988
• Weather Modification - Doc Type: Report

JULY 1988

RAUBER ET AL.

817

catelli and Hobbs (1974). Four particle habits were
considered. Two equations were used for each particle,
the first for an unrimed particle and the second for a
heavily rimed particle. A smooth transition between
equations was used as the particles grew, based on the
time of onset of riming and time of heavy rime coverage
(see Eqs. 5 and 6 below). The fall velocity equations
for each habit class are summarized in Table I.
In Table I, VI is the particle terminal velocity (meters
per second) and c or a is the particle major axis (cen-
timeters). For dendrites, it was assumed that it would
become heavily rimed but recognizable when rime
completely covered the particle (see Locatelli and
Hobbs 1974). Plates were assumed to rime into spher-
ical shape and become graupel. The available equations
for columns have opposite inflections (see Fig. 5) with
common points at 0 and 0.09 cm. At sizes smaller than
0.09 cm, the equation of Davis (1974) was used for
un rimed particles while Locatelli and Hobbs (1974)
was used for rimed particles. At sizes ~ 0.09 cm, the
equation of Locatelli and Hobbs was used independent
of rime coverage. Locatelli and Hobbs reported that
the maximum dimension of columns was near 0.2 cm.
The fall velocity of a column of length 0.2 cm was
considered as the upper fall velocity limit. Columns
with length> 0.2 cm were assumed to fall at the rate
of a column with length equal to 0.2 cm. The equations
for unrimed needles are linear fits to the data ofNakaya
(1954) and Brown (1970) for three size ranges. As with
columns, a maximum velocity limit was imposed.
However, this maximum velocity corresponded to a
larger size particle (0.35 cm) since needles are often
observed to be larger than 0.2 cm. We were unable to
find any studies in the literature which provided mea-
surements of the fall velocity of rimed needles. To sim-
ulate their fall velocity, it was assumed that these par-
ticles achieved a fall velocity equal to 1.5 Vtn, where
Ytn is the fall velocity of the unrimed single needle.

4) PARTICLE GROWTH REGIMES

An ice crystal experiences a wide range of conditions
during its transit from nucleation to impact with the

ground. For targeting purposes, these conditions were
parameterized into four growth stages. During the first
stage, which extended from the time of nucleation to
300 s, particle diffusional growth was allowed to pro-
ceed independently along the a and c axes. Riming was
not pe:rmitted. A 60 s time step was used. This time
step was found to be sufficient to resolve small changes
in particle fall velocity and changes in environmental
winds along the trajectory. The fall velocity of the par-
ticle was that of an unrimed plate (a axis> c axis) or
column (c axis> a axis). At the end of 300 s, the habit
was established. The particle was assumed to retain
this habit throughout its trajectory. The habit criteria
at 300 s growth was as follows:

Temperature
(oC)

Axis

Particle type

~-I3
>-13
<: -6
~ -6

a axis ~ c axis
a axis ~ c axis
c axis > a axis
c axis > a axis

dendrite
plate
column
needle

During the second growth stage, from 300 s to onset
of riming, particle diffusional growth continued. Rim-
ing was not permitted. The fall velocity was that of the
appropriate habit.
Tht~ third stage extended from onset of riming to
heavy rime coverage. The particle growth continued
at a rate specified by the diffusional growth rate. In
addition, a smooth transition between the fall velocity
for the unrimed and rimed particles of the form

VI = AVtr + (I - A)Vtu
was employed. Here,
A = (t - to)/(tr - to)

(5)

(6)

when: t is the current time, to the time of onset of rim-
ing, t,. the time when heavy rime coverage developed,
Vtr the fall velocity of the rimed particle and Vtu the
fall velocity of the unrimed particle.

Type

TABLE 1. Fall velocity (V" m S-I) equations as a function of crystal major axis (centimeters) used in SCPP targeting calculations.

Equation

Reference

I. Dendrite, unrimed
Dendrite, rimed
2. Plate, unrimed
Graupel
3. Column unrimed (c < 0.09 cm)
Column unrimed (c > 0.09 cm)
Column rimed
Column (c > 0.2 cm)
4. Needles unrimed (0 < c < 0.1 cm)
Needles unrimed (0.1 < c < 0.2 cm)
Needles unrimed (0.2 < c < 0.35 cm)
Needles unrimed (c :> 0.35 cm)
Needles (rimed or aggregated)

V, = 0.6197.t.217
V, = 1.32ao.330
V, = 2.96aO.l124
V, = 3.34.t.460
V, = 24.3cl.309
V, = 3.99dl.S6
V, = 3.99dl.S6
V, = 1.62
V, = 5c
V, = 2.1c + 0.29
V, = 1.2c + 0.47
V, = 0.89
V, = 1.5 v,(unrimed)

Brown (1970)
Locatelli and Hobbs (1974)
Davis (1974)
Locatelli and Hobbs (1974)
Davis (1974)
Locatelli and Hobbs (1974)
Locatelli and Hobbs (1974)
Locatelli and Hobbs (1974)
Brown (1970), Nakaya (1954)
Brown (1970), Nakaya (1954)
Brown (1970), Nakaya (1954)