Geoscience Reference
In-Depth Information
If
R
is much greater than
r
, then
v
R
is much greater than
v
r
and if (for the purposes
of this illustration) it is also assumed that the large droplet is a perfect sphere, then
v
R
is proportional to
R
0.5
and it follows that:
dR
dt
≈
wR
0.5
(11.2)
Equation (11.2) implies that drop growth occurs at an accelerating rate.
Although the model just described illustrates some relevant features of droplet
growth in a warm cloud, it is clearly overly simplistic. In fact the collision between
droplets has stochastic aspects that involve spatial and temporal dependency. But
more realistic statistical collision models have been created which simulate droplet
growth reasonably well. These show that the predisposition of bigger droplets to
get bigger means that after about 15 minutes the droplet distribution becomes bi-
modal, and that after some time drops with radius greater than 500
μ
m are formed
which are able to fall from the warm cloud.
Precipitation formation in other clouds
In cold clouds, aggregation of ice particles is the only mechanism available for par-
ticle growth. The physics involved in the aggregation is broadly similar to that of
coalescence although there are additional complicating mechanisms involved. The
terminal velocities of ice crystals in clouds tends to be very slow and to vary with the
shape of the particles, with the more complex shapes such as plate-shaped crystals
having little variation in velocity with increasing size. Generally the terminal veloci-
ties of pure ice crystals are small, usually less than 0.1 m s
−1
and commonly around
0.05 m s
−1
and the range of terminal velocities is narrow. This lowers the opportunity
for pure ice particles to grow by aggregation. The solid nature of ice particles also
means they have a tendency to bounce off each other - hence collection efficiency
is further reduced. For all these reasons, the opportunity for ice particle growth by
aggregation to precipitation-sized entities in cold clouds is somewhat limited.
In mixed clouds that occur above the 0°C isotherm, but which have a tempera-
ture greater than -40°C, all the growth processes mentioned in the introduction
can occur, i.e., coalescence of water droplets, aggregation of ice particles, and
accretion of water droplets onto ice particles, along with the Bergeron-Findeisen
process. Aggregation can be more effective in mixed clouds if the ice particles have
a thin film of supercooled water on their surface. This makes them 'sticky' because
the thin layer of water between the colliding ice particles freezes instantaneously.
The efficiency with which this aggregation occurs seems to be greater in the tem-
perature range -4°C to 0°C. Snowflakes are formed by this process with the largest
snowflakes produced in the warmest regions of clouds.
Although the terminal velocities of ice particles are small, differential motion of ice
particles and water droplets within mixed clouds results in collisions, so accretion is a
