Geoscience Reference
In-Depth Information
obviously only give growth in mixed cloud where both phases of water coexist. It is
worth noting that there are more growth processes available for mixed clouds, i.e.,
all the collision processes as well as the Bergeron-Findeisen process, and their ability
to produce precipitation is therefore greater than for warm clouds or cold clouds.
Precipitation formation in warm clouds
It is clear from the discussion above that, in clouds that ultimately produce pre-
cipitation, the growth of cloud particles is complex, and that it is particularly so for
mixed clouds. A full description of the microphysics of cloud evolution is beyond
the scope of this text. However, it is helpful to consider at least the simplest case of
droplet growth in warm clouds to provide basic insight into the complex process
of collision growth.
By definition, the air temperature in a warm cloud is above 0°C. Consequently,
warm clouds are found below the 0°C isotherm, which means they have a limited
depth at middle and high latitudes where they make only a small contribution to
precipitation. But their contribution to tropical precipitation and to warm season
precipitation can be appreciable. In warm clouds, coalescence is the only collision
mechanism available for cloud particle growth. It occurs between droplets or drops
of different size that are, therefore, falling at different rates. The larger drop falls more
quickly and collides with and potentially captures the slower moving smaller drop.
The likelihood of two water droplets colliding can be expressed in terms of an
impact parameter,
y
, which is equal to the distance between the geometric centers of
the two droplets (Fig. 11.1a). Collision is likely if
y
=0 and unlikely if
y
>> (
R
r
),
where
R
is the radius of the larger 'collector' drop and
r
is the radius of the smaller
drop with which the collector drop collides. However, the distinction between
whether there is or is not a collision is blurred because complications arise, some of
which are illustrated in Fig. 11.1b. The collision efficiency,
E
1
, is defined to be the
effective area for which collision of the two cloud droplets is certain relative to the area
[
+
r
)
2
] for which collision would be certain in the absence of these complicating
processes. The value of
E
1
varies from near zero when both cloud droplets are small to
near unity when both are large (Fig. 11.2). However, not all collisions will result in the
two droplets coalescing because, having collided, they can then subsequently break
apart. So it is necessary to multiply
E
1
by the
coalescence efficiency, E
2
, which decreases
markedly for droplets of similar size, to give the
collection efficiency, E
c
, with which a
falling droplet will collide with and then absorb another droplet, hence
E
c
= (
E
1
E
2
).
Attempts have been made to estimate
E
1
,
E
2
, and
E
c
theoretically, but it is very difficult
to validate these theoretical estimates experimentally.
Given a (perhaps approximate) description of the collection of droplets by a
single droplet, the next step is to imagine a large droplet of radius
R
falling though
a field of smaller droplets that are of uniform radius
r
and equally distributed in
space. Assuming
R
>>
r
, it can be easily shown that the resulting rate of growth in
the radius
R
is given by:
π
(
R
+
