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4. Initiation of Raindrops by Collision and Coalescence. 4.1 Introduction to precipitation physics. 4.2 Setting the stage for coalescence. 4.3 Droplet growth by collision and coalescence. 4.4 Growth models and discussion. 4.1 Precipitation Physics.
Collision and Coalescence
4.1 Introduction to precipitation physics
4.2 Setting the stage for coalescence
4.3 Droplet growth by collision and coalescence
4.4 Growth models and discussion
A drop with a radius of 40 micrometers is
at the cloud base (z=0). The cloud has a
liquid water content of 1.5g/m and a steady
updraft of 2m/s. The terminal velocity of the
drop is given by u=(8X10 s )R. R is in mm.
Assume a collection efficiency of unity.
The liquid water content of a cloud 2 km in depth varies linearly from 1
at the base to 3
at the top. A drop of 100 diameter starts to fall from
the top of the cloud. What will be its size when it leaves the cloud base?
Assume that the collection efficiency is 0.8 and that there is no updraft.
The Bowen Model
* Statistical-discrete growth
The Telford and Robertson Models
- Initial bimodal size distribution of droplets
- A drop grows by discrete collision and capture
events, not by continuous growth processes
- Some drops have more collisions than others
- Rain is produced when one drop in 10 gets an
initial head start and then grows by gravitational
- Require shorter time for a droplet to reach raindrop
than continuous growth
- Collision efficiencies are not unity
- The next collisions are more favorable
giving a further widening of the drop
changes with collection
- 10 of 100 large droplets will
collect a small droplet during
a given time
- Then 1 in 10 of each large size
will collect a smaller droplet
- Large droplets then grow at
- The distribution spreads
for broadening size distributions
- Large hydrometeor
Three possible mechanisms:
i. Drops of different sizes respond differently to
a fluctuating velocity
ii. The overlapping of turbulent eddies
iii. Abrupt inhomogenieties – a few intense turbulence
surrounded by areas of weak turbulence
- The collision-coalescence process is how precipitation
forms in warm clouds (those clouds that remain above
- For the process to work efficiently, the droplet spectrum
cannot be too narrow. Otherwise, the droplets will have
similar terminal velocities and collisions will be infrequent.
- As the large drops get larger than 4 or 5 mm, they
become unstable and break apart. This creates some
additional large drops which can themselves start to
i. Rain has been observed to occur in warm clouds within 15 minutes. Yet, our current understanding of collision-coalescence suggests a much longer time period is needed.
iii. The answer probably lies in a better understanding
of how turbulence affects droplet populations.
Statistical methods are probably also needed to
better understand and model the process by which
warm cloud precipitation develops.
1. Problem 8.1
2. A drop with an initial radius of 100 micrometers falls through
a cloud containing 100 droplets per cubic centimeter, which
it collects in a continuous manner with a collection efficiency
of 0.8. If all the cloud droplets have a radius of 10 micrometers,
how long will it take for the drop to reach a radius of 1 millimeter?
Assume a drop fall speed similar to that in problem 1. Also assume
the cloud droplets are stationary and that the updraft velocity in
the cloud is negligible.