Lecture 11
Cloud Microphysics
Wallace and Hobbs – Ch. 6
Ignore most of the math – concentrate
on descriptive conclusions and graphs
Cloud Types
Outline
Cooling
Supersaturation
Droplet
Formation
Droplet Growth
Precipitation
Formation
Nucleation
Usually refers to the initial formation of a
droplet
More general definition: AMS Glossary
Homogeneous nucleation


Droplet spontaneously forms in pure air
No particles present
Heterogeneous nucleation

Droplets form on particles called cloud
condensation nuclei (CCN)
Homogeneous Nucleation
Formation of a curved water surface
requires energy
 maintenance of a small droplet requires large
supersaturations
RH to Form Droplet of Radius r
RH
W & H, Fig. 6.2
112%
Such large RHs do not occur
in nature.
0.01
r (m)
Heterogeneous Nucleation
Hygroscopic CCN are particularly effective
condensation initiators

Generally made of soluble salts
When droplet forms, solution has a much
lower vapor pressure than pure water
 Condensation begins when RH < 100%
Droplet growth requires supersaturations of
less than 1%

Such supersaturations are achieved in updrafts
Köhler Curves
Give the equilibrium droplet size for a
given RH.
“Saturation ratio” = RH/100
Köhler
Curves
10-19 g
10-18g
10-17g
Numbers indicate mass
of dissolved salt (NaCl)
Suppose RH =
100.1%
10-19 g
10-18g
10-17g
Droplets grow until they
reach equilibrium
radius
10-19 g
10-18g
10-17g
Droplets grow until they
reach equilibrium
radius
10-19 g
10-18g
10-17g
Droplets grow until they
reach equilibrium
radius
10-19 g
10-18g
10-17g
Droplets grow until they
reach equilibrium
radius
10-19 g
10-18g
10-17g
Droplets grow until they
reach equilibrium
radius
Typical cloud
droplet radius
10-19 g
10-18g
10-17g
Droplets grow until they
reach equilibrium
radius
Droplet Growth
If ambient RH < value at peak of curve,
droplets stop growing when much smaller
than typical cloud drop
They are called haze droplets
10-19 g
10-18g
10-17g
Suppose RH =
100.3%
10-19 g
10-18g
10-17g
Droplets growing on
smaller nuclei behave
as before
10-19 g
10-18g
10-17g
Look at largest nucleus
10-19 g
10-18g
10-17g
10-19 g
10-18g
10-17g
10-19 g
10-18g
10-17g
10-19 g
10-18g
10-17g
10-19 g
10-18g
10-17g
10-19 g
10-18g
10-17g
Droplet keeps growing!
Droplet “Activation”
If ambient RH > peak value, droplet grows
indefinitely
Once droplet has gotten “over the hump”,
it is said to be activated.
Slowing of Growth
Rate of droplet growth decreases as
droplets grow
Let r = droplet radius
It can be shown that
dr 1

dt r
Depletion of Water Vapor
Also, growth of large number of droplets
reduces supersaturation
Result: Droplet radius tends to level off at
about 10m
Fall velocity of such a droplet is < 1 cm-1
 droplets tend to be carried upward
Droplets must be much larger to actually
fall
Microphysical Parameters
Liquid water content (LWC)

grams of liquid water per m3 of cloud
Droplet concentration, N

Number of droplets per cm3
Mean droplet size, r

Usually given in m
Not independent – knowledge of any two
determines the third
Relationship Between
Microphysical Parameters
4
3
LWC  N   L r ,
3
where L is the density of
liquid water.
See W & H, p. 217 for typical values of microphysical parameters
Supercooled Water
Definition: Liquid water with T < 0C
Freezing


Homogeneous nucleation occurs at -40C!
Heterogeneous nucleation occurs in presence
of a freezing nucleus
(Typically occurs at temps much higher than -40C)
Freezing Point
Common experience: Water freezes at 0C
This works when mass of water >> cloud droplet


Only one nucleation event is required to freeze entire
mass
Such an event is virtually certain for masses of water
normally encountered
Cloud droplets very small


Probability of a nucleation event at 0C is small
Probability increases as temperature falls
Ice Crystals
When T < 0C, ice crystals can form
directly from vapor
Homogeneous nucleation requires
unrealistically large super-saturations
Heterogeneous nucleation occurs on
particles called deposition nuclei
Ice Nuclei
General name for various types of nuclei

e.g., freezing nuclei, deposition nuclei
Relatively rare

1 particle in 108 suitable!
Nucleation Temps
Substance
Kaolinite
Temp. (C)
-9
Silver Iodide
-4
Bacteria!
-3
Source: Table 9.1 in A Short Course in Cloud
Physics, 3rd Ed. Rogers, R. and M. Yau.
Pergamon Press, 293 pp.
Supercooled Water and Ice
Let es,w(T) be the saturation vapor pressure
over liquid water at temperature T
Let es,i(T) be the saturation vapor pressure
over ice at temperature T
es,i(T) < es,w(T) for T < 0C
es,i vs. es,w
T (C)
0
-5
-10
-15
-20
-25
-30
-35
-40
es,i(hPa)
6.11
4.02
2.60
1.65
1.03
0.63
0.38
0.22
0.13
es,w(hPa)
6.11
4.21
2.87
1.91
1.25
0.81
0.51
0.31
0.19
(Source: Smithsonian Meteorological Tables, 6th Ed.)