Water in the atmosphere
Water content of air
mass water vapour
Mass mixing ratio, x 
mass dry air
~ 10gkg1 1%
Saturated vapour pressure, equilibrium over flat surface
Rate of evaporation = rate of condensation
svp is a function of T only
Saturated vapour pressure
Condensation
vapour pressure
Relative Humidity, R.H. 
100%
svp at same T
Condensation when R.H.≥100%
R.H. can increase by
(i)
increasing x,
(ii)
cooling air
Cooling damp air
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Radiation loss
Ascent (of air mass)
Descent, through inversion
Advection, over cool region
Influx of cold dry air
Convection
radiation fog
hill fog/cloud, fronts
steam fog
advection fog, har
Arctic sea smoke
cumulus clouds
Warm Rain Process
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Saturation
Nucleation
Growth by condensation
Growth by accretion
Rainfall
Nucleation
s.v.p. over curved surface > s.v.p. over flat surface
svp  r 
 1 2 
1.2 109
 exp 
  1
svp   
r

RT
r
 w 
For typical molecule, r~0.6nm, would need RH=740% (SS=640%)
In atmosphere maximum SS observed is ~1%
Condensation must be on particles with r~100nm
Radius
Name
Conc. (cm-3)
SS
< 0.1 µm
Aitken nuclei
10,000
1%
0.1 - 1 µm
large nuclei
100
0.1%
> 1 µm
giant nuclei
1
0.01%
Nucleation
Hygroscopic nuclei
Fewer water molecules in surface so lower evaporation rate
svp  r 
1.2 109 Bm
 1
 3
svp   
r
r
Kohler curves
Sizes of droplets
Growth by Condensation
To grow by dr require this much water
dm   w dV   w 4 r 2 dr
r
dr
dr
1
dm

dt  w 4 r 2 dt
dr
F
D


p
2
dt  w 4 r
wr
Mass flux of water vapour diffusing through
shell of radius n
dm
dp
2
F
 4 n D
dt
dn
Same flux through every shell, so integrate to find Δp
r
F dn
F 1

p   dp  

2

 4 D n
4 D r
r
Vapour pressure at droplet = svp (T)
Vapour pressure in cloud = svp * RH
p  pcloud  pdrop surface
 svp  RH  1  svp  SS
dr D  svp  SS 1

dt
w
r
Growth by condensation
Terminal
velocity of
drops
For laminar flow, at terminal velocity
drag force=weight
mg  6 rv
3
4
mg
3  r w g
v

6 r
6 r
v
2 w g 2
r
9 
Growth by Collision/Accretion
dm
   r1  r2
dt
Continuous collection model
 v  v  w E
2
1
dr1
 w 4 r
   r1  r2
dt
2
1
1
dr1 xs  air E

v1
dt
4w
dr1
 r1
dt
collection
efficiency
 v  v  x 
For large drops (>40µm) v1  r1
2{r1+r2}
l
2
if r1  r2 and v1  v2
r2
v2
2
relative volume swept
out per unit time
r1
v1
liquid water content of cloud
2
s
air
E
Arial view of convection cells
Cloud streets