When Saturation Occurs
Occurs…
…
• Heterogeneous Nucleation
• Supersaturations very small in atmosphere
distrib
ibution
i sensiitive
i to siize
• Drop siize di
distribution of cloud condensation nuclei
1
2
ICE NUCLEATION PROBLEMATIC
Percentage of clouds with ice particle
concentrations above detectable level
15
16 16
80
7 1 2 1 1 1
8
23
60
25
40
12
10
14
25
20
33
15
20
0
0
4
3
100
1
1
-5
-10
-15
-20
-25
Cloud top temperature (oC)
Image by MIT OpenCourseWare.
3
Precipitation Formation:
• Stochastic coalescence (sensitive to drop
size distributions)
geron-Findeisen Process
• Berg
• Strongly nonlinear function of cloud water
concentration
• Time scale of precipitation formation ~1030 minutes
4
Stability
No simple criterion based on entropy:
T 
 p
sd  c p ln    Rd ln  
 T0 
 p0 
    sd , p 
T 
 p 
q
L
s  c ln    R ln 
 qR ln 
p T 
d  p  vT
v
 0
 0
    s, p, qt 
5

Virtual Temperature and Density
Temperature
Assume all condensed water falls at
terminal velocity
Va  Vc

Md  Mv  Mc
pV  nR *T
R *T
Va 
p
 Md Mv 


,
 md mv 
6
1
md 
1
Md
Rd T
 Va 
p
where
here

mv
Mi
i m
i
 M  Mv
 d


md
 0.622
0 622
Rd  R *
7
,


md



qc  a 
Va  Vc
Rd T
q


1 qt 
1



Md  Mv  Mc
p
1 qc c 
 1
Rd T
q

1  qt 

p
Mv  Mc
Mv
qt 
,
q
M
M


Density temperature:

q
T  T 1 qt 

Rd T
p
8


Trick:
D fi a saturati
Define
t tion entropy,
t
s** :
ss*  s T , p, qq*
    s*, p, qt 
We can add an arbitrary function of qt to s* such that
    s*', p 
9
10
Stability Assessment using Tephigrams:
100
Press
sure (mb)
200
300
400
500
600
700
800
900
1000
-40
-30
-20
-10
0
10
Temperature (C)
11
20
30
40
50
Stability Assessment using Tephigrams:
Convective Available Potential Energy
(CAPE):
CAPEi   p  p   e dp
pi
n


  p Rd T  T d ln  p 
pi
p
e
12
Other Stability Diagrams:
13
“Air
Air--Mass
Mass”” Showers:
14
MIT OpenCourseWare
http://ocw.mit.edu
12.811 Tropical Meteorology
Spring 2011
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
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