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12.842 / 12.301 Past and Present Climate
Fall 2008
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Above a thin boundary layer, most atmospheric convection involved phase change of water:
Moist Convection
Moist Convection
• Significant heating owing to phase
changes of water
• Redistribution of water vapor – most
important greenhouse gas
• Significant contributor to stratiform
cloudiness – albedo and longwave
trapping
Water Variables
Mass concentration of water vapor (specific humidity):
q≡
MH O
2
M air
Vapor pressure (partial pressure of water vapor):
Saturation vapor pressure:
C-C:
e*
17.67(T −273)
T +30
e* = 6.112 hPa e
Relative Humidity:
H ≡ e e*
e
The Saturation Specific Humidity
Ideal Gas Law:
R *T
p=ρ
m
R*T
e = ρv
mv
mv e
ρ
v
q= ρ =
m p
mv e*
q* =
m p
Phase Equilibria
Bringing Air to Saturation
e = qp  m m 

v
e* = e *(T )
1. Increase q (or p)
2. Decrease e* (T)
When Saturation Occurs…
• Heterogeneous Nucleation
• Supersaturations very small in atmosphere
• Drop size distribution sensitive to size
distribution of cloud condensation nuclei
Ice Nucleation Problematic
ICE NUCLEATION PROBLEMATIC
4
3
100
Percentage of clouds with ice particle
concentrations above detectable level
15
16 16
80
7 1 2 1 1 1
8
23
60
14
25
40
12
10
20
33
15
20
1
0
0
25
1
-5
-10
-15
Cloud top temperature (oC)
Figure by MIT OpenCourseWare.
-20
-25
Precipitation Formation:
• Stochastic coalescence (sensitive to drop
size distributions)
• Bergeron-Findeisen Process
• Strongly nonlinear function of cloud water
concentration
• Time scale of precipitation formation ~10
30 minutes
Stability
No simple criterion based on entropy:
T 
 p
sd = c p ln   − Rd ln  
 T0 
 p0 
α = α ( sd , p )
T 
 p 
q
+ L
s = c ln   − R ln 
− qR ln ( H
p T 
d  p  vT
v
 0
 0 α = α ( s, p, qt )
) Trick:
Define a saturation entropy, s* :
s* ≡ s (T , p, q *)
α = α ( s*, p, qt )
We can add an arbitrary function of qt to s* such that
α ≅ α ( s*', p )
Stability Assessment using Tephigrams:
Convective Available Potential Energy
(CAPE):
CAPEi ≡ ∫ p (α p − α e )dp
pi
n
(
)
= ∫ p Rd Tρ − Tρ d ln ( p )
pi
p
e
Other Stability Diagrams:
Tropical Soundings
“Air-Mass” Showers:
Image courtesy of AMS.
Precipitating Convection favors Widely Spaced Clouds (Bjerknes, 1938)
Properties:
• Convective updrafts widely spaced
• Surface enthalpy flux equal to vertically
integrated radiative cooling
c pT ∂θ
M
= −Q
•
θ ∂z
• Precipitation = Evaporation = Radiative
Cooling
• Radiation and convection highly interactive
Simple Radiative-Convective Model
Enforce convective
neutrality:
T1 = T2 + ∆T ,
Ts = T2 + 2∆T
TOA : T2 = Te → T1 = Te + ∆T , Ts = Te + 2∆T
Surface : Fs + σ Ts 4 = σ Te 4 + σ T14
Layer 2 : 2σ Te = σ T + Fc
4
Define x ≡ ∆
T
Te
4
1
,
4
4

Fs = σ Te 1 + (1+ x ) − (1 + 2 x ) 
,


4
4

Fc = σ Te 2 − (1 + x ) 


4
Manabe and Strickler 1964 calculation:
Effect of Moist Convective Adjustment on Climate Sensitivity