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12.842 / 12.301 Past and Present ClimateFall 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 VariablesMass concentration of water vapor (specific humidity):

2q ≡ MH O

Mair

Vapor pressure (partial pressure of water vapor): e

Saturation vapor pressure: e*

17.67(T −273) C-C: e* 6.112 = hPa e T +30

Relative Humidity: H ≡ ee*

*v

v

R Te mρ=

*R Tp mρ=

vv m eq m pρρ= =

** vm eq m p=

The Saturation Specific Humidity

Ideal Gas Law:

Phase Equilibria

Bringing Air to Saturation

e qp m

= mv

* = *( )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 Pe

rcen

tage

of c

loud

s w

ith ic

e pa

rticl

eco

ncen

tratio

ns a

bove

det

ecta

ble

leve

l

100

80

60

40

20

0

10

15

12 33

25 25

23

20 14

16 16 8

3 15

4

7 1

1 1

2 1 1 1

0 -5 -10 -15 -20 -25

Cloud top temperature (oC)

Ice Nucleation Problematic

Figure by MIT OpenCourseWare.

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 psd = cp ln − Rd ln T p 0 0

α =α (sd , p) T p qs c= ln − R ln + L − qR ln ( ) H p d p v vT T 0 0

=α (s p q )α , , t

Trick:

Define a saturation entropy, s* :

s* ≡ s T p q ( , , *) α =α ( s*, p q, t )

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):

pi −CAPE ≡ ∫ (α α )dpi pn p e

pi= ∫ R T( −T )d ln ( )pp d ρ p ρe

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 coolingc T ∂θ • M p = −Q� θ ∂z

• Precipitation = Evaporation = Radiative Cooling

• Radiation and convection highly interactive

Simple Radiative-Convective Model

=Enforce convective T T + ∆T ,1 2 neutrality: + ∆TT T = 2s 2

TOA : T2 = Te → T1 = Te + ∆ T , Ts = Te + 2∆T

Surface : Fs +σTs 4 =σTe

4 +σT14

Layer 2 : 2 σTe 4 =σT1

4 + Fc

Define x ≡ ∆

F =σT 4 1 1+ x 4 − 1 2

4 s e + ( ) ( + x) ,

Fc =σTe 4

2 1− ( + x)4

, e

T T

Manabe and Strickler 1964 calculation:

Effect of Moist Convective Adjustment on Climate Sensitivity