The Atmosphere: Part 3: Unsaturated convection Composition / Structure Radiative transfer Vertical...
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Transcript of The Atmosphere: Part 3: Unsaturated convection Composition / Structure Radiative transfer Vertical...
The Atmosphere: Part 3: Unsaturated convection
• Composition / Structure• Radiative transfer
• Vertical and latitudinal heat transport• Atmospheric circulation
• Climate modeling
Suggested further reading:
Hartmann, Global Physical Climatology (Academic Press, 1994)
Full calculation of radiative equilibrium
surface much too warm
tropopause too cold
stratosphere about right
tropospheric lapse rate too large
Atmospheric energy balance
Hydrostatic balance
Mass of cylinder M A z
Forces acting:(i) gravitational force Fg gM g A z,(ii) pressure force acting at the top face, FT p A, and(iii) pressure force acting at the bottom face, FB p pA
Fg FT FB 0 p A g A z, i.e.,
p
z g
p z
g
pRT
p z
gRT
p
p p0 exp zHp p0 exp z
H; H RT
g
Pressure and density profiles in a compressible atmosphere
hydrostatic balance
perfect gas law
Isothermal atmosphere
p p0 exp 0
z dz
Hz
More generally, H=H(z) and
gas constant for dry air R = 287 J kg-1K-1
p z
g
pRT
p z
gRT
p
p p0 exp zHp p0 exp z
H; H RT
g
Pressure and density profiles in a compressible atmosphere
hydrostatic balance
perfect gas law
Isothermal atmosphere
p p0 exp 0
z dz
Hz
More generally, H=H(z) and
(T=237K)
ConvectionI: Incompressible fluid, no condensation
T
s sT
T and ρ are conserved under adiabatic displacement
z
0 T z
0
z
0 T z
0
stable
unstable
Thermodynamics of dry air
p,T p
RT Cp = 1005 J kg-1K-1
dQ cv dT p d 1
cp dT 1 dp
cp dT RTdpp
Thermodynamics of dry air
p,T p
RT
s sp,T
Cp = 1005 J kg-1K-1
specific entropy
dQ cv dT p d 1
cp dT 1 dp
cp dT RTdpp
ds dQ
T cp
dTT
R dpp cp
d
Thermodynamics of dry air
p,T p
RT
s sp,T
s cp ln
Cp = 1005 J kg-1K-1
p0 = 1000 hPa κ = R/cp = 2/7 (diatomic ideal gas)
T p 0
p
potential temperature
(+ constant)
specific entropy
dQ cv dT p d 1
cp dT 1 dp
cp dT RTdpp
ds dQ
T cp
dTT
R dpp cp
d
Thermodynamics of dry air
p,T p
RT
s sp,T
s cp ln
Cp = 1005 J kg-1K-1
p0 = 1000 hPa κ = R/cp = 2/7 (diatomic ideal gas)
T p 0
p
potential temperature
Adiabatic processes : ds 0 d 0
θ is conserved under adiabatic displacement
(N. B. θ=T at p =p0= 1000 hPa)
(+ constant)
specific entropy
dQ cv dT p d 1
cp dT 1 dp
cp dT RTdpp
ds dQ
T cp
dTT
R dpp cp
d
0 d p0p
cpdT RT
p dp
p0p
cpdT 1
dp
p0p
cpdT g dz
ConvectionII: Compressible ideal gas, no condensation
adiabatic displacement
T p 0
p
0 d p0p
cpdT RT
p dp
p0p
cpdT 1
dp
p0p
cpdT g dz
ConvectionII: Compressible ideal gas, no condensation
hydrostatic balance
dp g dz
adiabatic displacement
T p 0
p
0 d p0p
cpdT RT
p dp
p0p
cpdT 1
dp
p0p
cpdT g dz
ConvectionII: Compressible ideal gas, no condensation
hydrostatic balance
dp g dz
adiabatic displacement
T z
gcp
9.76 10 3 Km 1
— adiabatic lapse rate
Following displaced parcel
T p 0
p
dTdz parcel
z
0
0 d p0p
cpdT RT
p dp
p0p
cpdT 1
dp
p0p
cpdT g dz
ConvectionII: Compressible ideal gas, no condensation
hydrostatic balance
dp g dz
adiabatic displacement
T z
gcp
9.76 10 3 Km 1
— adiabatic lapse rate
Following displaced parcel
T p 0
p
unstable
stable
T z environment
T z environment
dTdz env
ddz
0
dTdz parcel
z
0
0 d p0p
cpdT RT
p dp
p0p
cpdT 1
dp
p0p
cpdT g dz
ConvectionII: Compressible ideal gas, no condensation
hydrostatic balance
dp g dz
adiabatic displacement
T z
gcp
9.76 10 3 Km 1
— adiabatic lapse rate
Following displaced parcel
T p 0
p
unstable
stable
T z environment
T z environment
z
0
dTdz parcel
dTdz env
ddz
0
Stability of Radiative Equilibrium Profile
• Radiative equilibrium is unstable in thetroposphere
-10 K/km
radiative equilibrium solution
Effects of convection
Model aircraft observations in an unsaturated convective region (Renno & Williams)
Effects of convection
radiative-convective equilibrium
Effects of convection
radiative-convective equilibrium
TR
OP
OS
PH
ER
ES
TR
AT
OS
PH
ER
E
Radiative-Convective Equilibrium
• Radiative equilibrium is unstable in thetroposphere Re-calculate equilibrium subject to the constraint that tropospheric stability is rendered neutral by convection.
-10 K/km
radiative equilibrium solution
Radiative-convective equilibrium(unsaturated)
Better, but:
• surface still too warm
• tropopause still too cold
Moist convection
Above a thin boundary layer, most atmospheric convection involves phase change of water: condensation releases latent heat