the atmosphere: part 3: unsaturated convection
DESCRIPTION
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). - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: The Atmosphere: Part 3: Unsaturated convection](https://reader036.vdocument.in/reader036/viewer/2022062720/5681358b550346895d9cf0cf/html5/thumbnails/1.jpg)
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)
![Page 2: The Atmosphere: Part 3: Unsaturated convection](https://reader036.vdocument.in/reader036/viewer/2022062720/5681358b550346895d9cf0cf/html5/thumbnails/2.jpg)
Full calculation of radiative equilibrium
surface much too warm
tropopause too cold
stratosphere about right
tropospheric lapse rate too large
![Page 3: The Atmosphere: Part 3: Unsaturated convection](https://reader036.vdocument.in/reader036/viewer/2022062720/5681358b550346895d9cf0cf/html5/thumbnails/3.jpg)
Atmospheric energy balance
![Page 4: The Atmosphere: Part 3: Unsaturated convection](https://reader036.vdocument.in/reader036/viewer/2022062720/5681358b550346895d9cf0cf/html5/thumbnails/4.jpg)
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
![Page 5: The Atmosphere: Part 3: Unsaturated convection](https://reader036.vdocument.in/reader036/viewer/2022062720/5681358b550346895d9cf0cf/html5/thumbnails/5.jpg)
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
![Page 6: The Atmosphere: Part 3: Unsaturated convection](https://reader036.vdocument.in/reader036/viewer/2022062720/5681358b550346895d9cf0cf/html5/thumbnails/6.jpg)
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)
![Page 7: The Atmosphere: Part 3: Unsaturated convection](https://reader036.vdocument.in/reader036/viewer/2022062720/5681358b550346895d9cf0cf/html5/thumbnails/7.jpg)
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
![Page 8: The Atmosphere: Part 3: Unsaturated convection](https://reader036.vdocument.in/reader036/viewer/2022062720/5681358b550346895d9cf0cf/html5/thumbnails/8.jpg)
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
![Page 9: The Atmosphere: Part 3: Unsaturated convection](https://reader036.vdocument.in/reader036/viewer/2022062720/5681358b550346895d9cf0cf/html5/thumbnails/9.jpg)
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
![Page 10: The Atmosphere: Part 3: Unsaturated convection](https://reader036.vdocument.in/reader036/viewer/2022062720/5681358b550346895d9cf0cf/html5/thumbnails/10.jpg)
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
![Page 11: The Atmosphere: Part 3: Unsaturated convection](https://reader036.vdocument.in/reader036/viewer/2022062720/5681358b550346895d9cf0cf/html5/thumbnails/11.jpg)
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
![Page 12: The Atmosphere: Part 3: Unsaturated convection](https://reader036.vdocument.in/reader036/viewer/2022062720/5681358b550346895d9cf0cf/html5/thumbnails/12.jpg)
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
![Page 13: The Atmosphere: Part 3: Unsaturated convection](https://reader036.vdocument.in/reader036/viewer/2022062720/5681358b550346895d9cf0cf/html5/thumbnails/13.jpg)
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
![Page 14: The Atmosphere: Part 3: Unsaturated convection](https://reader036.vdocument.in/reader036/viewer/2022062720/5681358b550346895d9cf0cf/html5/thumbnails/14.jpg)
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
![Page 15: The Atmosphere: Part 3: Unsaturated convection](https://reader036.vdocument.in/reader036/viewer/2022062720/5681358b550346895d9cf0cf/html5/thumbnails/15.jpg)
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
![Page 16: The Atmosphere: Part 3: Unsaturated convection](https://reader036.vdocument.in/reader036/viewer/2022062720/5681358b550346895d9cf0cf/html5/thumbnails/16.jpg)
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
![Page 17: The Atmosphere: Part 3: Unsaturated convection](https://reader036.vdocument.in/reader036/viewer/2022062720/5681358b550346895d9cf0cf/html5/thumbnails/17.jpg)
Stability of Radiative Equilibrium Profile
• Radiative equilibrium is unstable in thetroposphere
-10 K/km
radiative equilibrium solution
![Page 18: The Atmosphere: Part 3: Unsaturated convection](https://reader036.vdocument.in/reader036/viewer/2022062720/5681358b550346895d9cf0cf/html5/thumbnails/18.jpg)
Effects of convection
Model aircraft observations in an unsaturated convective region (Renno & Williams)
![Page 19: The Atmosphere: Part 3: Unsaturated convection](https://reader036.vdocument.in/reader036/viewer/2022062720/5681358b550346895d9cf0cf/html5/thumbnails/19.jpg)
Effects of convection
radiative-convective equilibrium
![Page 20: The Atmosphere: Part 3: Unsaturated convection](https://reader036.vdocument.in/reader036/viewer/2022062720/5681358b550346895d9cf0cf/html5/thumbnails/20.jpg)
Effects of convection
radiative-convective equilibrium
TR
OP
OS
PH
ER
ES
TR
AT
OS
PH
ER
E
![Page 21: The Atmosphere: Part 3: Unsaturated convection](https://reader036.vdocument.in/reader036/viewer/2022062720/5681358b550346895d9cf0cf/html5/thumbnails/21.jpg)
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
![Page 22: The Atmosphere: Part 3: Unsaturated convection](https://reader036.vdocument.in/reader036/viewer/2022062720/5681358b550346895d9cf0cf/html5/thumbnails/22.jpg)
Radiative-convective equilibrium(unsaturated)
Better, but:
• surface still too warm
• tropopause still too cold
![Page 23: The Atmosphere: Part 3: Unsaturated convection](https://reader036.vdocument.in/reader036/viewer/2022062720/5681358b550346895d9cf0cf/html5/thumbnails/23.jpg)
Moist convection
Above a thin boundary layer, most atmospheric convection involves phase change of water: condensation releases latent heat