Tropical Meteorology
Kerry Emanuel
Course Outline• Radiative-Convective Equilibrium
– General principles of radiative transfer– Simple models without phase change– General principles of moist convection– Simple models with phase change– Quantitative assessments of the equilibrium state -
comparisons to observations• The Zonally-Averaged Circulation
– The observed climatology– Breakdown of the radiative-convective equilibrium state– Dry theory– Moist theory– Regulation of intensity
• Asymmetric Steady Circulations– Monsoons
• Development and onset of the Asian monsoon• Monsoon breaks• Nonlinear, asymmetric theory
– The Walker Circulation• Observations• Theory
• Interannual Fluctuations of the Walker Circulation – ENSO
– Observed behavior– Theory and modeling of ENSO
• Intraseasonal Oscillations– Observations– GCM simulations– Theory of equatorial waves
• Dry• Moist
– WISHE– Cloud-radiation interactions and ISOs
• Higher Frequency Disturbances– Monsoon depressions– Equatorial waves– Easterly waves
• Tropical Cyclones– Structure and climatology– Steady-state physics– Genesis– Ocean interaction
Brief Overview of the Global Atmosphere
0.000004%O3*Ozone
0.00003%N2O*Nitrous Oxide
0.00005%H2Hydrogen
0.00017%CH4*Methane
0.0005%HeHelium
0.0018%NeNeon
0.0360%CO2*Carbon Dioxide
0.93%ArArgon
0 to 4%H2O*Water
20.95%O2Oxygen
78.08%N2Nitrogen
Percent VolumeChemical FormulaGas Name
* variable gases
Atmospheric Composition
Sea Surface Temperature
Seasonal variation of solar radiation
A One-Dimensional Description of the Tropical Atmosphere
Elements of Thermal Balance:Solar Radiation
• Luminosity: 3.9 x 1026 J s-1 = 6.4 x 107 Wm-2
at top of photosphere
• Mean distance from earth: 1.5 x 1011 m• Flux density at mean radius of earth
20 13700 24
LS Wm
dπ−≡ =
4Stefan-Boltzmann Equation:8 2 45.67 10
74 2Sun: 6.4 106,000
F TWm K
T WmT K
σ
σ
σ
=− − −= ×
−= ×
→
Disposition of Solar Radiation:
( )
2Total absorbed solar radiation 10planetary albedo 30%
2Total surface area 4
0Absorption per unit area 14
S a rp pap
rpS
ap
π
π
= −
≡
=
= −
Absorption by clouds, atmosphere, and surface
Terrestrial Radiation:Effective emission temperature:
4 0 14
Earth: 255 18
Observed average surface temperature 288 15
ST ae p
T K Ce
K C
σ ≡ −
= = − °
= = °
Highly Reduced Model• Transparent to solar radiation• Opaque to infrared radiation• Blackbody emission from
surface and each layer
Top of Atmosphere:
Radiative Equilibrium:
4 40 14
ST a TA p eσ σ = − =
Surface:
( )4 4 40 1 24s A p eST T a Tσ σ σ= + − =
A eT T→ =
142 303s eT T K→ = =
Surface temperature too large because:
• Real atmosphere is not opaque• Heat transported by convection as well as
by radiation
Energy Balance
Principal Atmospheric Absorbers
• H2O: Bent triatomic, with permanent dipole moment and pure rotational bands as well as rotation-vibration transitions
• O3: Like water, but also involved in photodissociation
• CO2: No permanent dipole moment, so no pure rotational transitions, but temporary dipole during vibrational transitions
• Other gases: N2O, CH4
Radiative Equilibrium
• Equilibrium state of atmosphere and surface in the absence of non-radiative enthalpy fluxes
• Radiative heating drives actual state toward state of radiative equilibrium
Extended Layer Models
4 42 2
4 4 4 4 41 2
4 4 41
1 14 4
1
:
: 2
:
3 2
e e
s e s
s e
s e e
TOA T T T T
Middle Layer T T T T T
Surface T T T
T T T T
σ σ
σ σ σ σ σ
σ σ σ
= → =
= + = +
= +
→ = =
Effects of emissivity<1
( )
( )
4 4 41
14
4 42
14
: 2
5 3212: 2
1 2142
A A A A s
A e s
t t A
t e e
Surface T T T
T T K T
Stratosphere T T
T T K T
ε σ ε σ ε σ
ε σ ε σ
= +
→ = <
=
→ = <
Full calculation of radiative equilibrium:
Time scale of approach to equilibrium:
Contributions of various absorbers:
Problems with radiative equilibrium solution:
• Too hot at and near surface• Too cold at a near tropopause• Lapse rate of temperature too large in the
troposphere• (But stratosphere temperature close to
observed)
Missing ingredient: Convection
• As important as radiation in transporting enthalpy in the vertical
• Also controls distribution of water vapor and clouds, the two most important constituents in radiative transfer
When is a fluid unstable to convection?
• Pressure and hydrostatic equilibrium• Buoyancy• Stability
Hydrostatic equilibrium:
( )::
:
1,
Weight g x y zPressure p x y p p x y
dwF MA x y z g x y z p x ydt
dw pg specific volumedt z
ρδ δ δδ δ δ δ δ
ρδ δ δ ρδ δ δ δ δ δ
α α ρ
−
− +
= = − −
∂= − − = =
∂
Pressure distribution in atmosphere at rest:
0
*: ,
1 ln( ):
: , " "zH
RT RIdeal gas Rp mp p gHydrostatic
p z z RTRTIsothermal case p p e H scale heightg
α
−
= ≡
∂ ∂= = −
∂ ∂
= ≡ =
Earth: H~ 8 Km
Buoyancy:
( )::
:
b
b b
be
b e
e
Weight g x y zPressure p x y p p x y
dwF MA x y z g x y z p x ydt
dw p p gg butdt z z
dw g Bdt
δ δ δδ δ δ δ δ
δ δ δ
ρ
ρ ρ
α αα
δ δ δ δ δ δ
αα
−
− +
= = −
−
−
∂ ∂= − − = −
∂ ∂
→ = ≡
Buoyancy and Entropy
Specific Volume: 1α ρ=
Specific Entropy: s
( , )p sα α=
( ) pp s
Ts ss pαδα δ δ
∂ ∂= =∂ ∂
( ) pss
g T TB g s s sp zδα
δ δ δα α
∂ ∂= = = − ≡Γ∂ ∂
:p s
TMaxwells pα ∂ ∂ = ∂ ∂
The adiabatic lapse rate:
( )
( )
( )
:
: 0
: 0
revv
v
v
p
p
p
ds p
First Law of Thermodynamicsds dT dQ T c pdt dt dt
d pdT dpcdt dt dt
dT dpc Rdt dt
dT dpcdt dt
Adiabatic c dT dp
Hydrostatic c dT gdz
gdTdz c
α
αα
α
α
α
= = +
= + −
= + −
= −
− =
+ =
→ = − ≡ −Γ
p
gcΓ =
Earth’s atmosphere: 1100
KmΓ =
Model Aircraft Measurements(Renno and Williams, 1995)
Radiative equilibrium is unstable in the troposphere
Re-calculate equilibrium assuming that tropospheric stability is rendered neutral by
convection:
Radiative-Convective Equilibrium
Better, but still too hot at surface, too cold at tropopause