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