Brief Overview of the Global Atmosphere

Images on pages 21, 57-58, and 69 are copyrighted by Oxford, NY: Oxford University Press, 2005. Book title is Divine wind: the history and science of hurricanes. ISBN: 0195149416. Used with permission.

Images on pages 3, 5 through 9, 19, 77 through 80 and 90 are copyrighted by Academic Press, NY, 1999. The images are in a chapter entitled "Quasi-equilibrium thinking" (author is Kerry Emanuel) that appears in the book entitled General circulation model development: past, present and future. Edited by D. Randall. ISBN: 0125780109. Used with permission.

Atmospheric CompositionGas Name Chemical Formula Percent Volume

Nitrogen N2 78.08%

Oxygen O2 20.95%

*Water H2O 0 to 4%

Argon Ar 0.93%

*Carbon Dioxide CO2 0.0360%

Neon Ne 0.0018%

Helium He 0.0005%

*Methane CH4 0.00017%

Hydrogen H2 0.00005%

*Nitrous Oxide N2O 0.00003%

*Ozone O3 0.000004%

* variable gases

See figure of “Humidity Profiles -- Annual”In book:Global Physical ClimatologyISBN: 0123285305 Author: Dennis L. HartmannPublisher: Academic PressNumber of pages: 411

0-100

Troposphere

Tropopause

Stratosphere

StratopauseMesosphere

Mesopause

Thermosphere

-80 -60 -40 -20 0 20

10000

20000

30000

40000

50000

60000

Alti

tude

(met

ers)

Temperature oC

70000

80000

90000

100000

Figure by MIT OCW.

See Figure 1.6 and Figure 1.7In book:Global Physical ClimatologyISBN: 0123285305 Author: Dennis L. HartmannPublisher: Academic PressNumber of pages: 411

See figure Temperature vs LatitudeIn book:Global Physical ClimatologyISBN: 0123285305 Author: Dennis L. HartmannPublisher: Academic PressNumber of pages: 411

See figure of seasonal variation of solar radiationIn book:Global Physical ClimatologyISBN: 0123285305 Author: Dennis L. HartmannPublisher: Academic PressNumber of pages: 411

See figure Insolation vs LatitudeIn book:Global Physical ClimatologyISBN: 0123285305 Author: Dennis L. HartmannPublisher: Academic PressNumber of pages: 411

A One-Dimensional Description of the Tropical Atmosphere

0-100

Troposphere

Tropopause

Stratosphere

StratopauseMesosphere

Mesopause

Thermosphere

-80 -60 -40 -20 0 20

10000

20000

30000

40000

50000

60000

Alti

tude

(met

ers)

Temperature oC

70000

80000

90000

100000

Figure by MIT OCW.

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−≡ =

Disposition of Solar Radiation:

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

Radiative Equilibrium:Top of Atmosphere:

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

See diagram of Energy BalanceIn book:Global Physical ClimatologyISBN: 0123285305 Author: Dennis L. HartmannPublisher: Academic PressNumber of pages: 411

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

http://www.divinewindbook.com/figures/image013.htm

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

Full calculation of radiative equilibrium:

Problems with radiativeequilibrium 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( ):

: , " "z

H

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

1α ρ=Specific Volume:

Specific Entropy: s

( , )p sα α=:

p s

TMaxwells pα ⎛ ⎞∂ ∂⎛ ⎞ = ⎜ ⎟⎜ ⎟∂ ∂⎝ ⎠ ⎝ ⎠

( ) pp s

Ts ss pαδα δ δ

⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

∂ ∂= =∂ ∂

( ) p

ss

g T TB g s s sp zδα

δ δ δα α⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠

∂ ∂= = = − ≡Γ∂ ∂

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 =

1100

KmΓ =Earth’s atmosphere:

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

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):

2H O

air

Mq M≡

Vapor pressure (partial pressure of water vapor): e

Saturation vapor pressure: e*

( )17.67 27330* 6.112

TTe hPa e

−+=C-C:

*e

e≡HRelative Humidity:

The Saturation Specific Humidity

*v

v

R Te mρ=

*R Tp mρ=Ideal Gas Law:

vv m eq m pρρ= =

** vm eq m p=

Phase Equilibria

Bringing Air to Saturation

vme qp m⎛ ⎞⎜ ⎟⎝ ⎠

=

* *( )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

00

Perc

enta

ge o

f clo

uds

with

ice

parti

cle

conc

entra

tions

abo

ve d

etec

tabl

e le

vel

-5 -10 -15 -20 -25

20

4010

15

1233

25 25

23

2014

16 168

315

4

7 1

1 1

2 1 1 1

60

80

100

Cloud top temperature (oC)

ICE NUCLEATION PROBLEMATIC

Figure by MIT OCW.

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

StabilityNo simple criterion based on entropy:

0 0

ln lnd p d

T ps c RT p⎛ ⎞ ⎛ ⎞

= −⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

( ),ds pα α=

( )ln ln ln0 0

T p qs c R L qRp d v vT p T

⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟= − + −⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

H

( ), , ts p qα α=

Virtual Temperature and Density Temperature

Assume all condensed water falls at terminal velocity

a c

d v c

V VM M M

α +=

+ +

*pV nR T=

* ,d va

vd

M MR TVp mm

⎛ ⎞= +⎜ ⎟

⎝ ⎠

11d

i

id i

m MM m

≡∑

,d va d

R T MV Mp ε

⎛ ⎞→ = +⎜ ⎟⎝ ⎠

0.622v

d

mm

ε ≡ ≅where

*d

d

RRm

≡

( )( )

1 11

1

a c d c at

d v c c c

dt

V V R T qqqM M M p q

R T qqp

ρα ε ρ

ε

⎛ ⎞+= = − + +⎜ ⎟+ + −⎝ ⎠

≅ − +

Density temperature:

,v c vt

M M Mq qM M+

≡ ≡

( )1 tqT T qρ ε≡ − +

dR Tp

ρα =

Trick:

Define a saturation entropy, s* :

( )* , , *s s T p q≡

( )*, , ts p qα α=

We can add an arbitrary function of qt to s* such that

( )*',s pα α≅

Stability Assessment using Tephigrams:

-40 -30 -20 -10 0 10 20 30 40 50

100

200

300

400

500

600700800900

1000

Temperature (C)

Pre

ssur

e (m

b)

Stability Assessment using Tephigrams:

Convective Available Potential Energy(CAPE):

( )( ) ( )ln

i

n

i

p e

pi p ep

pdp

CAPE dp

R T T d pρ ρ

α α≡ −∫

= −∫

Other Stability Diagrams:

“Air-Mass” Showers:

See Figure 15 and 16 In Journal:Byers Braham. Journal of Meteorology 5 (1948): 71-86

Tropical Soundings

Annual Mean Kapingamoronga:

Radiative-Moist Convective Equilibrium

Precipitating Convection favors Widely Spaced Clouds (Bjerknes, 1938)

Properties:

• Convective updrafts widely spaced• Surface enthalpy flux equal to vertically

integrated radiative cooling•• Precipitation = Evaporation = Radiative

Cooling • Radiation and convection highly interactive

pc TM Q

zθ

θ∂

= −∂

&

Manabe and Strickler 1964 calculation:

0 1 2 3 4 5 6 7 8 9 100.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Time (days)

Pre

cipi

tatio

n (m

m/d

ay)

See figures on pages 241-242 In book:General Circulation Model Development : Past, Present, and Future, Vol. 70ISBN: 0125780109 Author: David A. Randall (Editor)Publisher: Academic PressNumber of pages: 416

Recovery from mid-level specific humidity perturbation

1 2 3 4 5 6 7 8 9 10-1000

-900

-800

-700

-600

-500

-400

-300

-200

-100

Specific humidity perturbation (g/Kg), from -5.479 to 2.645

Time (days)

P (m

b)

1 2 3 4 5 6 7 8 9 10-1000

-900

-800

-700

-600

-500

-400

-300

-200

-100

Tv Perturbation, from -6.87 to 0.848

Time (days)

P (m

b)

Robe and Emanuel, J. Atmos. Sci., 1996

Islam et al. Predictability Experiments

See figure on page 238 In book:General Circulation Model Development : Past, Present, and Future, Vol. 70ISBN: 0125780109 Author: David A. Randall (Editor)Publisher: Academic PressNumber of pages: 416

Frequency histogram of rawindsonde relative humidities from 1600ascents at the tropical Pacific islands of Yap, Koror, Ponape and Majuro, January-May, 1994-95. Spencer and Braswell, Bull. Amer. Meteor. Soc.,1997.

The Three-Dimensional Circulation

What causes lateral enthalpy transport by atmosphere?

1: Large-scale, quasi-steady overturning motion in the Tropics,

2: Eddies with horizontal dimensions of ~ 3000 km in middle and high latitudes

Observed Characteristics of the Time Mean Tropical Atmosphere

• Monthly and seasonal means• Zonal means

Objective Analysis

Provides “Best Guess” as to the State of the Atmosphere

1. Start with “First Guess” Analysis

2. Ingest Data-Radiosondes-Surface Observations-Ship Reports and Buoy Observations-Aircraft Observations-Satellite Observations

3. Data Assimilation

-Blend data to produce an “initialized” (balanced) analysis(or not....)

4. Run General Circulation Model to Obtain next First Guess

-A six hour “cycle” is typical-“Asynoptic” Observations can also be assimilated

.

ζ = ∇ ×

r V =

∂ v∂ x

−∂ u∂ yVorticity

D = ∇ •

r V =

∂ u∂ x

+∂ v∂ yDivergence

∇ 2 ψ = ζStreamfunction

∇ 2 χ = DVelocityPotential

Non-divergent (Rotational) Wind

v ψ =∂ ψ∂ x

u ψ = −∂ ψ∂ y

Divergent Wind

u χ =∂ χ∂ x

v χ =∂ χ∂ y