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NATS 101

Lecture 6Greenhouse Effect and

Earth-Atmo Energy Balance

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Review Items

• Heat Transfer

• Latent Heat

• Wien’s Displacement Law Ramifications

• Stefan-Boltzman Law Ramifications

max2900 mKm

Tμμλ ⎛ ⎞

⎜ ⎟⎝ ⎠

≈

8-2 -2 -4 4(W m ) (5.67 10 Wm K )E T−= ×

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New Business

• Selective Absorption and Emission

• Earth-Atmo Energy Balance

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Modes of Heat Transfer

Conduction Convection Radiation

Williams, p. 19

Latent Heat

Remember this thought experiment and

the incandescent light bulb demo

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Latent Heat Take 2

Williams, p 63

Takes energy from environment

Emits energy to environment

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General Laws of Radiation

• All objects above 0 K emit radiant energy• Hotter objects radiate more energy per unit

area than colder objects, result of Stefan-Boltzman Law

• The hotter the radiating body, the shorter the wavelength of maximum radiation, result of

Wien’s Displacement Law• Objects that are good absorbers of radiation

are also good emitters…today’s lecture!

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Sun’s Radiation Spectrum

Ahrens, Fig. 2.7Planck’s Law

Key concept: Radiation is spread unevenly across all wavelengths

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Sun - Earth Radiation SpectraAhrens, Fig. 2.8

Planck’s Law

Key concepts: Wien’s Law and Stefan-Boltzman Law

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What is Radiative Temperature of Sun if Max Emission Occurs at 0.5 m?

• Apply Wien’s Displacement Law

max

max

2900

2900

29000.5

5800

mKT

mK

mKm

T K

T

T

μ

μλ

μμ

λ

≈

≈

≈

≈

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How Much More Energy is Emitted by the Sun than the Earth?

• Apply Stefan-Boltzman Law

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2

-2 -2 -4 48

8 4 4 54448

25 43

(W m ) W m K(5.67 10 )

(5.67 10 ) 5800 5800 1.6 10202905.67( 10 ) 290

4 7.0 10 1.2 10 (12,000 )4 6.4 10

2.0 1

Sun

Earth

Sun Sun

Earth Earth

Sun Sun

EarthEarth

E T

EE

A r times largerA r

A EA E

ππ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

−

−

−

= ×

× = ×≈ ==×

×= ×≈ ≈×

×≈ 90 (2 )billion times more

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Radiative Equilibrium

• Radiation absorbed by an object increases the energy of the object.– Increased energy causes temperature to increase

(warming).

• Radiation emitted by an object decreases the energy of the object.– Decreased energy causes temperature to decrease

(cooling).

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Radiative Equilibrium (cont.)

• When the energy absorbed equals energy emitted, this is called Radiative Equilibrium.

• The corresponding temperature is the Radiative Equilibrium Temperature.

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Why Selective, Discrete Absorption/Emission?

Life as we perceive it: A continuous world!

Atomic perspective: A quantum world!

Gedzelman 1980, p 103

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Energy States for Atoms

Electrons can orbit in only permitted states

A state corresponds to specific energy level

Only quantum jumps between states

Intervals correspond to specific wavelengths

Gedzelman 1980, p 104

Hydrogen Atom

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Energy States for Molecules

Molecules can also rotate, vibrate, librate

But only at specific energy levels or frequencies

Quantum intervals between modes correspond to specific wavelengths

Gedzelman 1980, p 105

H2O molecule H2O Bands

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Selective Absorption

The Bottom Line

Each molecule has a unique distribution of quantum states!

Each molecule has a unique spectrum of absorption and emission frequencies of radiation!

H2O molecule

Williams, p 63

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Absorption Visible (0.4-0.7 m) is

absorbed very little

O2 an O3 absorb UV (shorter than 0.3 m)

Infrared (5-20 m) is selectively absorbed

H2O & CO2 are strong absorbers of IR

Little absorption of IR around 10 m – atmospheric window

Visible

IR

Ahrens, Fig. 2.9

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Total Atmospheric Absorption

Visible radiation (0.4-0.7 m) is not absorbed

Infrared radiation (5-20 m) is selectively absorbed, but there is an emission window at 10 m

Ahrens, Fig. 2.9

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Simple Example of the Greenhouse Effect

(0% Solar absorbed, 100% IR absorbed)

1 Unit Incoming Solar

1

1/2 1/4 1/8 1/16

1/2 1/4 1/8 1/16

1 Unit Outgoing IR to Space

2 Units IR Emitted by Ground

½ emitted to space

½ emitted to ground

Take Home Point: Surface is warmer with selectively absorbing atmosphere than it would be without it.

Radiative Equilibrium

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Global Solar Radiation Balance (Not all Solar Radiation SR reaches the surface)

Ahrens, Fig. 2.13

70% SR absorbed by earth-atmosphere

~50% SR absorbed by surface~50% SR absorbed by surface

30% SR reflects back to space30% SR reflects back to space

Albedo: percent of total SR reflected

~20% absorbed by atmosphere

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Atmosphere Heated from Below

Ahrens, Fig. 2.11 old ed.

Solar radiation heats the ground

Air contacting ground heats by conductionAir contacting ground heats by conduction

Air above ground heats by convection and absorption of some IR from ground

Ground heats further through absorption of IR from atmosphere

Net Effect: Net Effect: Atmosphere is Heated Atmosphere is Heated

From BelowFrom Below

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Global Atmo Energy BalanceAhrens, Fig. 2.14

SolarSolar

GroundGround

AtmosphereAtmosphere

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Summary

• Greenhouse Effect (A Misnomer)SFC Warmer than Rad. Equil. Temp

Reason: selective absorption of air

H2O and CO2 most absorbent of IR

• Energy Balance Complex system has a delicate balance

All modes of Heat Transfer are important

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Assignments for Next Lectures

• Ahrens (next lecture)

Pages 42-50

Problems 2.15, 2.16, 2.18