# Heat transfer by electromagnetic radiation the Greenhouse Effect

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```					    Heat transfer by electromagnetic
the Greenhouse Effect

•   Energy balance in the Earth’s atmosphere
•   Greenhouse effect

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Electromagnetic waves
y
c

x

x1

Frequency f (s-1). Wavelength λ (metres).
Speed c = 3 x 108 m/s. c = f λ .
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Type of EM wave λ (metres)               Units normally
used
Radio waves        > 0.1                 > 0.1 m
Microwaves         10-1 – 10-4           100 mm – 0.1 mm
Infrared (IR)      10-4 – 7 x 10-7       100 μm – 0.7 μm
Visible            7 x 10-7 – 4 x 10-7   700 – 400 nm
Ultraviolet (UV)   4 x 10-7 – 10-8       400 – 10 nm
X Rays             10-8 – 10-11          10 – 0.01 nm
Gamma rays         < 10-11               < 0.01 nm
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How does Intensity of EM radiation
depend on distance from source S ?

Point source emits P Joules /sec ie
P watts
Define intensity I as power through
unit area

I1 = P / 4 π r 12   and I2 = P / 4 π r22
So I1 / I2 = ( r2 / r1 )2
Inverse square law
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If a hot object (eg the Sun) emits EM
radiation, what is the distribution over
wavelengths?

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Properties of this continuous spectrum
emitted by an object at temperature T
• Area under curve is total power per unit
surface area of emitting object - I(T)
• I(T) is proportional to T4
I(T) = σ T4 : σ = Stefan’s constant
• For a less-than-perfect radiator (eg
tungsten filament in a light bulb)
I(T) = ε σ T4 and the emissivity ε < 1
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Properties ctd
• Emitted distribution peaks at wavelength value
λm given by Wien’s Law
• λm = 2.8972 x 106 / T in units of nm and K
• (Sunlight peaks in visible region around 500 nm)
• These various aspects of the radiation emitted
by a hot body are explained by Quantum Theory
where radiation is seen as a stream of discrete
quanta or photons each carrying energy E = h f
where h is Planck’s constant (6.626x10-34)

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above the atmosphere and at earth’s
surface

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• Above the atmosphere we see normal spectrum with
shape expected from physics
• Atmospheric gases, ice crystals, clouds, dust, ice
caps, oceans scatter (i.e. reflect) 35% of intensity
back into space
α = 0.35 = planetary albedo
• Large albedo means Earth is bright when seen from
space (c/f Mars has α = 0.16, less bright)
• Look at regions where there is special absorption of
the radiation by specific molecules eg CO2 and H2O

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• The total solar radiation intensity is 1368
W/m2 above the atmosphere, and the Earth
presents a circular “catching area” πR2.

But Earth’s rotation plus air and ocean circulation
distribute this intensity over the entire 4 πR2
planetary surface area; so average “insolation” is
342 W/m2                                          12
Energy balance in our atmosphere

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Greenhouse effect
Suppose sunlight falls on a perfect radiator; it is in
equilibrium at temperature T1 with energy radiated =
energy absorbed. If T1 = 300K then the emitted
radiation is in the IR region
Place a sheet of glass
over the surface to
absorb a “band” of IR:
to keep emission equal
to absorption the
must increase to T2
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Atmospheric Greenhouse Effect
• We had earlier: Io = 1368 W/m2
• And fraction α is reflected/scattered away
• So Power delivered through disc of area π
R2 and thence spread by weather over all the
surface of the planet = π R2 I0 (1- α). This is
• Power RADIATED out from surface is
(Stefan) 4 π R2 σ T4
• Ignore the atmosphere, and set these two
quantities equal: then (1/4) I0 (1- α) = σ T4

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Atmospheric Greenhouse effect 2

• Solve (1/4) I0 (1- α) = σ T4 with given α and σ
T = 254 K
• Actual mean T = 288 K
• So atmosphere causes a 34 K warming of
earth’s surface on average
• Need to develop a better model that includes
the atmosphere’s absorbing effects
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Atmospheric Greenhouse effect 3
Remember sun
provides Io/4 per unit
area at top of atmos,
and albedo reflects
fraction α

Remember atmos is
a VERY thin skin

Simplify by assuming Earth radiates IE per unit area, and
atmosphere absorbs all of this. Then assume earth gets
IA per unit area from atmosphere. But atmosphere radiates
up as well as down. So there is another IA going outward
from the atmosphere.
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• We already know that solar energy absorbed per
unit area by earth/atmos system is (1/4)Io(1- α)
• Power arriving from sun = Power departing back to
space
so (1/4)Io(1- α) = IA           (1)
• Power into atmos= Power radiated by atmos
so IE = 2 IA                          (2)
• Therefore IE = 2 (1/4)Io(1- α) = σ TE4
• This gives TE = 298 K which is close to the actual
288K
• This shows greenhouse warming effect of
atmosphere – SUPPORTS LIFE
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Energy balance in our atmosphere -
again

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Enhancement of the greenhouse
effect:
• Consider the 390 units radiated from the
earth and the 350 of these absorbed in the
atmosphere
• What happens if the atmosphere becomes
MORE ABSORBING to the outgoing radiation
(due to CO2 buildup)
• Remember that CO2 is much more absorbant
for the long-λ outgoing radiation than for the
• How will the overall system re-adjust to such
a change?                                      20
Greenhouse ctd: Introduction of CO2

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Greenhouse ctd: Mean annual
temperature

Reference line is 1960-1990 mean. Ref. U. East
Anglia - see text                          22
NASA-Goddard plot 2005

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Greenhouse warming: greenhouse
gases
• Warming is now generally accepted, although
debate continues re magnitude; 1-5 K in next
50 years
• Contributors are:
- CO2 (fossil fuels, deforestation)
- CH4 (cattle, landfill, natural gas leaks)
- CFCs (refrigerants, aerosol sprays)
- ozone (photo-chemical smog)
- N2O (fossil fuels – transport)
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Greenhouse gases 2

Species        Decay time (y)
CO2            120
CH4            12
CFC            65-120
O3             0.1
N2O            114

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Effects of greenhouse warming

• Global temperature up by 1-5K in next 100 y
• Higher ocean levels through water expansion
and icecap melting
• Increased ocean evaporation causes
increased rainfall on land masses - flooding
• Longer summers increase evaporation so soil
moisture decreases – increased
desertification and loss of productivity in
semi-arid grasslands (Prairies)

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Amelioration ??
• Montreal protocol for CFCs is avery successful
precedent
• Kyoto protocol for greenhouse gases is a vastly
greater challenge
• Must move away from fossil fuels: Must shift from
private to public transport: Must re-forest: Must
conserve. BUT political will has rarely been so tested
• AND the Copenhagen Consensus argues that many
more lives could be saved by other investments –
e.g. micronutrients for malnourished children,

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• See links on course website to the
website of the Inter-Governmental
Panel on Climate change

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