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greenhouse effect, radiation budget,
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Solar Spectrum
The sun emits radiation at all wavelengths
Most of its energy is in the
IR-VIS-UV
portions of the spectrum
~50% of the energy is in the visible region
~40% in the near-IR
~10% in the UV
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Wavelength (m)
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Blackbody Radiation
Blackbody radiationradiation emitted by a body that
emits (or absorbs) equally well at all wavelengths
Planck
function
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Basic Laws of Radiation
1) All objects emit radiant energy.
2) Hotter objects emit more energy than colder objects. The amount of energyradiated is proportional to the temperature of the object raised to the
fourth power.
This is the Stefan Boltzmann Law
F = T4F = flux of energy (W/m2)
T = temperature (K)
= 5.67 x 10
-8
W/m
2
K
4
(a constant)
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Basic Laws of Radiation
1) All objects emit radiant energy.
2) Hotter objects emit more energy than colder objects (per unit area).The amount of energy radiated is proportional to the temperature of
the object.
3) The hotter the object, the shorter the wavelength () of the peak in
emitted energy.
This isWiens Law:
.)(2898
maxT
Km
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Stefan-Boltzmann law
F = T4F = flux of energy (W/m2)
T = temperature (K)
= 5.67 x 10-8 W/m2K4 (a constant)
Wiens law
.)(2898
maxT
Km
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We can use these equations to calculate properties of energy radiating from
the Sun and the Earth.
6,000 K 300 K
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T(K)
max(m)
region inspectrum F
(W/m2)
Sun 6000
Earth 300
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T(K)
max(m)
region inspectrum F
(W/m2)
Sun 6000 0.5
Earth 300 10
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Electromagnetic Spectrum
(m)
1000 100 10 1 0.1 0.01
ultraviolet
visible
lightinfraredmicrowaves x-rays
High
Energy
Low
Energy
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T(K)
max(m)
region inspectrum F
(W/m2)
Sun 6000 0.5 Visible
(yellow?)
Earth 300 10 infrared
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Blue light from the Sun is removed from the beam
by Rayleigh scattering, so the Sun appears yellow
when viewed from Earths surface even though its
radiation peaks in the green
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T(K)
max(m)
region inspectrum F
(W/m2)
Sun 6000 0.5 Visible
(green)
Earth 300 10 infrared
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Stefan-Boltzman law
F = T4F = flux of energy (W/m
2
)T = temperature (K)
= 5.67 x 10-8 W/m2/K4 (a constant)
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T(K)
max(m)
region inspectrum F
(W/m2)
Sun 6000 0.5 Visible
(green)
7 x 107
Earth 300 10 infrared 460
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Solar Radiation and Earths Energy Balance
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Planetary Energy Balance
We can use the concepts learned so far to
calculate the radiation balance of the Earth
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Some Basic Information:
Area of a circle = r2Area of a sphere = 4 r2
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Energy Balance:
The amount of energy delivered to the Earth is equal to the energy lost
from the Earth.
Otherwise, the Earths temperature would continually rise (or fall).
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Energy Balance:
Incoming energy = outgoing energy
Ein
= Eout
Ein
Eout
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How much solar energy reaches the Earth?
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How much solar energy reaches the Earth?
As energy moves away from the sun, it is spread over a greater and
greater area.
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How much solar energy reaches the Earth?
As energy moves away from the sun, it is spread over a greater and
greater area.
This is the Inverse Square Law
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Define So as the energy flux reaching
the Earth from the Sun.
We can calculate So:
So = L / A,
where L = The Suns luminosity
and A = area of a sphere with a radius
equal to Earths orbital distance
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So is the solar constant for Earth
.W/m1370
105.14
W109.34
W109.3
2
211
26
0
2
26
0
S
RA
LS
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So is the solar constant for Earth
It is determined by the distance between Earth (rs-e) and the Sun and the Sun
luminosity.
.W/m1370105.14W109.3
4
W109.3
2
211
26
0
2
26
0
S
RA
LS
E h l t h it l t t
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Each planet has its own solar constant
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How much solar energy reaches the Earth?
Assuming solar radiation covers the area of a circle defined by the radius of
the Earth (re)
Einre
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How much solar energy reaches the Earth?
Assuming solar radiation covers the area of a circle defined by the radius of
the Earth (re)
Ein = So (W/m2) x re2 (m2)
Einre
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How much energy does the Earth emit?
300 K
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How much energy does the Earth emit?
Eout = F x (area of the Earth)
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How much energy does the Earth emit?
Eout = F x (area of the Earth)
F = T4
Area = 4 re2
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How much energy does the Earth emit?
Eout = F x (area of the Earth)
F = T4
Area = 4 re2
Eout = ( T4) x (4 re2)
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(m)
1000 100 10 1 0.1 0.01
Hotter objects emit more
energy than colder objects
Earth
Sun
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(m)
1000 100 10 1 0.1 0.01
Hotter objects emit more
energy than colder objects
F = T4
Earth
Sun
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(m)
1000 100 10 1 0.1 0.01
Earth
Sun
Hotter objects emit at shorter
wavelengths.
max = 3000/T
Hotter objects emit more
energy than colder objects
F = T4
h d h h i ?
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How much energy does the Earth emit?
Eout = F x (area of the Earth)
Eout
H h d h E h i ?
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How much energy does the Earth emit?
Eout = F x (area of the Earth)
F = T4
Area = 4 re2
Eout = ( T4) x (4 re2)
Eout
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How much solar energy reaches the Earth?
Ein
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How much solar energy reaches the Earth?
We can assume solar radiation covers the area of a circle defined by the radius
of the Earth (re).
Einre
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How much solar energy reaches the Earth?
We can assume solar radiation covers the area of a circle defined by the radius
of the Earth (re).
Ein = So x (area of circle)
Ein
re
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So is the solar constant for Earth
It is determined by the distance between Earth and the Sun (R) and the Sunsluminosity (L).
Remember
.W/m1370
105.14W109.3
4
W109.3
2211
26
0
2
26
0
S
RA
LS
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How much solar energy reaches the Earth?
We can assume solar radiation covers the area of a circle defined by the radius
of the Earth (re).
Ein = So x (area of circle)
Ein = So (W/m2) x re2 (m2)
Ein
re
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How much solar energy reaches the Earth?
Ein = So re2BUT THIS IS NOT QUITE CORRECT!
**Some energy is reflected away**
Ein
re
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How much solar energy reaches the Earth?
Albedo (A) = % energy reflected away
Ein = So re2 (1-A)
Ein
re
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How much solar energy reaches the Earth?
Albedo (A) = % energy reflected away
A= 0.3 today
Ein = So re2 (1-A)Ein = So re2 (0.7)
re
Ein
Energy Balance:
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Incoming energy = outgoing energy
Ein = Eout
Eout
Ein
Energy Balance:
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Ein = Eout
Ein = So re2 (1-A)
Eout
Ein
Energy Balance:
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Ein = Eout
Ein = So re2 (1-A)Eout = T4(4 re2)
Eout
Ein
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Energy Balance:
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Ein = Eout
So re2 (1-A) = T4 (4 re2)
Eout
Ein
Energy Balance:
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Ein = Eout
So (1-A) = T4 (4)
Eout
Ein
Energy Balance:
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Ein = Eout
So (1-A) = T4 (4)T4 = So(1-A)
4
Eout
Ein
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T4 = So(1-A)
4If we know So and A, we can calculate the temperature of the Earth.
We call this the expected temperature (Texp). It is the temperature we
would expect if Earth behaves like a blackbody.
This calculation can be done for any planet, provided we know its
solar constant and albedo.
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T4 = So(1-A)
4For Earth:
So = 1370 W/m2
A = 0.3 = 5.67 x 10-8 W/m2K4
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T4 = So(1-A)
4For Earth:
So = 1370 W/m2
A = 0.3 = 5.67 x 10-8
T4 = (1370 W/m2)(1-0.3)
4 (5.67 x 10-8 W/m2K4)
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T4 = So(1-A)
4For Earth:
So = 1370 W/m2
A = 0.3
= 5.67 x 10-8
T4 = (1370 W/m2)(1-0.3)
4 (5.67 x 10-8 W/m2K4)
T4 = 4.23 x 109 (K4)
T = 255 K
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Expected Temperature:
Texp = 255 K
(oC) = (K) - 273
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Expected Temperature:
Texp = 255 K
(oC) = (K) - 273
So.
Texp= (255 - 273) = -18oC
(which is about 0 oF)
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Is the Earths surface really -18 oC?
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Is the Earths surface really -18 oC?
NO. The actual temperature is warmer!
The observed temperature (Tobs) is 15 oC, or about 59 oF.
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Is the Earths surface really -18 oC?
NO. The actual temperature is warmer!
The observed temperature (Tobs) is 15 oC, or about 59 oF.
The difference between observed and expected temperatures
(T):
T = Tobs - Texp
T = 15 - (-18)
T = + 33 oC
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T = + 33 oCIn other words, the Earth is 33 oC warmer than expected based on
black body calculations and the known input of solar energy.
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T = + 33 oCIn other words, the Earth is 33 oC warmer than expected based on
black body calculations and the known input of solar energy.
This extra warmth is what we call the GREENHOUSE EFFECT.
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T = + 33 oC
In other words, the Earth is 33 oC warmer than expected based on
black body calculations and the known input of solar energy.
This extra warmth is what we call the GREENHOUSE EFFECT.
It is a result of warming of the Earths surface by the absorption of
radiation by molecules in the atmosphere.
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The greenhouse effect:
Heat is absorbed or trapped by gases in
the atmosphere.
Earth naturally has a greenhouse effect of
+33 oC.
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The concern is that the amount of greenhouse warming will increase with the
rise of CO2 due to human activity.
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T = + 33 oC
In other words, the Earth is 33 oC warmer than expected based on
black body calculations and the known input of solar energy.
This extra warmth is what we call the GREENHOUSE EFFECT.
It is a result of warming of the Earths surface by the absorption of
radiation by molecules in the atmosphere.
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Earths Radiation transfer
It is easier to visualize earth's radiation heat transfer with the diagram. The units used to measure the radiant flux energy are the same watts
that are used for electricity; at the top of the atmosphere, the inputenergy is 341 watts per square meter (Wm-2),
which is exactly balanced by a return of that radiant energy; 102 Wm-2 isreflected by the clouds or the surface and 239 Wm-2 is returned as a net
result of the earth-atmosphere heat exchange interaction - and 102 +239 = 341.
The heated atmosphere sends 333 Wm-2of infrared radiation back to theearth, called back radiation.
The key to the global warming issue is that the earth must heat up sothat it can return 396 Wm-2 to restore the balance.
As the greenhouse gases build up, more infrared rays are absorbed inthe atmosphere, and more are sent back to the earth as back radiation.Since greenhouse gases are causing the problem, the only solutionafforded by physics is to reduce them.