The greenhouse effect
Lecture 19 :
Greenhouse effect
Reminders:
HW 8 available
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EM radiation so far
• Spectrum of EM radiation emitted by many objects may be approximated by the
blackbody spectrum
• Blackbody spectrum (plot of emitted intensity versus l)depends only on temperature
• Temperature determines
a) Total emitted EM power  S-B law: P = s a e T4
b) Shape of spectrum range of l, lpeak  1/T
Today’s lecture
• Brief look at IR radiation.
•Apply BB spectrum and S-B law to understand green house effect/global warming
• What determines the temperature of the earth’s surface?
• Why do greenhouse gases in the atmosphere cause it to heat up?
The electromagnetic spectrum
The greenhouse effect.
What are green house gases?
CO2, H2O and others
Why does the temperature of the earth’s surface depend on the presence of green
house gases in the atmosphere?
Greenhouse gases insulate the earth, increase its temperature (Without them, life
would not survive.)
Exactly how does the temperature change now we are adding more CO2?
Details of this get complicated
But the basic GH effect can be understood by considering a power balance and
using just the BB spectrum and SB law
Your car is sitting in the bright sun. The inside of the car gets much hotter than
the air next to it. Why?
a. The car absorbs light energy from sun better than the pavement.
b. Sunlight causes chemical reactions in car materials that give off heat.
c. Electrical appliances such as clock that run all the time in car causes it to heat up.
d. The windows let in energy but do not let it escape.
e. None of the above make sense, must be different explanation.
The greenhouse effect in your car
EM energy gets into car but can’t get out? How does that happen?
• We all know visible light travels easily through glass (windows!)
• But remember this? The glass blocked the IR from the hot plate, so we
could not detect the IR from the hot plate.
The greenhouse effect in your car
BB spectra of emitted
EM radiation from sun and car
UV Visible
power
IR
sun
40 C inside car
wavelength
• Remember effect of T on shape of BB spectrum
• Sun is very hot (5800K) and emits most power as visible light, which goes through the
car window.
• The interior of the car absorbs this energy and heats up.
• Inside of car is less hot than sun (310 K) so emits most power in the IR, which cannot
go out through the glass.
• Extra energy is trapped inside car making it hotter than the surrounding environment
How does the green house effect affect the temperature of the earth?
We can calculate the effect of GH gases on the temperature of the earth by considering a
power balance
1) Power in: Visible light energy from hot sun hits the earth and is absorbed
2) Power out: The cool earth (at temp. TE) radiates power out mainly as IR radiation
3) If earth remains at a constant temperature (ignoring the v.v.v. slow temperature
increase due to global warming), it must have constant thermal energy:
Power in from sun = Power out from earth, radiated into space.
Depends on TE, so we can
calculate temperature of earth!
Calculating the temperature of the earth TE
Power in from sun = Power out from earth, radiated into space.
Pin = Pspace
First lets calculate the power arriving at the earth from the sun:
If Re is the radius of the earth, what is the
area of the earth absorbing sunlight?
a)
b)
c)
d)
2pRe
pRe2
4pRe2
4/3 p Re3
Calculating the temperature of the earth TE
Power in from sun = Power out from earth, radiated into space.
Pin = Pspace
Pin = 1380 W/m2 x pRe2 x 0.7 = 1.22 x 1017 W
solar power/m2 at earth
area of earth absorbing sunlight
fraction of sunlight absorbed by earth
Calculating the temperature of the earth TE
Power in from sun = Power out from earth, radiated into space.
Pin = Pspace
Now lets calculate the power radiated from earth at temperature TE:
Use S-B law for a black body: P = s x TE4 x a
If Re is the radius of the earth, what is the
area of the earth that emits EM radiation
(mainly IR)?
a) 2pRe
b) pRe2
c) 4pRe2
d) 4/3 p Re3
Calculating the temperature of the earth TE
Power in from sun = Power out from earth, radiated into space.
Pin = Pspace
From Stefan Boltzman law:
Pspace = s x TE4 x surface area of Earth X f
Fraction of radiation that
actually makes it through
atmosphere to space.
If there are no greenhouse gases in the
atmosphere, f = 1.
As GH gases increase, f decreases.
Calculating the temperature of the earth TE
Pin
=
Powerspace
1380 W/m2 x pRe2 x 0.7 = s X TE4 X 4pRe2 X f
Power balance
equation
Can we rearrange this to find a value for TE ?
1380 x 0.7 = 4 x (5.67 x 10-8) x TE4 x f
4.26 x 109 = TE4 x f
TE4 = 4.26 x 109 / f
TE = sqrt (sqrt (4.26 x 109 / f ))
More greenhouse gases:
 Smaller fraction of earth’s IR radiation gets through atmosphere
 f decreases
 TE increases
 Earth is warmer!
First consider a world with NO GH gases…….
TE = sqrt (sqrt (4.26 x 109 / f ))
Lets try some numbers!
First assume that we have NO GH gases around the earth  f=1
Now lets consider the role of GH gases around the earth……
• Why doesn’t all of the radiated IR go directly into space?
• Certain types of molecules in the atmosphere called “greenhouse
gases” absorb IR and send it back towards earth. Carbon dioxide,
H2O, but not oxygen or nitrogen.
• Because of GH gases (mostly naturally occurring) only about 61% of
IR radiated from surface of earth actually makes it to space (f = 0.61)
No GH gases
Now lets consider the role of GH gases around the earth……
• Why doesn’t all of the radiated IR go directly into space?
• Certain types of molecules in the atmosphere called “greenhouse
gases” absorb IR and send it back towards earth. Carbon dioxide,
H2O, but not oxygen or nitrogen.
• Because of GH gases (mostly naturally occurring) only about 61% of
IR radiated from surface of earth actually makes it to space (f = 0.61)
With GH gases
So what TE does f = 0.61 imply?
Now lets consider the role of GH gases around the earth……
So what TE does f = 0.61 imply?
TE = sqrt (sqrt (4.26 x 109 / f ))
With GH gases
Naturally occurring greenhouse
gases keep the planet habitable.
Another way to think about the effect of GH gases
• Stable temp at surface, so Pspace = Pin
• No GH gases, all radiation from earth makes it to space
• With GH gases, not all radiation from earth makes it to space
 surface must radiate more for same Pspace
From SB law, if surface radiates more then TE must be higher
 GH gases result in warmer earth surface!
 Some naturally occurring GH gases essential for life
 But extra GH gases affect delicate balance of life
What is the current state of global warming?
• Temperature of earth has risen 1F (~0.5 C) in the 20th century.
• 2.5 to 10 F rise predicted for the next century.
• Is that significant?
-
At peak of last ice age (20,000 years ago), global temp was only
10F colder and most of North America was under 3000 feet of ice.
http://climate.nasa.gov/effects
http://geology.utah.gov/surveynotes/gladasked/gladice_ages.htm
Lets process all that with some clicker questions………..
When we increase the concentration of GH gases in the atmosphere by burning fossil
fuels etc, what happens?
a.
b.
c.
d.
e.
Less IR reflected back to earth, (lower f value)
Less IR reflected back to earth, (higher f value)
More IR reflected back to earth, (lower f value)
More IR reflected back to earth, (higher f value)
None of the above
After the concentration of greenhouse gases has gone up due to burning fossil fuels
(assume the temperature of the earth has stabilized), the total power emitted by
earth and making it through the atmosphere to space,
a. goes up
b. goes down
c. stays the same
To maintain the SAME amount of EM power reaching outer space (still balancing
power in from the sun), what changes must occur at the surface of the earth?
a.
b.
c.
d.
e.
More EM power must be emitted  higher surface temperature
More EM power must be emitted  lower surface temperature
Less EM power must be emitted  lower surface temperature
Less EM power must be emitted  lower surface temperature
Neither emitted power or surface temperature changes
If we look at Earth from outer space with remote temperature probe
(measures the amount of IR radiation arriving at the probe from earth to
determine temperature), what temperature do we measure?
a. 255K
b. 287 K
No GH gases: TE = 255 K
c. 295 K
d. 2000 K
With GH gases: TE = 287 K
Now add clouds to the simulation. What is their effect?
a. Clouds decrease temperature because they reflect part of sunlight back to space.
b. Clouds increase temperature because they absorb IR radiation from earth.
c. Clouds increase temperature because the sunlight is reflected then absorbed by
the greenhouse gases in the atmosphere.
d. a or b,
e. a or c
GH gas summary:
- Transmit all EM power from sun at visible l
- Partially reflect EM power from surface of earth at IR l
- Surface temperature must rise in presence of GH gases to maintain power balance
Why is earth surface hotter in
presence of GH gases?
WITH GH GASES
• Thickness of arrows represents amount of power
• Color of arrows represents wavelength
NO GH GASES
1. In both cases, the earth is at a stable T (constant thermal energy)
2. For stable T, Pin (from sun) = Pspace (lost to space)
3. Since Pin never changes (is same in both cases), Pspace is the same in both cases
4. No GH gases: Pearth (power radiated from surface of earth) = Pspace
5. With GH gases: Pearth = Pspace + Preflected
 Pearth is BIGGER in presence of GH gases
 Temp of surface higher in presence of GH gases (from SB law)