Solar Radiation Emission and Absorption

1
Solar Radiation Emission and Absorption
V1003 - Climate and Society
2
Take away concepts

• Conservation of energy.
• Black body radiation principle
• Emission wavelength and temperature (Weins Law).
  
• Radiation vs. distance relation
• Black body energy flux (Stefan-Boltzmann Law)
• Effective temperature calculation, differences
  from actual temperature.

3
What is Energy?

• Energy The ability to do work.
• Energy measured in Joules (1 J 0.24 calories).
• Power measured in Watts (1 J/s)
• Energy is always conserved (1st law of TD).
• Energy can be changed from one form to another,
  but it cannot be created or destroyed.

4
Solar Energy

• Nuclear fusion H to He
• Emits Electromagnetic radiation (radiant E)
• EM waves behave like particles and waves
• EM travels at c
• (3 x 108 m/s)

5
EM Radiation
Since c is constant, frequency of EM wave
emission related to electron vibration Warm
things have more energy than cold things, so .?
6
Properties of waves

• Amplitude (A)
• Wavelength (µm)
• Period (sec)
• Frequency (1/sec)
• c is constant

7
Blackbody Radiation

• A blackbody absorbs and emits radiation at 100
  efficiency (experimentally, they use graphite, or
  carbon nanotubes)
• energy in energy out
• Across all wavelengths

8
Weins Law emission wavelength and temperature

• ?max a / T
• Where
• ?max is wavelength of emitted radiation (in µm)
  
• a 2898, constant
• T emitter temperature (in K)
• Recall that K TC 273.15

Suns temperature is 5800K Whats its wavelength?
9
The Suns temperature is 5800 K, that is the
wavelength of its radiation?

• ?max a / T

• 5000 µm
• 50 µm
• 0.5 µm
• 2 µm
• 20µm

• ?max is wavelength of emitted radiation (in µm)
  
• a 2898, constant
• T emitter temperature (in K)
• Recall that K TC 273.15

10
Whats your wavelength?

• ?max a / T
• (a 2898)
• Your body is 37C
• or 37273 310K
• ?max ?

9.4 µm (far infrared)
11
Earth as we see it (visible)
12
Earths Infrared Glow 15µm
13
Electromagnetic spectrum
hot
cold
1 µm 1000 nm
14
Visualizing emission temperatures
Sunny day 6000K Sunset 3200K Candlelight
1500K
Blackbody applet http//qsad.bu.edu/applets/black
body/applet.html
15
The effect of distance on radiation the 1 / r2
rule
Sun emission decreases in proportion to 1 / r2 of
the Sun-Planet distance
16
Mars is 1.52 AU (1 AU earth-sun distance
1.5 x 1011 m)

• Using 1/ r2 rule
• 1 / (1.51.5) 0.44
• Mars receives 44 of the Earths solar radiation.

17
Jupiter is roughly 5 AU from the Sun, what
fraction of Earths solar radiation does it get?

• 1/2
• 1/5
• 1/10
• 1/25
• 1/125

18
Summary so far

• Weins Law (emission freq. and temperature)
• The 1 / r2 law (radiation amt and distance)
• Now lets calculate the total radiative energy
  flux into or out of a planet using the
• Stefan - Boltzmann Law

19
Stefan - Boltzmann Law

• Energy emitted by a black body is greatly
  dependent on its temperature
• I (1-a) ? T4
• Where
• I Black body energy radiation
• ? (Constant) 5.67x10-8 Watts/m2/K4
• T temperature in Kelvin
• a? albedo (reflectivity)
• Example Sun surface is 5800K, so I 6.4 x 107
  W/m2

20
Calculating the Earths Effective Temperature

• Easy as 1-2-3
• Calculate solar output.
• Calculate solar energy reaching the Earth.
• Calculate the temperature the Earth should be
  with this energy receipt.

21
1. Calculate solar output.

• Calculate Sun temperature assuming it behaves as
  a blackbody (knowing that ?sun 0.5µm).
• From S-B law Isun 6.4 x 10 7 W/m2
• We need surface area of sun
• Area 4?r2 4??(6.96x108 m) 6.2 x 10 18 m2
• Total Sun emission 3.86 x 1026 Watts (!)

Solar Emission Power
22
2. Calculate solar energy reaching the Earth.

• Simple Geometry.
• (recall the inverse square law..)
• Earth-Sun distance (D) 1.5 x 1011 m
• Area of sphere 4? r 2
• So, 3.86 x 10 26 Watts / (4? (1.5 x 1011 m)2 )
• Earths incoming solar radiation 1365 W/m2

23
3. Earth energy in energy out

• You have Iearth, solve for Tearth
• Stefan - Boltzmann law Iearth (1-a) ? Tearth4
  
• Incoming solar radiation 1365 W/m2
• About 30 is reflected away by ice, clouds, etc.
  reduced to 955 W/m2
• Incoming on dayside only (DISK), but outgoing
  everywhere (SPHERE), so outgoing is 1/4 of
  incoming, or 239 W/m2
• that is (0.7)(0.25)1365 energy that reaches
  Earth surface
• Energy in 239 W/m2 ? T4

24
Solve for Teffective 255K

• Earth Effective temp 255 K, or -18C
• Earth Actual temp 288K, or 15C
• the difference of 33C is due to the natural
  greenhouse effect.

25
So what Earths radiation wavelength?

• ?max a / T
• Where
• ?max is wavelength of emitted radiation (in µm)
  
• a 2898, constant
• T emitter temperature (in K)

If Earth effective temperature is 255K Whats the
wavelength?
26
Emission Spectra Sun and Earth
27
Radiation and Matter
Also dependent upon the frequency of radiation!
(next lecture)
28
Emission Spectra Sun and Earth
29
Blackbody emission curves and absorption bands
30
Why is the Sky blue?

• Rayleigh scattering of incoming, short wavelength
  radiation (photons with specific energy)
• Radiation scattered by O3, O2 in stratosphere
  (10-50 km)

31
Why are sunsets red?

• Blue wavelengths are scattered/absorbed
• Red and orange pass through to surface