1. Solar Radiation Emission and Absorption
V Climate and Society

2. Take away concepts Conservation of energy.
Black body radiation principle
Emission wavelength and temperature (Wein’s 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. Wein’s 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 = T°C
Sun’s temperature is 5800K
What’s its wavelength?

9. The Sun’s 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 = T°C

10. What’s your wavelength?
max = a / T
(a = 2898)
Your body is 37°C
or = 310K
max = ?
9.3 µm readiation
9.4 µm (far infrared)

11. Earth as we see it (visible)

12. Earth’s 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:

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 / (1.5*1.5) = 0.44
Mars receives ~44% of the Earth’s solar radiation.

17. Jupiter is roughly 5 AU from the Sun, what fraction of Earth’s solar radiation does it get?
1/2
1/5
1/10
1/25
1/125

18. Summary so far… Wein’s Law (emission freq. and temperature)
The “1 / r2” law (radiation amt and distance)
Now let’s 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 Earth’s “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 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 Watts / (4 (1.5 x 1011 m)2 )
Earth’s incoming solar radiation: 1365 W/m2
Earth radius (r): 6.7 x 108 m

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 -18°C
Earth Actual temp: 288K, or +15°C
… the difference of +33°C is due to the natural greenhouse effect.

25. So what Earth’s 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
What’s 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