1. Blackbody Radiation/ Planetary Energy Balance
Chapter 3—Part 2
Blackbody Radiation/
Planetary Energy Balance

2. Blackbody Radiation
Planck
function
Blackbody radiation—radiation emitted by a body that
emits (or absorbs) equally well at all wavelengths

3. Basic Laws of Radiation
All objects emit radiant energy.

4. Basic Laws of Radiation
All objects emit radiant energy.
Hotter objects emit more energy than colder objects.

5. Basic Laws of Radiation
All objects emit radiant energy.
Hotter objects emit more energy than colder objects. The amount of energy radiated is proportional to the temperature of the object raised to the fourth power.

6. Basic Laws of Radiation
All objects emit radiant energy.
Hotter objects emit more energy than colder objects. The amount of energy radiated is proportional to the temperature of the object raised to the fourth power.
 This is the Stefan Boltzmann Law
F =  T4
F = flux of energy (W/m2)
T = temperature (K)
 = 5.67 x 10-8 W/m2K4 (a constant)

7. Scientific Notation
10 = 101
100 = 102
1,000 = 103
1,000,000 = 106
1,000,000,000,000 = 1012

8. Basic Laws of Radiation
All objects emit radiant energy.
Hotter objects emit more energy than colder objects (per unit area). The amount of energy radiated is proportional to the temperature of the object.
The hotter the object, the shorter the wavelength () of emitted energy.

9. T(K) Basic Laws of Radiation All objects emit radiant energy.
Hotter objects emit more energy than colder objects (per unit area). The amount of energy radiated is proportional to the temperature of the object.
The hotter the object, the shorter the wavelength () of emitted energy.
This is Wien’s Law
max  3000 m
T(K)

10. max  3000 m T(K)  Stefan-Boltzmann law F =  T4
F = flux of energy (W/m2)
T = temperature (K)
 = 5.67 x 10-8 W/m2K4
(a constant)
 Wien’s law
max  3000 m
T(K)

11. We can use these equations to calculate properties of energy radiating from the Sun and the Earth.
6,000 K
300 K

12. T
(K)
max
(m)
region in spectrum F
(W/m2)
Sun
6000
Earth
300

13. T (K) max (m) F (W/m2) Sun 6000 0.5 Earth 300 10
region in spectrum F
(W/m2)
Sun
6000
0.5
Earth
300 10
Wien’s law: max  3000 m
T(K)

14. Electromagnetic Spectrum
visible
light
microwaves
infrared
ultraviolet
x-rays
1000
100 10 1
0.1
0.01
Low
Energy
High
Energy
 (m)

15. T (K) max (m) F (W/m2) Sun 6000 0.5 Visible Earth 300 10 infrared
region in spectrum F
(W/m2)
Sun
6000
0.5
Visible
(yellow?)
Earth
300 10
infrared

16. Blue light from the Sun is removed from the beam
by Rayleigh scattering, so the Sun appears yellow
when viewed from Earth’s surface even though its
radiation peaks in the green

17. T (K) max (m) F (W/m2) Sun 6000 0.5 Visible Earth 300 10 infrared
region in spectrum F
(W/m2)
Sun
6000
0.5
Visible
(green)
Earth
300 10
infrared

18. Stefan-Boltzmann law: F =  T4
(K)
max
(m)
region in spectrum F
(W/m2)
Sun
6000
0.5
Visible
(green)
7 x 107
Earth
300 10
infrared
460
Stefan-Boltzmann law: F =  T4

19. Solar Radiation and Earth’s Energy Balance

20. Planetary Energy Balance
We can use the concepts learned so far to calculate the radiation balance of the Earth
(The rest of this lecture will be done on the blackboard. The slides are included, though, for people who want to study them.)

21. Some Basic Information:
Area of a circle =  r2
Area of a sphere = 4  r2

22. Energy Balance:
The amount of energy delivered to the Earth is equal to the energy lost from the Earth.
Otherwise, the Earth’s temperature would continually rise (or fall).

23. Energy Balance:
Incoming energy = outgoing energy
Ein = Eout
Eout
Ein

24. How much solar energy reaches the Earth?

25. How much solar energy reaches the Earth?
As energy moves away from the sun, it is spread over a greater and greater area.

26. 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

27. So = L / area of sphere

28. So is the solar constant for Earth
So = L / (4  rs-e2) = 3.9 x 1026 W = 1370 W/m2
4 x  x (1.5 x 1011m)2
So is the solar constant for Earth

29. So is the solar constant for Earth
So = L / (4  rs-e2) = 3.9 x 1026 W = 1370 W/m2
4 x  x (1.5 x 1011m)2
So is the solar constant for Earth
It is determined by the distance between Earth (rs-e) and the Sun and the Sun’s luminosity.

30. Each planet has its own solar constant…

31. 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 re

32. 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)
Ein re

33. How much energy does the Earth emit?
300 K

34. How much energy does the Earth emit?
Eout = F x (area of the Earth)

35. How much energy does the Earth emit?
Eout = F x (area of the Earth)
F =  T4
Area = 4  re2

36. How much energy does the Earth emit?
Eout = F x (area of the Earth)
F =  T4
Area = 4  re2
Eout = ( T4) x (4  re2)

37.  (m) Sun Earth Hotter objects emit more energy than colder objects
1000
100 10 1
0.1
0.01
Hotter objects emit more energy than colder objects
 (m)

38.  (m) Sun Earth Hotter objects emit more energy than colder objects
1000
100 10 1
0.1
0.01
Hotter objects emit more energy than colder objects
F =  T4
 (m)

39. Hotter objects emit at shorter wavelengths.
max = 3000/T
Sun
Earth
1000
100 10 1
0.1
0.01
Hotter objects emit more energy than colder objects
F =  T4
 (m)

40. How much energy does the Earth emit?
Eout = F x (area of the Earth)
Eout

41. 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

42. How much solar energy reaches the Earth?
Ein

43. 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 re

44. 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

45. So is the solar constant for Earth
Remember…
So = L / (4  rs-e2) = 3.9 x 1026 W = 1370 W/m2
4 x  x (1.5 x 1011m)2
So is the solar constant for Earth
It is determined by the distance between Earth (rs-e) and the Sun and the Sun’s luminosity.

46. 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

47. **Some energy is reflected away**
How much solar energy reaches the Earth?
Ein = So  re2
BUT THIS IS NOT QUITE CORRECT!
**Some energy is reflected away**
Ein re

48. How much solar energy reaches the Earth?
Albedo (A) = % energy reflected away
Ein = So  re2 (1-A)
Ein re

49. 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

50. Energy Balance:
Incoming energy = outgoing energy
Ein = Eout
Eout
Ein

51. Energy Balance:
Ein = Eout
Ein = So  re2 (1-A)
Eout
Ein

52. Ein = Eout Energy Balance: Ein = So  re2 (1-A) Eout =  T4(4  re2)

53. Energy Balance:
Ein = Eout
So  re2 (1-A) =  T4 (4  re2)
Eout
Ein

54. Energy Balance:
Ein = Eout
So  re2 (1-A) =  T4 (4  re2)
Eout
Ein

55. Energy Balance:
Ein = Eout
So (1-A) =  T4 (4)
Eout
Ein

56. Ein = Eout Energy Balance: So (1-A) =  T4 (4) T4 = So(1-A) 4 Eout

57. T4 = So(1-A) 4
If 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.

58. T4 = So(1-A) 4 For Earth: So = 1370 W/m2 A = 0.3
 = 5.67 x 10-8 W/m2K4

59. T4 = So(1-A) 4 For 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)

60. T4 = So(1-A) 4 For 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

61. Expected Temperature:
Texp = 255 K
(oC) = (K) - 273

62. Expected Temperature:
Texp = 255 K
(oC) = (K) - 273
So….
Texp = ( ) = -18 oC
(which is about 0 oF)

63. Is the Earth’s surface really -18 oC?

64. Is the Earth’s surface really -18 oC?
NO. The actual temperature is warmer!
The observed temperature (Tobs) is 15 oC, or about 59 oF.

65. Is the Earth’s 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

66. 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.

67. 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.

68. 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 Earth’s surface by the absorption of radiation by molecules in the atmosphere.

69. The greenhouse effect:
Heat is absorbed or “trapped” by gases in the atmosphere.
Earth naturally has a greenhouse effect of +33 oC.

70. The concern is that the amount of greenhouse warming will increase with the rise of CO2 due to human activity.