1. Blackbody Radiation/ Planetary Energy Balance

2. Electromagnetic Spectrum
visible
light
1000
100 10 1
0.1
0.01
0.7 to 0.4 m
 (m)

3. Electromagnetic Spectrum
visible
light
ultraviolet
1000
100 10 1
0.1
0.01
 (m)

4. Electromagnetic Spectrum
visible
light
infrared
ultraviolet
1000
100 10 1
0.1
0.01
 (m)

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

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

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

8. The Planck Function
Blackbody radiation follows the Planck function

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

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

11. 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.

12. 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)

13. 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.

14. 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)

15. 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)

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

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

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

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

20. 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

21. 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

22. 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

23.  Stefan Boltzman Law.
F =  T4
F = flux of energy (W/m2)
T = temperature (K)
 = 5.67 x 10-8 W/m2K4 (a constant)

24. T (K) max (m) F (W/m2) Sun 6000 0.5 Visible 7 x 107 Earth 300 10
region in spectrum F
(W/m2)
Sun
6000
0.5
Visible
(green)
7 x 107
Earth
300 10
infrared
460

25. Solar Radiation and Earth’s Energy Balance

26. Planetary Energy Balance
We can use the concepts learned so far to calculate the radiation balance of the Earth

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

28. 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).

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

30. (The rest of this derivation will be done on the
board. However, I will leave these slides in here
in case anyone wants to look at them.)

31. How much solar energy reaches the Earth?

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

33. 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

34. So = L / area of sphere

35. 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

36. 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’ luminosity.

37. Each planet has its own solar constant…

38. 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

39. 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

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

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

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

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

44.  (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)

45.  (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)

46. 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)

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

48. 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

49. How much solar energy reaches the Earth?
Ein

50. 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

51. 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

52. 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.

53. 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

54. **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

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

56. 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

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

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

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

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

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

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

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

64. 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.

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

66. 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)

67. 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

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

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

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

71. 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.

72. 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

73. 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.

74. 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.

75. 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.

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

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