1. MET 61 1 MET 61 Introduction to Meteorology MET 61 Introduction to Meteorology - Lecture 8 “Radiative Transfer” Dr. Eugene Cordero San Jose State University Class Outline: Absorption and emission Scattering and reflected light Global Energy Balance

2. MET 61 2 MET 61 Introduction to Meteorology Radiation Emission B - Monochromatic Irradiance (Plank’s Law) F - Irradiance (Stefan Boltzmann Law) max – Peak emission at a wavelength

4. MET 61 4 MET 61 Introduction to Meteorology Energy distribution Radiative energy propagates at speed of light. Energy per unit area decrease as square of distance from emitter: R 1,, R 2 =radius

5. MET 61 5 MET 61 Introduction to Meteorology Energy distribution Radiative energy propagates at speed of light. Energy per unit area decrease as square of distance from emitter: R 1,, R 2 =radius

6. MET 61 6 MET 61 Introduction to Meteorology Example Estimate the value of the solar constant; the irradiance at the top of the Earth’s atmosphere.

7. MET 61 7 MET 61 Introduction to Meteorology Solution earth sun

8. MET 61 8 MET 61 Introduction to Meteorology Example Estimate the value of the solar constant; the irradiance at the top of the Earth’s atmosphere. S-Solar Constant

9. MET 61 9 MET 61 Introduction to Meteorology Absorption, Reflection and Transmission  - emissivity: Fraction of blackbody that is actually emitted (0-1) a - absorptivity: fraction of radiation striking an object that is absorbed. t - transmissivity: fraction of radiation striking an object that is transmitted. r - reflectivity: fraction of radiation striking an object that is reflected. Energy is conserved, so:

10. MET 61 10 MET 61 Introduction to Meteorology Absorption, Reflection and Transmission  - emissivity: Fraction of blackbody that is actually emitted (0-1) a - absorptivity: fraction of radiation striking an object that is absorbed. t - transmissivity: fraction of radiation striking an object that is transmitted. r - reflectivity: fraction of radiation striking an object that is reflected. Energy is conserved, so: a + r + t = 1

11. MET 61 11 MET 61 Introduction to Meteorology Or in terms of irradiance

12. MET 61 12 MET 61 Introduction to Meteorology Or in terms of irradiance

13. MET 61 13 MET 61 Introduction to Meteorology Kirchhoff’s law Describes how good emitters are also good absorbers This relationship is wavelength dependent. Albedo considers the net effect over a range of wavelengths.

14. MET 61 14 MET 61 Introduction to Meteorology Kirchhoff’s law Describes how good emitters are also good absorbers This relationship is wavelength dependent. Albedo considers the net effect over a range of wavelengths.

15. MET 61 15 MET 61 Introduction to Meteorology

16. MET 61 16 MET 61 Introduction to Meteorology

17. MET 61 17 MET 61 Introduction to Meteorology Activity 7 Inclass question: If the Earth’s albedo was to increase by 10%: A) By how much would surface solar radiation change? B) How would the Earth’s surface energy budget change? C) How would the Earth’s top of the atmosphere budget change?

18. MET 61 18 MET 61 Introduction to Meteorology Energy Balance Energy at any level must be in balance: Energy in = Energy out Example: Calculate the blackbody temperature of the earth assuming a planetary albedo of 0.3 and that the earth is in radiative equilibrium

19. MET 61 19 MET 61 Introduction to Meteorology Solution E (in; solar) = E (out; terrestrial)

20. MET 61 20 MET 61 Introduction to Meteorology Solution F (in; solar) = F (out; terrestrial) SF

21. MET 61 21 MET 61 Introduction to Meteorology Example A completely gray surface on the moon with an absorptivity of 0.9 is exposed to overhead solar radiation. What is the radiative equilibrium temperature of the surface?

22. MET 61 22 MET 61 Introduction to Meteorology Solution Since the moon has no atmosphere, the incoming solar radiation is the total incident radiation upon the surface. For radiative equilibrium:

23. MET 61 23 MET 61 Introduction to Meteorology Solution Since the moon has no atmosphere, the incoming solar radiation is the total incident radiation upon the surface. For radiative equilibrium:

24. MET 61 24 MET 61 Introduction to Meteorology Atmospheric absorption The amount of radiation that is absorbed by the atmosphere is proportional to the number of molecules per unit area that are absorbing.  (sigma) – optical depth or optical thickness k - absorption coefficient (m 2 /kg)  - density (kg/m 3 ) Angle of incidence (from vertical)

25. MET 61 25 MET 61 Introduction to Meteorology So the transmissivity of the layer is now: And neglecting scattering, then the absorptivity is:

26. MET 61 26 MET 61 Introduction to Meteorology So the transmissivity of the layer is now: And neglecting scattering, then the absorptivity is:

27. MET 61 27 MET 61 Introduction to Meteorology Example Parallel radiation is passing through a layer 100m in thickness containing a gas with an average density of 0.1 kg/m 3. The beam is directed at 60° from normal to the layer. Calculate the optical thickness and transmissivity and absorptivity of the layer at wavelength where the absorption coefficient is 10 -1.

28. MET 61 28 MET 61 Introduction to Meteorology Solution Assuming the absorption coefficient and density do not vary within the layer:

29. MET 61 29 MET 61 Introduction to Meteorology Solution Assuming the absorption coefficient and density do not vary within the layer: t =0.135 a =0.865

30. MET 61 30 MET 61 Introduction to Meteorology Sun angle

31. MET 61 31 MET 61 Introduction to Meteorology

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34. MET 61 34 MET 61 Introduction to Meteorology What month do you think this graph represents? a) December b) March c) June d) September

35. MET 61 35 MET 61 Introduction to Meteorology What month do you think this graph represents? a) December b) March c) June d) September Answer: December

36. MET 61 36 MET 61 Introduction to Meteorology

37. Simplified radiative energy cascade for the Earth-atmosphere climate system Energy Input Energy Output E-A Climate System Extraterrestrial Short Wave Radiation Reflected Extraterrestrial Short Wave Radiation Terrestrial Long Wave Radiation Planetary Albedo Solar Temperature Planetary Temperature

38. MET 61 38 MET 61 Introduction to Meteorology Assigned Reading for Feb 14 Ahrens Ch 2 (continuing)Ahrens Ch 2 (continuing) Stull Ch 2: Pages 26-28Stull Ch 2: Pages 26-28 Quiz 1 (30 minutes) on Feb 16 th from material through Feb 14 th.Quiz 1 (30 minutes) on Feb 16 th from material through Feb 14 th.

39. MET 61 39 MET 61 Introduction to Meteorology Activity 7: Due March 21 st Question 1: Concrete has an albedo of around.25 and yet the typical infrared emissivity of concrete is 0.8. Explain why these are different and the implication of this on climate change? Question 2: Consider a flat surface subject to overhead radiation. If the absorptivity is 0.1 for solar radiation and 0.8 in the infrared, compute the radiative equilibrium temperature. Question 3: Calculate the radiative equilibrium temperature of the Earth’s surface and Earth’s atmosphere assuming that the earth’s atmosphere can be regarded as a thin layer with an absorptivity of 0.1 for solar radiation and 0.8 for terrestrial radiation. Assume the earth’s surface radiates as a blackbody at all wavelengths.