MET 61 Introduction to Meteorology - Lecture 8

1. 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 MET 61 Introduction to Meteorology

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

4. Energy distribution • Radiative energy propagates at speed of light. • Energy per unit area decrease as square of distance from emitter: R1,, R2=radius MET 61 Introduction to Meteorology

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

6. Solution earth sun MET 61 Introduction to Meteorology

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

8. 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 MET 61 Introduction to Meteorology

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

10. 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. MET 61 Introduction to Meteorology

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13. 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? MET 61 Introduction to Meteorology

14. 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 MET 61 Introduction to Meteorology

15. Solution • F (in; solar) = F (out; terrestrial) S F MET 61 Introduction to Meteorology

16. 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? MET 61 Introduction to Meteorology

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

18. 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 (m2/kg) •  - density (kg/m3) • Angle of incidence (from vertical) MET 61 Introduction to Meteorology

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

20. Example • Parallel radiation is passing through a layer 100m in thickness containing a gas with an average density of 0.1 kg/m3. 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. MET 61 Introduction to Meteorology

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

22. Sun angle MET 61 Introduction to Meteorology

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

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

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

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

31. Activity 7: Due March 21st • 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. MET 61 Introduction to Meteorology