1. Physics of Planetary Climate Cors221: Physics in Everyday Life Fall 2009 Module 3 Lecture 2: Equilibrium Temperature and The Greenhouse Effect

2. From Last Time ✔ Science can only disprove, not prove ✔ Climate is what you expect; weather is what you get ✔ Light, all light from radio to gamma rays, is electromagnetic radiation ✔ Shorter, bluer wavelengths have more energy and are more dangerous than longer, redder wavelengths. ✔ All bodies emit blackbody radiation; hotter bodies emit more ( T 4 ) light and bluer (shorter wavelength) light. ✔ Earth cools by radiating infrared light to space by blackbody radiation

3. Radiative Equilibrium In equilibrium, the Earth is neither heating up nor cooling off; its average temperature stays pretty much constant. Therefore the same amount of total energy that Earth receives each second must be being radiated to keep Earth in long-term equilibrium.

4. Radiative Equilibrium How much power does Earth absorb in total?  R E 2 AF/a 2 = total power radiated Planet cross-sectional area Solar irradiance at a AU from the Sun

5. Radiative Equilibrium How much power does Earth radiate in total? 4  R E 2  T 4 = total power radiated Planetary surface area Blackbody power radiated per square meter

6. Radiative Equilibrium Setting power in = power out:    AF/a 2 = 4  R E 2  T 4 AF/a 2 = 4  T 4 AF / (4  a 2 ) = T 4 T = (AF / (4 s a 2 ) ).25 F = 1370 W / m 2  = 5.67 x 10 -8 W / (m 2 K 4 ) a = distance from Sun in AU A = fraction of light absorbed

7. Equilibrium Temperatures T = (AF / (4  a 2 ) ).25 F = 1370 W / m 2  = 5.67 x 10 -8 W / (m 2 K 4 ) a = distance from Sun in AU A = fraction of light absorbed Earth: a=1 A=0.7 Mercury: a=0.39 A=0.82 Venus: a=0.72 A=0.25 Moon: a=1.00 A=0.89 Mars: a=1.52 A=0.75

8. Equilibrium Temperatures T = (AF / (4  a 2 ) ).25 F = 1370 W / m 2  = 5.67 x 10 -8 W / (m 2 K 4 ) a = distance from Sun in AU A = fraction of light absorbed Earth: a=1 A=0.7 Actual T = 288K T eq = 254.3K Mercury: a=0.39 A=0.82 Actual T = 440K T eq = 442.5K Venus: a=0.72 A=0.25 Actual T = 737K T eq = 231.7K Moon: a=1.00 A=0.89 Actual T = 273K T eq = 274.5K Mars: a=1.52 A=0.75 Actual T = 210K T eq = 210.1K

9. Interaction of Light & Matter T = fraction of light transmitted R = fraction of light reflected A = fraction of light absorbed T + R + A = 1 All the light goes someplace; it doesn't disappear

10. Absorption Lines

11. Earth Atmosphere Absorption

12. Light and the Atmosphere

13. The Greenhouse Effect

14. Atmospheric Structure

15. Earth's Emitted Spectrum

16. Leading Greenhouse Gases Family Feud style: #1: #2: #3:

17. Leading Greenhouse Gases Family Feud style: #1: Water Vapor (~55% or 19K) #2: Carbon Dioxide (~18% or 6K) #3: Methane (~7% or ~2K)

18. Key Points In equilibrium, a body in space emits the same amount of energy as it absorbs Equilibrium Temperature Earth's equilibrium T = 255K (-18 o C!). Teq is good for airless worlds, not for ones with air Transmission + Reflection + Absorption =1 Gases in Earth's atmosphere absorb at different wavelengths The greenhouse effect comes about because atmospheric gases transmit sunlight at visible wavelengths, but absorb Earth's blackbody emission in the infrared #1: H 2 O #2: CO 2 #3: CH 4 T = (AF / (4  a 2 )).25 This has been true throughout the past 500 million years