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

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

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.

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

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

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 W / (m 2 K 4 ) a = distance from Sun in AU A = fraction of light absorbed

Equilibrium Temperatures T = (AF / (4  a 2 ) ).25 F = 1370 W / m 2  = 5.67 x 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

Equilibrium Temperatures T = (AF / (4  a 2 ) ).25 F = 1370 W / m 2  = 5.67 x 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

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

Absorption Lines

Earth Atmosphere Absorption

Light and the Atmosphere

The Greenhouse Effect

Atmospheric Structure

Earth's Emitted Spectrum

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

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

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