Physics of Planetary ClimateCors221: 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 ( T4) 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 coolingoff; its average temperature stays pretty much constant.

Therefore the same amount of total energy that Earthreceives each second must be being radiated to keepEarth in long-term equilibrium.

Radiative Equilibrium

How much power does Earth absorb in total?R

E2 AF/a2 = total power radiated

Planet cross-sectional areaSolar irradiance at a AU from the Sun

Radiative Equilibrium

How much power does Earth radiate in total?4R

E2 T4 = total power radiated

Planetary surface areaBlackbody power radiated per square meter

Radiative Equilibrium

Setting power in = power out:

AF/a2 = 4RE

2 T4

AF/a2 = 4 T4

AF / (4 a2) = T4

T = (AF / (4 s a2) ).25

F = 1370 W / m2

= 5.67 x 10-8 W / (m2 K4)a = distance from Sun in AUA = fraction of light absorbed

Equilibrium TemperaturesT = (AF / (4 a2) ).25 F = 1370 W / m2

= 5.67 x 10-8 W / (m2 K4)a = distance from Sun in AUA = 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 TemperaturesT = (AF / (4 a2) ).25 F = 1370 W / m2

= 5.67 x 10-8 W / (m2 K4)a = distance from Sun in AUA = fraction of light absorbed

Earth: a=1 A=0.7 Actual T = 288K Teq

= 254.3K

Mercury: a=0.39 A=0.82 Actual T = 440K Teq

= 442.5K

Venus: a=0.72 A=0.25 Actual T = 737K Teq

= 231.7K

Moon: a=1.00 A=0.89 Actual T = 273K Teq

= 274.5K

Mars: a=1.52 A=0.75 Actual T = 210K Teq

= 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 goessomeplace; it doesn'tdisappear

Absorption Lines

Earth Atmosphere Absorption

Light and the Atmosphere

The Greenhouse Effect

Atmospheric Structure

Earth's Emitted Spectrum

Leading Greenhouse GasesFamily Feud style:

#1:

#2:

#3:

Leading Greenhouse GasesFamily 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 (-18oC!). 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

2O #2: CO

2 #3: CH

4

T = (AF / (4 a2)).25

This has been true throughout the past 500 million years