EXPLAIN

2. Earth’s Energy Balance

Energy Balance

• Let the rate of energy flow from the Sun to the Earth be called Fin

• Let the rate of energy flow from the Earth to outer space be called Fout

Energy In = Energy Out

Energy Balance

• Assume both Sun and Earth are blackbodies, so F = s T4

• Fin = absorbed sunlight x daylight area

• Fout = s Tearth4 x total area

Fin = Fout

Energy Balance

Fin = Fout

Fin = Solar brightness x (1 – albedo) x (area of Earth’s shadow)

Fout = s (Tearth)4 x (area of Earth’s surface)

• 30% reflected by clouds, air, dust, and surface• 19% absorbed by the atmosphere (mostly

clouds)• 51% absorbed at the surface

Solar Radiation

Energy Balance

Fin = Fout

Fin = Solar brightness x (1 – a) x p r2

Fout = s (Te)4 x 4p r2

Energy Balance

Fin = Fout

Energy Balance

Fin = Fout

But the observed surface temperature is about 288 K

Both are almost perfect blackbodies!

The hot sun radiates at shorter (visible) wavelengths that carry more energy

Energy absorbed by the cooler earth is then re-radiated at longer (thermal infrared) wavelengths

Earth & Sun Emission

SUN

EARTH255 K

Bare Rock Model• If sunlight were

the only source of energy, the surface of the Earth would be way too cold for life!

• 255 °K = -18 °C = -1 °F

Surface

Sunlig

ht

Fsurface

Fin = Fout

Two-Layer Model• Now imagine

a layer of glass above the solid rock

• Glass is transparent to sunlight

• Glass is opaque to “Earthlight”(thermal IR)

Glass

Surface

Sunlig

ht

Fglass

Fglass

Fsurface

Seen from Above

Both models: • Absorb the same sunshine• Reflect the same amount of sunlight back out• Emit the same amount of Earthlight

Glass

Surface

Sunlig

ht

Fglass

Fglass

Fsurface

Sunlig

ht

Fsurface

boundary

Summary• Layer models are not meant to be

accurate or predictive, just to help us understand how the world works

• Energy balance of “bare rock” model is way too cold to support life!

• Adding a layer of glass makes the surface nice and toasty

• Where did the heat come from?

Bathtub Analogy• If faucet runs faster than

drain, level rises• And vice versa• Drain runs faster when

water is deep• Adding glass to layer

model acts like a clog in the drain

• Water rises until drainage = inflow again

Faucet ~ SunDrain ~ Thermal emissionWater level ~ temperature

Greenhouse Gases

Gases• Gases are made of

moving molecules separated by empty space

• Kinetic energy of molecular motion is proportional to temperature

• Gases don’t behave as blackbodies or even graybodies!

• Let’s take a look!99% of Earth’s

atmosphere is N2 & O2

Waves and Photons

Experiments show both kinds of behavior:

– Oscillating fields with troughs and crests (waves)

– Individual packets of energy (particles)

Long Waves = small photons

Short Waves = BIG PHOTONS

Electromagnetic radiation behaves as both waves and particles!

Energy is “Quantized”• When radiation

interacts with atoms and molecules, only certain “jumps” in energy are possible

• Electrons orbit at specific energy levels above an atomic nucleus

• Absorption of a photon of just the right energy can make them “jump up” to the next level

• Emission of a photon occurs when an electron “falls” down to a level below

UV & Visible Light• Big jumps take

lots of energy, small jumps take less

• Big drops emit energetic photons (short wavelengths)

• Small drops emit less energetic photons (longer wavelengths)

Most electron transitions in gases absorb/emit visible or UV light

Molecules and IR light• Molecules are groups of atoms

that share electrons (chemical bonds)

• Molecular transitions involve changes in vibration, rotation, bending, and stretching of chemical bonds

• Photons can interact with molecules to change states

• Transitions involve specific amounts of energy, so only certain wavelengths are active

Molecular transitions typically absorb & emit in thermal infrared

Dancing Molecules and Heat Rays!

• Nearly all of the air is made of oxygen (O2) and nitrogen (N2) in which two atoms of the same element share electrons

• Infrared (heat) energy radiated up from the surface can be absorbed by these molecules, but not very well

N N

O O

Diatomic molecules can vibrate back and forth like balls on a spring, but the ends are identical

No electric dipole!

Dancing Molecules and Heat Rays!

• Carbon dioxide (CO2) and water vapor (H2O) are different!

• They have many more ways to vibrate and rotate, so they are very good at absorbing and emitting infrared (heat) radiation Molecules that have

many ways to wiggle are called “Greenhouse” molecules

O OC

H H

O

Atmospheric Absorption

• Visible radiation passes almost freely through Earth's atmosphere

• Earth's emitted thermal energy either fits through a narrow “window” or is absorbed by greenhouse gases and reradiated

• Complete absorption from 5-8 mm (H2O) and > 14 mm (CO2)

• Little absorption between about 8 m and 11 mm (“window”)

Earth-Atmosphere Energy Balance

Earth's surface absorbs the 51 units of shortwave and 96 more of longwave energy units from atmospheric gases and clouds.These 147 units gained by earth are due to shortwave and longwave greenhouse gas absorption and emittance. Earth's surface loses these 147 units through convection, evaporation, and radiation.

9 PM surface temperature = 25 °C = 77 °F

Summer Nightin Colorado

6 AM surface temperature = -50 °C = -58 °F

radiationemittedby soil

390 W m-2 4 inches= 10 cm

6 AM surface temperature = 15 °C = 50 °F

Summer Nightin Colorado

radiationemittedby soil

390 W m-2 4 inches= 10 cm

radiationemittedby air

340 W m-2

The strongest evidence for the

Greenhouse Effect

is that we can survive night!

Common Sense• Doubling CO2

would add 4 watts to every square meter of the surface of the Earth, 24/7

• Doing that would make the surface warmer

• This was known before light bulbs were invented!

4 Watts

1 m

1 m

John Tyndall, January 1863

Common Myth #1“Scientists are worried about climate change

because it’s been warming up recently”

WRONG! We’re worried

because we know that when we add heat to things, they warm up

Cause and Effect

• Climate is a result of physical, chemical, & biological processes

• Forcing causes a response

• Strength of response to unit forcing is called “sensitivity”