Goals for Today1. PREDICT the consequences of varying the factors that

determine the (a) effective radiating temperature and (b) mean surface temperature of a planet

2. DESCRIBE how incoming and outgoing electromagnetic radiation interacts with Earth’s surface and its atmosphere

3. PREDICT how changes in solar constant, greenhouse gases, and albedo will affect a planet’s mean surface temperature

4. BALANCE a radiation budget by accounting for reflection, absorption, and transmission of radiation throughout a system

5. PREDICT the consequences for Earth’s surface temperature of latent heat and sensible heat transfer from the Earth’s surface to the atmosphere

Radiation Balance II [http://www.elearning.ubc.ca/vista]

RELEVANCE

Venus(too hot) Earth (just right)

Mars(too cold)

The flux of solar radiation reaching Earth is one of the main factors dictating its mean temperature,

and therefore its habitability

Amount of solar radiation that reaches the top of the Earth’s atmosphere

Next…how do we use this information to figure out the mean temperature of Earth?

(Solar Constant)/4342 W/m2

30% of the incoming solar radiation is directly reflected back to outer space

Earth’s ALBEDO = fraction of incoming

solar radiation that is reflected back to

space = 0.3

Earth’s surface reflects about 4% of the total

What’s doing the reflecting? Clouds (& dust) reflect about 26% of the total

Clicker Q: Considering ONLY the effects of ALBEDO, which of the following scenarios do you think would make Earth WARMER?

A. Turn desert into forestB. Turn tundra into desert C. Lower sea levelD. Produce more cloudsE. Expand ice caps

INPUT= Fin = 342 W/m2

ALBEDO = 30%

What’s doing the absorbing?

How much energy does Earth absorb?

342 W/m2

ENERGY ABSORBED = Fabs = Fin * (1-0.3)

= 342 W/m2 x 0.7

= 240 W/m2

Fem = Fabs = 240 W/m2

Fem

Earth’s radiation balanceWhat comes in must go out (or else…)

Fabs

…rearrange…calculate…

Te = 255°K (-18°C) Earth’s “EFFECTIVE RADIATING TEMPERATURE”

(brrrrr…..)

How hot must Earth be to emit 240 W/m2?

F = T4

Recall Stefan-Boltzmann’s equation…

T?

240 W/m2

240 W/m2

240 W/m2

240 W/m2

240 W/m2

240 W/m2 = Fem = Te4

Earth’s effective radiating temperature63.5 million W/m2

(Stefan-Boltzmann)1370 W/m2

(solar constant)

Geometry ofspheres& circles

Earth is a spinning sphere

342 W/m2

Earth’s albedois 0.3

240 W/m2What comes in

must go out255KEarth’s effective

radiating temperature is…

(Stefan-Boltzmann again)

5785 K(Wien’s law)

Clicker Q: Over its lifetime (billions of years), the Sun has been getting hotter, which

should influence Earth’s effective radiating temperature (how?). Which

of the following could counteract this effect (that is, influence Earth’s effective

radiating temperature in the opposite sense)?

A. Increase the size of the SunB. Decrease the Earth-Sun distanceC. Increase Earth’s spinning rateD. Decrease Earth’s spinning rateE. Increase Earth’s albedo

“Effective Radiating Temperature” VS “Mean Surface Temperature”

Te = -18°CTs = +15°C

240 W/m2

Ts > Te by about 33°Cdue to GREENHOUSE WARMING

Emissions Spectra for Sun and Earth

INFRAREDVISUV

Most energy from the Sun

passes through Earth’s

atmosphere

Most energy emitted by the

Earth gets absorbed by the atmosphere.

UV VIS IR

Short Long

CO2

H2O

O3

N2O

CH4

Total

What’s doing the absorbing?

Mostly O3

INCOMING OUTGOING

A bit of water vapour

Gree

nhou

se G

ases

Atmosphere

Fabs=240 W/m2 IRsurf = Tsurf4 = 240 W/m2

Fem=240 W/m2

Scenario 1: No greenhouse gases

How do atmospheric greenhouse gases increase the temperature of Earth’s

surface?

Stefan-Boltzmann Tsurf = 255K (or -18°C)

Assume 100% of IRsurf absorbed by greenhouse gases

IRsurf

Fabs = 240 W/m2 0.5 IRsurf

0.5 IRsurf

Scenario 2: With greenhouse gases

Fem = 240 W/m2

-18°C

+30°C

IN still equals OUT:Fem = Fabs = 240 W/m2

Since Fem = 0.5 IRsurf

IRsurf = (240/0.5) W/m2

= 480 W/m2

Stefan-Boltzmann Tsurf = 303K (or +30°C)

Fin? A. 250 W/m2

B. 500 W/m2

C. 1000 W/m2

D. 2000 W/m2

E. 4000 W/m2

Clicker Q: Here’s a diagram of a planet with greenhouse gases (like Scenario 2). This planet is also SPINNING. Its solar constant is 2000 W/m2. At the top of the planet’s atmosphere, how much solar radiation does the average

square meter get?

Fin= 500 W/m2

Fabs?

A. 100 W/m2

B. 250 W/m2

C. 500 W/m2

D. 1000 W/m2

E. 2000 W/m2

Clicker Q: Same planet. Its solar constant is 2000 W/m2. Its albedo is 50%. What is the flux of solar radiation the planet ABSORBS

(Fabs)?

250 W/m2

500

W/m

2

250

W/m

2

A. 100 W/m2

B. 250 W/m2

C. 500 W/m2

D. 1000 W/m2

E. 2000 W/m2IRsurf?

Clicker Q: Same planet. Its solar constant is 2000 W/m2. Its albedo is 50%. What is the

flux of infrared radiation emitted by the surface of the planet (IRsurf)?

IRsurf

Fabs = 240 W/m2

Fem = 240 W/m2

This simple model predicts a surface temperature significantly higher than measured

-18°C

+30°C

240 W/m2

480 W/m2

WHY?

Te = -18°CTs = +15°C RealityThe model

IRsurf

Fabs = 240 W/m2

Fem = 240 W/m2

Clicker Q: Which of these simplifying assumptions contributed to overestimating the temperature of the surface?

-18°C

+30°C

240 W/m2

480 W/m2

A. None of the incoming solar radiation is absorbed by the atmosphere and 240 W/m2 reach the surface

XX

B. All IRsurf is absorbed by the atmosphere and none leaks out to outer space

C. IR radiation is the only means whereby energy is transferred from the surface to the atmosphere

X

IRsurf

Fabs = 240 W/m2 0.5 IRsurf

0.5 IRsurf

Fem = 240 W/m223% of incoming shortwave radiation are absorbed by the atmosphere

Earth’s surface transfers energy to the atmosphere in the form of latent and sensible heat too

Atmosphere is not 100% opaque to IR radiation

Te = -18°CTs = +15°C

Earth’s radiation balance

SURFACE

Earth’s radiation balance: SURFACE

Input: 47% from the Sun96% from the atmosphere

Total: 143%

Output:109% as IR to the atmosphere5% as IR to outer space29% as heat to the atmosphere

Total: 143%

=114%

SURFACEEarth’s surface radiates 114% of 342 W/m2 = 390 W/m2

SURFACE TEMPERATURE:

390 W/m2 … Stefan-Boltzmann… 288K (15°C)

Earth’s surface temperature

• Earth’s mean surface temperature is higher than its effective radiating temperature because of greenhouse gases• Earth’s atmosphere lets most of the incoming, short wavelength, solar radiation through, but absorbs much of the outgoing, long wavelength, infrared radiation emitted by Earth• Latent and sensible heat transfer from Earth’s surface to its atmosphere help keep the surface cooler than it would otherwise be• The radiation budget for Earth’s surface, its atmosphere, and the planet as a whole are typically in balance. Changes in solar constant, albedo, and greenhouse gases can all perturb the system, leading to a new equilibrium temperature.

Summary: Radiation Balance II

Relevance: Earth’s habitability, greenhouse warming

Slide about the negative feedback that keeps Earth’s T in whack?Increased T, more radiation emitted, decreased T, less radiation emitted