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Global Energy Balance

What determines global surfacetemperature?

Blackbody radiation

Energy emitted by an object depends on

temperature.

Energy Flux (W/m2)

= Energy/(Time x Area) = !T4

where ! = constant = 5.67x10-8 W/(m2K4)

1 W= 1 Joule/second (Energy/time)

T is temperature in K

wavelength proportional to 1/T:

"max = 2898/T, where " is in µm (10-6m)

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Energy emitted by the sun (W)

= Flux at sun's surface (W/m2) x Area of

sun (m2)

= !Tsun4 x 4"rs2

Flux at some distance r from sun:

Flux = Energy emitted by the sun (W), area

over which this energy is spread

Flux = (!Tsun4)(4"rs2)/(4"r2) ~ 1/r2

sun earth

Flux at the distance of the earth's orbit = ( Tsun4)(4 rs2)/(4 reo2) = S S = 1373 W/m2 = "solar constant" Energy absorbed by earth = Flux at the distance of the earth's orbit x cross section of earth = [( Tsun4)(4 rs2)/(4 reo2)][ re2] = S[ re2] Incoming energy from the sun is determined by the orbital parameters and the temperature of the sun.

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An object will heat up if energy is added:

c x dT/dt = dE/dt where c is the heatcapacity

If more energy is absorbed by the earth thanis emitted, earth will heat up. If more energyis emitted than absorbed earth will cooldown. How is a balance achieved?

Emission of energy depends on thetemperature of the earth

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Global Energy Balance

A temperature at the surface of the earth will

be reached such that Energy in = Energy out

Energy in = Energy out

S[!re2] = ("Tearth4)(4!re2)

T = 275 K = 2°C

0

5E+16

1E+17

2E+17

2E+17

3E+17

3E+17

200 220 240 260 280 300

Energy received from sun(Watts)

With albedo

Energy emitted by Earth

Earth heats up

Earth cools

down

Ener

gy in

to/o

ut fr

om E

arth

(W)

Earth’s Temperature (K)

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35% of sunlight reflected backout to space

• Clouds [24%]• Scattering by the

atmosphere [7%]• Earths surface [4%]

– Snow– Vegetation– Ocean– Desert

Energy in = Energy out (1-.35) S[ re2] = ( Tearth4)(4 re2) where .35 is the Albedo (reflected fraction of visible light) of the earth. T = 255 K = -18°C

This is actually the temperature somewhere in the atmosphere. It is the temperature that we would see from space (emission temperature). Actual surface temperature is 15°C. Difference reflects the greenhouse effect.

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0

5E+16

1E+17

2E+17

2E+17

3E+17

3E+17

200 220 240 260 280 300

Energy received from sun(Watts)

With albedo

Energy emitted by Earth

Earth heats up

Earth cools

down

Ener

gy in

to/o

ut fr

om E

arth

(W)

Temperature (K)

Earth’s surface T = 5°C

Incoming shortwave Outgoing longwave

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Greenhouse gas: can absorb and emit

infrared (heat) radiation

Greenhouse gases:

concentration (ppm)

Water vapor variable

CO2 350 ppm

methane 1.7

N2O (nitrous oxide) .3

ozone variable

Water vapor is the most important

greenhouse gas. Carbon dioxide comes in

second (rarer, but very effective at trapping

radiation).

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Energy Balance

Energy absorbed = Energy emitted (T)

How to change earth's surface temperature:

1) Change Energy coming in from the sun

(increase reflectance).

2) Change amount of greenhouse gasses

(emission T stays the same, but surface T is

increased.

More than 1 way to satisfy energy balance!

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Positive feedback: Process in which

perturbation causes system to travel further

away from initial state:

Negative feedback: Process which causes a

system to return to it's initial state upon

perturbation:

Positive (de-stabilizing) feedbacks on earth's

temperature:

1) Ice-albedo feedback

Colder T - > more ice -> more sunlight

reflected - > colder T

Cold limit: Totally frozen earth

Warmer T - > less ice -> less sunlight

reflected - > warmer T

Warm limit: Earth with no ice

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2) Water vapor feedback

Warm air can hold more moisture than cold

air:

Colder T -> less water vapor in atmosphere -

> colder T

Warmer T -> more water vapor in

atmosphere - > warmer T

What stabilizes earth’s climate?

Long term CO2 regulation byweathering and volcanism

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What controlsatmospheric CO2?

1) Partitioning of Cbetween DeepOcean andatmosphere/surface ocean (103-104

yr)2) Partitioning of C

between ocean/atmosphere/biosphere andsediments/rocks(>106 yr)

Simplified Earth:

Crust = CaSiO3 (wollastonite)

Process which tends to draw down CO2

3H20 + 2CO2 + CaSiO3 -> Ca++ + 2HCO3- + H4SiO4 -> SiO2 +CaCO3 + 3H20 + CO2

1) CO2 dissolves in water to form a weak acid, which with timewill break up CaSiO3 into Ca++, 2HCO3-,H4SiO4. This is calledchemical weathering. These ions are soluble, and are washedinto streams and eventually into the ocean by rainwater.

2) In the ocean, plants and animals form hard shells (CaCO3=

SiO2). This draws the Ca++, 2HCO3-,H4SiO4 out of the ocean.

These shells are eventually buried in the ocean sediments.

Net reaction: CO2 + CaSiO3 -> SiO2 + CaCO3

Whole cycle: Take up 2CO2, release 1CO2 => net uptake of 1CO2 from atmosphere.

Weathering limits rate at which CO2 is drawn down

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Weathering Rates

• Temperature• Moisture• CO2

• Mechanical breakdown

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Process which tends to build up CO2:

The mantle contains CO2. As seafloor is

created, this CO2 is released to the

atmosphere.

When seafloor sediments are subducted

(subjected to heat and pressure), some CO2

from CaCO3 is released back into the

atmosphere.

SiO2 + CaCO3 -> CaSiO3 + CO2

This reaction will proceed faster when plate

tectonics moves faster.

Stabilizing mechanism: fact that uptake of

CO2 is proportional to amount of CO2 in

atmosphere.

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How is a balance achieved?

CO2Rate

of C

O2 i

n/ou

t of a

tmos

pher

e

In from volcanoes

Out from weathering

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The Carbonate-Silicate Cycle

Examples

• Frozen Earth• Faster plate tectonics• Weaker sun• Continents near equator• Rise of land plants

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The Faint Young Sun Problem

Faint young sun paradox

Sun increases intensity with time. As moreof the H is converted to He, the suncontracts. This increases the rate of fusion,and the temperature will increase.

Q: Why wasn't early earth frozen??

A: More carbon was in the atmosphere.Early on, CH4 was also an important factor.

How will this play out in the future as thesun gets brighter?