Download Global Energy Balance

Global Energy Balance
What determines global surface
temperature?
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
sun
earth
Flux = (!Tsun4)(4"rs2)/(4"r2) ~ 1/r2
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 heat
capacity
If more energy is absorbed by the earth than
is emitted, earth will heat up. If more energy
is emitted than absorbed earth will cool
down. How is a balance achieved?
Emission of energy depends on the
temperature 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)
Energy into/out from Earth (W)
T = 275 K = 2°C
3E+17
3E+17
Energy received from sun
(Watts)
With albedo
Energy emitted by Earth
2E+17
Earth cools
down
2E+17
Earth heats up
1E+17
5E+16
0
200
220
240
260
280
300
Earth’s Temperature (K)
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35% of sunlight reflected back
out 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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Energy into/out from Earth (W)
3E+17
3E+17
Energy received from sun
(Watts)
With albedo
Energy emitted by Earth
2E+17
Earth cools
down
2E+17
Earth heats up
1E+17
5E+16
0
200
220
240
260
280
300
Temperature (K)
Incoming shortwave
Outgoing longwave
Earth’s surface T = 5°C
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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 by
weathering and volcanism
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What controls
atmospheric CO2?
1) Partitioning of C
between Deep
Ocean and
atmosphere/surfac
e ocean (103-104
yr)
2) Partitioning of C
between ocean/
atmosphere/
biosphere and
sediments/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 time
will break up CaSiO3 into Ca++, 2HCO3-,H4SiO4. This is called
chemical weathering. These ions are soluble, and are washed
into 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 1
CO2 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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Rate of CO2 in/out of atmosphere
How is a balance achieved?
g
o
t fr
m
n
eri
h
t
ea
w
Ou
In from volcanoes
CO2
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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 more
of the H is converted to He, the sun
contracts. 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 the
sun gets brighter?
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