Earth’s Energy Budget• Earth has 2 heat engines:

– Internal– External

• Internal Heat Engine– Energy that drives plate tectonics– Source = radioactive decay– ~1/10000th the energy provided by the sun

Earth’s Energy Budget

• Earth’s External Heat Engine– Energy provided by the sun– Average global surface temperature = 15°C

• Balance between* Incoming solar radiation (electromagnetic

spectrum, mostly visible light)* Outgoing terrestrial radiation (infrared radiation)

Solar radiation• Stephan-Boltzman Law (Energy emitted), E = T4

= Stephan-Boltzman constant = 5.67 x 10-8 Wm-2K-4

• P is proportional to the area under the Planck function curve• Psun = 6.3 x 107 W/m2 (every second)• Only a small fraction of sun’s energy is received by the Earth every

second: 1368 W/m2, as measured by satellites at top of atmosphere

• Wien’s Law - Peak wavelength emitted by a body peak (in microns) = 2877/TK

• For Sun: 5780K = temp of photosphere peak sun = 2877/5780

= 497 nm = 4.97 x 10-7 m

Peak wavelength of the sun is around 500 nm (497)

Earth

• Incoming radiation is short wave.• Outgoing radiation is long wave.

• If the Earth is a blackbody at steady state– Incoming = outgoing (remember our assumption)

– Powerin = Powerout

Geometry & assumptions

From: http://www.windows2universe.org/earth/climate/sun_radiation_at_earth.html accessed 3.26.12

Earth- Incoming Radiation• Solar radiation intersects Earth as a disk (r2)

• Powerin = Powerin from sun (S) – Reflected Solar power= r2 S - r2 SWhere:r = radius of Earth (6360 km)S = solar constant (1368 W/m2) = albedo (earth’s reflectivity) (~30%)

= r2 S (1-

Earth- Outgoing Radiation

• Earth radiates as a sphere with area 4r2

• Stephan-Boltzmann equations defines outgoing energy based on radiating temperature

• Powerout = 4r2 Te4

(units (m2)(Wm-2K-4)(K4) = WTotal energy emitted by the Earth

Earth’s Radiation Budget

• If the earth were a black body the in = out

• Set incoming = outgoingr2 S (1- 4r2 Te

4

Simplify:S/4 (1- Te

4

Solve for Te

Te = 255K (-18 °C)

What if it were different?

Earth as a Black Body• Earth’s actual surface temperature

Ts = 288K (15°C)peak (m) = 2877/288 = 10 m (IR)

Ts - Te = 288 – 255 = 33 difference

• Interactions within atmosphere alter radiation budget • Earth is not a perfect black body, some of the outgoing

radiation is reflected & re-radiated• Greenhouse Effect

Greenhouse Gases

H2O = 1-3%

CO2 = .035%

CH4

N2O

O3

CFC’s

HighConc.

Trace

Naturally occurring

Anthropogenic

Sources referenced

• Ruddiman, W. “Earth’s Climate: Past and Future”. Online: http://bcs.whfreeman.com/ruddiman/

• Archer & Rahmstorf. “The Climate Crisis”. 2010. • Martin, E. Energy budget Powerpoint. Accessed

online 3.23.12.• Climate and Earth’s Energy Budget. NASA. Online:

http://earthobservatory.nasa.gov/Features/EnergyBalance