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Earth’s Energy Budget

Earth’s Energy Budget. Earth has 2 heat engines: Internal External Internal Heat Engine Energy that drives plate tectonics Source = radioactive decay ~1/10000 th the energy provided by the sun. Earth’s Energy Budget. Earth’s External Heat Engine Energy provided by the sun

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Earth’s Energy Budget

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  1. 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

  2. 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)

  3. Solar radiation • Stephan-Boltzman Law (Energy emitted), E = sT4 • = 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 lpeak (in microns) = 2877/TK • For Sun: 5780K = temp of photosphere lpeak sun = 2877/5780 = 497 nm = 4.97 x 10-7 m

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

  5. 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

  6. Geometry & assumptions

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

  8. Earth- Incoming Radiation • Solar radiation intersects Earth as a disk (pr2) • Powerin = Powerin from sun (S) – Reflected Solar power = pr2 S - pr2 Sa Where: r = radius of Earth (6360 km) S = solar constant (1368 W/m2) • = albedo (earth’s reflectivity) (~30%) = pr2 S (1- a)

  9. Earth- Outgoing Radiation • Earth radiates as a sphere with area 4pr2 • Stephan-Boltzmann equations defines outgoing energy based on radiating temperature • Powerout = 4pr2sTe4 (units (m2)(Wm-2K-4)(K4) = W Total energy emitted by the Earth

  10. Earth’s Radiation Budget • If the earth were a black body the in = out • Set incoming = outgoing pr2 S (1- a) = 4pr2sTe4 Simplify: S/4 (1- a) = sTe4 Solve for Te Te = 255K (-18 °C) What if it were different?

  11. Earth as a Black Body • Earth’s actual surface temperature Ts = 288K (15°C) lpeak (mm) = 2877/288 = 10 mm (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

  12. Greenhouse Gases H2O = 1-3% CO2 = .035% CH4 N2O O3 CFC’s High Conc. Naturally occurring Anthropogenic Trace

  13. 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

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