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 – 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 =  T 4  = Stephan-Boltzman constant = 5.67 x Wm -2 K -4 P is proportional to the area under the Planck function curve P sun = 6.3 x 10 7 W/m 2 (every second) Only a small fraction of sun’s energy is received by the Earth every second: 1368 W/m 2, 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 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) – Power in = Power out

Geometry & assumptions

From: accessed http://

Earth- Incoming Radiation Solar radiation intersects Earth as a disk (  r 2 ) Power in = Power in from sun (S) – Reflected Solar power =  r 2 S -  r 2 S  Where: r = radius of Earth (6360 km) S = solar constant (1368 W/m 2 )  = albedo (earth’s reflectivity) (~30%) =  r 2 S (1- 

Earth- Outgoing Radiation Earth radiates as a sphere with area 4  r 2 Stephan-Boltzmann equations defines outgoing energy based on radiating temperature Power out = 4  r 2  T e 4 (units (m 2 )(Wm -2 K -4 )(K 4 ) = W Total energy emitted by the Earth

Earth’s Radiation Budget If the earth were a black body the in = out Set incoming = outgoing  r 2 S (1-  4  r 2  T e 4 Simplify: S/4 (1-  T e 4 Solve for T e T e = 255K (-18 °C) What if it were different?

Earth as a Black Body Earth’s actual surface temperature T s = 288K (15°C) peak (  m) = 2877/288 = 10  m (IR) T s - T e = 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 H 2 O = 1-3% CO 2 =.035% CH 4 N 2 O O 3 CFC’s High Conc. Trace Naturally occurring Anthropogenic

Sources referenced Ruddiman, W. “Earth’s Climate: Past and Future”. Online: Archer & Rahmstorf. “The Climate Crisis” Martin, E. Energy budget Powerpoint. Accessed online Climate and Earth’s Energy Budget. NASA. Online: yBalance yBalance