# EOSC 112: THE FLUID EARTH - University of British Columbia

EOSC 112: THE FLUID EARTH RADIATION, ENERGY BALANCE AND THE GREENHOUSE EFFECT E12 Read: Kump et al. Chap.3, p. 34-43 Check: Key Terms, Review Questions. Objectives: 1. To describe the spectrum of electromagnetic radiation 2. To calculate the energy balance of a planet

devoid of atmosphere 3. To calculate the magnitude of the greenhouse effect 1. Spectrum of electromagnetic radiation Figure representing a wave in motion The regions of the spectrum that are most important to climate and life are: the visible, the infrared, and the ultraviolet (fig.). The Sun radiates energy in all of these

spectral regions, while Earth emits in the infrared (fig.). Stefan-Boltzmann law: F = T4 where, F = energy flux (Watts/m2), T = temperature (Kelvins), and = 5.67x10x10-8 W/(m2K4). Figure representing the solar and terrestrial spectra

2. Energy Balance The principle to apply to determine the surface temperature of a planet: Energy Balance. For a planet without atmosphere, the surface T depends on 2 factors: 1) the solar flux available at the distance of the planets orbit, and 2) the reflectivity of the planet. (See box titled Planetary Energy Balance) Figure representing the calculation of

Planetary Energy Balance Calculation of Planetary Energy Balance ENERGY EMITTED BY EARTH = ENERGY ABSORBED BY EARTH ENERGY EMITTED = 4 R 2 earth 4

e T EN. ABSORBED = EN. INTERCEPTED EN. REFLECTED = R 2 earth S - R

2 earth SA Introducing the above expressions into our top equation yields: or 4 e

4 T S (1 - A) Te 4 (S / 4 )(1 A) radiussun where, S T distancesun earth 2 4 sun

and using, Tsun= 57x1080K, radiussun= 695 000km, distancesun-earth= 1.496x108km then, S = 1366W/m2; A = 0.3 Te = 255K = -18C. But, Ts = 15C. For Venus, Te = -53C, Ts = 457x10C 3. Magnitude of the Greenhouse Effect

For a planet with an atmosphere, the surface T also depends on the greenhouse effect (that is, the amount of warming provided by the atmosphere): Tg Tsurface(actual) Tsurface(calculated) Earth: Tg 15 ( 18) 33 C Venus: Tg 457 ( 53) 510 C Mars: Tg 55 ( 61) 6 C

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