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02EnergyBalance - Energy balance principles ESM 203...

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Unformatted text preview: 10/02/2007 Energy balance principles ESM 203: Earth-Sun* energy balance EarthJeff Dozier & Thomas Dunne Fall 2007 Energy is the capacity for doing work (i.e. motivating some change in a system) "Energy" and "heat" are equivalent Energy in energy out = energy storage energy storage either t ith temperature "phase" of water (solid, liquid, gas) 1 Temperature (measure of ( f energy storage) "sensible heat" energy in gy energy out requires energy ("latent heat") melt ice freeze water vaporize vapor condense * We will cover terrestrial energy sources later (onethousandth of the solar flux at the surface, but capable of moving continents and building mountain ranges) gives up energy 3 How Earth operates (simplified) less Methods of energy transfer Radiation: electromagnetic waves propagate through space all bodies radiate, warmer bodies more interactions depend on wavelength 1370 Wm2 Conduction: molecule-tomolecule Some fraction (20-30%) is reflected by atmosphere and surface Remainder (70-80%) is absorbed and emitted at longer wavelengths Some emitted radiation is absorbed in atmosphere Imbalance between Equator and Poles causes circulation of atmosphere and ocean Heated surface transfers energy to atmosphere Water at surface evaporates and moves into atmosphere and the energy ... and condenses to fall back to surface as precipitation also moves hot to cold temperature T d night day typical soil temperatures moves heat & vapor 4 Convection: mixing in air or water enhances transfer sensible: temperature difference between warmer and colder fluid latent: change of phase of water during mixing 2 } ESM 203: EarthSun energy balance 1 10/02/2007 Sensible and latent heat Temperature steady steady. Energy converts water to steam, which leaves the pot. Latent heat. 100 There is a spectrum (range) of wavelengths of electromagnetic radiation Wavelength () For radiation in the climate, we usually use m (micrometer, 106m) or nm (nanometer, 109m) to measure wavelength. Wate temperature (C) er Temperature rising, energy stored in water Sensible water. heat 20 Time Input of energy (heating) 5 http://www.yorku.ca/eye/spectrum.gif 7 Radiation A body radiates energy when electrons in its atoms receive or generate so much energy that they release a small packet of energy (photon) If the atoms are receiving or generating a lot of energy (i.e. they are hot) they emit photons in large numbers and frequently. Thus, both the intensity (energy per unit time) and the frequency of emission are high. Since energy (E) travels through a vacuum at a constant speed (c, the speed of light), if the frequency () of particle (wave) emission is high, the wavelength () is short: = c Planck's law: energy per photon = h = h h is Planck's constant 6 Two rules describing radiation were derived from this simple postulate Planck's equation L = 2hc 2 hc , where x = 5 x k T ( e - 1) At a given temperature a body emits a spectrum of wavelengths and the intensity of radiation varies with the wavelength en nergy Peak radiation for hotter object is higher and at shorter wavelength c = speed of light = 3.0 x 108 ms1 h = Planck's constant = 6.63 x 1034 Js k = Boltzmann's constant = 1.38 x 1023 JK1 0 .00 E + 00 0 Hotter object radiates more at all wavelengths 40 wavelength 8 ESM 203: EarthSun energy balance 2 10/02/2007 Integration over all wavelengths (derived from Planck's equation) Stefan-Boltzmann equation Planck equation for Sun and Earth 10 8 0 R Radiance, Wm m sr -1 E = T = temperature (K) L d = T 10 -1 6 Sun (5800K) Earth (288K) Scaled for Earth-Sun Distance Lightbulb (2840K) 4 -2 E = energy emitted (W m2) = Stefan-Boltzmann constant = 5.67 x 108 W m2 deg4 = emissivity ( ti of radiation f i i it (ratio f di ti from th material t th t from an ideal `blackbody' at the t i l to that f id l `bl kb d ' t same temperature). 0.9-0.99 for most natural materials, but 0.01-0.05 for aluminum foil, for example. 10 4 10 2 10 0 Energy from the Sun (T = 5800K) = 6.4 x 107 W m2 Energy from Earth (T = 288K) = 390 Wm2 10 9 -1 10 0 See Dingman Fig 3-1 & 3-3 Wavelength, m 10 1 10 2 11 Intensity of solar radiation (W m2) is reduced at (W Earth's orbital distance, from ~108 to ~103 Wm2 R = Sun s radius Sun's P = radius of Earth's orbit Result from Planck equation Wavelength of peak radiation (m) = 2897/T(K) Peak of Sun's radiation = 2897/5800 = 0.5 m Peak of Earth's radiation = 2897/288 = 10 m From Sun, most energy in range 0.35 m From Earth, most energy in range 350 m W Let E = Energy generated at Sun 2 m So, total energy at Sun = E4R2 Watts That same amount of energy spreads out over the surface of a sphere at a distance of Earth's radius (4P2) So, energy at Earth is P R S0 = E 4R 2 R W = E 2 4P 2 P m 2 At upper edge of Earth's atmosphere S0 = 1370 W m2 : the `solar constant' 10 12 ESM 203: EarthSun energy balance 3 10/02/2007 Units for measuring energy Joule (J): (mechanically) 1 J is amount of energy expended in accelerating a 1 kg mass by 1 m/sec for 1 sec Mechanical energy can be converted to heat gy specific heat of water is 4185 J/deg/kg (a calorie is 4.185 J) Latent heat (correct term is "enthalpy") of: fusion (melt-freeze) is 335,000 J/kg vaporization is 2.5 million J/kg Rate of energy exchange is called power A Watt (W) is a power. Joule per second A person uses about 2,500 kilocalories/day 10 million Joules/day 120 Watts 13 Incoming solar radiation 15 Atmospheric absorption and scattering Atmospheric transmission of solar and infrared radiation emission absorption scattering NASA Goddard Institute for Space Studies http://www.giss.nasa.gov 14 16 ESM 203: EarthSun energy balance 4 10/02/2007 How Earth intercepts radiation from the Sun less r 1370 Wm2, S0 Radiation intercepted by a tilted plane Consider a plane normal to Earth's surface at a latitude of . r - 90-(- ) Total solar radiation = S0 r2 Total surface area over which the rotating earth spreads the radiation = 4r2 Average intensity of solar radiation = S0/4 = 342 Wm2 This value averages zones where the radiation falls from nearly overhead (tropics) to grazing angles (towards poles) 17 1 L - Radiation on a plane perpendicular to sun's rays, 1 m high and 1 m wide = S0 x 1 x 1 Radiation on 1 m wide plane tilted at angle 90- to sun's rays is S0/L L = 1/cos (- ) Radiation on tilted plane = S0 cos (- ). Intensity of solar radiation varies with sun's height above the horizon (latitude and season) S0 19 The intensity of radiation intercepted by a tilted plane varies with the height of the Sun (i.e. with latitude and (i.e. season) Consider a plane normal to Earth's surface at a latitude of . Height of sun above horizon at noon = 90 ( ) 90-(NP Seasonality of solar radiation (intensity per m2 and duration per day) at top of atmosphere depends on tilt of Earth's axis as it orbits the Sun S0 Eq 90-(-) Latitude at which sun is directly overhead (varies seasonally) 18 Duxbury, A.C. & Duxbury, A. B. (1989) An Introduction to the World's Oceans 20 ESM 203: EarthSun energy balance 5 10/02/2007 The simplest climate model--energy model-- balance with a non-absorbing atmosphere nonSolar radiation at top of atmosphere (MJ m2day1) Solar radiation absorbed by whole Earth = infrared radiation emitted by whole planet h l l t i.e., net all-wave radiation = 0 300 S0 = solar radiation = planetary average albedo F = infrared radiation T = planetary surface temperature So (1 - ) = F = T 4 4 S so, T = 0 (1 - ) 4 0.90-0.95, = 5.67108 1/ 4 250 Tem perature (K) 200 150 100 S0 = 1370 W m2 normal to Sun 50 Divide by 4 to average over Earth, 342.5 Wm2 Dingman, Figure 3-6 21 0 0 0.2 0.4 Albedo 0.6 0.8 1 Albedo 0.27-0.33 (see Charlson) Thus T 255K = 18C 23 Wavelengths of radiation and the atmosphere Ultraviolet (<0.4 m): absorbed by stratospheric ozone (less ozone more UV) Visible (0.40.7 V bl (0 4 0 7 m): scattered b air molecules, dust, soot, ) d by l l d salt, clouds Scattering by air greater for shorter wavelengths (blue). Near-infrared (0.7-3.0 m) (from Sun): scattered less, but absorbed by water vapor, especially at 1.4 and 1.9 m, and by clouds Middle infrared (3 5 m) (from Sun and Earth) and thermal (3-5 infrared (>5 m) (from Earth): absorbed by clouds, water vapor, carbon dioxide, methane, ozone, and other "greenhouse" gases Some "windows" (3.5-4.0m and 10.5-12.5m) when no clouds 22 Interpretation If the atmosphere didn't absorb radiation, the global average temperature should be about 18C 18 C. Near the surface, average air temperature is measured to be about 16C. The discrepancy must be due to the role of the atmosphere in absorbing energy and storing it near the surface. This interaction between solar radiation and the atmosphere begins the processes of energy transfer that create climate 24 ESM 203: EarthSun energy balance 6 10/02/2007 Variation of atmospheric temperature with elevation reflects absorption of radiation emitted from surface and absorbed by atmospheric gases < 0.1m absorbed by N2, O2, N, O Harte's more realistic energy-balance model, energybut still 1-D (Homework 1) 1- (Homework 1) Sav=S/4 apSav Fu (1-)Fs < 0.2m absorbed by O2 O3 absorbs < 0.31 m and ~8 m upper kuSav Fl 0.5L lower klSav Fu H 0.5L W Fs > 0.31m warms surface, which radiates and warms atmosphere surface Fl 25 27 Graedel, T. E. and P. J. Crutzen (1995) Atmosphere, Climate and Change Harte's 1-D climate model with atmosphere 1Mean annual global energy balance for Earth's atmosphere A simple model of this type allows us to anticipate the general nature of changes in atmospheric g p temperature if various controlling factors were to change e.g. solar radiation, albedo, or the absorbing capacity of the atmosphere caused by changes in concentrations of absorbing gases. Layered atmosphere, most infrared absorption in lower layer. y Some solar absorption in upper atmosphere. Sensible and latent heat from surface up into atmosphere. Latent heat estimated from global average of precipitation. We are concerned about such changes because we have come to recognize that surface albedo has changed due to regional-scale vegetation changes; there are feedback effects between climate and albedo because of snow and ice; several greenhouse gases have changed over recent Earth history. Graedel, T. E. and P. J. Crutzen (1995) Atmosphere, Climate and Change 26 Also includes energy released from human activities, although negligible. This is a "steady state" model: no time element; in contrast with a transient model. 28 ESM 203: EarthSun energy balance 7 10/02/2007 Structure of the Harte model apSav Fu (1-)Fs kuSav Fl=Tl4 klSav Upper layer, Tu 0.5L Fu Lower layer, Tl Fs H W Fs=sTs4 29 Absorption of short and long wave radiation by atmospheric constituents Fl=Tl4 Sav(1-ku-kl) 0.5L Surface, Ts Graedel, T. E. and P. J. Crutzen (1995) Atmosphere, Climate and Change 31 Structure of energy balance models in general Top boundary They have compartments Energy (a mass) fluxes e gy (and ass) u es into and out of each must balance Temperature affects some of the fluxes, so T can adjust to make them balance Tx,y,z Layers (e atmosphere) e.g., Most of the atmospheric constituents that absorb outoutgoing long-wave radiation long(relatively large asymmetric molecules) although natural, are augmented by pollutant gases. If we change these concentrations, expect more outgoing radiation to be absorbed and the atmospheric temperature to rise, especially in the lower parts of the atmosphere. Graedel, T. E. and P. J. Crutzen (1995) Atmosphere, Climate and Change 32 Fluxes are: Radiative Convective (vertical) and advective (horizontal) Both sensible and latent Surface (lower boundary) Conductive (not important in atmosphere) 30 ESM 203: EarthSun energy balance 8 10/02/2007 (Karl & Trenberth 2003) Lean 2005, Physics Today 33 35 Radiation imbalance varies with latitude excess Absorbed solar radiation deficit Emitted infrared radiation 0 Equator 30 latitude 60 90 Pole 34 ESM 203: EarthSun energy balance 9 ...
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