Energy Balance and Greenhouse Gases. E out. Summer Seminar Conceptual Climate Models. Energy Balance and Greenhouse Gases

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1 Summer Seminar Conceptual Climate Models Jim Walsh Oberlin College Global climate is determined by the radiation balance of the planet. There are three fundamental ways in which this balance can change 1 : *changing the incoming solar radiation (insolation) *changing the albedo *altering the Outgoing Longwave Radiation (OLR) July 23, 2013 Anthropogenic interference with climate occurs first of all through a perturbation of the radiation balance (e.g., greenhouse effect, air pollution, land use change) 2 1 Intergovernmental Panel on Climate Change AR4 (2007), p. 465 ( 2 M. Wild, Institute for Atmospheric and Climate Science, ETH, Zurich. Budyko s EBM: = sine(latitude) E in E out Mikhail Budyko ( ) insolation albedo outgoing longwave radiation (OLR) Units: W/m 2 = J/(s m 2 ) M.I. Budyko, The effect of solar radiation variations on the climate of the Earth, Tellus 21 (1969)

2 NASA: Earth Radiation Budget Experiment IPCC Assessment Report 4 (2007), Working Group 1, p. 96 Budyko s EBM: = sine(latitude) Principles of Planetary Climate Cambridge, 2010 (PPC) OLR Ray Pierrehumbert University of Chicago Chapter 4: Radiative transfer in temperature-stratified atmospheres Chapter 3: Elementary models of radiation balance. D. Hartmann, Global Physical Climatology, Academic Press, G. Plass, Infrared radiation in the atmosphere, Amer. J. Physics 24 (1956),

3 Solid Angles and Steradians Radiation: characterized by direction of propagation and frequency frequency (Hz) wavelength (m) Electromagnetic spectrum The measure in radians of an angle made by a collection of rays emanating from a point P is the length of the arc of the unit circle centered on P which the rays intersect. P (PPC, p. 137) wavenumber relevant in climatology The measure in steradians of a solid angle made by a collection of rays emanating from a point P is the area of the patch of the unit sphere centered on P which the rays intersect. steradians P steradians Energy of radiation: measured by its intensity or radiance I Solid Angle Differential Hemisphere surface area The amount of corresponding radiant energy is magnitude of radiant intensity

4 Energy of radiation: measured by its intensity or radiance The amount of corresponding radiant energy is Energy of radiation: Flux density The amount of radiant energy per unit frequency per unit area per unit time: Total energy per unit frequency passing across a unit area of a plane surface from one side to the other (integrate over the upper hemisphere): Energy per unit frequency per unit area per unit time: Spectral flux density Integrate spectral flux density over all frequencies: Flux density Blackbody radiation: radiation reacts so strongly with matter that it achieves thermodynamic equilibrium at same temperature as the matter ( perfect absorbers and emitters ). Blackbody radiation isotropic: equally intense in all directions Planck s Function: k = Boltzman thermodynamic constant h = Planck s constant c = speed of light frequency (Hz) Stefan-Boltzman Law: Total power exiting from each unit area of the surface of a blackbody: wavelength (m) wavenumber n spectral F.D. with T at all n

5 Blackbody radiation isotropic: equally intense in all directions Radiation balance of planets: An idealized example the planetary albedo is spatially uniform. the planet radiates like a perfect blackbody (uniform surface temp. T ) the planet s atmosphere is perfectly transparent to the electromagnetic energy emitted by the surface Total power exiting from each unit area of the surface of a blackbody: (T E = 255 K) n Planet loses energy through emission at a lower wavenumber than that at which it receives energy from the star. Flux absorption: Beer s Law Greenhouse gas (GG): Absorption is proportional to the flux F times the mass of the absorber along the path. Prevalence of clouds in the high, cold regions of the tropical atmosphere (condensed water small enough small enough to stay suspended for a long time.) (Figure from PPC, p. 149) absorption coefficient density of the absorber Assumes : (i) no scattering: a parallel beam of radiation (ii) plane-parallel approximation: atmospheric properties are functions only of the vertical coordinate The Earth s observed zonal-mean OLR for January, 1986 (solid curve). (dashed curve).

6 Greenhouse gas (GG): Greenhouse gas (GG): Nitrogen N % Oxygen O % Argon Ar % Carbon Dioxide CO % Neon Ne % Methane CH % Ozone O % Water vapor -- highly variable; typically makes up about 1% R. Pierrehumbert et al, On the relative humidity of the atmosphere, The Global Circulation of the Atmosphere, T. Schneider and A Sobel, eds. Princeton University Press, 2007, p This is composition of air in percent by volume, at sea level at 15 C and Pa. (CRC Handbook of Chemistry and Physics, edited by David R. Lide, 1997) Greenhouse gas: Absorption coefficient and OLR spectrum. Toy example with one (fictitious) GG p Transmission spectra of major atmospheric gases tropopause T strat T s T 600 n wavenumber (T s = 280 K, T strat = 200 K) (PPC, p. 218) Sun Earth

7 Greenhouse gas: Absorption coefficient and OLR spectrum. Toy example with one (fictitious) GG Greenhouse gas: Absorption coefficient and OLR spectrum. p T Tstrat Ts 600 n wavenumber Infrared emission peak for Earth centered on ~ n = 670 cm-1 The strength of the greenhouse effect is not so much a matter of how deep the ditch is, but how wide. (Ts = 280 K, Tstrat = 200 K) (Ts = 280 K, Tstrat = 200 K) (PPC, p. 217) Greenhouse gas: Absorption coefficient and OLR spectrum. Rather than being unquestionably lethal, the results of a doubling of CO2 may be merely catastrophic. --R. Pierrehumbert Greenhouse gases T = 260 K p = 500 mb R. Pierrehumbert, Infrared radiation and planetary temperature, Physics Today (January 2011). R. Pierrehumbert, Infrared radiation and planetary temperature, Physics Today (January 2011). SUN Absorption coefficient for pure CO2 at T = 293 K, p = 1000 mb tropopause

8 Greenhouse gases: Logarithmic dependence of OLR on CO 2 H. Marshall, J. Walker and W. Kuhn, Long-term climate change and the geochemical cycle of carbon, J. Geophys. Res. 93 (D1) (1988), Equilibrium solutions A = ln P, B = ln P, P = pco 2 K. Caldeira and J. Kasting, Susceptibility of the early Earth to irreversible glaciation caused by carbon dioxide clouds, Nature 359 (1992), A( )= B( )= , =ln(pco 2 /300) A. McC. Hogg, Glacial cycles and carbon dioxide, Geophys. Res. Lett. 35 (2008) Equilibrium solutions

9 Geological and paleomagnetic evidence indicate that during at least two Neoproterozoic glacial periods (~630 Ma and ~715 Ma) continental ice sheets flowed into the ocean near the equator. Positive ice-albedo feedback; snowball Earth hypothesis Alternative theory: thin strip of open ocean about the equator. --evidence that photosynthetic eukaryotes thrived both before and immediately after the Snowball Episodes. --evidence that multiple lineages of sponges may have survived these glaciations D. Abbot, A. Viogt and D. Koll, The Jormungand global climate state and implications for Neoproterozoic glaciations, J. Geophys. Res. 116 (2011) (D18103) Net evaporation Abbot et al, p. 4 Henry Fuseli (1788) Abbot et al, p. 4

10 Summary Lots of good science involved in the study of the atmosphere and its effects on climate. Involve physics and chemistry colleagues? Greenhouse gases and their effects on outgoing longwave radiation can be incorporated into conceptual climate models. Conceptual climate models are versatile: adjustments in the albedo function, for example, can lead to model behavior appropriate for different eras in the Earth s past. Homework: Worksheet problems 2, 3, 4, 6, 7, 8, 13, 14 Thank You!

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