Monday 9 September, :30-11:30 Class#03
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1 Monday 9 September, :30-11:30 Class#03 Topics for the hour Solar zenith angle & relationship to albedo Blackbody spectra Stefan-Boltzman Relationship Layer model of atmosphere OLR, Outgoing longwave Radiation Radiative Balance, Heat transport in Ocean & Atmosphere Radiative Transfer Selective absorption by gases 1
2 TOA Insolation and Average Solar Zenith Angle determine seasonal & latitudional variations Solar zenith angle 90 sun rise/set Θs Hartmann, 1994 Solar Flux per Area Q = S 0 d d 2 cosθ s dbar - mean sun-earth distance while d is actual distance. Amount by which area is increased 2
3 Daily Average Solar Zenith Angle & Latitude 90 - polar darkness Albedohigher when zenith larger Θs = = , polar minimum Θs avg at subsolar latitude =38.3 Hartmann,
4 Theoretical Blackbody Spectra Blackbodies vibrate & interact with light at many frequencies Earth, ocean and land are blackbodies but gases are not since they only interact at certain frequencies Units of plot As T increases, peaks move to the right & total energy emitted increases [Archer 2011] 4
5 Blackbody Radiation Blackbody radiation - perfect absorber and emits a maximum of energy at a particular temperature Dependence of total blackbody emission (over all wavelengths) on temperature follows Stefan-Boltzman Law ( Tell us how quickly energy is radiated from an object): E R = εσt 4 σ = Wm 2 K 4 ER is the total rate of energy emaission from the object at all frequencies in Watts/m2. ε is emissivity, a number between 0 & 1 telling us how good a blackbody we have (1=best) σ is the Stefan-Boltzman constant T is emission temperature Compare spectra of Sun and Earth 5
6 Normalized Spectra of Sun and Earth (same heights) Visible not absorbed Ozone absorbs most incoming solar radiation 4 micron break CO 2 vibration-rotation absorption key wavelength Water vapor absorption between microns You can imagine that radiation is NOT easy to model! 6
7 Layer Model of the Atmosphere Recall bare rock model had an emission temperature of 255 K, much cooler than real temperature of 288 K. Atmosphere is transparent to visible light (solar) Solar energy all reaches the surface and converts into Terrestrial radiation and points up. Terrestrial radiation (LW) is absorbed in atmosphere and emitted upwards and downwards 7
8 Solve for temperature of surface and atmosphere. Simple energy balance model Assume LW blackbody Solar transparent Hartmann, 1994 S 0 4 (1 α p ) = σt 4 4 A = σt Energy Balance TOA e σt 4 4 S = 2σT Energy Balance of Atmosphere A sd S 0 4 (1 α ) + σt 4 4 p A = σt S Energy Balance of Surface T e =T a =255K T S = is ~20% warmer 8
9 Infrared Radiation emitted by earth, some absorbed by atmosphere 0.4-7µm µm 7-25µm incoming solar radiation outgoing terrestrial radiation Solar Absorption (yellow) µm (visible, 45% ) transparent µm (near i.r., 37% ) Atmospheric Absorption (green) 7-25 µm (far i.r., 37% ) 9.6 µm Ozone < 8 µm Water Carbon Dioxide > 15 Water Vapor Atmospheric Window 9
10 10
11 11
12 12
13 Latitudional Energy Balance Hartmann, 1994 Steep gradient due to increasing albedo with lat. Ruddiman, 2001 Heat must be transported poleward to balance heat imbalance 13
14 Energy Balance Climate Rate of change of energy E ao t Storage small when averaged over a year so it is ignored. = R TOA ΔF ao Divergence of horizontal flux R TOA = ΔF ao Hartmann,
15 Take Figure 2.12 & integrate Energy Transport Hartmann, 1994 How we get this total curve and then atmospheric, then ocean as a residual. 50%/50% atmosphere/ocean, More on this later 15
16 Homework for Wed Sept 18, 2013 Problems 2, 3, and 4 in Hartmann Chapter 2 2. Calculate the emission temperature of Earth if the solar luminosity is 30% less as it is hypothesized to have been early in Solar System History. Use todays s albedo and today s Earth-Sun distance. 3.Calculate the emission temperature of Earth, if the planetary albedo is changed to that of ocean areas without clouds, about 10%. 4.Using the model illustrated in Figure 2.3, calculate the surface temperature if the insolation is absorbed in the atmosphere, rather than at the surface. 16
17 Electromagnetic Radiation Wave (scattering) - particle or discrete parcels of energy photons (emission & absorption) duality Frequency and wavelength of electromagnetic radiation * c * = 3 x 10 8 m s -1 ν frequency λ wavelength ν = c λ Radiant energy propagates in quantum bits, called photons and a photon has energy proportional to its frequency: E υ = υ Planck's_ Constant _ = 6.625x10 34 Js 1. High-frequency have energy than lower frequency? 17
18 Complex Geometry of Radiative Energy Energy measured by intensity or radiance More details than Fig 3.1 df ν = I ν cosθ dω da dν dt Solid Angle Concept Radiant Intensity in complex units W m -2, integrate over all solid angles Spectral Flux density π 2π F ν = dω (thisfigure) or dω = sinθ dθ dφ I ν (θ,φ) cosθ sinθdθ dφ Flux density - integrate over frequency F = 0 F ν dν 18
19 Radiation encounters object Perfect Transmission - radiation passes through object unchanged Pure scattering - change direction with no change in energy Absorption - energy transmitted to object, which can then re-radiate it Nature of the above depends on frequency and properties of object EX: water vapor & CO2 19
20 Wien s Law: Wavelength of maximum emission inversely proportional to Temperature Visible not absorbed Ozone absorbs most incoming solar radiation 4 micron break CO 2 vibration-rotation absorption key wavelength Water vapor absorption between microns You can imagine that radiation is NOT easy to model! 20
21 This figure was prepared by Robert A. Rohde
22 Selective Absorption by Gasses To understand Greenhouse effect examine interaction of radiation with matter. Planck postulated that energy levels of atomic and molecular vibrations were discrete values. E υ = n υ (n = 0,1,2,...) Discrete energy levels that differ by hν. Release or absorption of energy changes molecules energy level. Photon (of proper energy ) hits particle and if absorbed then it appears as increased internal energy of molecule. E total = E translational + E rotational + E vibrational + E electronic 22
23 Relationship between Gases, Vibration and Light Mass of an atom in nuclei (analogy to sun) Chemical bond linking atoms are like a spring, so the bonds can vibrate at particular frequencies Gases absorb and emit radiation at specific frequencies N2 and O2 are symmetric so don t have dipole moments (electric fields created due to asymmetry) so are not greenhouse gases. CO and NO are asymmetric, but reactive so do not lead to much greenhouse effect. CO2 and H2O have charge imbalances. Atmospheric Composition? 23
24 CO2 and H2O vibrate and interact with longwave (IR) radiation Water has a dipole moment in its resting state. Water vapor can absorb and emit at many frequencies due to its shape. More complex structure of multiple weights and springs that can oscillate in more complicated fashion. Need to bend CO2 to create dipole moment. Infrared active, absorbs and emits IR light in key part of spectrum Asymmetric stretch not in key part of spectrum. [Archer 2011] 24
25 Spectrum of outgoing Longwave (InfraRed) Radiation optically thick optically thin [Archer 2011, based on model] Theoretical Blackbody spectra for various temperatures from K. Jagged line is IR spectrum at TOA. Few gases that absorb along yellow part of spectrum. (Atmospheric window). Follows warmer curve. Around 700 cycles/cm, the spectra follows cooler curve, due to bending vibration of CO2 (absorbs at this frequency and emits at lower intensity). Figure constructed so area under curve proportional to total energy flux. CO2 versus CH4 absorption? 25
26 Summary 26
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