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Space Science : Atmosphere Part-5 Planck Radiation Law Local Thermodynamic Equilibrium: LET Radiative Transport Approximate Solution in Grey Atmosphere Skin Temperature Greenhouse Effect Radiative Balance Radiative Time Constant Reading Ionosphere for Previous part Radiation Transport Greenhouse Effect
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Windows and Absorptions in the Solar Spectrum 0.2 0.6 1.0 1.4 1.8 2.2 2.6 3.0 m
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Radiation: Solar and Earth Surface Atmosphere is mostly transparent in visible but opaque in UV and IR; IR window 8-13um B (T) Fraction absorbed
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Before Discussing Radiation Define Solid Angle r sin d r d x z y dd dd r sin
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Planck’s Law for Thermal Emission of Photons
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GREY ATMOSPHERE Chap 3 G+W, H p10-17 Gray vs. Black vs. Transparent Also, absorption independent of frequency over the range of relevant frequencies Processes Surface heated by visible Warm Surface emits IR ~ 3 – 100 m peak ~ 15 m IR absorbed by CO 2, O 3, H 2 O, etc. Remember why not O 2 and N 2 ?
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Vibrational Bands CO 2 (IR active?) Symmetric Stretch O C O 7.46 m (N) Asymmetric Stretch O C O 4.26 m (Y) Bending O C O 15.0 m (Y) H 2 O Symmetric Stretch O 2.73 m (Y) H H Asymmetric Stretch O 2.66 m (Y) H H Bending O 6.27 m (Y) H H You can have combination bands or 2 vib. levels
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IR Emission and Absorption Ground Emits Primarily Triatomc Molecules Absorb and Re-emit: vibrational and rotational states To determine T we assume excited molecules heat locally by collisions. CO 2 (v=1) + M --> CO 2 (v=0) + M + K.E.
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Slab of Atmosphere Absorption I + dI dz I
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Solution: Absorption Only (did earlier; new notation)
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What about EMISSION Slab of atmosphere has a T emits IR Assume LTE LTE Local Thermodynamic Equilibrium molecular motion and the population of the vibrational and rotational states are all described by Boltzmann distribution and photons by Planck’s law ---using the same T Kirchhoff’s Law In LTE the emissivity of a body (or surface) equals its absorptivity.
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Radiative Transport with Emission + Absorption
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Flux (cont) I dA = r 2 d r
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Radiative Transport (cont.) include angles dz = cos
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Radiation Transport (cont.) I and B are isotropic
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Not Quite Isotropic * 5/3 Use * not in transport eq. dz
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Third Equation is the Heat Equation
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Radiative Transport Solution (cont.) Use Eqs. (1) and (2) with (3).
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Radiative Transport Solution (cont.) Use Eq. (3) and (4)
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Radiative Transport: Solution use C 1 in (5) and (6)
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Solution to the radiative transfer equations for a grey atmosphere Conductive Transport (Adiabatic Lapse Rate) Radiative Transport Becomes radiative dominated near tropopause * Optical Thickness in IR g*g*
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Finally: we do not know T g we know only T e for emission to space! This is the Green House Effect Ground T exceeds T for emission to space
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A Real Green House How do you get IR out equal to Visible light absorbed inside: RAISE T Note: For a real green house convection may be as important: i.e. glass a thermal barrier IR Visible OutsideInside
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Greenhouse Effect is Complex
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PLANETARY ENERGY BALANCE G+W fig 3-5 11386 Convective 30 IR Radiation To Space 67 GROUND Incoming solar radiation mesopause
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Radiation Transport (Review) dz Atmospheric Slab IR
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Integrate (*) for upward moving and downward moving IR photons
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(Review continued)
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Ground T (review)
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G + W (simple version; 4 layers) 0123401234 Ground Space F1F1 F1F1 F2F2 F2F2 F3F3 F3F3 F4F4 F4F4 FgFg F VIS =F out
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Earth g 2
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VENUS (Problem for set 2) T e = 230 T g = 750 Therefore: g * = ? Therefore: Use cross section from previous slide, pure CO2 N = ?
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Top Why isn’t T e = T( ) at the top? =emissivety T e 4 (1- ) T 4 T4 T4
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Thermal Structure Tropopause to Mesopause
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TIME CONSTANT FOR RADIATIVE EQUILIBRIUM
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Carbon concentration vs. time
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Carbon Concentration Long Term Later we will look at the carbon cycle
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GREEN HOUSE EFFECT
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However,
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#4 Summary Things you should know Planck Radiation Law Local Thermodynamic Equilibrium: LET Radiative Transport Greenhouse Effect Surface temperature Skin Temperature Radiative Time Constant
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