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Space Science: Atmosphere Part -2 Thermal Structure Stability of an Air Mass Absorption of Radiation Chapman Layer Ozone

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HW Assignments and Reading: 1 Reading CH Secs 1.1,1.3, 1.5.1 Prob. 1.1, 1.2, 1.4 dePL Secs 4.1, 4.2 Prob: 4.1, 4.2, 4.12, 4.13 Houghton Probl: 1.2, 1.4, 1.6, 1.9

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Temperature vs. Altitude Earth’s Atmosphere Radiation Absorption Indicated We have described Heating of and rough T profile in troposhere

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Temperature (Heat) vs. Altitude Radiation absorption + heat transport Bottom: troposphere Heat Surface (Visible Rad) + Convective Transport (Lapse Rate) Middle: Stratosphere and Mesosphere Near UV Absorption + Radiative Transport Top: Thermosphere Far UV absorption + Conduction Dominates

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Heating at a Cloud Layer Assume clouds are where sunlight is absorbed and IR re-radiated to space, then a simple model gives: Adiabatic Lapse rate above and isothermal below But Venus was found to have an increasing temperature with decreasing altitude below the cloud layer. Therefore, some radiation must get through T z dd vis IR

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Troposphere STABILITY of a PARCEL of AIR Bouyant Force Parcel of air, allowed to move vertically roughly follows adiabatic lapse rate. Therefore, T of the parcel differs from ambient T stable unstable dd T T0T0 Z Actual Lapse rate is dT/z a (z) = Density vs. z for Which air can move up or down adiabatically p =p a Pressure Equalizes to ambient by expanding or contracting volume d d

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Mesosphere and Stratosphere Radiative Transport ABSORPTION of LIGHT Wavelength~eVEffect 0.1cm0.001excite rotations of molecules 10 m0.1excite vibrations of molecules 3. photodissociation excite the electrons in the outer shells of atoms and molecules 0.1 m10ionize atoms or molecules 0.01 m100ionize inner shell electrons O 2 (+h >5eV) -> O + O

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Altitude at which various frequencies are absorbed from Chamberlain and Hunten 0.3 m 0.05 m

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ABSORPTION of SUNLIGHT ∆z F s F’ s ∆z is a layer thickness (positive up) is the solar zenith angle F s is the solar energy flux at frequency (comment) ∆ F s = F s - F’ s n (∆z/cos ) F s (up is positive; n = number of absorbers/volume) ∆ F s = n (∆z/cos ) F s where = effective cross section of the absorber cos dF s / dz = n F s

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Optical Path Length cos d F s / dz = n F s Rewrite d F s / F s = n dz /cos Solve using a density decreases with z. The flux transmitted to altitude z is F s (z) = F s ( ) exp[ - ] where F s ( ) is the solar onto the planet and is = ∫ z n dz /cos ~ abs N abs (z) /cos = optical path length for frequency Thickness of atmosphere to radiation from outside: will depend on frequency, density of absorbing species at that frequency with a cross section (should write abs, and N abs.) Light can also scatter (blue sky) so need to add scat, Note: (n abs, ) often written as ( k abs, ) the mass density.

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Direct Heating by Absorption of Sunlight Absorption in Atmosphere as a Source in Energy Equation Heating Rate/ Vol = n abs F s (z) / cos (Energy flux absorbed in ∆z)/∆z Earlier we used dq as the change in energy of the gas per unit mass dq/dt = [c v dT + p dV]/dt = Energy absorption rate/ vol at a given z (fixed p) c p T/ t = n abs F s (z) / cos Dropped subscript as one averages over all absorbed frequencies Can also think of the Heating Rate = Photon Flux x Photon Energy/( ab cos ) abs = mean free path for absorption 1/ abs = density x cross section = n abs

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z zz nono F (z) Maxim in the Heating rate: Chapman n abs Chapman Layer heating rate = n abs F s (z) / cos for a particular absorption process (dropped ) Remember z dependence: n(z) = n o exp[ -z/H] F s (z) = F s ( ) exp[ - (z)] (z) = ∫ z abs n abs dz /cos = abs N abs /cos ≈ [H/ abs cos ] exp[ -z/H] Temperature Maxima -> Layered Atmospheres n abs small F (z) small n abs x F -->

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Find the Heating Maximum The column where absorption is a max is The inverse of the absorption cross section Cross section and concentration give structure

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What Occurs Near Stratopause (~ 50 km) Near UV light absorbed in atmosphere primarily by O 3 Surface is heated by the visible and cooled by the IR But the IR does not go straight to space, some of it is absorbed by CO 2, H 2 O, etc. It must then be re-emitted. m m O 3 O=C=O IR Surface Before considering heating consider O 3 formation

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Absorb Potential Energy O +O R O 2 Two states shown: Ground Attractive a higher state: here repulsive Photon energy greater than energy to dissociate Vibrations slow-- Transition is at a fixed R (Franck-Condon Principle) Photoabsorption in a Molecule Diatomic

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Some Oxygen Molecule Energy Curves

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Energy Levels for Triatomic Molecule Tri-atomic molecules has a potential energy surface for each state: represents three distances

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O 3 + h O 2 + O( 1 D) mixing ratio: ~ 0.3 ppm only absorber at 230 290 nm Large absorption cross section Dissociation energy 1.05 eV Atmospheric ‘depth’ of O 3 is equivalent to ~0.3cm at STP: {250nm] = 10 -17 cm 2 x 0.3cm x2.7x10 19 /cc = 81 5eV

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Hartley Band: allowed transitions Chappius Band: ‘forbidden’ transitions Much smaller cross section

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Definitions Reaction and Photoabsorption Coefficients

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CHAPMAN EQUATIONS C+H chap 1 O 2 + h EUV O + O J 2 slow (flux small) >~7eV; 0.17 m) O + O + M O 2 + M k 11 slow (few O and 3 bodies) O + O 2 + M O 3 + M k 12 fast (use O 2 ) O 3 + O O 2 + O 2 k 13 slow (few O and O 3 ) O 3 + h (UV) O 2 + O J 3 fast eV; ~0.2-0.31 m) J 3 k 12 OO3O3 O2O2 k 11 k 13 J2J2 <--large density in stratosphere J3J3

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Densities of O 2,O 3 and O C+H we need to calculate

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Another O 3 Destruction Process Reactive Species that are recycled X + O XO + O 2 k 4 XO O X + O 2 k 5 Equivalent to O O 3 2 O 2 X Cl, H, OH, SO 2 Nitrous Oxides: N 2 O --> N + NO Fertilizers, Sewage, Lightning, Aurora etc. Chlorine: ClO x, Cl x Volcanoes (HCl); Chloroflourocrabons (CFCl 3 CF 2 CL 2 ) Ice clouds (Noctalucent Clouds -> H H + O 3 -> O 2 + OH* (airglow)

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The above does not say anything about how heat gets in; only how O 3 is formed and lost How Does Heat Get In ? O 2 + O + M Recombine Absorb O + O( 1 D) + KE ‘hot’ O and O( 1 D) O 2 cool by collisions O 3 Formed vibrationally hot: cools by collisions

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SUMMARY Ozone Heating in Upper Atmosphere forms the stratosphere Start : O 2 + h Form O 3 : O + O 2 +M 3 VE Destroy O 3 : Photo Absorption in Stratosphere : O +h + KE Also Reactions:O 3 + O Cooling CO 2 Radiation in IR ( 15 m) (not much gaseous H 2 O in stratosphere)

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Temperature vs. Altitude Earth’s Atmosphere again Radiation Absorption Indicated to get T(z) need IR emission also See structure of other atmosphere dePL What does lapse rate say about stratosphere?

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#2 Summary Things you should know Earth’s Thermal Structure Stability of an Air Mass Absorption of Radiation Optical Path Length Photo-absorption Cross Section Chapman Layer Reactions Rates Stratospheric Heating

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