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

2. 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

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

4. 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

5. 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 dd vis IR

6. 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 dd 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

7. 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

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

9. 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

10. 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.

11. 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

12. 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 -->

13. 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

14. 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

15. 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

16. Some Oxygen Molecule Energy Curves

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

18. 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

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

20. Definitions Reaction and Photoabsorption Coefficients

21. 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

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

23. 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)

24. 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

25. 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)

26. 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?

27. #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