1. Copyright R. R. Dickerson 20111 LECTURE 2 AOSC 637 Atmospheric Chemistry R. Dickerson

2. Copyright R. R. Dickerson 20112 ATMOSPHERIC PHYSICS Seinfeld & Pandis: Chapter 1 Finlayson-Pitts: Chapter 2 1.Pressure: exponential decay 2.Composition 3.Temperature The motion of the atmosphere is caused by differential heating, that is some parts of the atmosphere receive more radiation than others and become unstable.

3. VERTICAL PROFILES OF PRESSURE AND TEMPERATURE Mean values for 30 o N, March Tropopause Stratopause

4. Copyright R. R. Dickerson 20114 N2N2 O2O2 Ar O3O3 Inert gasesCO 2 H2H2 ←SO 2, NO 2, CFC’s, etc PM CO CH 4 N2ON2O Composition of the Earth’s Troposphere

5. Copyright R. R. Dickerson 20115 Banded iron formation.

6. Copyright R. R. Dickerson 20116 Units of pressure: 1.00 atm. = 14.7 psi = 1,013 mb = 760 mm Hg (torr) = 33.9 ft H ₂ O = 29.9” Hg = 101325 Pa (a Pascal is a Nm ⁻ ² thus hPa = mb) Units of Volume: liter, cc, ml, m³ Units of temp: K, °C Units of R: 0.08206 1 atm mole -1 K -1 8.31 J mole -1 K -1 R’ = R/M wt = 0.287 J g -1 K -1 For a mole of dry air which has the mass 29 g. Problem for the student: calc Mwt. Wet (2% H ₂ O vapor by volume) air.

7. Copyright R. R. Dickerson 20117 Derive the Hypsometric Equation Start with The Ideal Gas Law PV = nRT or P = ρR’T or P = R’T/α Where R’ = R/Mwt Mwt = MOLE WT. AIR ρ = DENSITY AIR (g/l) α = SPECIFIC VOL AIR = 1/ρ We assume that the pressure at any given altitude is due to the weight of the atmosphere above that altitude. The weight is mass times acceleration. P = W = mg But m = Vρ For a unit area V = Z P = Zρg

8. Copyright R. R. Dickerson 20118 For a second, higher layer the difference in pressure can be related to the difference in height. dP = − g ρ dZ But ρ = P/R’T dP = − Pg/R’T * dZ For an isothermal atmosphere g/R’T is a constant. By integrating both sides of the equation from the ground (Z = 0.0) to altitude Z we obtain:

9. Copyright R. R. Dickerson 20119 Where H ₀ = R’T/g we can rewrite this as: *HYPSOMETRIC EQUATION* Note: Scale Height: H ₀ ~ 8 km for T = 273K For each 8 km of altitude the pressure is down by e ⁻ ¹ or one “e-fold.”

10. Copyright R. R. Dickerson 201110 Problems left to the student. 1.Show that the altitudes at which the pressure drops by a factor of ten and two are 18 and 5.5km. Rewrite the hypsometric Eq. for base 2 and 10. 2.Calculate the scale-height for the atmospheres of Venus and Mars. 3.Derive an expression for pressure as a function of altitude for an atmosphere with a temperature that varies linearly with altitude. 4.Calculate the depth of a constant density atmosphere. 5.Calculate, for an isothermal atmosphere, the fraction of the mass of the atmosphere between 200 and 700 hPa.

11. Results of Diagnostic Test Basic Thermo 14 Thermo Diag 10 Aerosols (10)Clouds 10 Biogeoche m 11 Photo Chem 12Sow ice 10 Cld models 10 Kinetics 20 student a 1491077 5818 student b 14107 126920 student c 14106.510316811 student d 1210037 4012 student e 1423190007 pass 5/54/53/5 4/53/52/53/5

12. Solubility of CO 2 = f(T)

13. Copyright R. R. Dickerson 201113 Temperature Lapse Rate Going to the mountains in Shenandoah National Park the summer is a nice way to escape Washington’s heat. Why? Consider a parcel of air. If it rises it will expand and cool. If we assume it exchanges no heat with the surroundings (a pretty good assumption, because air is a very poor conductor of heat) it will cool “adiabatically.” CALCULATE: ADIABATIC LAPSE RATE First Law Thermodynamics: dU = DQ + DW

14. Copyright R. R. Dickerson 201114 WHERE U = Energy of system (also written E) Q = Heat across boundaries W = Work done by the system on the surroundings H = Internal heat or Enthalpy ASSUME: a)Adiabatic (dH = 0.0) b)All work PdV work (remember α = 1/ρ) dH = Cp dT – α dP CpdT = α dP dT = (α/Cp) dP

15. Copyright R. R. Dickerson 201115 Remember the Hydrostatic Equation OR Ideal Gas Law Result: This quantity, –g/C p, is a constant in a dry atmosphere. It is called the dry adiabatic lapse rate and is given the symbol γ ₀, defined as −dT/dZ. For a parcel of air moving adiabatically in the atmosphere:

16. Copyright R. R. Dickerson 201116 Where Z ₂ is higher than Z ₁, but this presupposes that no heat is added to or lost from the parcel, and condensation, evaporation, and radiative heating can all produce a non-adiabatic system. The dry adiabatic lapse rate is a general, thermodynamic property of the atmosphere and expresses the way a parcel of air will cool on rising or warm on falling, provided there is no exchange of heat with the surroundings and no water condensing or evaporating. The environmental lapse rate is seldom equal to exactly the dry adiabatic lapse rate because radiative processes and phase changes constantly redistribute heat. The mean lapse rate is about 6.5 K/km. Problem left to the students: Derive a new expression for the change in pressure with height for an atmosphere with a constant lapse rate,

17. Copyright R. R. Dickerson 201117 Stability and Thermodynamic Diagrams (Handout) Solid lines – thermodynamic property Dashed (colored) lines – measurements or soundings day γ a > γ ₀ unstable γ b = γ ₀ neutrally stable γ c < γ ₀ stable On day a a parcel will cool more slowly than surroundings – air will be warmer and rise. On day b a parcel will always have same temperature as surroundings – no force of buoyancy. On day c a parcel will cool more quickly than surroundings – air will be cooler and return to original altitude.

18. Copyright R. R. Dickerson 201118 This equation is easily corrected for a wet air parcel. The heat capacity must be modified: Cp' = (1-a)Cp + aCp(water), where "a" is the mass of water per mass of dry air. If the parcel becomes saturated, then the process is no longer adiabatic. Condensation adds heat. DQ = -Lda Where L is the latent heat of condensation -dT/dZ = g/Cp + (L/Cp) da/dZ Because the amount of water decreases with altitude the last term is negative, and the rate of cooling with altitude is slower in a wet parcel. The lapse rate becomes the wet adiabat or the pseudoadiabat.

19. Copyright R. R. Dickerson 201119 (HANDOUT) Very important for air pollution and mixing of emissions with free troposphere. Formation of thermal inversions. (VIEWGRAPH) In the stratosphere the temperature increases with altitude, thus stable or stratified. DFN: Potential temperature, θ : The temperature that a parcel of air would have if it were brought to the 1000 hPa level (near the surface) in a dry adiabatic process. You can approximate it quickly, or a proper derivation yields: θ z = T ( 1000 hPa/P z ) ** R’/Cp = T ( 1000 hPa/P z ) ** 0.286

20. DIURNAL CYCLE OF SURFACE HEATING/COOLING: z T 0 1 km MIDDAY NIGHT MORNING Mixing depth Subsidence inversion NIGHTMORNINGAFTERNOON

21. Copyright R. R. Dickerson 201121 Plume looping, Baltimore ~2pm.

22. Copyright R. R. Dickerson 201122

23. Copyright R. R. Dickerson 201123

24. Copyright R. R. Dickerson 201124 Plume Lofting, Beijing in Winter ~7am.

25. Copyright R. R. Dickerson 201125 Atmospheric Circulation and Winds

26. Copyright R. R. Dickerson 201126 ITCZ

27. Copyright R. R. Dickerson 201127 Mid latitude cyclone with fronts

28. Copyright R. R. Dickerson 201128 Fig. 9.13 Warm Front

29. Copyright R. R. Dickerson 201129 Fig. 9.15 Cold front

30. Copyright R. R. Dickerson 201130 Fig. 1-17, p. 21

31. Copyright R. R. Dickerson 2011 31 Fig. 1-16, p. 19

32. Copyright R. R. Dickerson 201132 Fig. 1-16, p. 19

33. Copyright R. R. Dickerson 201133 Detailed weather symbols

34. Copyright R. R. Dickerson 201134 Electromagnetic Radiation

35. Copyright R. R. Dickerson 201135 Electromagnetic spectrum

36. Copyright R. R. Dickerson 201136 Planck’s Law for blackbody radiation: Take first derivative wrt T and set to zero: Wien’s Law: Integrate over all wavelength: Stephan-Boltzmann Law:

37. Copyright R. R. Dickerson 201137 UV-VISIBLE SOLAR SPECTRUM

38. Copyright R. R. Dickerson 201138 Planck’s Law says that the energy of a photon is proportional to its frequency. Where Planck’s Const., h = 6.6x10 -34 Js The energy associated with a mole of photons at a given wavelength in nm is: