Understanding the Earth's Atmosphere: Composition, Circulation, and Energy Balance

1. CE 5326 AIR POLLUTION CONTROLFall 2008 Session 5: The Atmosphere The Atmosphere

2. H.W.: Due October 1, 2008 • De Nevers Problems 5.5; 5.6; 5.7 • Reading Assignment: • De Nevers: Chap. 5 • SP: Chap 16.1 – 16.2;16.4.1 The Atmosphere

3. The Atmosphere • Origin of the Atmosphere • History of the Atmosphere • Structure of the Atmosphere The Atmosphere

4. The Atmosphere The Atmosphere

5. Chemical Composition of the Atmosphere The Atmosphere

6. Atmospheric Circulation The Atmosphere

7. Atmospheric Circulation The Atmosphere

8. Energy Balance The Atmosphere

9. Energy Balance The Atmosphere

10. Water in the Atmosphere • Absolute Humidity • Relative Humidity • Specific Humidity • Dew Point • Supersaturation • Wet-bulb Temperature • Dry-bulb Temperature The Atmosphere

11. Coriolis Force F= 2(V x Ω) V= u i + v j +w k ΩW = Ωxi + Ωy j + Ωzk ΩW = Ωcos φ j + Ω sin φ k The Atmosphere

12. Geostrophic Wind • Balance between the pressure gradient and the Coriolis force in the upper atmosphere The Atmosphere

13. Gradient Wind • Balance between the pressure gradient, the Coriolis force, and the centrifugal force caused by the curved isobar VGR f + VGR2 /r = (dp/dn) /ρ For cyclonic winds, For anticyclonic winds, The Atmosphere

14. Surface Wind • Balance between the pressure gradient, the Coriolis force, and surface friction force • Ekman Spiral The Atmosphere

15. Surface Wind • Logrithmic Velocity Profile • τ = µ du/dy • PowerLaw Velocity Profile The Atmosphere

16. Determining The Vertical Velocity Profile Ex: On a windy day, the following wind observations were made: z, m 0.5 1.0 2.0 4.0 8.0 16.0 u, m/s 1.6 2.3 3.0 3.7 4.4 5.1 Determine the roughness length and friction velocity for the site. The Atmosphere

17. Temperature in the Lower Atmosphere • The Equation of State The Atmosphere

18. Temperature in the Lower Atmosphere • The Hydrostatic Equation • dp/dz = -ρg • dp(z)/dz = - ρ(z)g and dp(z)/p(z) = -g/RT(z) dz • If T(z) ~ Constant, then • p = po exp(-z g / RT) The Atmosphere

19. Temperature in the Lower Atmosphere The First Law of Thermodynamics DU = dQ + dW applies to the total mass and dU/m = dQ/m + dW/m or du = dq + dw applies to a unit mass where dU, du = change of internal energy dQ, dq = heat input across the boundary of the system, dW, dw = work done on the system The Atmosphere

20. Temperature in the Lower Atmosphere Specific Heat for Ideal Gas cp = cv + R or cp = cv + R*/M for unit mass, or Cp = Cv + mR → Cp = Cv + mR*/M → Cp = Cv + nR* where cp = specific heat at constant pressure per unit mass, J K-1 kg-1 cv = specific heat at constant volume per unit mass, J K-1 kg-1 Cp = specific heat at constant pressure for the system, J K-1; Cv = specific heat at constant volume for the system, J K-1 The Atmosphere

21. Temperature in the Lower Atmosphere • The Adiabatic Process • Relationship between Temperature and Pressure in the Atmosphere • For dry air, R/cp = 0.288. The Atmosphere