Thermal Structure of the Atmosphere: Lapse Rate, Convection, Clouds, Storms

1. Thermal Structure of the Atmosphere: Lapse Rate, Convection, Clouds, Storms

2. Take away concepts and ideas Heat convection vs. conduction Atmospheric lapse rate Pressure as a function of altitude Convection in a dry vs. wet atmosphere Atmospheric heat transport Moist convection and CISK

3. Atmosphere Very poor conductor Very good convection Important radiation properties

4. Convection.. • Why does water in a kettle heat up to boil? • Why is air on the ceiling warmer than the floor? • Why does smoke rise? • Why does lava ooze out of cracks on the ocean floor? • How do clouds form?

5. “State” Properties of Air The interdependence of air temperature, pressure, and density

6. Temperature and Pressure profiles of the atmosphere

7. Thermodynamic properties of Dry Air Assume (for now) the atmosphere has no water. Dry air pressure (P), Temperature, and Density all linked through Ideal Gas Law Hydrostatic balance

8. A. “Ideal Gas Law” P V = n R T Pressure “Ideal Gas Law” = “Equation of State” (just “perfect” gas with no other phases, like water) n / V = density =  so can rewrite as: P =  R T Number of molecules Temperature Volume Constant

9. P =  R TorP V = n R T R = constant Pressure (P, force exerted by gas molecular motion) Temperature (T, energy of molecular motion) Density (number of atoms per unit volume, n/V)

10. Q1: Hot air balloon and fun with the ideal gas law P = ∆ R ∆T If you increase temperature but keep pressure constant what happens to density? • Pressure increases • Pressure decreases • Density increases • Density decreases • R decreases

11. Rigid walls = constant Flexible walls P = constant

12. constant P=∆ R ∆T Cooling a balloon in liquid nitrogen (-∆T) increases the density (+∆) Link

13. B. Hydrostatic equation The atmosphere under gravity - hydrostatic balance Gravity “pushes down” … the atmosphere “pushes back” When equal, this is Hydrostatic balance equation ΔP = - ρ g Δz where g = grav. accel. (9.8 m/s2)

14. Impress your friends! Deriving the dry adiabatic lapse rate (rate at which the atmosphere cools with altitude): Easy as 1…2…3: 1) 1st Law of Thermodynamics ∆Heating = ∆internal energy + ∆work ∆Q = ∆U + ∆W (conservation of energy, signs are right here) No heating for an adiabatic process, therefore: 0 = ∆U + ∆W

15. 2)0 = ∆U + ∆W 0 = (change in temperature * air heat capacity) + (pressure * change in volume) 0 = n cv ∆T + P ∆V Combining, 0 = Cp ∆T + ∆P/ρ (Cp is heat cap of air) Rearranging, ∆T/∆P = -1 / ( Cp ρ) Now, substitute into hydrostatic equation (∆P = -  g ∆z) You’ve derived the Dry Adiabatic Lapse Rate equation Rearrange… ∆T/∆z = g / Cp ∆T/∆z = (9.8 m/s2) / (1004 J/kg/K) = 9.8 K per km <-- Dry Lapse Rate !!

16. Q2: Hiking You’re planning a hike in some desert mountain range and the temperature at basecamp is 20°C. What is the temperature at the summit which is 2000m higher? • 10°C • 0°C • -10°C • -20°C • Can’t tell

17. Atmospheric temperature profile: Heat transfer by DRY convection = 9.8°C / km Surface warming By conduction Adiabatic = No heat is lost or gained within a parcel of air Diabatic = Heat is lost or gained within a parcel of air

18. Now just add water…Wet Convection So far we’ve just considered a “dry atmosphere” Dry adiabatic lapse rate: -9.8 °C/km typical adiabatic lapse rate: - 6 to -7 °C/km why aren’t they the same? Water vapor!

19. 7°C/km 9.8°C/km Dry Air and Dry Convection Think of a “parcel” of air… If the air is heated, how does its density change? P = ∆ R ∆T Is the parcel stable or unstable relative to adjacent parcels? … dry air convection! (no clouds just yet…)

20. Thermodynamic properties of moist air The atmosphere in most places isn’t dry. Energetics of water phase changes: Liquid --> Vapor requires 540 cal/gram H2O (Latent heat of evaporation; takes heat AWAY) Vapor --> Liquid releases 540 cal/gram H2O (Latent heat of condensation; ADDS heat)

21. Phase changes of water

22. Temperature Controls Water Vapor Saturation in Air Warm air holds A LOT more water than cold air. What is saturation? Saturation water vapor content increases exponentially with temperature Clausius-Clapeyron relation-->

23. Consider a rising parcel of air, but this time it has water vapor (typically 0.5% by weight)… • Air parcel rises… starts to cool • Follows DRY ADIABATIC lapse rate until 1st condensation (cloud) • 1st condensation --> release of latent heat of condensation inside of parcel • Warming in parcel offsets cooling, so • Rising parcel no longer follows dry adiabatic lapse rate of -9.8°C/km, but follows the MOIST ADIABATIC lapse rate of -6-7 °C/km Tropical atmosphere follows MOIST adiabat Polar atmosphere follows DRY adiabat

24. Moisture affects stability unstable stable -7 °C/km -6.5 °C/km -7 °C/km -9.8 °C/km MOIST PARCEL rising in warm environment DRY PARCEL rising in warm environment

25. Comparing the dry and moist lapse rates

26. California Coastal Range Coast Desert

27. down Moist adiabatic lapse rate = 7°C/km Dry adiabatic lapse rate = 9.8°C/km up

28. unstable

29. Why Hurricanes are so powerful CISK = Convective Instability of the Second Kind

30. Galveston, TX: Hurricane of 1900