GEU 0047: Meteorology Lecture 6 Stability and Cloud Development

1. GEU 0047: MeteorologyLecture 6Stability and Cloud Development

2. Equilibrium vs. Stability • Equilibrium’s 2 States: • Stable • Unstable Perturbed from its initial state, an object can either tend to return to original point (A. stable) or deviate away (B. unstable)

3. Atmospheric Stability

4. Atmospheric Stability • If perturbed vertically, a stable air parcel will tend to go back to its original altitude, whereas an unstable parcel will usually accelerate away vertically. • If rising/sinking, the air parcel tends to cool down/warm up, due to the change in ambient pressure with altitude. • Remember e-1 change for every 7.29 km (scale height Hp) P = Po e-z/Hp

5. Γd: a constant Dashed lines: unsaturated parcel’s lapse rate Solid lines: environmental lapse rate

6. Γw: NOT a constant ! Dashed lines: moist parcel’s lapse rate Solid lines: environmental lapse rate

7. Are the following 2 statements same (or contradictory)? • rising air cools • warm air rises Hhh…? Let’s think about it for a while!

8. Rising and Sinking Air

9. Determining the temperature in a rising air parcel consider a rising parcel of air -->> • As the parcel rises, it will adiabatically expand and cool (recall our discussion in chapter 5 about rising parcels of air) • adiabatic - a process where the parcel temperature changes due to an expansion or compression, no heat is added or taken away from the parcel • the parcel expands since the lower pressure outside allows the air molecules to push out on the parcel walls • since it takes energy for the parcel molecules to "push out" on the parcel walls, they use up some of their internal energy in the process. • therefore, the parcel also cools since temperature is proportional to molecular internal energy

10. Eureka!(Archimedes’ Law) In air, scale reads the weight T1 = W. Immersed in water, the additional buoyant force reduces the objects weight because of buoyancy Fb . Thereby, T2 = W - Fb Fb = rfVf g = displaced fluid weight Fb T2 T1 W W

11. Buoyancy • Archimedes Law: The buoyancy force is equal to theweight of the volume of fluid displaced. Weight of the volume of fluid* displaced rfVog Weight (m g) of the object roVo g The net force on an object is its weight minus the buoyancy Fn = ro Vo g – rfVog = (ro– rf) Vo g *The environmental air is treated as a fluid in which a parcel of air is immersed.

12. Buoyancy and Acceleration Acceleration = Force/mass F = Weight - Fb = ro Vo g - rfVog Acceleration = F/ (ro Vo ) = g(ro Vo - rfVo)/m = g(ro - rf)/ro

13. Buoyancy and Acceleration In air, replacing densities with temperatures using the ideal gas law, P = r R T, yields an equation for the acceleration of the air parcel, given the temperature and pressure of the parcel (To, Po) and those of the environment (Tf, Pf). acceleration = g(Po - Pf)/Po = g(Tf- To)/Tf Therefore, A large temperature difference means instability. a ~ DT Your HW#3 Due Nov. 29

14. Determining stability involves asking what happens to an air parcel if there is a small perturbation (vertical motion).What is its equilibrium like, stable or unstable?

15. Expansion and cooling (or compression and heating) without any thermal exchange with the environment • Adiabatic process does NOT mean isothermal process (What the hell …? Is Q = mcDT wrong?) Adiabatic Process: Rigid walls: ris constant Black: isothermal Blue: adiabatic Flexible walls: P is constant

16. Dry Adiabats Gdry: Temperature change within an unsaturated air parcel. ~-9.8oC/1000m

17. Moist Adiabats Gwet : Temperature change within a saturated air parcel. ~ -6oC/1000m

18. Lapse Rate: change in Temperature with Altitude G = -DT/Dz Environmental Lapse Rate: • Radiosondes yield information about the environmental lapse rate. It is what it is…on average G ~ 6.5oC/1000m. • This lapse rate is used to estimate the stability after comparing with either the dry adiabatic lapse rate (Gdry) or moist adiabatic lapse rate (Gwet) of our imageryair parcel.

19. Some things you need to know: The gas laws • Apply p = r R T to an air parcel with a unit mass, • p α = R T; α: specific volume (α = r-1) • p Δα + Δp α = R ΔT • If this air parcel is in hydrostatic balance, • r gDz = ptop – pbottom = - Dp • Δp = - ρ g Δz • Now, if this air parcel takes in some heat energy Dq while performing some work Dw and causes an amount of internal energy change Du, • Dq = Dw + Du = pΔ α + Du (1st law of thermodynamics)

22. The specific heats Cv : Spceific heat at constant volume Cv ≡ Dq / DT, Cv ≡ Du / DT when α is constant Cp : Spceific heat at constant pressure Cp ≡ Dq / DT when p is constant Cp = Cv + R

23. Adiabatic process and lapse rate Dq = pΔ α + Du = pΔ α+ CvDT = D (p α) - α Δp + CvDT = D(RT) - α Δp + CvDT = RDT - α Δp + CvDT = (Cv + R)DT - α Δp = Cp DT - α Δp = Cp DT + g Δz p α = RT Cp ≡ Dq / DT when p is const. Δp = - ρ g Δz If dry adiabatic, Dq = 0 Gdry = - DT/D z = g/Cp

24. Moist Adiabatic Lapse Rate Unlike Gdry, Gwet = - DT/Dz is NOT a constant, but varies with temperature and moisture content !

25. Saturation Vapor Pressure (SVP) es = eo exp{L/Rv (1/To-1/T)} Known as Clausius-Clapeyron relation discovered when two engineers were working on the thermodynamics of water vapor to produce a more efficient steam engine. eo = 611 Pascals Rv = 461 J/K/kg (e α = RvT) To = 273o K (i.e., 0oC) L = { Lv = 2.50 x 106 J/kg} = { Ld = 2.83 x 106 J/kg}

26. Mixing Ratio r r = mass of water vapor / mass of dry air = rv/rd How does the Td change in rising and sinking air? For an air parcel at T and P, what is its water vapor content? Note: Drs/ΔT > 0 P T

27. Moist adiabatic process • Dq = Cp DT + g Δz • Dq = -LvDrs, for a saturated air parcel (rs: saturation mixing ratio) • -LvDrs = Cp DT + g Δz • Gwet = - DT/ Δz = Lv/Cp *Drs/Δz + g/Cp = Lv/Cp *Drs/Δz + Gdry =Lv/Cp *Drs/ΔT *ΔT/ ΔZ + Gdry =- Lv/CpDrs/ΔT Gwet + Gdry • (1 + Lv/CpDrs/ΔT) Gwet=Gdry BecauseDrs/ΔT is always positive, Gwet<Gdry

28. Air Parcel Adiabatic Plot X Air parcel representation (Pressure, Temperature, mixing ratio) = Temperature = Humidity thin solid: Gd thick dashed: Gw thin dashed: r(isohume)

29. Dry Adiabatic Process Both air parcel points (temperature, humidity) move together to the new pressure. Temperature along the dry adiabat, Humidity along an isohume or constant moisture content, because NO moisture leaves the parcel.

30. Moist Adiabatic Process At some level, the adiabats and isohumes converge. T and Td then cool along the moist (saturated) adiabat. The difference between the actual mixing ratio in a cloud and the original mixing ratio is the distance between X and O on the plot. It is equal to the amount of condensation produced.

31. Lifting Condensation Level (LCL) • When unsaturated air is lifted, it cools at the dry adiabatic rate. If lifted high enough, the temperature will drop below the dew point. • Drier air must be lifted higher than moist air to encounter LCL. • The height at which saturation just occurs is called the saturation level or the lifting condensation level (LCL). • This height (in meters) can be estimated for cumulus-type clouds and is approximated by ZLCL = 125/(T - Td), where Td is the dew point temperature derived from the vapor pressure equation encountered before: e = eo exp{Lv/Rv (1/To-1/Td)}

32. Absolute Stability (Dry) The parcel of air is cooler and heavier than the surrounding air around it at all levels. G < Gdry When perturbed it will tend to return to its original position.

33. Absolute Stability (Wet) • The atmosphere is • always stable when • the environmental • lapse rate is less • than the moist • adiabatic rate. • G < Gwet

34. Stratus clouds (cirrostratus, altostratus, nimbostratus) form in stable air.

35. A Stable Atmosphere • Stability favors a small environmental lapse rate. • Ways to make the lapse rate small…. • Warm the air aloft (Inversions) • warm advection (warm front) • slowly sinking air (high pressure) • Cool the air near the ground (Fogs) • calm night radiative cooling • cold advection (cold front) • air moving over a cold surface Dashed: before Solid: after

36. When the surface air is saturated in a stable atmos., a persistent fog (or haze) may form. Fig. 6-5, p. 143

37. Subsidence (sinking air) • Descending of a layer of air causes it to warm and shrink via adiabatic compression. • A temperature inversion can develop (warm air over cool).

38. Subsidence inversion Fig. 1, p. 144

39. Absolutely Unstable (Dry) The atmosphere is always unstable when the environmental lapse rate is greater than the dry adiabatic rate. G > Gdry > Gwet

40. Absolutely Unstable (Wet) The parcel of air is warmer and lighter than the surrounding air around it at all levels. When perturbed it will tend to accelerate away from its original position.

41. Cumulus-type clouds

42. Stability Conditions An atmosphere with an environmental lapse rate G will be... • Always Stable if G < GDry G < GWet • Always Unstable if G > GDry G > GWet What About Between?

43. Conditional Stability (Dry) In this example the dry air is cooler and heavier than the air around it at all levels. It is stable. The environmental lapse rate is less than the dry adiabatic lapse rate. But, GDry > G>GWet

44. Conditionally Unstable (Wet) A saturated parcel is warmer than the surrounding air at all levels. It is unstable. With an environmental lapse rate between the dry and moist adiabatic rates, stability depends upon whether the air is saturated or not.

45. Conditional Stability If air can be lifted to a level where it is saturated, instability would result.

46. Instability Causes • Instability favors a large environmental lapse rate. • Ways to increase the lapse rate …. • Cool the air aloft • cold advection (jet stream) • radiative cooling (emitting IR to space) • Warm the air near the ground • influx of warm air (warm advection) • daytime solar heating of the surface • air moving over a warm surface Dashed: before Solid: after

48. 胞狀層積雲 雲階

49. Mixing Instability Mixing may occur via convection or turbulence.

50. Stratus Formation Mixing stable air close to saturation can cause stratus-type clouds. The upper layer cools and saturates while the lower layer warms and dries out, increasing the environmental lapse rate.