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We just the covered the large-scale hydrostatic environment…

Atmospheric Stability and Buoyancy. ?. We just the covered the large-scale hydrostatic environment… We now need to understand whether a small-scale moist air parcel will spontaneously rise or sink through the atmosphere. Atmospheric Stability and Buoyancy. Outline: Review

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We just the covered the large-scale hydrostatic environment…

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  1. Atmospheric Stability and Buoyancy ? We just the covered the large-scalehydrostatic environment… We now need to understand whether a small-scalemoist air parcel will spontaneously rise or sink through the atmosphere M. D. Eastin

  2. Atmospheric Stability and Buoyancy • Outline: • Review • Dry Adiabatic (unsaturated) Processes • Moist Adiabatic (saturated) Processes • Concepts Stability and Buoyancy • Forced vertical motions • Spontaneous vertical motions • Atmospheric Stability Analysis • Criteria for Unsaturated Air • Criteria for Saturated Air • Conditional Instability • Level of Free Convection (LFC) M. D. Eastin

  3. Review of Dry Adiabatic Processes • Basic Idea: • No heat is added to or taken from the system • which we assume to be an air parcel • Changes in temperature result from either • expansion or contraction • Many atmospheric processes are dry adiabatic • We shall see that dry adiabatic process play • a large role in deep convective processes • Vertical motions • Thermals Parcel M. D. Eastin

  4. Review of Dry Adiabatic Processes • Poisson’s Relation: • Relates the initial conditions oftemperature • and pressure to the final temperature and • pressure during a dry adiabatic process • Potential Temperature: • Special form of Poisson’s relationship • Compress all air parcels to 1000 mb • Provides a “standard” pressure level for • comparison of air parcels at different • altitudes M. D. Eastin

  5. Review of Dry Adiabatic Processes • Dry Adiabatic Ascent or Descent: • Air parcels undergoing dry adiabatic transformations • maintain a constant potential temperature (θ) • During dry adiabatic ascent (expansion) the parcel’s • temperature must decrease in order to preserve • the parcel’s potential temperature • During dry adiabatic descent (compression) the • parcel’s temperature must increase in order to • preserve the parcel’s potential temperature Constant θ M. D. Eastin

  6. Review of Dry Adiabatic Processes • Dry Adiabatic Lapse Rate (Γd): • Describes how temperature changes • with height for an air parcel moving up • or down during a dry adiabatic process • Potential temperature is constant • “Dry Adiabats” on the Skew-T diagram An air parcel moving between 1000-700 mb parallel to a dry adiabat Δz = 2.7 km Using Γd we should expect ΔT = 26.5ºC T700 = -12.5ºC z700 = 2.8 km Dry Adiabatic (Unsaturated) T1000 = 14°C z1000 = 0.1 km M. D. Eastin

  7. Review of Moist Adiabatic Processes • Saturated Ascent: • Once saturation is achieved (at the LCL), further ascent produces additional cooling (adiabatic expansion) and condensation (phase changes) occur • The parcel now contains liquid water (cloud drops) • The condensation process releases latent heat that warms the parcel • This heat partially offsets (cancels out) the expansion cooling • “Pseudo-adiabats” on Skew-T diagram Pseudo-adiabat Moist Adiabatic Ascent (Saturated) (a Cloud) TLCL Dry Adiabatic Ascent (Unsaturated) Dry adiabat Td T M. D. Eastin

  8. Review of Moist Adiabatic Processes • Saturated Descent: • A descending saturated air parcel that contains liquid water (cloud / rain drops) • will experience warming (adiabatic compression) • The parcel will become temporarily unsaturated → cloud/rain drops evaporate • The evaporation process absorbs latent heat that cools the parcel • This cooling partially offsets (cancels out) the compression warming • “Pseudo-adiabats” on Skew-T diagram Moist Descent (Saturated) (Cloud evaporation) Pseudo-adiabat Moist Descent (Saturated) (Rain evaporation) Pseudo-adiabat M. D. Eastin

  9. Concept of Stability Basic Idea: Ability of an air parcel to return to is level of origin after a displacement M. D. Eastin

  10. Temperature Dewpoint Temperature Concept of Stability Basic Idea: Ability of an air parcel to return to is level of origin after a displacement Depends on the temperature structure of the atmosphere M. D. Eastin

  11. Concept of Stability • Three Categories of Stability: • Stable: • Returns to its original position • after displacement • Neutral: • Remains in new position after • being displaced • Unstable: • Moves further away from its original • position after being displaced M. D. Eastin

  12. Concept of Stability • Evidence of stability type in the atmosphere: • The type of cloud depends on atmospheric stability Stratus – Stable Cumulus – Unstable M. D. Eastin

  13. Concept of Stability • How is air displaced? Forced Ascent • Flow over mountains • Flow over cold and warm fronts M. D. Eastin

  14. Concept of Stability • How is air displaced? Spontaneous Ascent • Air parcel is warmer than its environment • which means the parcel is “buoyant” • Air becomes buoyant through “heating” Warm Cool Hot Cool M. D. Eastin

  15. Concept of Buoyancy Basic Idea: Archimedes Principle: The buoyant force exerted by a fluid on an object in the fluid is equal in magnitude to the weight of fluid displaced by the object. Bubble in a tank of water B B = Buoyancy Force M. D. Eastin

  16. Concept of Buoyancy • Basic Idea: • Let’s forget the bubble for now… • Pressure in the tank increases • with depth • Pressure is the force per unit area • exerted by the weight of all the mass • lying above that height • Identical to our atmosphere • Water in the tank is in hydrostatic • balance Tank of water L P Z H M. D. Eastin

  17. Concept of Buoyancy • Basic Idea: • Water in the tank is in hydrostatic • balance • At any given point within the • tank the upward directed pressure • gradient force (dp/dz) must balance • the downward directed gravitational • force (-ρwg) imposed by the weight of • the water mass above that point • The water does not move up or down Tank of water L -ρwg P Z dp/dz H M. D. Eastin

  18. Concept of Buoyancy • Basic Idea: • Let’s return to our bubble! • If we examine the forces acting along • the black line located at the base of • the bubble: • On either side of the bubble ( ) • the upward and downward • directed forces balance • At the bubble base ( ), the upward • directed pressure gradient force • is the same, but the downward • directed gravitational force is • different • The mass of the bubble must be • taken into account (-ρbg) Bubble in a tank of water -ρwg -ρbg -ρwg dp/dz dp/dz dp/dz M. D. Eastin

  19. Concept of Buoyancy • Basic Idea: • Option #1: • If the mass of the bubble is less than • the mass of the water it replaces… • then the pressure gradient force will be • stronger than the gravitational force… • and the bubble will experience an • upward directed buoyancy force(B) • The bubble will accelerate upward! Bubble in a tank of water B -ρbg dp/dz M. D. Eastin

  20. Concept of Buoyancy • Basic Idea: • Option #2: • If the mass of the bubble is greater than • the mass of the water it replaces… • then the pressure gradient force will be • weaker than the gravitational force… • and the bubble will experience an • downward directed buoyancy force(B) • The bubble will accelerate downward! Bubble in a tank of water B -ρbg dp/dz M. D. Eastin

  21. Concept of Buoyancy Basic Idea: A Different View… At the moment of Archimedes’ famous discovery M. D. Eastin

  22. Concept of Buoyancy • Basic Idea: Applied to the Atmosphere… • Large-scale environment is in • hydrostatic balance • If the density of a moist air • parcel (ρp) is less than the • density of the environmental • air (ρe) that it displaces, then • the air parcel will experience • an upward directed buoyancy • force (B): B ρe ρp ρe M. D. Eastin

  23. Concept of Buoyancy • Basic Idea: Applied to the Atmosphere… • Large-scale environment is in • hydrostatic balance • If the density of a moist air • parcel (ρp) is greater than the • density of the environmental • air (ρe) that it displaces, then • the air parcel will experience • a downward directed buoyancy • force (B): B ρe ρp ρe M. D. Eastin

  24. Concept of Buoyancy • Basic Idea: Applied to the Atmosphere… • Recall from the Ideal Gas Law: • virtual temperature of an air parcel • is inversely proportional to density • If the virtual temperature of a moist • air parcel (Tvp) is greater than that • of the nearby environmental air (Tve), • then the air parcel will experience • an upward directed buoyancy • force (B): Warm Air Rises! B Tve Tvp Tve M. D. Eastin

  25. Concept of Buoyancy • Basic Idea: Applied to the Atmosphere… • Recall from the Ideal Gas Law: • virtual temperature of an air parcel • is inversely proportional to density • If the virtual temperature of a moist • air parcel (Tvp) is less than that of • the nearby environmental air (Tve), • then the air parcel will experience • a downward directed buoyancy • force (B): Cold Air Sinks! B Tve Tve Tve M. D. Eastin

  26. Concept of Buoyancy • Mathematical Definition of Buoyancy: • See your text for the full derivation • Other commonly used forms that are roughly equivalent… Buoyancy Force (Virtual Temperature Form) Potential Temperature Form Virtual Potential Temperature Form Temperature Form M. D. Eastin

  27. Atmospheric Stability Analysis • Basic Idea: Unsaturated Air • Use the observed atmospheric temperature profile to determine • the stability of an unsaturated air parcel after vertical displacement • Assume: Upward displacement • The air parcel will always cool at • the dry adiabatic lapse rate (Γd) • Compare Γd to the observed • lapse rate (Γ) • Will the new parcel temperature • be colder than, warmer than, • or equivalent to the nearby • environment? Γd (parcel) Height Γ (environment) Temperature M. D. Eastin

  28. Atmospheric Stability Analysis Criteria for Unsaturated Air Parcel: Stable: Neutral: Unstable: Γ Parcel becomes colder than nearby environment Parcel will return to original location Height Downward Buoyancy Force Γd Temperature Γ Parcel becomes equivalent to the nearby environment Parcel will remain at new location No Buoyancy Force Height Γd Temperature Γd Parcel becomes warmer than nearby environment Parcel will move further away from original location Upward Buoyancy Force Height Γ Temperature M. D. Eastin

  29. Atmospheric Stability Analysis Application: Unsaturated Air Compare the observed lapse rate (Γ) (temperature change with height) to the local dry adiabatic lapserate (Γd) Temperature Neutral Unstable Stable M. D. Eastin

  30. Atmospheric Stability Analysis Application: Unsaturated Air Compare the observed lapse rate (Γ) (temperature change with height) to the local dry adiabatic lapserate (Γd) G Temperature F E D C B A M. D. Eastin

  31. Atmospheric Stability Analysis • Basic Idea: Saturated Air • Use the observed atmospheric temperature profile to determine • the stability of a saturated air parcel after vertical displacement • Assume: Upward displacement • The air parcel will always cool at the • pseudo-adiabatic lapse rate (Γs) • Compare Γs to the observed • lapse rate (Γ) • Will the new parcel temperature • be colder than, warmer than, • or equivalent to the nearby • environment? Γs (parcel) Height Γ (environment) Temperature M. D. Eastin

  32. Γ Height Γs Temperature Γ Height Γs Temperature Γs Height Γ Temperature Atmospheric Stability Analysis Criteria for Saturated Air Parcel: Stable: Neutral: Unstable: Parcel becomes colder than nearby environment Parcel will return to original location Downward Buoyancy Force Parcel becomes equivalent to the nearby environment Parcel will remain at new location No Buoyancy Force Parcel becomes warmer than nearby environment Parcel will move further away from original location Upward Buoyancy Force M. D. Eastin

  33. Atmospheric Stability Analysis Application: Saturated Air Compare the observed lapse rate (Γ) (temperature change with height) to the local pseudo-adiabatic lapserate (Γs) Temperature Neutral Unstable Stable M. D. Eastin

  34. Atmospheric Stability Analysis Application: Saturated Air Compare the observed lapse rate (Γ) (temperature change with height) to the local pseudo-adiabatic lapse rate (Γs) G Temperature F E D C B A M. D. Eastin

  35. Γd Γs Height Γ Temperature Atmospheric Stability Analysis Combined Criteria for Moist Air (either saturated or unsaturated): Absolutely Unstable: Dry Neutral: Unsaturated parcel becomes warmer than nearby environment Saturated parcel becomes warmer than nearby environment Γd Unsaturated parcel becomes equivalent to the nearby environment Saturated parcel becomes warmer than nearby environment Γs Γ Height Temperature M. D. Eastin

  36. Atmospheric Stability Analysis • Combined Criteria for Moist Air (either saturated or unsaturated): • Conditionally Unstable: • The vertical temperature profile at most locations in our atmosphere • is conditionally unstable • This is an important special case that we will return to in a little bit… Γ Unsaturated parcel becomes colder than nearby environment Saturated parcel becomes warmer than nearby environment Γs Γd Height Temperature M. D. Eastin

  37. Atmospheric Stability Analysis Combined Criteria for Moist Air (either saturated or unsaturated): Moist Neutral: Absolutely Stable: Γ Unsaturated parcel becomes colder than nearby environment Saturated parcel becomes equivalent to the nearby environment Γs Γd Height Temperature Γs Γ Unsaturated parcel becomes colder than nearby environment Saturated parcel becomes colder than nearby environment Γd Height Temperature M. D. Eastin

  38. Atmospheric Stability Analysis Application: Moist Air Compare the observed lapse rate (Γ) (temperature change with height) to the local dry adiabatic lapse rate (Γd) and the pseudo-adiabatic lapserate (Γs) E D C B A M. D. Eastin

  39. Atmospheric Stability Analysis • Conditional Instability: • Unsaturated air parcels experiencing a smallvertical displacement will be • stable and experience a downward buoyancy force • However, if the unsaturated parcel can experience enough forced ascent • with a large vertical displacement, the parcel may become saturated and • reach an altitude at which it becomes warmer than its local environment Td Where will a parcel starting at the surface become buoyant due to forced ascent? T Lift the surface parcel M. D. Eastin

  40. Atmospheric Stability Analysis • Conditional Instability: • Unsaturated air parcels experiencing a smallvertical displacement will • stable and experience a downward buoyancy force • However, if the unsaturated parcel can experience enough forced ascent • with a large vertical displacement, the parcel may become saturated and • reach an altitude at which it becomes warmer than its local environment Td T Altitude at which parcel first becomes warmer than the environment LCL M. D. Eastin

  41. Atmospheric Stability Analysis Level of Free Convection (LFC): Definition: Altitude at which a lifted air parcel first becomes warmer than the nearby environment (acquires an upward buoyancy force) and begin to accelerate upward without additional forced ascent Td T Level of Free Convection (LFC) LCL M. D. Eastin

  42. Atmospheric Stability Analysis Application: Find the Level of Free Convection (LFC) Find the LFC for the surface air parcel M. D. Eastin

  43. Atmospheric Stability Analysis Application: Find the Level of Free Convection (LFC) Find the LFC for the surface air parcel M. D. Eastin

  44. Atmospheric Stability and Buoyancy • Summary: • Review • Dry Adiabatic (unsaturated) Processes • Moist Adiabatic (saturated) Processes • Concepts Stability and Buoyancy • Forced vertical motions • Spontaneous vertical motions • Atmospheric Stability Analysis • Criteria for Unsaturated Air • Criteria for Saturated Air • Conditional Instability • Level of Free Convection (LFC) M. D. Eastin

  45. References Houze, R. A. Jr., 1993: Cloud Dynamics, Academic Press, New York, 573 pp. Markowski, P. M., and Y. Richardson, 2010: Mesoscale Meteorology in Midlatitudes, Wiley Publishing, 397 pp. Petty, G. W., 2008: A First Course in Atmospheric Thermodynamics, Sundog Publishing, 336 pp. Tsonis, A. A., 2007: An Introduction to Atmospheric Thermodynamics, Cambridge Press, 197 pp. Wallace, J. M., and P. V. Hobbs, 1977: Atmospheric Science: An Introductory Survey, Academic Press, New York, 467 pp. M. D. Eastin

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