ThermodynamicsM. D. Eastin 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 ?

ThermodynamicsM. D. Eastin 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) Atmospheric Stability and Buoyancy

ThermodynamicsM. D. Eastin 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 Review of Dry Adiabatic Processes

ThermodynamicsM. D. Eastin Poisson’s Relation: Relates the initial conditions of temperature 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 Review of Dry Adiabatic Processes

ThermodynamicsM. D. Eastin 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 Review of Dry Adiabatic Processes

ThermodynamicsM. D. Eastin Dry Adiabatic Lapse Rate (Γ d ): 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 Review of Dry Adiabatic Processes Δz = 2.7 km T 1000 = 14°C T 700 = -12.5ºC z 1000 = 0.1 km z 700 = 2.8 km Using Γ d we should expect ΔT = 26.5ºC An air parcel moving between mb parallel to a dry adiabat Dry Adiabatic (Unsaturated)

ThermodynamicsM. D. Eastin 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 Review of Moist Adiabatic Processes Dry Adiabatic Ascent (Unsaturated) T LCL Dry adiabat T TdTd Moist Adiabatic Ascent (Saturated) (a Cloud) Pseudo-adiabat

ThermodynamicsM. D. Eastin 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 Review of Moist Adiabatic Processes Pseudo-adiabat Moist Descent (Saturated) (Cloud evaporation) Pseudo-adiabat Moist Descent (Saturated) (Rain evaporation)

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

ThermodynamicsM. D. Eastin 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 Concept of Stability Temperature Dewpoint Temperature

ThermodynamicsM. D. Eastin 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 Concept of Stability

ThermodynamicsM. D. Eastin Evidence of stability type in the atmosphere: The type of cloud depends on atmospheric stability Concept of Stability Stratus – StableCumulus – Unstable

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

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

ThermodynamicsM. D. Eastin 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. Concept of Buoyancy B Bubble in a tank of water B = Buoyancy Force

ThermodynamicsM. D. Eastin 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 Concept of Buoyancy Tank of water PZ H L

ThermodynamicsM. D. Eastin 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 (-ρ w g) imposed by the weight of the water mass above that point The water does not move up or down Concept of Buoyancy Tank of water PZ H L -ρwg-ρwg dp/dz

ThermodynamicsM. D. Eastin 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 (-ρ b g) Concept of Buoyancy Bubble in a tank of water -ρwg-ρwg dp/dz -ρwg-ρwg -ρbg-ρbg

ThermodynamicsM. D. Eastin 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! Concept of Buoyancy Bubble in a tank of water -ρbg-ρbg dp/dz B

ThermodynamicsM. D. Eastin 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! Concept of Buoyancy Bubble in a tank of water -ρbg-ρbg dp/dz B

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

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

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

ThermodynamicsM. D. Eastin 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 (T vp ) is greater than that of the nearby environmental air (T ve ), then the air parcel will experience an upward directed buoyancy force (B): Concept of Buoyancy B T vp T ve Warm Air Rises!

ThermodynamicsM. D. Eastin 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 (T vp ) is less than that of the nearby environmental air (T ve ), then the air parcel will experience a downward directed buoyancy force (B): Concept of Buoyancy B T ve Cold Air Sinks!

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

ThermodynamicsM. D. Eastin 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 (Γ d ) Compare Γ d to the observed lapse rate (Γ) Will the new parcel temperature be colder than, warmer than, or equivalent to the nearby environment? Atmospheric Stability Analysis Temperature Height Γ d (parcel) Γ (environment)

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

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

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

ThermodynamicsM. D. Eastin 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 (Γ s ) Compare Γ s to the observed lapse rate (Γ) Will the new parcel temperature be colder than, warmer than, or equivalent to the nearby environment? Temperature Height Γ s (parcel) Γ (environment) Atmospheric Stability Analysis

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

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

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

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

ThermodynamicsM. D. Eastin 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… Atmospheric Stability Analysis Unsaturated parcel becomes colder than nearby environment Temperature Height ΓsΓs Γ ΓdΓd Saturated parcel becomes warmer than nearby environment

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

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

ThermodynamicsM. D. Eastin Conditional Instability: Unsaturated air parcels experiencing a small vertical 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 Atmospheric Stability Analysis Where will a parcel starting at the surface become buoyant due to forced ascent? T TdTd Lift the surface parcel

ThermodynamicsM. D. Eastin Conditional Instability: Unsaturated air parcels experiencing a small vertical 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 Atmospheric Stability Analysis T TdTd LCL Altitude at which parcel first becomes warmer than the environment

ThermodynamicsM. D. Eastin 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 Atmospheric Stability Analysis T TdTd LCL Level of Free Convection (LFC)

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

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

ThermodynamicsM. D. Eastin 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) Atmospheric Stability and Buoyancy

ThermodynamicsM. D. Eastin 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.