Transcript Lecture #11: Parcel Buoyancy and Atmospheric Stability
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 Thermodynamics M. D. Eastin
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) Thermodynamics M. D. Eastin
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
Parcel
dq c v dT pdα 0 dq c p dT dp 0 • 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 Thermodynamics M. D. Eastin
Review of Dry Adiabatic Processes
Poisson’s Relation:
• Relates the
initial
conditions of temperature and pressure to the
final
temperature and pressure during a dry adiabatic process T final T initial p final p initial R d c p
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 Thermodynamics θ T p 0 p R d c p M. D. Eastin
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
Thermodynamics M. D. Eastin
Review of Dry Adiabatic Processes
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
d
dT dz g c p 9 .
8
C
/
km
An air parcel moving between 1000-700 mb parallel to a dry adiabat Dry Adiabatic (Unsaturated) Δz = 2.7 km Using Γ d we should expect ΔT = 26.5ºC T 700 = -12.5
ºC T 1000 = 14 °C z 700 = 2.8 km z 1000 = 0.1 km
Thermodynamics M. D. Eastin
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 Thermodynamics
Moist Adiabatic Ascent (Saturated) (a Cloud) Dry Adiabatic Ascent (Unsaturated) T d Pseudo-adiabat T LCL Dry adiabat T
M. D. Eastin
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 Thermodynamics
Moist Descent (Saturated) (Cloud evaporation) Moist Descent (Saturated) (Rain evaporation) Pseudo-adiabat Pseudo-adiabat
M. D. Eastin
Concept of Stability
Basic Idea: Ability of an air parcel to return to is level of origin after a displacement
Thermodynamics M. D. Eastin
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
Thermodynamics
Dewpoint Temperature Temperature
M. D. Eastin
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 Thermodynamics M. D. Eastin
Concept of Stability
Evidence of stability type in the atmosphere:
• The type of cloud depends on atmospheric stability
Stratus – Stable
Thermodynamics
Cumulus – Unstable
M. D. Eastin
Concept of Stability
How is air displaced? Forced Ascent
• Flow over mountains • Flow over cold and warm fronts Thermodynamics M. D. Eastin
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
Thermodynamics
Cool Hot Cool
M. D. Eastin
Basic Idea:
Archimedes Principle:
Concept of Buoyancy
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 = Buoyancy Force B
Thermodynamics M. D. Eastin
Concept of Buoyancy
Basic Idea:
•
Let’s forget the bubble for now… Tank of water
•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
L
• • Identical to our atmosphere Water in the tank is in hydrostatic balance
P H
dp
w g
dz
Z
Thermodynamics M. D. Eastin
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 (
ρ w g
) imposed by the weight of the water mass above that point F F
P L Tank of water ρ w g
dp/dz
dp
w g
dz
H
• The water does not move up or down Thermodynamics
Z
M. D. Eastin
Concept of Buoyancy
Basic Idea:
•
Let’s return to our bubble!
Bubble in a tank of water
• 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
)
ρ w g
dp/dz
ρ b g
dp/dz
ρ w g
dp/dz
Thermodynamics M. D. Eastin
Concept of Buoyancy
Basic Idea: Option #1:
• If the mass of the bubble is less than the mass of the water it replaces… b w
Bubble in a tank of water B
then the pressure gradient force will be stronger than the gravitational force…
ρ b g
dp dz
b g
and the bubble will experience an upward directed buoyancy force (
B
)
dp/dz
• The bubble will accelerate upward!
Thermodynamics M. D. Eastin
Concept of Buoyancy
Basic Idea: Option #2:
• If the mass of the bubble is greater than the mass of the water it replaces… b w
Bubble in a tank of water B ρ b g
then the pressure gradient force will be weaker than the gravitational force… dp dz
b g
and the bubble will experience an downward directed buoyancy force (
B
)
dp/dz
• The bubble will accelerate downward!
Thermodynamics M. D. Eastin
Concept of Buoyancy
Basic Idea: A Different View…
Thermodynamics At the moment of Archimedes’ famous discovery M. D. Eastin
Concept of Buoyancy
Basic Idea: Applied to the Atmosphere…
• Large-scale environment is in hydrostatic balance dp
e g
dz • 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
force (B): buoyancy p e
ρ e ρ p B ρ e
Thermodynamics M. D. Eastin
Concept of Buoyancy
Basic Idea: Applied to the Atmosphere…
• Large-scale environment is in hydrostatic balance dp
e g
dz • 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): p e
ρ e ρ p B ρ e
Thermodynamics M. D. Eastin
Concept of Buoyancy
Basic Idea: Applied to the Atmosphere…
• Recall from the Ideal Gas Law: p
ρ
R d T v virtual temperature of an air parcel is inversely proportional to density
Warm Air Rises!
• 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):
T ve T vp B T ve
T p T e Thermodynamics M. D. Eastin
Concept of Buoyancy
Basic Idea: Applied to the Atmosphere…
• Recall from the Ideal Gas Law: p
ρ
R d T v virtual temperature of an air parcel is inversely proportional to density
Cold Air Sinks!
• 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):
T ve T ve B T ve
T p T e Thermodynamics M. D. Eastin
Concept of Buoyancy
Mathematical Definition of Buoyancy:
• See your text for the full derivation B g T vp T ve T ve
Buoyancy Force (Virtual Temperature Form)
• Other commonly used forms that are roughly equivalent… B
Temperature Form
g T p T e T e
Potential Temperature Form
B g θ p θ e θ e
Virtual Potential Temperature Form
B g θ vp θ ve θ ve Thermodynamics M. D. Eastin
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
(
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?
Γ (environment) Γ d (parcel) Temperature
Thermodynamics M. D. Eastin
Atmospheric Stability Analysis
Criteria for Unsaturated Air Parcel: Stable:
d
Parcel becomes colder than nearby environment Downward Buoyancy Force Parcel will return to original location Γ d Temperature Γ Neutral:
d
Parcel becomes equivalent to the nearby environment No Buoyancy Force Parcel will remain at new location Γ d Γ Temperature Unstable:
d Thermodynamics
Parcel becomes warmer than nearby environment Upward Buoyancy Force Parcel will move further away from original location Γ d Γ Temperature
M. D. Eastin
Atmospheric Stability Analysis
Application: Unsaturated Air Compare the observed lapse rate ( Γ ) (temperature change with height) to the local dry adiabatic lapse rate ( Γ d ) Temperature Neutral
d
Unstable
d
Stable
d Thermodynamics M. D. Eastin
Atmospheric Stability Analysis
Application: Unsaturated Air Compare the observed lapse rate ( Γ ) (temperature change with height) to the local dry adiabatic lapse rate ( Γ d ) G Temperature F E D C B A
Thermodynamics M. D. Eastin
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
(
Γ s
) • Compare
Γ s
to the observed lapse rate (
Γ
) • Will the new parcel temperature be
colder than
,
warmer than
, or
equivalent to
environment?
the nearby
Γ s (parcel) Γ (environment) Temperature
Thermodynamics M. D. Eastin
Atmospheric Stability Analysis
Criteria for Saturated Air Parcel: Stable:
s
Parcel becomes colder than nearby environment Downward Buoyancy Force Parcel will return to original location Γ s Temperature Γ Neutral:
s
Parcel becomes equivalent to the nearby environment No Buoyancy Force Parcel will remain at new location Γ s Γ Temperature Unstable:
s
Parcel becomes warmer than nearby environment Upward Buoyancy Force Parcel will move further away from original location Γ Γ s
Thermodynamics
Temperature
M. D. Eastin
Atmospheric Stability Analysis
Application: Saturated Air Compare the observed lapse rate ( Γ ) (temperature change with height) to the local pseudo-adiabatic lapse rate ( Γ s ) Temperature Neutral
s
Unstable
s
Stable
s Thermodynamics M. D. Eastin
Atmospheric Stability Analysis
Application: Saturated Air Compare the observed lapse rate ( Γ ) (temperature change with height) to the local pseudo-adiabatic lapse rate ( Γ s ) G Temperature F E D C B A
Thermodynamics M. D. Eastin
Atmospheric Stability Analysis
Combined Criteria for Moist Air (either saturated or unsaturated): Absolutely Unstable:
Γ Γ d Γ s
Unsaturated parcel becomes warmer than nearby environment Saturated parcel becomes warmer than nearby environment Γ d Γ Temperature Γ s Dry Neutral:
Γ Γ d Γ s
Unsaturated parcel becomes equivalent to the nearby environment Saturated parcel becomes warmer than nearby environment Γ Γ d Γ s Temperature
Thermodynamics M. D. Eastin
Atmospheric Stability Analysis
Combined Criteria for Moist Air (either saturated or unsaturated): Conditionally Unstable:
Γ d Γ Γ s
Unsaturated parcel becomes colder than nearby environment Saturated parcel becomes warmer than nearby environment Γ d Γ Temperature Γ s
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… Thermodynamics M. D. Eastin
Atmospheric Stability Analysis
Combined Criteria for Moist Air (either saturated or unsaturated): Moist Neutral:
Γ d Γ Γ s
Unsaturated parcel becomes colder than nearby environment Saturated parcel becomes equivalent to the nearby environment Γ d Γ Temperature Γ s Absolutely Stable:
Γ d Γ s Γ
Unsaturated parcel becomes colder than nearby environment Saturated parcel becomes colder than nearby environment Γ d Γ s Γ Temperature
Thermodynamics M. D. Eastin
Atmospheric Stability Analysis
Application: Moist Air Compare the observed lapse rate ( Γ ) (temperature change with height) to the local dry adiabatic lapse rate and the pseudo-adiabatic lapse rate ( Γ d ) ( Γ s ) E D C B A
Thermodynamics M. D. Eastin
Atmospheric Stability Analysis
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
T d T Where will a parcel starting at the surface become buoyant due to forced ascent?
Lift the surface parcel
Thermodynamics M. D. Eastin
Atmospheric Stability Analysis
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
T d T Altitude at which parcel first becomes warmer than the environment LCL
Thermodynamics M. D. Eastin
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
T d T Level of Free Convection (LFC) LCL
Thermodynamics M. D. Eastin
Atmospheric Stability Analysis
Application: Find the Level of Free Convection (LFC) Find the LFC for the surface air parcel
Thermodynamics M. D. Eastin
Atmospheric Stability Analysis
Application: Find the Level of Free Convection (LFC) Find the LFC for the surface air parcel
Thermodynamics M. D. Eastin
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) Thermodynamics M. 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.
Thermodynamics M. D. Eastin