Todays lecture objectives:

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ATMS 305 Atmospheric Thermodynamics and Statics

• Todays lecture objectives
• The Concept of Static Stability (WH 3.6)
• Now that we know how to deal with phase changes
  inside the air (Polly) parcel, how does the
  temperature inside the air (Polly) parcel compare
  to the environmental air?

?
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ATMS 305 The Concept of Static Stability

• Todays lecture topics
• The Concept of Static Stability (WH 3.6)
• What is meant by stability?
• Unsaturated air
• Archimedes Principle and buoyancy
• Saturated air
• Conditional and convective instability

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Meteorological Stability

• The ability of the air to return to its origin
  after displacement

(courtesy F. Remer)
4
Stability

• Depends on the thermal structure of the atmosphere

(courtesy F. Remer)
5
Stability

• Can be classified into 3 categories
• Stable
• Neutral
• Unstable

(courtesy F. Remer)
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Stable

• Returns to original position after displacement

(courtesy F. Remer)
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Neutral

• Remains in new position after being displaced

(courtesy F. Remer)
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Unstable

• Moves farther away from its original position

(courtesy F. Remer)
9
Stability

• How is air displaced?
• Two methods
• 1.) Forced Ascent
• 2.) Auto-Convective Ascent

(courtesy F. Remer)
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Forced Ascent

• Some mechanism forces air aloft
• Usually synoptic scale feature

Cold air
Warm air
Cool Air
(courtesy F. Remer)
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Forced Ascent

• Type of clouds
• Depends on stability

Stable - Stratus Unstable - Cumulus
(courtesy F. Remer)
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Auto-Convective Ascent

• Air becomes buoyant by contact with warm ground
• Usually microscale or mesoscale

Hot
Cool
Cool
(courtesy F. Remer)
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Auto-Convective Ascent

• Type of Clouds
• Cumulus

(courtesy F. Remer)
14
Stability

• As parcel rises
• 1.) Parcel Temperature Changes
• Unsaturated?
• Dry Adiabatic Lapse Rate

(courtesy F. Remer)
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Dry Adiabatic Lapse Rate
(courtesy F. Remer)
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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.

Archimedes 287 211 BC
(courtesy F. Remer)
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Archimedes Principle

• Square bubble in a tank of water

B
B buoyancy force
(courtesy F. Remer)
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Archimedes Principle

• Water pressure in tank increases with depth

B
p
z
(courtesy F. Remer)
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Archimedes Principle

• Water is in hydrostatic equlibrium

B
(courtesy F. Remer)
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Archimedes Principle

• Force on bottom of bubble

Fbottom
(courtesy F. Remer)
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Archimedes Principle

• Force on top of bubble

Ftop
Fbottom
(courtesy F. Remer)
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Archimedes Principle

• Buoyancy Force

B
Ftop
Fbottom
(courtesy F. Remer)
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Archimedes Principle

• Horizontal Pressure Differences Balance

(courtesy F. Remer)
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Archimedes Principle

• Pressure Difference Between Top Bottom

ptop
pbottom
(courtesy F. Remer)
25
Archimedes Principle

• Combine Equations

B
ptop
pbottom
(courtesy F. Remer)
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Archimedes Principle
Archimedes 287 211 BC

• Cartoon here??

At the moment of Archimedes famous discovery.
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Buoyancy

• Similar to parcel of air in atmosphere
• At Equilibrium
• Density of Parcel Same as Density of Environment

(courtesy F. Remer)
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Buoyancy

• Density Difference Results in Net Buoyancy Force

B
(courtesy F. Remer)
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Buoyancy

• Density Difference Results in Net Buoyancy Force

B
(courtesy F. Remer)
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Buoyancy

• Net Buoyancy Force

B
(courtesy F. Remer)
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ATMS 305 The Concept of Static Stability

• A parcel of unsaturated air originally located at
  level O
• Environment A
• T-storm possible or not?

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ATMS 305 The Concept of Static Stability

• A parcel of unsaturated air originally located at
  level O
• Environment B
• T-storm possible or not?

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Stability

• As parcel rises
• 1.) Parcel Temperature Changes
• Saturated?
• Pseudoadiabatic Lapse Rate

(courtesy F. Remer)
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Pseudo-Adiabatic Lapse Rate

• Varies with dws/dT

Big
Small
4oC km-1 lt Gs lt 9.8oC km-1
(courtesy F. Remer)
35
ATMS 305 The Concept of Static Stability

• If a parcel of air is saturated
• Static stability
• Static instability
• Static neutrality

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ATMS 305 The Concept of Static Stability

• Conditional instability
• Level of free convection
• Altitude above which the parcel develops a
  positive buoyancy which carries it upward even in
  the absence of further lifting

37
ATMS 305 The Concept of Static Stability

• Conditional instability
• If the environmental lapse rate is between the
  dry and saturated adiabatic lapse rates, there is
  the possibility of gravitational instability if
  vertical motions are large enough to lift air
  parcels beyond their level of free convection

38
ATMS 305 The Concept of Static Stability

• Convective (or potential) instability
• An air parcel at A will reach its lifting
  condensation level almost immediately, and beyond
  that point it will cool moist adiabatically.
• An air parcel at B will cool dry adiabatically
  through a deep layer before it reaches its LCL.
• As the inversion layer is lifted, the top part
  cools much more rapidly than the bottom part and
  the lapse rate quickly becomes destabilized

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ATMS 305 The Concept of Static Stability

• Conditional and convective instability
• Throughout the tropics, the lapse rate is
  conditionally unstable up to 15 km convectively
  unstable up to 6 km
• Why doesnt deep convection break out everywhere
  in the tropics?

40
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