Baroclinic Instability Questions and Answers

Q: Which criterion gives a necessary condition for instability?

The criterion requires the meridional gradient of potential vorticity to change sign somewhere in the domain, with boundary temperature gradients counted as delta functions in that gradient. It generalises Rayleigh's barotropic result to the stratified rotating case. Charney-Drazin concerns wave propagation, and the Richardson and Miles-Howard criteria concern shear instability at much smaller scales. Reading the definition literally, rather than recalling a formula, is the reliable route through questions of this shape.

Q: Which distinction should be remembered about that criterion?

A flow satisfying the criterion may nonetheless be stable, so the condition rules out instability when it fails but does not guarantee it when it holds. Examination questions frequently turn on exactly this word. The criterion applies to arbitrary shear profiles, and its power lies in reducing a difficult stability calculation to an inspection of a single gradient. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Q: Which realistic feature does the Charney model add?

Charney worked on a beta plane with an unbounded atmosphere above, so the interior potential vorticity gradient is non-zero and instability arises from its interaction with the surface temperature gradient. The resulting modes are bottom-trapped with a depth set by the Rossby height. Latent heat, friction and realistic stability are absent from both idealised models, which is what keeps them tractable. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Q: Which vertical structure do Charney modes have?

The Charney mode is confined to a depth of order the Rossby height, which is the horizontal scale multiplied by the ratio of the Coriolis parameter to the buoyancy frequency. That gives roughly the depth of the troposphere for a synoptic scale disturbance, so the confinement is not severe. The absence of an upper lid is exactly what allows the mode to decay rather than being reflected back. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

Q: Which quantity gives the Rossby depth scale?

Multiplying the horizontal scale by \( f/N \), about one in a hundred in the troposphere, gives the depth over which a disturbance of that width influences the flow. A synoptic scale disturbance a thousand kilometres wide therefore reaches through about ten kilometres, which is the whole troposphere. This is the vertical counterpart of the deformation radius and explains the observed aspect ratio of weather systems.

Q: Which parameter is used operationally to map baroclinic instability?

The Eady growth rate parameter, proportional to the Coriolis parameter times the vertical shear divided by the buoyancy frequency, combines exactly the ingredients the theory identifies. Maps of it show maxima off the eastern coasts of Asia and North America in winter, coinciding with the observed storm tracks. The Richardson number and convective energy concern much smaller scale instabilities. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Q: Which regions show the largest values of that parameter?

Strong shear and modest stratification combine off the coasts of Japan and North America in winter, exactly where the observed storm tracks begin. The agreement between the theoretical parameter and the observed climatology is striking. The equator has almost no Coriolis parameter, deserts have weak shear despite hot surfaces, and continental inversions represent strong stratification that suppresses growth. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Q: Which surface feature contributes to the strong shear there?

The Gulf Stream and Kuroshio carry warm water poleward alongside cold continental air, producing intense low level baroclinicity that anchors the storm track entrance. Ocean circulation therefore controls where mid-latitude storms form. Uniform ocean temperature would remove the gradient entirely, and mountains and snow cover contribute elsewhere but not to this particular feature. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Q: Which term describes the geographical band of frequent cyclone activity?

Storm tracks are identified as bands of maximum synoptic scale variance, running northeastward across the Atlantic and Pacific in the northern hemisphere. They begin where the Eady growth rate is largest and decay downstream. The polar front and jet stream are related features of the same baroclinic zone, and the Ferrel cell is the zonally averaged circulation that the eddies themselves maintain. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

11.

Which criterion gives a necessary condition for instability?

A.The Richardson criterion
B.The Miles-Howard criterion, which requires the Richardson number to fall below one quarter somewhere
C.The Charney-Stern criterion
D.The Charney-Drazin criterion, which governs the vertical propagation of planetary waves into the stratosphere

Answer: C

The criterion requires the meridional gradient of potential vorticity to change sign somewhere in the domain, with boundary temperature gradients counted as delta functions in that gradient. It generalises Rayleigh's barotropic result to the stratified rotating case. Charney-Drazin concerns wave propagation, and the Richardson and Miles-Howard criteria concern shear instability at much smaller scales. Reading the definition literally, rather than recalling a formula, is the reliable route through questions of this shape.

Discuss in Forum

12.

Which distinction should be remembered about that criterion?

A.It is sufficient but not necessary, so a flow failing it may still become unstable under some conditions
B.It is both necessary and sufficient
C.It applies only to flows in which the vertical shear is constant throughout the depth of the domain
D.It is necessary but not sufficient

Answer: D

A flow satisfying the criterion may nonetheless be stable, so the condition rules out instability when it fails but does not guarantee it when it holds. Examination questions frequently turn on exactly this word. The criterion applies to arbitrary shear profiles, and its power lies in reducing a difficult stability calculation to an inspection of a single gradient. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Discuss in Forum

13.

Which feature supplies the required sign change in the Eady model?

A.The temperature gradients at the two boundaries
B.The beta effect, which provides a positive interior gradient of planetary vorticity across the domain
C.The vertical shear
D.The curvature of the mean flow profile, whose second derivative changes sign at the mid-level of the layer

Answer: A

The Eady model has zero interior potential vorticity gradient, so the required change of sign comes entirely from the two boundary temperature gradients, which Bretherton showed to be equivalent to delta functions of potential vorticity. The beta effect is absent by construction. This equivalence is what allows a model with no interior gradient at all to satisfy the criterion. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

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14.

Which realistic feature does the Charney model add?

A.A realistic vertical profile of static stability including the sharp increase found at the tropopause
B.The beta effect with no upper lid
C.Latent heat release within the ascending branch of the growing baroclinic wave being modelled here
D.Surface friction

Answer: B

Charney worked on a beta plane with an unbounded atmosphere above, so the interior potential vorticity gradient is non-zero and instability arises from its interaction with the surface temperature gradient. The resulting modes are bottom-trapped with a depth set by the Rossby height. Latent heat, friction and realistic stability are absent from both idealised models, which is what keeps them tractable. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Discuss in Forum

15.

Which vertical structure do Charney modes have?

A.Top-trapped
B.Amplitude that grows steadily with height as the density of the air decreases towards the tropopause
C.Bottom-trapped with amplitude decaying upward
D.Uniform amplitude throughout the depth of the atmosphere, since there is no upper boundary to confine them

Answer: C

The Charney mode is confined to a depth of order the Rossby height, which is the horizontal scale multiplied by the ratio of the Coriolis parameter to the buoyancy frequency. That gives roughly the depth of the troposphere for a synoptic scale disturbance, so the confinement is not severe. The absence of an upper lid is exactly what allows the mode to decay rather than being reflected back. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

Discuss in Forum

16.

Which quantity gives the Rossby depth scale?

A.The scale height of the atmosphere multiplied by the ratio of the buoyancy frequency to the Coriolis parameter
B.The wind speed divided by beta
C.The square root of the ratio of the static stability to the vertical shear of the wind at that level
D.The horizontal scale times f divided by N

Answer: D

Multiplying the horizontal scale by \( f/N \), about one in a hundred in the troposphere, gives the depth over which a disturbance of that width influences the flow. A synoptic scale disturbance a thousand kilometres wide therefore reaches through about ten kilometres, which is the whole troposphere. This is the vertical counterpart of the deformation radius and explains the observed aspect ratio of weather systems.

Discuss in Forum

17.

Which parameter is used operationally to map baroclinic instability?

A.The Eady growth rate parameter
B.The bulk Richardson number, which is used to assess the likelihood of turbulence within a sheared layer
C.The Rossby number
D.The convective available potential energy, which measures the buoyancy available to a rising moist parcel

Answer: A

The Eady growth rate parameter, proportional to the Coriolis parameter times the vertical shear divided by the buoyancy frequency, combines exactly the ingredients the theory identifies. Maps of it show maxima off the eastern coasts of Asia and North America in winter, coinciding with the observed storm tracks. The Richardson number and convective energy concern much smaller scale instabilities. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Discuss in Forum

18.

Which regions show the largest values of that parameter?

A.The interiors of the winter continents, where surface radiative cooling produces very strong inversions
B.The western oceanic storm track entrance regions in winter
C.The subtropical deserts in summer, where the surface temperature gradient reaches its greatest values
D.The equatorial belt

Answer: B

Strong shear and modest stratification combine off the coasts of Japan and North America in winter, exactly where the observed storm tracks begin. The agreement between the theoretical parameter and the observed climatology is striking. The equator has almost no Coriolis parameter, deserts have weak shear despite hot surfaces, and continental inversions represent strong stratification that suppresses growth. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Discuss in Forum

19.

Which surface feature contributes to the strong shear there?

A.Mountain ranges
B.The high albedo of the winter snow cover, which cools the surface uniformly across the whole continent
C.The sea surface temperature gradient across a western boundary current
D.The uniform temperature of the open ocean, which prevents any horizontal thermal contrast from forming

Answer: C

The Gulf Stream and Kuroshio carry warm water poleward alongside cold continental air, producing intense low level baroclinicity that anchors the storm track entrance. Ocean circulation therefore controls where mid-latitude storms form. Uniform ocean temperature would remove the gradient entirely, and mountains and snow cover contribute elsewhere but not to this particular feature. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Discuss in Forum

20.

Which term describes the geographical band of frequent cyclone activity?

A.The polar front, which is the surface boundary between polar and mid-latitude air masses in each hemisphere
B.The jet stream
C.The Ferrel cell, which is the indirect meridional circulation found in the middle latitudes of each hemisphere
D.The storm track

Answer: D

Storm tracks are identified as bands of maximum synoptic scale variance, running northeastward across the Atlantic and Pacific in the northern hemisphere. They begin where the Eady growth rate is largest and decay downstream. The polar front and jet stream are related features of the same baroclinic zone, and the Ferrel cell is the zonally averaged circulation that the eddies themselves maintain. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Discuss in Forum

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