Thermal Wind Balance Questions and Answers

Q: Which development principle relates surface pressure change to thermal advection?

Sutcliffe expressed surface development in terms of the thermal advection and the thermal vorticity advection, giving forecasters a practical rule based on the thickness field. It was the working method of British forecasting for decades before numerical models. Margules concerns frontal slope, Charney-Drazin wave propagation into the stratosphere, and Eady the idealised theory of baroclinic growth.

Q: Which configuration favours surface development in Sutcliffe's theory?

Development occurs where the thermal steering carries positive vorticity over the surface system, which in practice means a surface low downstream of an upper trough within a strong thermal gradient. A barotropic atmosphere permits no development at all, and thickness contours parallel to isobars indicate no thermal advection. The theory is essentially a practical rendering of the omega equation.

Q: Which quantity does thermal steering give?

A surface system tends to move along the thickness contours, which is the thermal steering rule, because the upper flow that steers it is itself largely determined by the thermal wind. The rate of deepening is given by the development terms rather than by the steering. Depth and intensity are separate properties, though a deepening system does tend to become more vertically upright as it matures.

Q: Which limitation does thermal steering have as a forecasting rule?

A mature occluded low becomes vertically upright and slow moving, and the thermal steering rule then gives little guidance because the system is no longer being carried by the flow above. The rule works best during the developing stage. It uses thickness rather than direct upper air observations, applies to deepening and filling systems alike, and does give an indication of speed from the strength of the thermal wind. Reading the definition literally, rather than recalling a formula, is the reliable route through questions of this shape.

Q: Which stage of a cyclone's life cycle shows the greatest vertical tilt?

Growth requires the upper trough to lie upstream of the surface low, so the tilt is greatest while the system is deepening most rapidly. As the system occludes the two become vertically aligned and deepening ceases. The wave stage has a modest tilt and the decaying stage may even tilt the other way. Recognising tilt as a signature of active development is one of the most useful practical applications of this theory. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Q: Which relationship exists between tilt and energy conversion?

A westward tilt with height means warm air rises and cold air sinks systematically, lowering the centre of gravity of the atmosphere and releasing available potential energy as kinetic energy. Eastward tilt reverses the conversion and describes a decaying system. Vertical alignment gives no net conversion at all, which is precisely why a vertically stacked low stops deepening.

Q: Which idealised model isolates the thermal wind as the source of instability?

Eady considered a uniformly stratified fluid with constant vertical shear between two rigid lids and showed that disturbances grow by drawing on the available potential energy of that shear. The shear is exactly the thermal wind. The barotropic model has no shear and hence no baroclinic instability, while the Ekman and Hadley models address friction and the meridional circulation respectively.

Q: Which wavelength grows fastest in the Eady model?

The Eady model gives a most unstable wavelength of roughly 4000 kilometres, close to the observed spacing of mid-latitude cyclones, and a growth rate corresponding to an e-folding time of about a day. The agreement with observation is what made the model so influential. The deformation radius is smaller by a factor of about four and sets the scale rather than the most unstable wavelength directly.

Q: Which growth rate does the Eady model predict?

The maximum growth rate is proportional to the shear divided by the buoyancy frequency, giving an e-folding time near 24 hours for typical mid-latitude values. That matches the observed pace at which cyclones develop from a barely visible wave to a mature system in two or three days. The rate depends strongly on the shear, which is the thermal wind, so it is not a function of latitude alone.

Q: Which boundary condition does the Eady model impose?

Eady placed rigid horizontal boundaries at the ground and at the tropopause, which allows edge waves to exist at each and lets the pair interact to produce growth. The interaction of two counter-propagating edge waves is the cleanest available account of baroclinic instability. A free surface, periodicity or a radiation condition would each change the character of the solution, and the Charney model, which replaces the upper lid with an unbounded atmosphere on a beta plane, gives a somewhat different and more realistic answer at the cost of much greater complexity.

71.

Which development principle relates surface pressure change to thermal advection?

A.The Charney-Drazin criterion
B.The Eady model, which describes the growth of baroclinic waves in a uniformly sheared basic state
C.The Sutcliffe development theory
D.The Margules relation, which gives the slope of a frontal surface from the wind change across it

Answer: C

Sutcliffe expressed surface development in terms of the thermal advection and the thermal vorticity advection, giving forecasters a practical rule based on the thickness field. It was the working method of British forecasting for decades before numerical models. Margules concerns frontal slope, Charney-Drazin wave propagation into the stratosphere, and Eady the idealised theory of baroclinic growth.

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72.

Which configuration favours surface development in Sutcliffe's theory?

A.A surface low lying directly beneath the axis of the upper level ridge at the same longitude as it
B.A barotropic atmosphere
C.A region in which the thickness contours run parallel to the surface isobars throughout the whole area
D.A surface low beneath positive thermal vorticity advection

Answer: D

Development occurs where the thermal steering carries positive vorticity over the surface system, which in practice means a surface low downstream of an upper trough within a strong thermal gradient. A barotropic atmosphere permits no development at all, and thickness contours parallel to isobars indicate no thermal advection. The theory is essentially a practical rendering of the omega equation.

Discuss in Forum

73.

Which quantity does thermal steering give?

A.The direction in which a surface system will move
B.The rate at which the central pressure of a system will fall over the following twenty four hours
C.The intensity of the system
D.The depth through which the circulation of the surface system extends upward into the troposphere

Answer: A

A surface system tends to move along the thickness contours, which is the thermal steering rule, because the upper flow that steers it is itself largely determined by the thermal wind. The rate of deepening is given by the development terms rather than by the steering. Depth and intensity are separate properties, though a deepening system does tend to become more vertically upright as it matures.

Discuss in Forum

74.

Which limitation does thermal steering have as a forecasting rule?

A.It gives the direction of movement but never any indication of the speed at which the system travels
B.It fails once a system becomes vertically stacked
C.It applies only to systems whose central pressure is falling rather than rising at the time concerned
D.It requires upper air data

Answer: B

A mature occluded low becomes vertically upright and slow moving, and the thermal steering rule then gives little guidance because the system is no longer being carried by the flow above. The rule works best during the developing stage. It uses thickness rather than direct upper air observations, applies to deepening and filling systems alike, and does give an indication of speed from the strength of the thermal wind. Reading the definition literally, rather than recalling a formula, is the reliable route through questions of this shape.

Discuss in Forum

75.

Which stage of a cyclone's life cycle shows the greatest vertical tilt?

A.The decaying stage
B.The initial wave stage, before any closed circulation has appeared at the surface on the chart
C.The rapidly deepening stage
D.The mature occluded stage, when the surface low is deepest and the circulation extends most deeply

Answer: C

Growth requires the upper trough to lie upstream of the surface low, so the tilt is greatest while the system is deepening most rapidly. As the system occludes the two become vertically aligned and deepening ceases. The wave stage has a modest tilt and the decaying stage may even tilt the other way. Recognising tilt as a signature of active development is one of the most useful practical applications of this theory. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Discuss in Forum

76.

Which relationship exists between tilt and energy conversion?

A.Eastward tilt allows the disturbance to extract kinetic energy from the mean flow around it directly
B.Tilt has no energetic role
C.Vertical alignment maximises the conversion because the circulations at the two levels then reinforce
D.Westward tilt allows potential energy to be converted to kinetic energy

Answer: D

A westward tilt with height means warm air rises and cold air sinks systematically, lowering the centre of gravity of the atmosphere and releasing available potential energy as kinetic energy. Eastward tilt reverses the conversion and describes a decaying system. Vertical alignment gives no net conversion at all, which is precisely why a vertically stacked low stops deepening.

Discuss in Forum

77.

Which idealised model isolates the thermal wind as the source of instability?

A.The Eady model
B.The barotropic vorticity model, which was used for the earliest numerical weather forecasts made
C.The Ekman model
D.The Hadley model, in which a direct thermally driven cell transports heat from the equator polewards

Answer: A

Eady considered a uniformly stratified fluid with constant vertical shear between two rigid lids and showed that disturbances grow by drawing on the available potential energy of that shear. The shear is exactly the thermal wind. The barotropic model has no shear and hence no baroclinic instability, while the Ekman and Hadley models address friction and the meridional circulation respectively.

Discuss in Forum

78.

Which wavelength grows fastest in the Eady model?

A.About 1000 kilometres, which is the deformation radius in the mid-latitude troposphere at present
B.About 4000 kilometres
C.About 400 kilometres, which is comparable with the width of an individual frontal rain band observed
D.About 40000 kilometres

Answer: B

The Eady model gives a most unstable wavelength of roughly 4000 kilometres, close to the observed spacing of mid-latitude cyclones, and a growth rate corresponding to an e-folding time of about a day. The agreement with observation is what made the model so influential. The deformation radius is smaller by a factor of about four and sets the scale rather than the most unstable wavelength directly.

Discuss in Forum

79.

Which growth rate does the Eady model predict?

A.An e-folding time of a week
B.A growth rate that depends only on the latitude and not on the strength of the vertical wind shear
C.An e-folding time of about one day
D.An e-folding time of about one hour, which matches the development of an individual convective cell

Answer: C

The maximum growth rate is proportional to the shear divided by the buoyancy frequency, giving an e-folding time near 24 hours for typical mid-latitude values. That matches the observed pace at which cyclones develop from a barely visible wave to a mature system in two or three days. The rate depends strongly on the shear, which is the thermal wind, so it is not a function of latitude alone.

Discuss in Forum

80.

Which boundary condition does the Eady model impose?

A.A free surface at the top which is allowed to deform in response to the motion beneath it below
B.Periodic vertical boundaries
C.A radiation condition at the top so that wave energy may escape upward into the stratosphere above
D.Rigid lids at the top and bottom of the domain

Answer: D

Eady placed rigid horizontal boundaries at the ground and at the tropopause, which allows edge waves to exist at each and lets the pair interact to produce growth. The interaction of two counter-propagating edge waves is the cleanest available account of baroclinic instability. A free surface, periodicity or a radiation condition would each change the character of the solution, and the Charney model, which replaces the upper lid with an unbounded atmosphere on a beta plane, gives a somewhat different and more realistic answer at the cost of much greater complexity.

Discuss in Forum

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