Geostrophic and Gradient Wind Questions and Answers

Q: Which name is given to a chart of geopotential height on a pressure surface?

An upper air or constant pressure chart contours the geopotential height of a chosen pressure surface, most often 850, 700, 500, 300 or 250 hectopascals. The contours act exactly as isobars do on a surface chart, so the geostrophic wind is read from their spacing and blows along them. A thickness chart shows the difference between two such surfaces, a surface chart uses mean sea level pressure, and a cross section is a vertical rather than a horizontal display. Knowing which chart answers which question is a basic operational skill.

Q: Which pressure level is conventionally used to represent the mid-troposphere?

The 500 hectopascal surface lies at about 5.5 kilometres, with half the mass of the atmosphere below it, which makes it the natural single level to represent the steering flow. The 850 level is used for low level thermal advection, 250 or 300 for the jet stream and 1000 for surface conditions. The special status of 500 follows directly from hydrostatic balance and is worth understanding rather than merely accepting, since it explains why so much synoptic reasoning is conducted at that one level.

Q: Which level is normally used to examine the jet stream?

The jet core sits near the tropopause, around 250 to 300 hectopascals in mid-latitudes, so charts at those levels display it best. Lower levels show progressively weaker westerlies because the thermal wind has not yet accumulated. The choice of level therefore follows directly from the thermal wind relation rather than being an arbitrary convention, and it shifts with season and latitude as the tropopause height changes. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

Q: Which quantity does the spacing of thickness contours give?

Because thickness is proportional to layer mean temperature, and the thermal wind is proportional to the horizontal temperature gradient, the spacing of thickness contours gives the thermal wind directly. The thermal wind blows along the thickness contours with low thickness, and therefore cold air, on the left in the northern hemisphere. This makes a thickness chart a direct display of the vertical shear, which is why it is such a useful analytical tool.

Q: Which rule places the thermal wind relative to the thickness contours?

The thermal wind obeys the same geometry as the geostrophic wind, with thickness playing the role of height, so it blows along the thickness contours with low values on the left in the northern hemisphere. Since low thickness means cold air, this is the familiar statement that the thermal wind blows with cold air on its left. The rule reverses in the southern hemisphere along with the sign of the Coriolis parameter, which is worth checking explicitly. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Q: Which construction gives the wind at an upper level from the surface wind?

The thermal wind is by definition the vector difference between the geostrophic winds at two levels, so adding it to the lower level wind gives the upper level wind. Drawing this triangle on a chart is the classical way of estimating upper winds from a surface analysis and a thickness field. The density ratio and the cross-isobaric rotation address quite different questions, and no averaging construction gives the correct result. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Q: Which situation gives a thermal wind of zero?

A barotropic layer has no horizontal temperature gradient, so the thermal wind vanishes and the geostrophic wind is the same at top and bottom. Strong wind with no directional change still implies a thermal wind if the speed changes with height. Perpendicular isotherms and contours describe strong thermal advection rather than the absence of a thermal wind, which is very nearly the opposite of the situation described. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

Q: Which term describes a layer in which the wind changes direction but not speed with height?

If the wind turns without changing speed, the thermal wind is perpendicular to the mean wind, which means the isotherms are perpendicular to the flow and thermal advection is at its maximum. Veering then means warm advection and backing cold advection. A barotropic layer has no directional change at all, and neutral stability and cyclostrophic balance concern quite different aspects of the flow.

Q: Which practical use has the geostrophic momentum approximation?

Replacing the actual momentum by the geostrophic momentum in the acceleration term gives the semi-geostrophic equations, which describe frontogenesis far better than the quasi-geostrophic system does. The cross-frontal ageostrophic circulation is retained and the fronts sharpen realistically. Coriolis is certainly retained, and neither gravity wave filtering nor density removal is what the approximation accomplishes. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

Q: Which deficiency of quasi-geostrophic theory does the semi-geostrophic system address?

Quasi-geostrophic theory advects by the geostrophic wind alone, which cannot produce the collapse to a genuine discontinuity that real frontogenesis approaches. The semi-geostrophic system includes the ageostrophic advection and reproduces frontal collapse in finite time. Vertical motion is present in quasi-geostrophic theory through the omega equation, and the beta effect can be retained if desired.

91.

Which name is given to a chart of geopotential height on a pressure surface?

A.A cross section, which displays the vertical structure of the atmosphere along a chosen line on the map
B.A constant pressure chart
C.A surface synoptic chart, on which mean sea level pressure is analysed with isobars drawn across it
D.A thickness chart

Answer: B

An upper air or constant pressure chart contours the geopotential height of a chosen pressure surface, most often 850, 700, 500, 300 or 250 hectopascals. The contours act exactly as isobars do on a surface chart, so the geostrophic wind is read from their spacing and blows along them. A thickness chart shows the difference between two such surfaces, a surface chart uses mean sea level pressure, and a cross section is a vertical rather than a horizontal display. Knowing which chart answers which question is a basic operational skill.

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92.

Which pressure level is conventionally used to represent the mid-troposphere?

A.250 hectopascals
B.1000 hectopascals, which is used to represent conditions at or very near to mean sea level itself
C.500 hectopascals
D.850 hectopascals, which lies just above the boundary layer over most lowland areas of the world

Answer: C

The 500 hectopascal surface lies at about 5.5 kilometres, with half the mass of the atmosphere below it, which makes it the natural single level to represent the steering flow. The 850 level is used for low level thermal advection, 250 or 300 for the jet stream and 1000 for surface conditions. The special status of 500 follows directly from hydrostatic balance and is worth understanding rather than merely accepting, since it explains why so much synoptic reasoning is conducted at that one level.

Discuss in Forum

93.

Which level is normally used to examine the jet stream?

A.500 hectopascals, which is the level conventionally used to represent the flow in the mid-troposphere
B.850 hectopascals
C.700 hectopascals, which is often chosen for examining vertical motion and the depth of cloud layers
D.250 hectopascals

Answer: D

The jet core sits near the tropopause, around 250 to 300 hectopascals in mid-latitudes, so charts at those levels display it best. Lower levels show progressively weaker westerlies because the thermal wind has not yet accumulated. The choice of level therefore follows directly from the thermal wind relation rather than being an arbitrary convention, and it shifts with season and latitude as the tropopause height changes. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

Discuss in Forum

94.

Which quantity does the spacing of thickness contours give?

A.The thermal wind
B.The geostrophic wind at the mid-point of the layer whose thickness the chart has been drawn for
C.The vertical velocity
D.The rate at which the mean temperature of the layer is changing with the passage of time at a point

Answer: A

Because thickness is proportional to layer mean temperature, and the thermal wind is proportional to the horizontal temperature gradient, the spacing of thickness contours gives the thermal wind directly. The thermal wind blows along the thickness contours with low thickness, and therefore cold air, on the left in the northern hemisphere. This makes a thickness chart a direct display of the vertical shear, which is why it is such a useful analytical tool.

Discuss in Forum

95.

Which rule places the thermal wind relative to the thickness contours?

A.Across them at an angle of about thirty degrees which increases as the layer becomes deeper still
B.Along them with low thickness on the left in the northern hemisphere
C.Across them from high thickness towards low thickness following the temperature gradient directly
D.Along them with low thickness on the right

Answer: B

The thermal wind obeys the same geometry as the geostrophic wind, with thickness playing the role of height, so it blows along the thickness contours with low values on the left in the northern hemisphere. Since low thickness means cold air, this is the familiar statement that the thermal wind blows with cold air on its left. The rule reverses in the southern hemisphere along with the sign of the Coriolis parameter, which is worth checking explicitly. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Discuss in Forum

96.

Which construction gives the wind at an upper level from the surface wind?

A.Rotating the surface wind through the cross-isobaric angle appropriate to the roughness of the surface
B.Taking the geometric mean of the surface wind and the wind observed at the top of the boundary layer
C.Adding the thermal wind vector to the surface geostrophic wind
D.Multiplying the surface wind by the ratio of the densities at the two levels being considered here

Answer: C

The thermal wind is by definition the vector difference between the geostrophic winds at two levels, so adding it to the lower level wind gives the upper level wind. Drawing this triangle on a chart is the classical way of estimating upper winds from a surface analysis and a thickness field. The density ratio and the cross-isobaric rotation address quite different questions, and no averaging construction gives the correct result. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Discuss in Forum

97.

Which situation gives a thermal wind of zero?

A.A layer in which the geostrophic wind is very strong but does not change its direction with height
B.A layer with strong shear
C.A layer in which the isotherms are perpendicular to the height contours throughout its whole depth
D.A barotropic layer

Answer: D

A barotropic layer has no horizontal temperature gradient, so the thermal wind vanishes and the geostrophic wind is the same at top and bottom. Strong wind with no directional change still implies a thermal wind if the speed changes with height. Perpendicular isotherms and contours describe strong thermal advection rather than the absence of a thermal wind, which is very nearly the opposite of the situation described. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

Discuss in Forum

98.

Which term describes a layer in which the wind changes direction but not speed with height?

A.Pure thermal advection
B.Barotropic, since the magnitude of the geostrophic wind is unchanged between the top and the base
C.Neutral stability
D.Cyclostrophic, because the change of direction implies curvature of the trajectory followed by parcels

Answer: A

If the wind turns without changing speed, the thermal wind is perpendicular to the mean wind, which means the isotherms are perpendicular to the flow and thermal advection is at its maximum. Veering then means warm advection and backing cold advection. A barotropic layer has no directional change at all, and neutral stability and cyclostrophic balance concern quite different aspects of the flow.

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99.

Which practical use has the geostrophic momentum approximation?

A.It allows the pressure gradient force to be computed without knowing the density of the air present
B.It simplifies frontal dynamics while retaining the ageostrophic circulation
C.It removes the Coriolis force entirely so that the equations become those of a non-rotating fluid
D.It filters gravity waves

Answer: B

Replacing the actual momentum by the geostrophic momentum in the acceleration term gives the semi-geostrophic equations, which describe frontogenesis far better than the quasi-geostrophic system does. The cross-frontal ageostrophic circulation is retained and the fronts sharpen realistically. Coriolis is certainly retained, and neither gravity wave filtering nor density removal is what the approximation accomplishes. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

Discuss in Forum

100.

Which deficiency of quasi-geostrophic theory does the semi-geostrophic system address?

A.Vertical motion is absent
B.The Coriolis parameter is treated as constant so that Rossby waves cannot propagate in the system
C.Fronts do not become sharp enough
D.Gravity waves are retained and so impose a severe restriction on the numerical time step available

Answer: C

Quasi-geostrophic theory advects by the geostrophic wind alone, which cannot produce the collapse to a genuine discontinuity that real frontogenesis approaches. The semi-geostrophic system includes the ageostrophic advection and reproduces frontal collapse in finite time. Vertical motion is present in quasi-geostrophic theory through the omega equation, and the beta effect can be retained if desired.

Discuss in Forum

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