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Geostrophic and Gradient Wind Questions and Answers

71.

Arrange the following balances in order of increasing Rossby number of the flow they describe.

1. Cyclostrophic

2. Geostrophic

3. Gradient wind

4. Inertial

Select the correct sequence.

Answer: C

Geostrophic balance describes the smallest Rossby number, gradient wind balance a somewhat larger one where curvature matters, inertial motion a case where the pressure gradient has dropped out, and cyclostrophic balance the largest where Coriolis is negligible, giving 2, 3, 4, 1. Arranging them this way shows the family as a progression along a single parameter rather than as four unrelated results.

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72.

Match each balance with the force it omits.

List I

A. Geostrophic

B. Cyclostrophic

C. Inertial

List II

P. centrifugal

Q. Coriolis

R. pressure gradient

Select the correct match.

Answer: D

Geostrophic balance omits the centrifugal term, cyclostrophic balance omits the Coriolis term, and inertial motion omits the pressure gradient force. Gradient wind balance, which omits none of the three, completes the family. Presented as a table of omissions the four balances become a single coherent scheme rather than four separate facts to be memorised independently.

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73.

Match each wind with what it describes.

List I

A. Geostrophic

B. Thermal

C. Ageostrophic

List II

P. vertical shear of the geostrophic wind

Q. two-force balanced flow

R. departure from balance

Select the correct match.

Answer: A

The geostrophic wind is the two-force balanced flow, the thermal wind is the vertical shear of that flow implied by a horizontal temperature gradient, and the ageostrophic wind is the departure of the actual wind from balance. The three together give a complete description of the horizontal wind at synoptic scales, with the small third member carrying the vertical motion and the evolution.

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Answer: B

Contour spacing gives the geopotential gradient and the latitude gives the Coriolis parameter, and those two quantities determine the geostrophic wind completely. Density has vanished because the chart is drawn on a pressure surface, so temperature is not required. The surface wind and the pressure tendency give other information: the former reflects friction and the latter is the source of the isallobaric wind.

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Answer: C

A pressure gradient is a spatial derivative, so it requires simultaneous readings from several stations rather than a time series from one. A barograph gives the local tendency, which is a quite different quantity used for the isallobaric wind. A radiosonde gives a vertical profile at one location. Inferring the gradient from the wind reverses the usual logic and would be circular if the balance is what is being tested. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

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Answer: D

Differentiation amplifies small-scale error, so a height analysis accurate to a few decametres can give a geostrophic wind in error by several metres per second. This is why modern analysis systems assimilate wind observations directly rather than deriving the wind from the mass field. Both speed and direction are affected. The general point, that derivatives amplify noise, recurs throughout the diagnosis of atmospheric fields. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

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Answer: A

Because the geostrophic relation involves a spatial derivative, small errors in the mass field produce large errors in the derived wind, whereas a direct measurement carries only its own instrumental error. This is why wind profilers, aircraft reports and satellite-derived winds are so valuable in data assimilation. Cost and latitude are not the relevant considerations, and pressure observations are in fact widely available. Naming the cost of a choice alongside its benefit is what turns a fact into a design decision.

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Answer: B

A small radius of curvature makes the centrifugal term comparable with the other two, so the Rossby number rises and gradient wind balance must replace geostrophic balance. Broad weak systems and straight flow are precisely where geostrophy works best. Alignment of contours with isotherms says something about the thermal wind rather than about the validity of the geostrophic approximation at a single level.

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Answer: C

Evaluating the three terms and taking their sum gives the net unbalanced force, which is what accelerates the parcel. The Rossby number indicates whether balance is likely rather than measuring the departure in a particular case. The Richardson number concerns stratification and shear, and the ageostrophic ratio measures departure from geostrophic rather than from gradient balance, which is a different question.

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Answer: D

An unbalanced state radiates inertia-gravity waves that carry the imbalance away, leaving a balanced residual on a timescale of hours. This geostrophic adjustment is why the atmosphere is observed to remain close to balance almost everywhere despite continual forcing. Friction and diabatic heating act far more slowly, and baroclinic instability generates rather than removes departures from the zonal state.

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