Geostrophic and Gradient Wind Questions and Answers

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.

Answer: D

Inverting a potential vorticity distribution to recover the wind and mass fields requires a balance condition, because potential vorticity alone does not determine the division between balanced and unbalanced motion. Geostrophic, gradient wind or nonlinear balance may be used depending on the accuracy required. Hydrostatic balance is necessary but far from sufficient, and cyclostrophic balance is inappropriate at synoptic scales. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Answer: A

A compact upper level potential vorticity anomaly induces a cyclonic circulation that decays downward over a depth set by the ratio of the Coriolis parameter to the buoyancy frequency times the horizontal scale. This action at a distance is the basis of the modern potential vorticity view of cyclogenesis, in which an upper anomaly overtakes a surface thermal anomaly and the two amplify each other.

Answer: B

The Rossby depth scale, equal to the horizontal scale multiplied by \( f/N \), determines how far the induced circulation penetrates. A larger anomaly therefore reaches further, and a more strongly stratified atmosphere confines it more closely. This is the vertical counterpart of the deformation radius and gives a clean physical criterion for whether an upper anomaly can interact with the surface at all.

Answer: C

When an upper level potential vorticity anomaly moves over a low level warm anomaly, each induces a circulation that reinforces the other, and the pair amplifies while remaining vertically tilted against the shear. This mutual amplification is the potential vorticity statement of baroclinic instability. Merging, friction and wave radiation all describe processes that occur but none of them is the mechanism of rapid development. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

Answer: D

Growth requires the upper anomaly to lie upstream of the surface anomaly, which in westerly flow means a westward tilt with height. A vertically stacked pair is the mature, non-growing configuration reached at the end of development. Eastward tilt corresponds to decay, with the disturbance giving energy back to the mean flow. This tilt criterion is one of the most useful practical signatures of an actively deepening system on a chart. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

Answer: A

In a deepening system the upper trough lies to the west of the surface low, so the surface feature is downstream, and the two become vertically aligned only as the system matures and stops deepening. This is the classical rule of thumb from synoptic analysis and it matches the tilt requirement derived from potential vorticity thinking, which is a satisfying convergence of empirical practice and theory.

Answer: B

A westward tilt with height allows warm air to rise and cold air to sink in a systematic way, converting the available potential energy of the horizontal temperature gradient into kinetic energy of the disturbance. This is the energetic statement of baroclinic instability. An eastward tilt reverses the conversion, which is why decaying systems adopt that configuration and why the tilt is such a reliable diagnostic of the stage of development. Naming the cost of a choice alongside its benefit is what turns a fact into a design decision.

Answer: C

Within the lowest kilometre, turbulent stress transmits surface drag into the flow, adding a third force and turning the wind across the isobars towards low pressure. The geostrophic wind remains a useful reference against which the actual wind is compared, but it is no longer a good approximation to it. The Coriolis parameter has no height dependence, and pressure is measured particularly well at the surface.

Answer: D

Boundary layer parameterisations often express the surface stress as a coefficient times the square of the geostrophic wind, since the geostrophic wind is known from the pressure field while the surface wind is not. The coefficient depends on roughness and stability. The other options describe the Ekman pumping relation, the cross-isobaric angle relation and a purely descriptive connection, none of which is what this coefficient does. The shared properties explain why these belong to one family, and the differences explain why more than one exists.