Geostrophic and Gradient Wind Questions and Answers

Answer: A

Geostrophic balance is the exact opposition of the horizontal pressure gradient force and the Coriolis force, and it is the leading order result of a scale analysis for small Rossby number. Because the Coriolis force is perpendicular to the velocity and the pressure gradient force is perpendicular to the isobars, the wind must blow along the isobars. The other options describe frictional flow near the ground, a combination that is not a balance at all, and the vertical hydrostatic relation, none of which is the horizontal balance being asked about here.

Answer: B

For the Coriolis force to oppose the pressure gradient force exactly, the velocity must be perpendicular to the pressure gradient, which means parallel to the isobars. Any cross-isobaric component would indicate that some third force, in practice friction, is present. The thirty degree figure belongs to the surface wind over rough terrain, a perpendicular wind describes the instant of release from rest before the Coriolis force has had time to act, and the angle has no dependence on latitude in the geostrophic case at all.

Answer: C

Buys Ballot's law states that in the northern hemisphere an observer standing with their back to the wind has lower pressure on their left, and the rule reverses in the southern hemisphere. It follows directly from the rightward Coriolis deflection: the force must point from low towards high pressure to oppose the pressure gradient, and it points to the right of the motion, so high pressure lies to the right. Reconstructing the law from the force balance is far more reliable than trying to remember it as an isolated fact.

Answer: D

On a constant pressure surface the geostrophic wind has magnitude \( |\nabla\Phi|/f \), with the wind directed along the height contours. Density has disappeared because pressure is being used as the vertical coordinate, which is the chief practical advantage of that choice. In height coordinates the equivalent expression is the pressure gradient divided by the product of density and \( f \), so the two forms agree but the pressure coordinate version is simpler and is what upper air charts are built around.

Answer: A

The geostrophic wind is proportional to the pressure gradient, so packing the isobars twice as closely doubles the wind. The absolute value of the pressure is irrelevant, since a uniform field of any magnitude exerts no force. Increasing the latitude increases the Coriolis parameter and therefore reduces the wind for a given gradient, and the depth of a layer plays no part in a purely horizontal balance. Reasoning from the formula rather than from intuition avoids the common mistake about absolute pressure.

Answer: B

Since the geostrophic wind equals the pressure gradient force divided by \( f \), and \( f \) increases with latitude, the same isobar spacing corresponds to a weaker wind nearer the pole. Physically, the stronger Coriolis force can balance the same pressure gradient at a lower speed. The effect is substantial in practice: the same spacing gives roughly forty per cent more wind at thirty degrees than at sixty, which forecasters allow for when reading charts spanning a wide range of latitude.

Answer: C

Dividing by a vanishing \( f \) would give an unbounded geostrophic wind, so the balance breaks down within roughly five degrees of the equator. Tropical pressure gradients are in fact very weak rather than strong, precisely because any appreciable gradient would immediately drive a strong ageostrophic response. Friction is no more important there than elsewhere in the free atmosphere. This breakdown is why numerical analysis and initialisation schemes must treat the tropics quite differently from mid-latitudes.

Answer: D

With \( f \) constant, the geostrophic wind is the gradient of geopotential rotated through ninety degrees and divided by \( f \), and the divergence of such a field vanishes identically. It follows that all horizontal divergence, and hence all vertical motion, is carried by the ageostrophic wind. The geostrophic wind certainly possesses vorticity, it is parallel to the isobars by construction, and its variation with height is the thermal wind, which is a separate relation with its own conditions.

Answer: A

Since mass continuity links horizontal divergence to vertical motion, and the geostrophic wind has no divergence on an f-plane, every cubic metre of ascent must be driven by the small ageostrophic residual. This is why a quantity roughly a tenth the size of the total wind receives so much attention in synoptic analysis. Vorticity is entirely compatible with zero divergence, and the flow does evolve, though the evolution too is driven by the ageostrophic part.

Answer: B

The ageostrophic wind is what remains when the geostrophic part is subtracted from the actual wind, and in mid-latitudes it is typically about ten per cent of the total. Small though it is, it carries the divergence, the vertical motion and the acceleration of the flow, so it is where the interesting dynamics lives. The second option describes only the frictional component near the ground, which is one contribution to the ageostrophic wind rather than the whole of it.