Thermal Wind Balance Questions and Answers

Answer: C

Barotropy means isobaric and isopycnal surfaces are parallel, so there is no horizontal temperature gradient on a pressure surface and the thermal wind vanishes. Baroclinicity is precisely the opposite case, in which the thermal wind is non-zero. The second statement therefore inverts the definition. Almost all interesting mid-latitude weather occurs in baroclinic conditions, which is why the barotropic case is treated mainly as a simplifying idealisation.

Answer: D

The hypsometric equation gives thickness as proportional to layer mean virtual temperature multiplied by the logarithm of the ratio of the bounding pressures, so the first statement is correct. The base pressure enters only through that logarithm, which is fixed once the two levels are chosen, so thickness varies with temperature alone for a given layer. That is what makes a thickness chart readable as a temperature chart.

Answer: A

The first two statements are correct, while the third inverts the definition: the thermal wind vanishes in a barotropic atmosphere and is non-zero in a baroclinic one. Confusing the two terms is the commonest error in this topic. A useful check is that baroclinic instability, the source of mid-latitude weather, requires a thermal wind and therefore requires baroclinicity by definition.

Answer: B

Thickness is a mass-weighted mean, so it conceals the vertical distribution and cannot give level by level temperatures, which makes the third statement false. The first two are correct. This limitation is exactly why a shallow warm layer aloft can defeat the 540 decametre rule, and why forecasters examine the full sounding rather than relying on a single bulk quantity.

Answer: C

The last pairing is wrong: barotropy means no vertical shear of the geostrophic wind, since the thermal wind vanishes. The other three are correctly matched. Setting the four terms out together makes the logical chain visible, from intersecting surfaces through a horizontal temperature gradient to a vertical shear, which is the whole content of thermal wind balance in one line.

Answer: D

A wind whose speed increases with height without turning has a thermal wind parallel to the flow, so there is certainly a thermal wind and the last pairing fails. The other three are correct for the northern hemisphere. Working through the four cases as a set clarifies that turning indicates advection while speed change alone indicates a gradient along the flow.

Answer: A

Friction is not part of the derivation: the relation follows from combining geostrophic and hydrostatic balance, and both of those require a non-zero Coriolis parameter. Friction does of course invalidate geostrophic balance within the boundary layer, but it enters through that route rather than as a separate condition. Distinguishing what a derivation actually uses from what happens to be true alongside it is a habit worth cultivating. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

Answer: B

The Ekman spiral arises from the balance between pressure gradient, Coriolis and frictional forces within the boundary layer, and has nothing to do with any horizontal temperature gradient. The other three are all direct consequences of the thermal wind relation. Both the spiral and the thermal wind describe wind turning with height, which is why the pair makes a useful test of whether the mechanisms have been kept distinct. Working one numerical case through both cases side by side fixes the distinction better than any rule of thumb.

Answer: C

Turning anticlockwise with height is backing, which places the thermal wind to the left of the lower wind and therefore implies cold advection in the northern hemisphere. No absolute temperatures are needed, only the sense of the turning, which is what makes this such a quick and useful check. The same profile in the southern hemisphere would indicate warm advection instead.

Answer: D

Thickness is proportional to layer mean virtual temperature, so a fall of 12 decametres corresponds to a cooling of roughly 6 kelvin averaged over the layer. This is a typical signature of cold advection behind a front. Humidity affects thickness only weakly through virtual temperature, and subsidence warms rather than cools, which would raise the thickness rather than lower it.