Questions: Thermal Wind Balance and the Relationship Between Temperature and Wind

Question 1

In winter, the temperature difference between the tropics and the poles is much larger than in summer. What does thermal wind balance predict about the jet stream?

• A. The jet stream weakens in winter because cold polar air reduces geostrophic wind speeds
• B. The jet stream intensifies in winter because the stronger pole-to-equator temperature gradient produces greater vertical wind shear, which accumulates with height into a stronger westerly maximum
• C. The jet stream strength is unrelated to temperature gradients — it depends only on upper-tropospheric pressure patterns
• D. The jet stream moves equatorward in winter and disappears in summer due to reduced Coriolis force

Answer: (B)

Thermal wind balance directly links the horizontal temperature gradient to vertical wind shear: a stronger temperature gradient produces stronger shear, meaning the westerly wind increases more rapidly with height. In winter, the equator-to-pole temperature contrast is greatest, so the thermal wind (the shear vector) is largest. This shear accumulates from the surface to the tropopause, producing the strongest jet streams of the year — often exceeding 200 km/h at tropopause level. In summer, the gradient weakens, the thermal wind weakens, and the jet relaxes.

Question 2

A warm air mass lies to the south and a cold air mass to the north over a mid-latitude region. Compared to the lower-tropospheric pressure gradient, what happens to the pressure gradient between the same two air masses at a higher pressure level?

• A. It weakens at higher levels because pressure decreases with altitude in both air masses equally
• B. It stays the same — horizontal temperature contrasts do not affect vertical pressure structure
• C. It strengthens at higher levels because warm air expands more vertically, creating greater height differences between the warm south and cold north at upper pressure surfaces
• D. It reverses — the cold air develops higher pressure at upper levels due to gravity pulling cold air downward

Answer: (C)

This is the hypsometric mechanism at the heart of thermal wind. Warm air is less dense and expands vertically: the same two pressure surfaces (say, 850 hPa and 500 hPa) are farther apart in warm air than in cold air. Over the warm south, the upper pressure surface is higher; over the cold north, it is lower. This creates a tilted upper pressure surface, which means a stronger pressure gradient at upper levels than at lower levels. The stronger gradient drives a stronger geostrophic wind — exactly the vertical wind shear that thermal wind balance describes.

Question 3

The 'thermal wind' is an actual wind that can be measured by a weather balloon at a specific pressure level.

• T. True
• F. False

Answer: False

The thermal wind is not an actual wind — it is the vector *difference* in geostrophic wind between two pressure levels. It is a measure of vertical wind shear, derived mathematically from the horizontal temperature gradient. You cannot fly through the thermal wind or measure it directly; you calculate it from temperature or thickness data. This is a common confusion: the name 'thermal wind' suggests a physical wind, but it is a diagnostic quantity describing how geostrophic winds change with height in a baroclinic atmosphere.

Question 4

If the atmosphere's temperature is perfectly uniform horizontally (no horizontal temperature gradient anywhere), thermal wind balance predicts that the geostrophic wind will not change with height.

• T. True
• F. False

Answer: True

The thermal wind equation states that vertical wind shear is proportional to the horizontal temperature gradient. If there is no horizontal temperature gradient, the thermal wind vector is zero — meaning no change in geostrophic wind with height. In such a barotropic atmosphere, the same geostrophic wind blows at every pressure level. Real atmospheres are never perfectly barotropic, but the concept is analytically important: it defines the baseline against which baroclinic (temperature-stratified) atmospheres are measured.

Question 5

Explain in physical terms why warm air to the south and cold air to the north produces westerly wind that increases with height in the Northern Hemisphere.

Model answer: Warm air is less dense and expands vertically, so the column of atmosphere between two pressure surfaces is thicker in the warm south than in the cold north. At the lower pressure surface, heights may be nearly flat, but at the upper pressure surface, the surface tilts downward from south (high) to north (low). This tilt creates a stronger southward pressure gradient aloft than at the surface. In the Northern Hemisphere, the Coriolis force deflects the geostrophic wind to the right of this gradient, producing a westerly wind. Because the tilt is greater at higher levels, the westerly wind is stronger at higher levels — vertical shear that increases with height.

This causal chain — temperature gradient → thickness gradient → upper-level pressure tilt → enhanced pressure gradient → stronger geostrophic wind — is the complete physical story of thermal wind. Understanding it mechanistically lets you predict seasonal and geographic jet stream behavior from first principles. The key conceptual step that students often miss is that the pressure gradient *changes with height* because of differential thermal expansion, not because of any wind force acting on the atmosphere.