Geostrophic and Thermal Wind Balance

On scales larger than a thunderstorm, the atmosphere settles into a near-balance between forces, so that knowing the pressure field and how temperature varies with height lets a forecaster reconstruct the wind itself.

Definition

Geostrophic balance is the approximate equality of the horizontal pressure-gradient force and the Coriolis force; the thermal wind is the resulting change of the geostrophic wind with height, which is proportional to the horizontal temperature gradient.

Scope

This topic covers geostrophic balance between the pressure-gradient and Coriolis forces, hydrostatic balance in the vertical, the thermal wind relation linking the vertical shear of the geostrophic wind to horizontal temperature gradients, and the related gradient and cyclostrophic balances for curved flow.

Core questions

• How does the balance of pressure-gradient and Coriolis forces set the large-scale wind?
• Why does horizontal temperature contrast imply vertical wind shear?
• When does balanced flow break down, and what follows?
• How do curvature and centrifugal effects modify geostrophic balance?

Key theories

Geostrophic approximation

For motions that are large in scale and slow to change, the acceleration is small compared with the dominant forces, so the wind is well approximated by the geostrophic value blowing parallel to the isobars.

Thermal wind relation

Combining geostrophic and hydrostatic balance shows that the vertical shear of the geostrophic wind is set by the horizontal temperature gradient, explaining why the strong upper-level jets sit above sharp temperature contrasts.

Mechanisms

Where air piles up as high pressure, the pressure-gradient force pushes it toward lower pressure, but Earth's rotation deflects the moving air until the Coriolis force balances the push and the wind flows along the isobars. Because pressure surfaces tilt more steeply where the air below is cold and dense, this geostrophic wind must change with height in proportion to the horizontal temperature gradient, the thermal wind, which is why the jet stream lies above the strongest temperature contrasts.

Clinical relevance

Geostrophic and thermal wind balance let forecasters infer winds aloft from temperature and pressure analyses, locate jet streams, and diagnose where the atmosphere is departing from balance, the regions where rising motion and weather development are concentrated.

History

Buys Ballot's nineteenth-century empirical law that wind blows with low pressure to the left in the Northern Hemisphere foreshadowed geostrophic balance; the formalization of geostrophic and thermal wind relations in the early twentieth century, and their central role in Charney's scale analysis, made them cornerstones of dynamic meteorology.

Key figures

• Christophe Buys Ballot
• Carl-Gustaf Rossby
• Jule Charney

Seminal works

• holton2013
• martin2006

Frequently asked questions

If I know the pressure pattern, can I estimate the wind?

Yes. On large scales the geostrophic relation gives the wind speed from how tightly the isobars are packed and its direction parallel to them, with low pressure to the left in the Northern Hemisphere.

Why is the jet stream located where it is?

The thermal wind relation ties the increase of wind with height to horizontal temperature contrasts, so the fastest upper-level winds, the jet stream, form above the sharp boundary between warm and cold air masses.