Thermal wind

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In atmospheric science, the thermal wind is the vector difference between the geostrophic wind at upper altitudes minus that at lower altitudes in the atmosphere. It is the hypothetical vertical wind shear that would exist if the winds obey geostrophic balance in the horizontal, while pressure obeys hydrostatic balance in the vertical. The combination of these two force balances is called thermal wind balance, a term generalizable also to more complicated horizontal flow balances such as gradient wind balance.

Since the geostrophic wind at a given pressure level flows along geopotential height contours on a map, and the geopotential thickness of a pressure layer is proportional to virtual temperature, it follows that the thermal wind flows along thickness or temperature contours. For instance, the thermal wind associated with pole-to-equator temperature gradients is the primary physical explanation for the jet stream in the upper half of the troposphere, which is the atmospheric layer extending from the surface of the planet up to altitudes of about 12–15 km.

Mathematically, the thermal wind relation defines a vertical wind shear – a variation in wind speed or direction with height. The wind shear in this case is a function of a horizontal temperature gradient, which is a variation in temperature over some horizontal distance. Also called baroclinic flow, the thermal wind varies with height in proportion to the horizontal temperature gradient. The thermal wind relation results from hydrostatic balance and geostrophic balance in the presence of a temperature gradient along constant pressure surfaces, or isobars.

The term thermal wind is often considered a misnomer, since it really describes the change in wind with height, rather than the wind itself. However, one can view the thermal wind as a geostrophic wind that varies with height, so that the term wind seems appropriate. In the early years of meteorology, when data was scarce, the wind field could be estimated using the thermal wind relation and knowledge of a surface wind speed and direction as well as thermodynamic soundings aloft.^[1] In this way, the thermal wind relation acts to define the wind itself, rather than just its shear. Many authors retain the thermal wind moniker, even though it describes a wind gradient, sometimes offering a clarification to that effect.