Near-by a zone of horizontal temperature gradient the geostrophic wind must have a vertical wind shear. The geostrophic wind is proportional to the horizontal pressure gradient and in accordance to the hydrostatic equation the isobars show different slopes in different altitudes. Both factors lead to a vertical wind shear. The rate of change of the vertical wind shear is called thermal wind. That means that the thermal wind refers to the difference between the geostrophic winds at different levels. The thermal wind blows parallel to the isotherms with warm air on the right and cold air on the left side of the streaming (Northern Hemisphere). By comparision of the wind directions in two levels we can conclude that we have warm air advection if the wind turns to the right (clockwise) with increasing height. Cold air advection is associated with its turning to the left (counter-clockwise).
A typical example for an increasing vertical temperature gradient is a clockwise turning of the wind (warm air advection) in low levels and neglectable or counter-clockwise turning above (small or cold air advection).
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