concept

Thermal wind balance

What you get when geostrophic balance is combined with hydrostatic balance: wherever a horizontal temperature gradient exists, the wind speed MUST change with height. The reason is homely — cold air is denser, so its pressure surfaces stack closer together, which makes the pressure gradient steeper aloft than near the ground, and the geostrophic wind has to strengthen to match. This is why jets sit near the tropopause: the equator-to-pole temperature difference accumulates eastward shear all the way up, so the wind only peaks where the temperature gradient runs out.