The height of the tropopause responds to the tropospheric column such that:
Why
Warm air is less dense and the column expands vertically, so the level at which the temperature stops falling is reached higher up: over the tropics and in warm air masses the tropopause is high (and cold), while in cold polar air it is low (and relatively warm). Across a front the tropopause height changes sharply, and this break in the tropopause is where jet streams are found. Above a cold, low tropopause the air at a given flight level may actually be warmer than above a high tropopause. Reference: syllabus 20.6.4; ICAO Doc 8896; WMO.