Foehn wind

A relatively warm, dry downslope wind on the lee side of a mountain. Condensation and condensate removal during ascent can produce precipitation-driven foehn warming; isentropic foehn drawdown, turbulent mixing and radiative warming can also contribute. Rainfall is therefore not a necessary condition for every foehn event. The atmosphere's upstream stratification, moisture and flow over or around the mountain determine the contributing mechanisms.^[ref]

Mountain blocking can prevent low-level upstream air from crossing the barrier while air from higher levels passes over and descends. In stable stratification that elevated source air has higher potential temperature; adiabatic descent can bring it into a lee valley warmer than the blocked low-level air. This source-air change permits a dry foehn without requiring condensation and rainout along the arriving parcel's path.

In the classical idealized parcel path, ascend dry adiabatically to condensation height $z_c$, continue at constant moist lapse rate ${\Gamma }_m$ to height $H>z_c$, lose condensate, then descend at dry lapse rate ${\Gamma }_d$ to the initial height. Adding the temperature changes gives the title. Complete condensate removal and an unsaturated descent are essential assumptions. A reversible dry ascent and descent with the same source air instead gives no net temperature increase at the same pressure.