 Precipitation-driven foehn warming

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.