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The difference between air temperature and its dew point. For unsaturated air it is positive. Near terrestrial surface conditions, a closed ascending parcel's lifting condensation level is approximately $125\mathrm{m}{\mathrm{K}}^{-1}$ times this difference, because its temperature decreases about $8\mathrm{K}\mathrm{k}{\mathrm{m}}^{-1}$ faster than its dew point.

A foehn wind is relatively warm, dry downslope air on a mountain's lee side. In the classical condensation pathway, ascending windward air expands and cools at the dry adiabatic lapse rate until the lifting condensation level. Condensation then releases latent heat, reducing the cooling rate to the moist adiabatic lapse rate. Atmospheric precipitation removes condensate, and the descending parcel warms by compression at approximately the dry rate. Its relative humidity falls.

For equal starting and finishing heights, complete condensate removal and a constant moist lapse rate above condensation height $z_c$, the precipitation-driven foehn warming isHere $H>z_c$ is the parcel's maximum height and ${\Gamma }_d>{\Gamma }_m$. The warming is adiabatic compression during descent, not heating by friction. Without condensation or a difference in source air, a reversible dry parcel returning to its original height would regain its original temperature.

Precipitation is not essential to every foehn event. Isentropic foehn drawdown can bring air of higher potential temperature from aloft down the lee slope; turbulent mixing and extra solar heating beneath clear skies can also contribute. The sketch shows the classical rainout pathway rather than asserting a unique mechanism.^[ref]

Below cloud base, an initially unsaturated closed parcel expands as ambient pressure falls. In the absence of heat exchange its temperature falls approximately at the dry adiabatic lapse rate $g/c_{p,d}$. Its vapour mixing ratio is conserved, but its saturation mixing ratio decreases strongly as it cools. Hence relative humidity rises until the lifting condensation level is reached. The density normally decreases through expansion; the environmental profile determines the parcel's buoyancy and thus whether ascent can continue.

Near saturation, slight atmospheric supersaturation permits suitable cloud condensation nuclei to activate. Köhler theory describes the competition between curvature, which raises equilibrium vapour pressure, and dissolved solute, which lowers it. Cooling generates supersaturation, while condensation onto the new droplets consumes it. Their balance normally keeps in-cloud relative humidity close to, but not identically at, saturation. The activated droplet number depends on the aerosol population and the maximum supersaturation produced by the ascent.

Above cloud base, condensation lowers the vapour content and raises the liquid-water content. The latent heat released partly offsets expansion cooling, so the moist adiabat has a smaller lapse-rate magnitude than the dry one. In a dilute approximation,A closed adiabatic parcel conserves total water $q_t=q_v+q_l$ and approximately its moist entropy; retaining condensate makes this a reversible-cloud idealization, rather than a precipitating pseudoadiabat. In a shallow cloud, the saturation-mixing-ratio decrease and slow density variation yield nearly constant condensation per height, so liquid-water content is approximately linear above base. Once activation is complete, assuming nearly fixed droplet number per volume gives increasing droplet size as condensate accumulates. Entrainment, continued activation, collision-coalescence and atmospheric precipitation can all violate that simplified description; they are excluded from the stated retrieval model.

At the lifting condensation level, the parcel temperature first equals its dew point. For $z/H\ll 1$, the first-order Taylor expansion gives $T_D\simeq T_{D,s}(1-z/H)$. Equating this with the dry-adiabatic process result givesNear terrestrial surface temperatures, $T_{D,s}/H\simeq 1.7$–$1.9\mathrm{K}\mathrm{k}{\mathrm{m}}^{-1}$, whereas ${\Gamma }_d\simeq 9.8\mathrm{K}\mathrm{k}{\mathrm{m}}^{-1}$. ConsequentlyUse absolute temperature for $T_{D,s}/H$. The temperature difference can be evaluated in kelvins or degrees Celsius, whose increments agree. The coefficient is an approximate near-surface terrestrial value, not independent of composition or ambient conditions for all atmospheres.

The dew-point depression is $6\mathrm{K}$, soKeeping $T_{D,s}=276.15\mathrm{K}$, $H\simeq 158.5\mathrm{km}$ and $c_p=1004\mathrm{J}\mathrm{k}{\mathrm{g}}^{-1}{\mathrm{K}}^{-1}$ gives approximately $747\mathrm{m}$, consistent with the rounded estimate.

The real cloud base can differ because entrainment changes the parcel's atmospheric mixing ratio and temperature, surface humidity varies, and the environmental pressure profile need not match the assumed parcel profile. Finite cloud-droplet activation requires some atmospheric supersaturation, so the first visible cloud droplets need not occur exactly at the thermodynamic lifting condensation level. A parcel must also actually be lifted that far; environmental static stability can prevent this. The constant-latent heat and first-order Taylor expansion approximations produce smaller numerical differences.