= Solution
Below <Lifting condensation level>[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 <Vapor pressure>[vapour pressure], and dissolved solute, which lowers it. Cooling generates <Atmospheric supersaturation>[supersaturation], while <condensation> onto the new <Cloud droplet>[droplets] consumes it. Their balance normally keeps in-cloud <relative humidity> close to, but not identically at, saturation. The activated <Number density>[droplet number] depends on the <aerosol> population and the maximum <Atmospheric supersaturation>[supersaturation] produced by the ascent.
Above <Lifting condensation level>[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,
$$
\Gamma_m\simeq\frac g{c_{p,d}}
\frac{1+L_vq_s/(R_dT)}{1+L_v^2q_s/(c_{p,d}R_vT^2)}.
$$
A closed adiabatic parcel conserves total water $q_t=q_v+q_l$ and approximately its <Entropy>[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 <Cloud-droplet activation>[activation] is complete, assuming nearly fixed <Number density>[droplet number] per volume gives increasing <Cloud droplet>[droplet] size as condensate accumulates. <Fluid entrainment>[Entrainment], continued <Cloud-droplet activation>[activation], <collision-coalescence> and <atmospheric precipitation> can all violate that simplified description; they are excluded from the stated retrieval model.
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