Energetically Stringent Quantification of Water Vapor Supersaturation at Cloud Base

Abstract. We quantify water vapor supersaturation (S_v) at warm cloud base by describing the ascent of a saturated (cloudy) air parcel as a reversible cloud-adiabatic process. In this framework, the parcel’s isobaric enthalpy is conserved along the ascent. The latent heat release (Q) during condensational growth of cloud condensation nuclei (CCN) and droplets is internally redistributed according to the first law of thermodynamics, such that the energy balance is partitioned between the parcel’s internal energy (U) and the saturation work of water vapor (W_s). We find that the fraction of Q associated with ∆U and W_s corresponds to liquid-phase supersaturation (S_l) and S_v, respectively. Closure analyses of airborne measurements at cloud bases of growing cumuli over the Amazon Basin demonstrate that the droplet number concentration N_d scales with S_v and agrees within the uncertainty range with the CCN(S_v) activation spectra measured below cloud base. The new methodology allows the calculation of N_d(S_v) spectra from airborne measurements at cloud bases. Our results suggest that adiabatic models assuming full conversion of phase-change energy into condensational growth tend to overestimate the liquid water content. During the cloud parcel ascent, a finite fraction of this energy is expended as vapor expansion work, reducing the amount available for vapor-to-liquid conversion. Neglecting this energetic partition leads to an overestimation of the latent heat released during condensational growth of particles, cloud parcel buoyancy and vertical acceleration.