A new method to derive water vapor supersaturation at cumulus cloud base from in situ measurements

Current in situ measurements of water vapor supersaturation ( S _v ) with respect to liquid water at cloud base are highly uncertain due to instrumental limitations. Consequently, S _v is commonly estimated using cloud microphysical models and parameterizations. Here, we derive S _v at warm cumulus cloud base from in situ measurements through calculations of the energy and water vapor budgets associated with cloud formation. The derived S _v provides a thermodynamic analogue to the supersaturation established in a cloud condensation nuclei (CCN) chamber, enabling direct comparison with independently measured CCN activation spectra below cloud base. To this end, we formulate the energy budget of a saturated rising air parcel at cloud base and treat the transition between saturated thermodynamic states locally as quasi-isobaric. Under these conditions, the latent heat ( Q ) released during condensational droplet growth is determined by the corresponding sensible enthalpy difference between the saturated-vapor and water vapor–liquid states. According to the first law of thermodynamics, Q is partitioned between the change in internal energy (Δ U ) and water vapor expansion work ( W _s ). Within this diagnostic framework, part of the condensational energy is, therefore, spent on W _s , reducing the amount of liquid water formed relative to the limiting case in which the entire condensational energy contributes to droplet growth. Accordingly, the cloud supersaturation ( S _c ) is diagnostically partitioned into liquid-phase ( S _l ) and vapor-phase ( S _v ) components based on the fractions of Q associated with Δ U and W _s , respectively. This framework enables the derivation of S _v from airborne cloud-base measurements through thermodynamic constraints on condensational energy partitioning. Here we use airborne measurements collected in growing convective cumuli over the Amazon Basin during the ACRIDICON-CHUVA campaign. Our results demonstrate that the derived cloud droplet number concentration as a function of S _v agrees, within measurement uncertainties, with S _v activation spectra of CCN measured below cloud base.