A New Bulk Shallow-Cumulus Model and Implications for Penetrative Entrainment Feedback on Updraft Buoyancy

Abstract A new refinement of Albrecht et al.’s bulk model for shallow-cumulus convection is presented. It is used to illuminate fundamental aspects of oceanic shallow-cumulus boundary layer structure, including updraft buoyancy and vertical velocity scales, cumulus mass flux, temperature and humidity profiles, and trade-inversion height. The new model, like Albrecht et al.’s, includes a subcloud mixed layer and a cumulus layer with linear gradients of conserved thermodynamic variables, topped by a sharp capping inversion. Albrecht et al.’s model was not mathematically well posed, leading to an inconsistency between its heat and moisture balances at the inversion base. The new bulk model resolves this problem by diagnosing, rather than prognosing, the cumulus-layer gradients and introducing a penetrative entrainment closure to determine the growth of the cumulus layer into the overlying free troposphere. It uses more realistic assumptions about lateral cumulus entrainment and detrainment and a simplified s...