A Refined Zero-Buoyancy Plume Model for Large-Scale Atmospheric Profiles and Anvil Clouds in Radiative-Convective Equilibrium

A simple analytical model, the zero-buoyancy plume (ZBP) model, has been proposed to understand how small-scale processes such as plume-environment mixing and evaporation affect the steady-state structure of the atmosphere. In this study, we refine the ZBP model to achieve self-consistent analytical solutions for convective mass flux, addressing the inconsistencies in previous solutions. Our refined ZBP model reveals that increasing plume-environment mixing can increase upper-troposphere mass flux through two pathways: increased cloud evaporation or reduced atmospheric stability. To validate these findings, we conducted small-domain convection-permitting Radiative-Convective Equilibrium simulations with horizontal resolutions ranging from 4 km to 125 m. As a proxy for plume-environment mixing strength, the diagnosed entrainment rate increases with finer resolution. Consistent with a previous study, we observed that both anvil cloud fraction and upper-troposphere mass flux increase with higher resolution. Analysis of the clear-sky energy balance in the simulations with two different microphysics schemes identified both pathways proposed by the ZBP model. The dominant pathway depends on the relative strengths of evaporation cooling and radiative cooling in the environment. Our work provides a refined simple framework for understanding the interaction between small-scale convective processes and large-scale atmospheric structure.