A Cumulus Parameterization with State-Dependent Entrainment Rate. Part I: Description and Sensitivity to Temperature and Humidity Profiles

A new cumulus parameterization is developed for which an entraining plume model is adopted. The lateral entrainment rate varies vertically depending on the surrounding environment. Two different formulations are examined for the rate. The cumulus ensemble is spectrally represented according to the updraft velocity at cloud base. Cloud-base mass flux is determined with prognostic convective kinetic energy closure. The entrainment rate tends to be large near cloud base because of the small updraft velocity near that level. Deep convection tends to be suppressed when convective available potential energy is small because of upward reduction of in-cloud moist static energy. Dry environmental air significantly reduces in-cloud humidity mainly because of the large entrainment rate in the lower troposphere, which leads to suppression of deep convection, consistent with observations and previous results of cloud-resolving models. The change in entrainment rate has the potential to influence cumulus convection through many feedbacks. The results of an atmospheric general circulation model are improved in both climatology and variability. A representation of the South Pacific convergence zone and the double intertropical convergence zone is improved. The moist Kelvin waves are represented without empirical triggering schemes with a reasonable equivalent depth. A spectral analysis shows a strong signal of the Madden-Julian oscillation. The scheme provides new insights and better understanding of the interaction between cumuli and the surrounding environment.