According to the convective quasi-equilibrium paradigm, moist convection may be viewed as acting to rapidly remove conditional instability that is produced by large-scale uplift or radiative processes. Indeed, the convective mass flux within climate models is often parameterised to be directly dependent on measures of conditional instability such as the convective available potential energy (CAPE). Observationally, however, tropical precipitation has only a weak relationship to instability, and it is instead highly correlated with the environmental humidity. For instance, recent observational analyses have revealed that while CAPE peaks when the free troposphere is relatively dry, the highest daily precipitation rates are observed in regions where the free troposphere is close to saturation.

Here, we seek to untangle the physical mechanisms that lead to the observed relationships between convection, humidity and instability in the tropics. We construct a simple bulk-plume model for an ensemble of convective clouds under the influence of large-scale moisture convergence, extending the work of Romps (2014) who examined the special case of radiative-convective equilibrium. According to this model, both high precipitation and high humidity are caused by large-scale convergence within the atmosphere, even in the absence of any direct sensitivity of convection to environmental moisture. Furthermore, the plume model predicts that CAPE is maximised for weak convergence, when the tropospheric humidity is low. These relationships are reproduced in a set of simulations with a cloud-resolving model run to equilibrium with imposed large-scale vertical velocity profiles.