Why does tropical convective available potential energy (CAPE) increase with warming?

Recent work has produced a theory for tropical convective available potential energy (CAPE) that highlights the Clausius-Clapeyron (CC) scaling of the atmosphere's saturation deficit as a driver of increases in CAPE with warming. Here we test this so-called zero-buoyancy theory for CAPE by modulating the saturation deficit of cloud-resolving simulations of radiative-convective equilibrium in two ways: changing the sea surface temperature (SST) and changing the environmental relative humidity (RH). For earthlike and warmer SSTs, undilute parcel buoyancy in the lower troposphere is insensitive to increasing SST because of a countervailing CC scaling that balances the increase in the saturation deficit; however, buoyancy increases dramatically with SST in the upper troposphere. Conversely, in the RH experiment, undilute buoyancy throughout the troposphere increases monotonically with decreasing RH. We show that the zero-buoyancy theory successfully predicts these contrasting behaviors, building confidence that it describes the fundamental physics of CAPE and its response to warming.