The Shape of CAPE: Undilute Parcel Buoyancy in the Tropics

CAPE is an elementary measure of convective instability. This work investigates the shape of the underlying undilute parcel buoyancy profiles that give rise to CAPE in the tropics. We first use a bulk-plume framework, due to Singh and O'Gorman, to predict how this buoyancy profile shape changes with sea surface temperature (SST) and environmental relative humidity (RH). The prediction is that, at earthlike and warmer SSTs, undilute buoyancy in the lower troposphere is insensitive to increasing SST but grows dramatically in the upper troposphere; as a result of the ballooning reservoir of buoyancy in the upper troposphere, CAPE should exhibit Clausius-Clapeyron scaling with SST. Conversely, when the environmental RH is reduced, undilute buoyancy throughout the troposphere is predicted to increase monotonically, yielding a linear dependence of CAPE on RH. We then confirm these predictions with cloud-resolving simulations of radiative-convective equilibrium. Finally, we show that this same bulk-plume framework provides an explanation for the large upper-tropospheric peak in buoyancy that is not related to the release of latent heat of fusion above the melting line. Further simulations with ice processes disabled confirm that ice is not responsible for the top-heaviness of undilute buoyancy profiles. The success of the bulk-plume theory in these starkly different contexts implies that it captures the fundamental physics of CAPE.