Convective available potential energy (CAPE), frequently regarded as an indicator of the potential intensity of deep convection, is strongly controlled by the properties of the planetary boundary layer (BL). Variations in CAPE observed during field experiments in midcontinent North America, the tropical east Atlantic, and the tropical west Pacific, can be accounted for mostly by changes in the temperature and humidity in the BL. The coupling between CAPE and the BL holds for both convective and nonconvective conditions. The coupling under conditions of deep convection implies a constraint on the intensity of deep convection which can be used as a closure for cumulus parameterization. This constraint requires equilibrium in the environment of the parcel used as a basis for calculating CAPE. Over many cases, parcel-environment equilibrium is observed to hold more robustly than equilibrium of CAPE itself. When observational uncertainties are considered, it is uncertain whether quasi-equilibrium, in which the rate of change of CAPE is substantially less than the rate at which mean advection and BL fluxes change CAPE, holds at subdiurnal timescales in the eastern Atlantic and the western Pacific. Quasi-equilibrium is a poor approximation at subdiurnal timescales in midcontinent North America. At timescales approaching diurnal, quasi-equilibrium holds in all cases. Cumulus parameterizations based on quasi-equilibrium may be limited in their ability to model diurnal cycles as a result. CAPE fluctuations related to large, subdiurnal variations in surface fluxes are much sharper than CAPE fluctuations related to changes in mean advection above the BL, especially over land. The strong BL control on CAPE indicates that deep convection does not equilibrate rapid, high-amplitude variations in CAPE originating there.