A new diagnostic convective closure, which is dependent on convective available potential energy (CAPE), is derived under the quasi-equilibrium assumption for the free troposphere subject to boundary layer forcing. The closure involves a convective adjustment time scale for the free troposphere and a coupling coefficient between the free troposphere and the boundary layer based on different time scales over land and ocean. Earlier studies with the ECMWF Integrated Forecasting System (IFS) have already demonstrated the model's ability to realistically represent tropical convectively coupled waves and synoptic variability with use of the "standard" CAPE closure, given realistic entrainment rates. A comparison of low-resolution seasonal integrations and high-resolution short-range forecasts against complementary satellite and radar data shows that with the extended CAPE closure it is also possible, independent of model resolution and time step, to realistically represent nonequilibrium convection such as the diurnal cycle of convection and the convection tied to advective boundary layers, although representing the late night convection over land remains a challenge. A more in-depth regional analysis of the diurnal cycle and the closure is provided for the continental United States and particularly Africa, including comparison with data from satellites and a cloud-resolving model (CRM). Consequences for global numerical weather prediction (NWP) are not only a better phase representation of convection, but also better forecasts of its spatial distribution and local intensity.