In the context of the European Cloud Systems project, the problem of the simulation of the diurnal cycle of convective precipitation over land is addressed with the aid of cloud-resolving (CRM) and single-column (SCM) model simulations of an idealized midlatitude case for which observations of large-scale and surface forcing are available. The CRM results are compared to different versions of the European Centre for Medium-Range Weather Forecasts (ECMWF) convection schemes using different convective trigger procedures and convective closures. In the CRM, maximum rainfall intensity occurs at 15 h (local time). In this idealized midlatitude case, most schemes do not reproduce the afternoon precipitation peak, as (i) they cannot reproduce the gradual growth (typically over 3 hours) of the deep convective cloud layer and (ii) they produce a diurnal cycle of precipitation that is in phase with the diurnal cycle of the convective available potential energy (CAPE) and the convective inhibition (CIN), consistent with the parcel theory and CAPE closure used in the bulk mass-flux scheme. The scheme that links the triggering to the large-scale vertical velocity gets the maximum precipitation at the right time, but this may be artificial as the vertical velocity is enforced in the single-column context.The study is then extended to the global scale using ensembles of 72-hour global forecasts at resolution T511 (40 km), and long-range single 40-day forecasts at resolution T159 (125 km) with the ECMWF general-circulation model. The focus is on tropical South America and Africa where the diurnal cycle is most pronounced. The forecasts are evaluated against analyses and observed radiosonde data, as well as observed surface and satellite-derived rainfall rates. The ECMWF model version with improved convective trigger produces the smallest biases overall. It also shifts the rainfall maximum to 12 h compared to 9.5 h in the original version. In contrast to the SCM, the vertical-velocity-dependent trigger does not further improve the phase of the diurnal cycle. However, further work is necessary to match the observed 15 h precipitation peak.