General Circulation Models (GCMs) have for decades exhibited difficulties in modelling the diurnal cycle of precipitation (DCP). This issue can be related to inappropriate representation of the processes controlling sub-diurnal phenomena like convection. In this study, 11 single-column versions of GCMs are used to investigate the interactions between convection and environmental conditions, processes that control nocturnal convections, and the transition from shallow to deep convection on a diurnal time-scale. Long-term simulations are performed over two continental land sites: the Southern Great Plains (SGP) in the USA for 12 summer months from 2004 to 2015 and the Manacapuru site at the central Amazon (MAO) in Brazil for two full years from 2014 to 2015. The analysis is done on two regimes: afternoon convective regime and nocturnal precipitation regime. Most models produce afternoon precipitation too early, likely due to the missing transition of shallow-to-deep convection in these models. At SGP, the unified convection schemes better simulate the onset time of precipitation. At MAO, models produce the heating peak in a much lower level compared with observation, indicating too shallow convection in the models. For nocturnal precipitation, models that produce most of nocturnal precipitation all allow convection to be triggered above the boundary layer. This indicates the importance of model capability to detect elevated convection for simulating nocturnal precipitation. Sensitivity studies indicate that (a) nudging environmental variables towards observations has a minor impact on DCP, (b) unified treatment of shallow and deep convection and the capability to capture mid-level convection can help models better capture DCP, and (c) the interactions of the atmosphere with other components in the climate system (e.g. land) are also important for DCP simulations in coupled models. These results provide long-term statistical insights on which physical processes are essential in climate models to simulate DCP.