A case of daytime development of deep convection over tropical semi-arid land is used to evaluate the representation of convection in global and regional models. The case is based on observations collected during the African Monsoon Multidisciplinary Analysis (AMMA) field campaign and includes two distinct transition phases, from clear sky to shallow cumulus and from cumulus to deep convection. Different types of models, run with identical initial and boundary conditions, are intercompared: a reference large-eddy simulation (LES), single-column model (SCM) version of four different Earth system models that participated in the Coupled Model Intercomparison Project 5 exercise, the SCM version of the European Centre for Medium-range Weather Forecasts operational forecast model, the SCM version of a mesoscale model and a bulk model. Surface fluxes and radiative heating are prescribed preventing any atmosphere-surface and cloud-radiation coupling in order to simplify the analyses so that it focuses only on convective processes. New physics packages are also evaluated within this framework. As the LES correctly reproduces the observed growth of the boundary layer, the gradual development of shallow clouds, the initiation of deep convection and the development of cold pools, it provides a basis to evaluate in detail the representation of the diurnal cycle of convection by the other models and to test the hypotheses underlying convective parametrizations. Most SCMs have difficulty in representing the timing of convective initiation and rain intensity, although substantial modifications to boundary-layer and deep-convection parametrizations lead to improvements. The SCMs also fail to represent the mid-level troposphere moistening during the shallow convection phase, which we analyse further. Nevertheless, beyond differences in timing of deep convection, the SCM models reproduce the sensitivity to initial and boundary conditions simulated in the LES regarding boundary-layer characteristics, and often the timing of convection triggering.