Organized tropical convection is a crucial mechanism in the climate system, but its representation in climate models through parametrization schemes has numerous shortcomings. One of these shortcomings is that they are deterministic despite the statistical nature of the relationship they are representing. Several attempts at devising a stochastic parametrization scheme have been made, many of which assume a local approach, that is, one in which the convection in a grid box is determined without consideration of the previous time steps and the surrounding boxes. This study seeks to explore the effect of this assumption on the coherence of convection using cloud regimes, which represent various modes of tropical convection. First, we analyze the coherence of observed convection beyond the typical size of a model grid box and time step. Then, we evaluate the consequences of the local assumption on this coherence in simple statistical models. Cloud regimes in the real world show high degrees of coherence, manifesting in their lifetimes, areas, and inter-regime relationships. However, in a local statistical model, they are too small, too short-lived, and have incorrect relationships between each other. This can be improved by incorporating time memory and spatial dependence in the modeling. Our results imply that a local approach to a statistical representation of convection is not viable, and a statistical model must account for nonlocal influence in order to have large-scale convective coherence that more closely resembles the real world. Key Points Observed convection has coherence beyond the grid box and the time step A model local in space and time does not produce such coherence Incorporating spatial and temporal memory recovered some of this coherence.