Clouds are a key player in the global climate system, affecting the atmospheric water and energy budgets, and they are strongly coupled to the large-scale atmospheric circulation. Here we examine the co-variability of the atmospheric energy and water budget imbalances in three different global model configurations - radiative-convective equilibrium, aqua-planet and global simulations with land. The gradual increase in the level of complexity of the model configuration enables an investigation of the effects of rotation, meridional temperature gradient, land-sea contrast and seasonal cycle on the co-variability of the water and energy imbalances. We demonstrate how this co-variability is linked to both the large-scale tropical atmospheric circulation and to cloud properties. Hence, we propose a co-variability-based framework that connects cloud properties to the large-scale tropical circulation and climate system and is directly linked to the top-down constrains on the system – the water and energy budgets. In addition, we examine how the water and energy budget imbalances co-variability depends on the temporal averaging scale, and explain its dependency on how stationary the circulation is in the different model configurations. Finally, we demonstrate the effect of an idealized global warming and convective aggregation on this co-variability.