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<p>The initiation of deep convection in a diurnal cycle is still one of the most important uncertainties in a climate numerical model. This is partially due to our poor understanding of the physical mechanisms leading to the transition from shallow to deep convection. In this work, we discuss the role of shallow cumulus clouds in the initiation of deep convection. By using a simple entraining plume model, we show that the interaction between an active and a passive shallow cumulus helps the former to reach higher altitudes and, in the right conditions, may initiate deep convection. It is also shown that the organization of passive and active clouds due to the formation of cold pools may act as a positive feedback. Furthermore, based on the proposed mechanism, a stochastic triggering function is derived, which can be implemented in climate models. As an important feature, the stochastic function is scale-aware, which makes it suitable for simulations at the gray-zone.</p>

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