Shallow clouds impose a large uncertainty on climate models, as the computational power required to directly simulate them is unavailable. While much cloud research focusses on representing these unresolved processes, we propose a different perspective: Understanding and modelling only system-wide properties of cloud fields that emerge at the large scales resolved by climate models. Combining satellite data, high-resolution simulations and machine learning, we will i) systematically map these emergent properties, ii) search for simplified models that capture their essentials, iii) study how they form and iv) investigate whether they are likely to dramatically change in a warming climate.