Tropical deep convection and global warming: what do we know?

Tropical deep convection, and the anvil clouds it produces, are key players in the climate system. But, these phenomena are typically unresolved in global climate models, so their response to global warming is uncertain. In this talk we highlight some key uncertainties, including a marked resolution-dependence of anvil clouds even in cloud-resolving models, as well as uncertainty in the tropical anvil cloud area feedback. We also, however, discuss the constraint that tropical convective mass fluxes should robustly decrease with global warming, especially when evaluated in temperature coordinates. This constraint is derived with pencil-and-paper, and confirmed across a hierarchy of cloud-resolving and global climate simulations.