Mean precipitation change from a deepening troposphere

Global climate models robustly predict that global mean precipitation should increase at roughly 2-3% K-1, but the origin of these values is not well understood. Here we develop a simple theory to help explain these values. This theory combines the well-known radiative constraint on precipitation, which says that condensation heating from precipitation is balanced by the net radiative cooling of the free troposphere, with an invariance of radiative cooling profiles when expressed in temperature coordinates. These two constraints yield a picture in which mean precipitation is controlled primarily by the depth of the troposphere, when measured in temperature coordinates. We develop this theory in idealized simulations of radiative-dconvective equilibrium and also demonstrate its applicability to global climate models.