How tropical convection couples high moist static energy over land and ocean

What is a zeroth-order picture of the tropical atmosphere? Isaac Held once wrote in his blog: "My picture of the tropics is that of a circus tent (the temperature in the tropical upper troposphere) held up by poles (deep tropical convection) of different heights.” Here we show that if the "heights" of the "poles" are interpreted as the subcloud moist static energy (MSE), this picture depicts the observed climate with surprising accuracy. More quantitatively, we demonstrate the utility of convective quasi-equilibrium and weak temperature gradient assumptions in interpreting subcloud MSE over land and ocean. The large difference in zonal-mean subcloud MSE (left panel) over land and ocean has been interpreted as convective quasi-equilibrium being inaccurate in the observations. However, here we weight subcloud MSE with corresponding rainfall and show that the subcloud MSE where convection occurs (right panel) is actually latitudinally uniform and very similar over land or ocean. Furthermore, the entire distribution of rainfall amount in subcloud MSE is very similar over land and ocean with the peak at 343\,J/g and a half width at half maximum of 3\,J/g, which is surprising in light of the well-documented land-ocean contrast of tropical convection. An important implication is that the highest subcloud MSE at each location, whether over land or ocean, is subject to a uniform upper bound set by the convective regions.