Instabilities of Radiative Convective Equilibrium with an Interactive Surface

Moist radiative-convective equilibrium (RCE) is the statistical equilibrium state the atmosphere would reach in the absence of lateral energy transport. It is arguably the simplest climatic equilibrium, where the vertically-integrated radiative cooling balances the convective heating. If the solar forcing is large enough, RCE can be unstable to water vapor perturbations, leading to a dry state with mean descent or a moist state with mean ascent. This instability is believed to correspond to the phenomenon of self aggregation of convection, where a convecting moist cluster surrounded by a broad region of dry subsiding air forms. The temperature perturbations of the surface play an important role in the organization of convection, through surface turbulent and radiative fluxes. However, it is very computationally intensive to run cloud resolving models and large eddy simulations of convection without artificially imposing a fixed surface temperature. This explains why the instabilities of RCE with an interactive surface remain an open problem. By using the MIT single column model and an idealized two-layers model of the atmosphere with a slab ocean, we are able to study the potential instabilities of the fully interactive system. We find that allowing for surface temperature perturbations adds a new air-sea potential instability to the purely atmospheric radiative-convective instability found by Emanuel et al. (2013). Furthermore, we are able to study the stability of the system for all values of solar forcing and surface heat capacities; we can then numerically compute the bifurcation diagram of the system. Finally, we show that the instability preferentially leads to a dry than a moist state, which helps explaining why self-aggregation of convection is observed to make the free-troposphere drier.