A two‐column radiative–convective equilibrium (RCE) model is used to study the depth of convection that develops in the subsiding branch of a Walker‐like overturning circulation. The model numerically solves for two‐dimensional non‐rotating hydrostatic flow, which is damped by momentum diffusion in the boundary layer and model interior, and by convective momentum transport. Convection, clouds and radiative transfer are parametrized, and the convection scheme does not include explicit freezing or melting.
While integrating the model towards local RCE, the level of neutral buoyancy (LNB) fluctuates between mid‐ and high levels. Evaporation of detrained moisture at the LNB locally cools the environment, so that the final RCE state has a stable layer at mid‐levels (550 hPa ≈ 50–100 hPa below 0 °C), which is unrelated to melting of ice. Preferred detrainment at mid‐ and high levels leaves the middle‐to‐upper troposphere relatively dry.
A circulation is introduced by incrementally lowering the sea‐surface temperature in one column, which collapses convection: first to a congestus mode with tops near 550 hPa, below the dry layer created in RCE; then to congestus with tops near 650 hPa; and finally to shallow cumulus with tops near 850 hPa. Critical to stabilizing congestus near 650 hPa is large radiative cooling near moist cumulus tops under a dry upper atmosphere. This congestus mode is very sensitive, and only develops when horizontal temperature gradients created by evaporative and radiative cooling can persist against the work of gravity waves. This only happens in runs with ample momentum diffusion, which are those with convective momentum transport or large domains.
Compared to the shallow mode, the congestus mode produces a deep moist layer and more precipitation. This reduces radiative cooling in the cloud layer and enhances stability near the cloud base, which weakens the circulation, and leads to less precipitation over the warm ocean.