A Linear Response Framework for Radiative‐Convective Instability

Radiative‐convective equilibrium is a simple paradigm for the tropical climate, in which radiative cooling balances convective heating in the absence of lateral energy transport. Recent studies have shown that a large‐scale circulation may spontaneously develop from radiative‐convective equilibrium through the interactions among water vapor, radiation, and convection. This potential instability, referred to as radiative‐convective instability, may be posed as a linear stability problem for the water vapor profile by combining a linear response framework with the weak temperature gradient approximation. We design two analytic models of convective linear response to moisture perturbations, which are similar to Betts‐Miller and bulk‐plume convection schemes. We combine these convective responses with either clear‐sky gray or real‐gas radiative responses. In all cases, despite consistent radiative feedbacks, the characteristics of convection dominate the vertical structure of the most unstable linear mode of water vapor perturbations. For Betts‐Miller convection, the stability critically depend on a key parameter: the heating to advection of moisture conversion rate (HAM); warmer atmospheres with higher HAM exhibit more linear instability. In contrast, bulk‐plume convection is stable across temperatures but becomes linearly unstable with a moisture mode peaking in the midtroposphere once combined to radiation, with approximate growth rates of 10 days.