A Linear Response Framework for Radiative-Convective Instability

Abstract

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.