Radiatively-Cooled Moist Convection under an Idealised Climate Change Scenario: Linear Analysis

In order to explore the effects of climate change on atmospheric convection and the water cycle, we develop and analyse an extension of the Rainy-B\'enard model, which is itself a moist version of the Rayleigh-B\'enard model of dry convection. Including moisture changes the character of the convection, with condensation providing a source of buoyancy via latent heating. The climate change model is set up by imposing a variable radiative cooling rate, prescribing surface temperature and relative humidity, and imposing a moist-pseudoadiabatic profile at the top boundary (a flux boundary condition). The model is analysed across the climate parameter space by examining diagnostics of the model's basic state, and its stability, with Convective Available Potential Energy (CAPE) calculations and a linear stability analysis. We use the linear stability results to identify new parameters relevant for this moist convective system, and to understand how the linear instability responds to the climate parameters. In particular, we define the "Rainy number" as a scaled ratio of positive-area CAPE and diffusion parameters. An alternative radiative-based Rainy number also is shown to describe the parameter space, especially for problems relating to changes in flux conditions. The analysis provides a novel theoretical understanding of how the dynamics and scales of moist convection and hence precipitation will change under climate change.