Radiatively-cooled moist convection under idealised climate change scenarios: 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-Bénard model, which is itself a moist version of the Rayleigh-Bénard model of dry convection. Including moisture changes the character of the convection, with condensation providing a source of buoyancy via latent heating and the system exhibiting moist conditional instability. A range of idealised climate change scenarios are constructed by appropriate choice of both the radiative cooling rate and the surface temperature, and these scenarios are investigated over a wide range of surface relative humidity values. We impose moist-pseudoadiabatic conditions at the top boundary, which allow the temperature and specific humidity values to vary at the top boundary in response to convection. The model is analysed across the different climate change scenarios 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 Rainy number acts like the traditional Rayleigh number for dry Rayleigh-Bénard convection, and provides a novel theoretical tool for understanding how the dynamics and scales of moist convection and hence precipitation will change under climate change. The linear analysis predicts an intensification of the hydrological cycle under climate change. The model set up and linear analysis provide a basis for future investigation into the non-linear dynamics of (idealised) moist convection.