Sensitivity of radiative-convective equilibrium simulations to horizontal resolution

This paper investigates the impacts of horizontal resolution on the statistical behavior of convection. An idealized radiative-convective equilibrium is simulated for model resolutions ranging between 2 and 50 km. The simulations are compared based upon the analysis of the mean state, the energy and water vapor transport, and the probability distribution functions for various quantities. It is shown that, at a coarse resolution, the model is unable to capture the mixing associated with shallow clouds. This results in a dry bias in the lower troposphere, and in an excessive amount of water clouds. Despite this deficiency, the coarse resolution simulations are able to reproduce reasonably well the statistical properties of deep convective towers. This is particularly apparent in the cloud ice and vertical velocity distributions that exhibit a very robust behavior. A theoretical scaling for the vertical velocity as function of the grid resolution is derived based upon the behavior of an idealized air bubble. It is shown that the vertical velocity of an ascending air parcel is determined by its aspect ratio, with a wide, flat parcel rising at a much slower pace than a narrow one. This theoretical scaling law exhibits a similar sensitivity to that of the numerical simulations. It is used to renormalize the probability distribution functions for vertical velocity, which show a very good agreement for resolutions up to 16 km. This new scaling law offers a way to improve direct simulations of deep convection in coarse resolution models.