Impacts of updraft size and dimensionality on the perturbation pressure and vertical velocity in cumulus convection. Part II: Comparison of theoretical and numerical solutions and fully dynamical simulations

The theoretical and numerical solutions give a scaling of updraft velocity with R (~Δx) consistent with fully dynamical 2D and 3D simulations in the gray zone, with a rapid decrease of maximum w at relatively small R and a slower decrease at large R. These results suggest that an incorrect representation of perturbation pressure may be an important contributor to biases in convective strength at these resolutions. The theoretical solutions also provide a concise physical interpretation of the "virtual mass" coefficient in convection parameterizations and can be easily incorporated into these schemes to provide a consistent scaling of perturbation pressure effects with R, updraft height, and the buoyancy profile.