Vertical Velocity in the Gray Zone

We describe how convective vertical velocities wc vary in the ‘gray zone’ of horizontal resolution, using both hydrostatic and non-hydrostatic versions of GFDL's FV3 dynamical core, as well as analytical solutions to the equations of motion. We derive a simple criterion (based on parcel geometries) for a model to resolve convection, and find that O(100m) resolution can be required for convergence of wc. We also find, both numerically and analytically, that hydrostatic systems over-estimate wc, by a factor of 2 - 3 in the convection-resolving regime. This over-estimation is simply understood in terms of the ‘effective buoyancy pressure’ of Jeevanjee and Romps (2015, 2016).