The dependence of the climate simulated in a global storm-resolving model on its vertical resolution

In global atmospheric modeling the importance of an appropriate ratio of vertical to horizontal model resolution has been emphasized earlier. Theoretical considerations for appropriate ratios have been based, e.g., on quasi-geostrophic considerations for large-scale flows and the dissipation conditions for gravity waves. In limited-area convection-permitting simulations it has been shown that in particular the simulation of shallow cloud layers depends on the vertical model resolution. 
A recent focus in global climate modeling is to increase horizontal resolutions down to a few kilometers grid spacing in order to resolve processes like convection that need to be parameterized at coarser resolutions. In these simulations, often the vertical model resolutions haven’t been changed much in comparison to traditional approaches. Questions like the following may arise: Is this appropriate? How strongly does the climate at storm-resolving horizontal scales depend on vertical resolution? Can convergence of the simulated climate be expected at a certain vertical resolution? Is it useful to invest in further increases of horizontal resolution without a refinement of the vertical grid?
To start answering these questions we have performed simulations with the ICON global atmospheric model at a horizontal resolution of 5 km with three different vertical grids comprising 55, 110, and 190 layers and corresponding vertical resolution in the troposphere of 400, 200, and 100 m, respectively, for a period of 6 weeks.  Here we will show the dependence of selected climate parameters, including the global energy budget, on the vertical resolution.