A Quasi-steady Baroclinic Eddy with Hypohydrostatic Convection

Upscale feedback of underresolved moist convection to baroclinic eddies is investigated using a beta-plane model without convective parameterization. At a typical GCM resolution, the aspect ratio of the grid-scale convection renders it hydrostatic, leading to a resolution-dependent vertical velocity and mean stratification. In the first set of experiments, the grid spacing is decreased from 40 km to 10 km to allow nonhydrostatic effects; in the second set of experiments, the hypohydrostatic rescaling is applied to artificially increase the nonhydrostasy of the model. Similarity theory predicts wider and slower convective motions in the rescaled model and is quantitatively verified by the experiments. The dependence of convection-associated vertical velocity on the effective resolution, defined as the grid spacing divided by the rescaling factor, is mapped out, with scalings in the hydrostatic and nonhydrostatic regimes identified. Between the two regimes is the resolution gray zone, having drastically decreasing vertical velocity and increasing fraction of resolved convection as functions of effective resolution. The mean climate is found to be insensitive to the hypohydrostatic rescaling unless the effective resolution is beyond the gray zone. However, the significant slowing of convection leads to biases in the mean stratification in the warm sector, despite better resolving the convective cells. The results highlight the role of convection in the warm sector and suggest that the hypohydrostatic rescaling might be more useful when applied at resolutions higher than 10 km than at GCM resolutions.