The hypohydrostatic rescaling and its impacts on modeling of atmospheric convection

The atmospheric circulation spans a wide range of spatial scales, including the planetary scale (∼10,000 km), synoptic scale (∼2,000 km), mesoscale (∼200 km), and convective scales (<20 km). The wide scale separation between convective motions, responsible for the vertical energy transport, and the planetary circulation, responsible for the meridional energy transport, has prevented explicit representation of convective motions in global atmospheric models. Kuang et al. (Geophys. Res. Lett. 32: L02809, 2005) have suggested a way to circumvent this limitation through a rescaling that they refer to as Diabatic Acceleration and REscaling (DARE). We focus here on a modified version of the procedure that we refer to as hypohydrostatic rescaling. These two strategies are equivalent for inviscid and adiabatic flow in the traditional meteorological setting in which the vertical component of the Coriolis acceleration is ignored, but they differ when atmospheric physics is taken into account. It is argued here that, while the hypohydrostatic rescaling preserves the dynamics of the planetary scale circulation, it increases the horizontal scale of convective motions. This drastically reduces the computational cost for explicit simulation of hypohydrostatic convection in a global atmospheric model. A key question is whether explicit simulations of hypohydrostatic convection could offer a valid alternative to convective parameterization in global models. To do so, radiative–convective equilibrium is simulated with a high-resolution non-hydrostatic model using different model resolutions and values of the rescaling parameter. When the behavior of hypohydrostatic convection is compared with coarse-resolution simulations of convection, the latter set of simulations reproduce more accurately the result from a reference high-resolution simulation. This is particularly true for the convective velocity and cloud ice distributions. Scaling arguments show that hypohydrostatic rescaling increases the convective overturning time. In particular, this convective slowdown associated with the hypohydrostatic rescaling is more significant than the slowdown resulting from Communicated by R. Klein. O. Pauluis (B) Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA E-mail: [email protected] Dargan M. W. Frierson Department of Geophysical Sciences, University of Chicago, Chicago, IL, USA Stephen T. Garner · Isaac M. Held Geophysical Fluid Dynamics Laboratory/NOAA, Princeton, NJ, USA Geoffrey K. Vallis Atmospheric and Oceanic Sciences Program, Princeton University, Princeton, NJ, USA 486 O. Pauluis et al. under-resolving the convective elements. These results cast doubt on the practical value of the hypohydrostatic rescaling as an alternative to convective parameterization.