Nonlinear Hydrostatic Conditional Symmetric Instability: Implications for Numerical Weather Prediction

Abstract

A simplified two-dimensional version of the Pennsylvania State University-NCAR Mm scale Model (MM4) was used to investigate the nonlinear evolution of unforced conditional symmetric instability (CSI). Sensitivity tests examines the effects of the model resolution, the magnitudes and formulation of the vertical and horizontal diffusion, and the Prandtl number on various aspects of the CSI circulations. Aspects of the circulations that are considered include the transverse velocity, the growth rate, and the updraft slope, as well as the existence of a CSI circulation. With the fairly unstable initial conditions used in these tests, unstable CSI modes are explicitly resolved with horizontal grid spacing of at most 30 km, using a fairly weak horizontal diffusion. The vertical grid spacing needs to be no greater than 340 m to be consistent with the horizontal grid spacing and the sloping thermal structures. To resolve the most unstable nonlinear CSI modes, horizontal resolutions of no more than 15 km and vertical resolutions less than 170 m are necessary. The magnitude of the horizontal diffusion, the magnitude and the formulation of the vertical diffusion, and the Prandtl number all affect the simulated CSI circulations. Comparisons to linear theory allow the generalization of the results. These generalizations suggest that the combined effects of model resolution, model diffusion, scale height of the instability, and environmental conditions (e.g., N2) determine whether CSI will be explicitly released in a numerical model, and also whether the resolved unstable modes include the desirable most unstable mode. Unstable CSI modes that do not correspond to the most unstable mode can be explicitly resolved with a grid spacing that is coarser than that necessary for the most unstable mode. If the resolved modes do not include the most unstable mode, the evolution of the CSI circulations will be substantially slower and the amplitudes reduced from what should be expected in the real atmosphere in which the most unstable mode should be present.