Three-Dimensional Scaling and Consistent Truncation of Global Atmospheric Models

Abstract

A three-dimensional scale index based on spherical domain and quasigeostrophic scale analysis indicates a truncation limit of global atmospheric models that includes both horizontal and vertical dimensions. Applying such a scale index, a numerical experiment is designed using a simplified adiabatic version of the National Center for Atmospheric Research (NCAR) Community Climate Model (CCM0B) to examine, incorporating nonlinear dynamics alone, whether an optimal horizontal resolution for a nine-vertical-level (modes) global general circulation model can be achieved. In establishing appropriate vertical modes that can be uniquely scaled and are independent and physically relevant, an optimal distribution of levels, which has been developed, is utilized in the experiment. The experimental results, which consist of a total of 110 individual integrations of the CCM0B with ten initial states for each of six horizontal truncations, appear to agree with the conclusions implied by the above referenced three-dimensional scale index; that is, a consistent horizontal resolution for a nine-vertical-level model should be in the range of triangular truncation T25 to T30 to yield optimal prediction results, considering, however, only the nonlinear dynamical aspect. It should be noted that due to the simplifications and idealizations made to carry out our experiment, additional studies under more realistic atmospheric conditions are necessary and are encouraged based on the results presented herein to further validate the existence of the consistency of three-dimensional model resolutions.