Vertical Resolution Requirements for NWP models

Even though existing operational global NWP model configurations use similar horizontal grid spacing, they employ a wide range of vertical grid spacings, especially in the free atmosphere. We examine the role of vertical mesh spacing in the convergence of full-physics global atmospheric model solutions for synoptic, mesoscale and cloud-scale horizontal meshes. Using the Model for Predication Across Scales (MPAS) Atmosphere, convergence is evaluated for three solution metrics; the horizontal kinetic energy spectrum, the Richardson-number probability density function, and resolved flow features. For a 15 km horizontal mesh (similar to current operational mesh densities), all three metrics exhibit convergence in the free atmosphere when the vertical grid spacing is less than or equal to 200 meters through the free troposphere and lower stratosphere. Non-convergence is accompanied by noise, spurious structures, reduced levels of mesoscale kinetic energy, and reduced Richardson number peak frequencies. Coarser horizontal mesh solutions converge in a similar manner but contain much less noise than the 15 km solutions for coarse vertical resolution. For convective-scale resolution simulations with 3 km cell spacing on a variable-resolution mesh, solution convergence is almost attained with a vertical mesh spacing of 200 meters. The boundary layer scheme is the dominant source of vertical filtering in the free atmosphere and the dominant sink for horizontal kinetic energy. Although the increased vertical mixing at coarser vertical mesh spacing depresses the kinetic energy spectra and Richardson number convergence, it does not produce sufficient dissipation to effectively halt scale collapse. These results confirm and extend the results from a number of previous studies, and further emphasize the sensitivity of the energetics to the vertical mixing formulations in models.

Among operational models, the ECMWF IFS uses the finest vertical mesh in the free troposphere, with a vertical mesh spacing of approximately 300 meters and a total of 137 levels in its configuration. Both the UM and the GFS use many fewer levels (70 and 64, respectively), although the UM has smaller vertical mesh spacing in the troposphere, averaging around 500 meters, compared to 700 meters for the GFS. The MPAS results suggest that the IFS configuration is nearly optimally balanced with regard to horizontal and vertical mesh spacing, while the configurations used by other centers may be significantly suboptimal, with the vertical grids being too coarse. While implicit and explicit model filters, and sub-grid physics, may ameliorate noise created by too-coarse vertical grid spacing, the resolving capabilities of the models are likely compromised.