On the Need of Orography Filtering in a Semi-Lagrangian Atmospheric Model with a Terrain-Following Vertical Coordinate

Operational numerical weather prediction (NWP) systems are increasingly focusing on higher spatial resolutions, often approaching the non-hydrostatic scales. One of the principal objectives is to improve the flow representation at the finer scales, particularly over complex terrain. As a result, the emphasis on representing the dynamical effects of the finest orography scales is also on the rise. For the previous generation of NWP systems, the Global Environmental Multiscale (GEM) model of Environment and Climate Change Canada (ECCC) has been relying on orography filters that, in addition to removing variance at the Nyquist limit, would to some extent smooth scales as large as 20 times the grid resolution (Δ). However, with the changing focus on high resolution forecasting, the orography filter in GEM has recently been modified to make it sharper with reduced cut-off wavelength for the smallest scales. In particular, the latest implementation of ECCC’s operational 15-km global deterministic prediction system (GDPS) employs a filter that retains at least 95% variance of orography scales larger than 3Δ.

The use of very high resolution orography, as in the GDPS, when implemented in ECCC’s 10-km continental-scale regional deterministic prediction system, is found to result in severe under-prediction of freezing rain accumulations in the valleys around the Canadian Rockies. Further investigation reveals a pattern of spurious winter-time warming in these valleys, which is also evident in the GDPS simulations to some extent. In order to better comprehend the underlying issues, theoretical test models with the characteristic numerical details identical to GEM, i.e. terrain-following vertical coordinate with semi-Lagrangian treatment for advection, were developed to simulate one-dimensional and two-dimensional flows in the presence of mountains and valleys of specified resolutions.

With the help of one dimensional shallow water problem in the presence of orography, the effective resolution, i.e., the smallest scales that are resolved by a model with sufficient accuracy, has been found to be larger than 6Δ for the GEM numerics. The one-dimensional problem shows that orography scales below the effective resolution can lead to considerable distortions in the solution. Super-critical flow over two-dimensional valleys with statically stable conditions reconfirms these findings. Furthermore, the two-dimensional model demonstrates that error in the flow representation at scales below a model’s effective resolution can lead to secondary erroneous signals similar to valley warming in the full three-dimensional case. The results from this study highlight the importance of appropriately filtering orography scales in accordance with a model’s effective resolution in order to obtain acceptable forecast guidance in the presence of complex terrain. The different test problems and the associated findings will be presented at the conference.