Global Environmental Multiscale Model with Height-Based Terrain-Following Vertical Coordinate for Improving Numerical Stability

A new dynamical core of the Global Environmental Multiscale (GEM) model has recently been developed at Environment and Climate Change Canada (ECCC) that adopts a height-based terrain-following vertical coordinate. The dynamical core of the GEM model, used operationally by ECCC for numerical weather prediction (NWP), employs a log-hydrostratic-pressure-type vertical coordinate. For very high spatial resolutions, e.g., for sub-kilometer horizontal grid spacing, the existing dynamical core suffers from severe numerical instability – particularly over complex terrain where the mountain slopes can become steeper than 45°. A number of approaches have been investigated to improve this stability aspect of the operational GEM model with limited success. The growing demand for very high-resolution operational NWP systems has, however, made improving model stability over steep mountains an imperative. The previous experience with the Mesoscale Compressible Community model at ECCC suggests that a dynamical kernel based on height-type vertical coordinate does not suffer from as severe orography-induced instability. Some of the existing scientific literature also point at the potential for height-based vertical coordinate to extend the stability limit through improved approximation of the horizontal gradients in the discretized dynamical system. Improving model stability over steep terrain has therefore been the primary motivation for developing this new dynamical core.

One of the major advantages of the pressure-type vertical coordinate – currently used in GEM – is that it permits the use of a direct solver for the discretized elliptic problem to resolve the dynamical component of the flow. However, recent investigations with ECCC’s new high performance computing infrastructure have revealed that the direct solver loses its scalability substantially for a very large number of processor cores. This implies that in order to take advantage of very large number of processor cores to integrate each model dynamical step, a highly optimized iterative solver will be essential in future. Such a requirement negates one of the most advantageous aspects of the existing pressure-based vertical coordinate system and makes the height-based system more attractive for future NWP systems.

The new dynamical kernel with height-based vertical coordinate has been tested for different theoretical benchmark cases. It has been found to be neutral in terms of accuracy while improving numerical stability for steep terrain slopes. When tested for full three-dimensional atmospheric flow simulations in the absence of parameterized physical forcing the two dynamical cores are found to be equivalent for operational NWP resolutions. At present, work is in progress to couple the new dynamical core with ECCC’s operational physical parameterization package. Results pertaining to the different aspects of the newly-developed GEM dynamical core will be presented at the conference.