Extend HOMME to non-hydrostatic scales

The High-Order Method Modeling Environment (HOMME) is a framework to develop global atmospheric models (dynamical cores) based on high-order accurate and conservative element-based Galerkin methods. HOMME employs the continuous Galerkin or Spectral Element (SE) and the Discontinuous Galerkin (DG) methods, on a cubed-sphere tiled with quadrilateral elements. The element-based Galerkin method possesses computationally desirable properties such as local and global conservation, geometric flexibility, high on-processor operations, and minimal communication footprints. The cubed-sphere geometry provides quasi-uniform rectangular elements on the sphere without polar singularities and suitable for SE or DG discretization schemes. HOMME can be configured to solve the hydrostatic primitive equations on a uniform or variable-resolution cubed-sphere grid with explicit time stepping. In addition, the HOMME framework facilitates multi-tracer transport modeling based on finite-volume approaches. Currently the SE version of HOMME is the default dynamical core for NCAR’s Community Atmosphere Model (CAM), and HOMME-SE can efficiently scale to hundreds of thousands processors on a supercomputer.

The objective of this project is to extend HOMME to a framework capable of providing the CAM and the Community Earth System Model (CESM) with high-resolution and parallel efficient global dynamical cores at non-hydrostatic (NH) scales. The next-generation atmospheric climate models will depend on numerical methods that scale to large numbers of processors, and element-based Galerkin methods provide one route to meet the need for high-resolution dynamical cores. Numerical development within HOMME is strategic because it is not only a robust numerical test bed, but it is also a framework to transfer numerical methods to the CESM. CISL’s strategic goal includes enhancing the effective use of current and future computational systems by improving mathematical and computational methods for Earth System models, and HOMME development plays a major role in this aspect. This work supports CISL’s science imperative to develop mathematical research codes that improve modeling. Specifically, it fulfills the strategic action item to further develop the HOMME dynamical core.

In FY2016, the HOMME framework has been further extended to a non-hydrostatic dynamical core named the “High-Order Multiscale Atmospheric Model (HOMAM),” and which is based on prior research. The horizontal aspects of the HOMAM discretization remain the same as that of the current HOMME cubed-sphere grid system, with the DG spatial discretization method. The vertical discretization relies on terrain-following height-based z-coordinates. Several measures have been taken to extend the HOMME framework in preparation for the NH model implementation. These include restructuring the code, improving the efficiency of the DG algorithms, enhancing the parallel communication, and incorporating various DCMIP (Dynamical Core Model Intercomparison Project) benchmark tests to validate the new 3D NH model formulation. To examine the ability for the solver to represent non-hydrostatic effects, we conduct the mountain waves test over a non-smooth idealized 3D mountain. The main purpose of this test is to study the impact of orography on an atmosphere at rest, and it is particularly interesting for models with terrain-following height-based vertical coordinates that invariably introduce numerous metric terms. The model correctly captures the mountain-induced gravity wave propagation as shown in the figure below, and results are comparable with that of the reference results presented in DCMIP tests (Nair et al. 2016, DOI:10.2514/6.2016-3888).

Mountain waves
Simulated results for non-hydrostatic mountain waves over a 3D idealized mountain (DCMIP test) with HOMAM. The figure shows the mountain-induced gravity wave propagation for the vertical slice of the horizontal wind perturbation (u' m/s) along the equator, after 3,600 seconds of simulation.

The maximum stable time step for explicit time discretizations is dictated by the Courant–Friedrichs–Lewy (CFL) stability limit. At a higher resolution (smaller grid spacing), the CFL limit requires extremely smaller time steps, and is not practical for global NH models simulating climate. However, the stringent CFL limit associated with vertical high resolution can be remedied by using a dimension-splitting procedure that treats the vertical component of the equations in an implicit manner and the horizontal components explicitly, and the HEVI (horizontally explicit and vertically implicit) scheme does it precisely. A major research effort in FY2016 was to test the accuracy and scalability of the HEVI scheme in the HOMME framework. The time-stepping scheme HEVI has been implemented in HOMAM, and its performance has been compared with a fully explicit Runge-Kutta (RK) method. The figure below shows the scaling results with HEVI and the standard RK method, which are close to ideal scaling (dotted line). Moreover, the HEVI scheme does not impede the parallel scalability of the HOMME framework.

HEVI scales well
The strong scaling results with the HEVI and explicit RK time stepping methods for the HOMAM non-hydrostatic dynamical core. The HEVI scheme does not affect the scalability of the model.

Primary support for HOMME is provided by NSF Core funding.