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.

A major drawback of the CAM-SE model used in HOMME is that the governing equations are based on the hydrostatic approximation, which limits the horizontal resolution to about 25 km. As spatial resolutions become finer, the use of the hydrostatic approximation becomes inappropriate at the smallest resolved scales. CAM-SE employs pressure (mass) based vertical coordinates with a “shallow” atmosphere approximation (with constant-radius Earth and simplified Coriolis term), this limits the top of the atmosphere to a height of about 30 km. A major design change is required to address these limitations and prepare the CAM-SE framework for future high-resolution climate modeling applications. Extending the CAM-SE framework to a non-hydrostatic (NH) model with the ability to handle deep atmospheric simulations is of great interest at NCAR Laboratories including CGD, ACD, and HAO.

New-generation climate models are based on NH dynamics following compressible Euler or Navier-Stokes system of equations, which are capable of high-resolution cloud-resolving global simulations with horizontal resolution of a few km or finer. The “deep” atmosphere is typically of O(100) km in the vertical where the radius of the Earth and its gravity varies radially, and allows accurate representation of the Coriolis force terms. The ultimate goal of this project is to extend CAM-SE dynamical core to an NH model with an option for deep atmosphere simulation.

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 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 testbed, 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. 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.

The major effort in FY2017 was preparing CAM-SE to achieve this goal. A prototype 2D NH model with SE discretization in the horizontal and FV/FD discretization in the vertical was developed. The split-explicit time integration and vertical boundary conditions associated with z-coordinates have been successfully tested for the 2D model. A prototype 3D NH model based on the DG method known as HOMAM (High-Order Multiscale Atmospheric Model) was incorporated into the HOMME framework in FY2016. In FY2017, the DCMIP benchmark test cases used for HOMAM were ported into the CAM-SE framework for initial development and for validation and verification of the new NH code. Substantial progress was made in the first of three stages of developing the new NH model in the CAM-SE framework. A new branch in the CAM-SE trunk was created exclusively for the NH development and established the software infrastructure:

  • Implemented vertical height-based z-coordinates without orographic metrics.
  • Used a simplified Euler system without orography and fully explicit time-stepping.
  • Validated the code with simple DCMIP tests such as inertia-gravity wave propagation.

Primary support for HOMME is provided by NSF Core funding.