Cubed-Sphere finite-volume dynamical core (fvcore) Overview

 

 

The finite-volume dynamical core (fvcore) is being implemented on the quasi-uniform cubed-sphere grid within a flexible modeling framework for direct implementation as a modular component within the global modeling efforts at NASA, GFDL-NOAA, NCAR, DOE and other interested institutions. The fvcore is an integral component within the NASA Goddard Earth Observing System (GEOS) modeling suite, as well as the global modeling efforts at GFDL and the Community Atmosphere Model (CAM) at NCAR. The development of a cubed-sphere version of the fvcore will expose a new level of parallelism (2-dimensional X-Y domain decomposition) that is not feasible within the current latitude-longitude (lat-lon) version, and allow for implementation of the purely flux-form algorithm at a massively parallel level on a variety of computational platforms.

The cubed-sphere grid is a projection of a cube onto a sphere represented as six adjoining grid faces which cover the globe. The cubed-sphere provides a quasi-uniform resolution, which offers several benefits over the standard lat-lon grid currently implemented within the fvcore. The quasi-uniform nature of the cubed-sphere grid eliminates the parallelization difficulties associated with the poles, allowing a far more efficient implementation of the horizontal 2-D domain decomposition, a feature that will be required of a truly scalable ultra-high resolution earth system model. Further, the clustering of grid points at the poles on the lat-lon grid requires special attention to avoid violating the Courant Friedrichs-Levy (CFL) stability requirements without dramatically reducing the integration time step. In particular, the flux-form transport algorithm applied within the lat-lon implementation requires a semi-lagrangian extension to allow the use of large time steps, and a polar filter is required to stabilize the high frequency gravity waves generated at high latitudes. The quasi-uniform nature of the cubed-sphere grid eliminates these problems at the poles and also allows for a reasonable time step within CFL limits without the need to extend the flux-form algorithm and without the use of a polar filter. In addition, the cubed-sphere can be implemented without significant algorithmic modifications and can be applied to support both the cubed-sphere and lat-lon grids within the same code using the same flux-form transport algorithm, a highly desirable feature as the popularity of the fvcore continues to grow within the modeling community.

The cubed-sphere grid is ideal for 2-dimensional domain decomposition in the X-Y direction; this is perhaps the most attractive feature of the cubed-sphere grid. While the pole problems associated with the lat-lon grid pose significant restrictions on the ability to impose 2-dimensional domain decomposition, this is a rather straight forward ghosting problem with the cubed-sphere. The ability to decompose in the X-Y direction provides great promise for producing a modeling system scalable to 100,000s of processors. On a system such as 'Halem' (a 1388 processor Compaq AlphaServer SC45 at the NASA Center for Computational Sciences at Goddard Space Flight Center) which supports the use of 4 shared memory processors for each of the 347 nodes the 0.25 degree cubed-sphere grid would allow the use of up to 345,600 processors in a hybrid message-passing/shared-memory configuration, as opposed to 960 processors for the current latitude decomposed fvGCM. As grid resolution is increased to 0.1 degrees the cubed-sphere would have the potential to use up to 2,000,000+ processors on a shared memory platform like the SGI Altix cluster 'Columbia' at the NASA Advanced Computing Division. Of course, efficient computing on such an immense scale will demand a great deal from the hardware in particular the interconnects between nodes; however, having the capability to utilize 100,000s of processors will be essential for timely execution of real-time numerical weather prediction systems with horizontal resolutions at and beyond the hydrostatic limit (~10 km horizontal resolution).

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