Global Coupled Modeling on the Expanded Spherical Cube

High-end coupled models are computationally too expensive to allow routine centenial and millenial timescale simulations. Instead dynamically intermediate models are typically used in this context, for example models based on QG dynamics and zonally averaged models. Here we present an alternative approach of using highly paramterized physics in conjunction with an efficient dynamical scheme model that uses a cube expanded onto a sphere.

Grid point models built on standard latitude-longitude grids have to deal with stringent stability criteria arising from the convergence of meridians at the poles and have a computational load that scales exponentially with resolution. Gridding the sphere using a cubic conformal mapping (Rancic et al., 1996) provides relatively uniform resolution and effectively overcomes the shortcomings of the standard grids.

Here, we describe the implementation of the MIT Isomorphic Dynamical Kernel on the conformal expanded cube, and the subsequent use of this model for coupled global atmosphere-ocean calculations. A vector invariant form of the fluid equations is used which overcomes the challenge of handling the "poles" (the corners of the cube) on this grid. This strategy is central to enabling the scheme to be applied generally. The underlying cubic geometry can be built from patching six rectilinear grids, each grid being curvilinear. The "tile and halo" approach to parallelization used in the model elegantly adapts to the cubic geometry while the finite volume method used naturally describes orthogonal curvilinear grids. As such, the implementation on the cubic grid represents only incremental modifications to the existing model.

Avoiding the extreme stability criteria of the latitude-longitude grid allows the model to take a longer time-step than previously and use less memory at an equivalent resolution, leading to overall improved efficiency. The resulting scheme provides a computationally viable approach for global coupled modeling. Using the same cubic grid for both the atmosphere and ocean simplifies the coupling procedure and allows for simple and exact