The Global Environmental Multiscale (GEM) model is the Canadian atmospheric model used for meteorological forecasting at all scales. A limited-area version now also exists. It is a gridpoint model with an implicit semi-Lagrangian iterative space-time integration scheme. In the ''horizontal,'' the equations are written in spherical coordinates with the traditional shallow atmosphere approximations and are discretized on an Arakawa C grid. In the ''vertical,'' the equations were originally defined using a hydrostatic-pressure coordinate and discretized on a regular (unstaggered) grid, a configuration found to be particularly susceptible to noise. Among the possible alternatives, the Charney-Phillips grid, with its unique characteristics, and, as the vertical coordinate, log-hydrostatic pressure are adopted. In this paper, an attempt is made to justify these two choices on theoretical grounds. The resulting equations and their vertical discretization are described and the solution method of what is forming the new dynamical core of GEM is presented, focusing on these two aspects.

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Abstract. Atmospheric dynamical cores are a fundamental component of global atmospheric modeling systems and are responsible for capturing the dynamical behavior of the Earth's atmosphere via numerical integration of the NavierStokes equations. These systems have existed in one form or another for over half of a century, with the earliest discretizations having now evolved into a complex ecosystem of algorithms and computational strategies. In essence, no two dynamical cores are alike, and their individual successes suggest that no perfect model exists. To better understand modern dynamical cores, this paper aims to provide a comprehensive review of 11 non-hydrostatic dynamical cores, drawn from modeling centers and groups that participated in the 2016 Dynamical Core Model Intercomparison Project (DCMIP) workshop and summer school. This review includes a choice of model grid, variable placement, vertical coordinate, prognostic equations, temporal discretization, and the diffusion, stabilization, filters, and fixers employed by each system.

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The overset grid nicknamed "Yin-Yang" grid is singularity free and has quasi-uniform grid spacing. It is composed of two identical latitude/longitude orthogonal grid panels that are combined to cover the sphere with partial overlap on their boundaries. The system of shallow-water equations (SWEs) is a hyperbolic system at the core of many models of the atmosphere. In this paper, the SWEs are solved on the Yin-Yang grid by using an implicit and semi-Lagrangian discretization on a staggered mesh. The resulting scalar elliptic equation is solved using a Schwarz-type domain decomposition method, known as the optimized Schwarz method, which gives better performance than the classical Schwarz method by using specific Robin or higher order transmission conditions.