DYNAMICO-1.0, an icosahedral hydrostatic dynamical core designed for consistency and versatility

Abstract

Abstract. The design of the icosahedral dynamical core DY-NAMICO is presented. DYNAMICO solves the multi-layer rotating shallow-water equations, a compressible variant of the same equivalent to a discretization of the hydrostatic primitive equations in a Lagrangian vertical coordinate, and the primitive equations in a hybrid mass-based vertical coordinate. The common Hamiltonian structure of these sets of equations is exploited to formulate energy-conserving spatial discretizations in a unified way.The horizontal mesh is a quasi-uniform icosahedral C-grid obtained by subdivision of a regular icosahedron. Control volumes for mass, tracers and entropy/potential temperature are the hexagonal cells of the Voronoi mesh to avoid the fast numerical modes of the triangular C-grid. The horizontal discretization is that of Ringler et al. (2010), whose discrete quasi-Hamiltonian structure is identified. The prognostic variables are arranged vertically on a Lorenz grid with all thermodynamical variables collocated with mass. The vertical discretization is obtained from the three-dimensional Hamiltonian formulation. Tracers are transported using a second-order finite-volume scheme with slope limiting for positivity. Explicit Runge-Kutta time integration is used for dynamics, and forward-in-time integration with horizontal/vertical splitting is used for tracers. Most of the model code is common to the three sets of equations solved, making it easier to develop and validate each piece of the model separately.Representative three-dimensional test cases are run and analyzed, showing correctness of the model. The design permits to consider several extensions in the near future, from higher-order transport to more general dynamics, especially deep-atmosphere and non-hydrostatic equations.

NCAR Release of CAM‐SE in CESM2.0: A Reformulation of the Spectral Element Dynamical Core in Dry‐Mass Vertical Coordinates With Comprehensive Treatment of Condensates and Energy

“…The thermodynamic equation, momentum equations, and dry air mass continuity equation in CAM-SE are evolved using the five-stage third-order RK scheme described in Guerra and Ullrich (2016; see their equation (56)). The stability of this class of time-stepping schemes is discussed in Dubos et al, 2015Dubos et al, (2015 see their section 3.4). For a given initial state vector at time step n, ⃗ Λ (0) = ⃗ Λ n , the updated state vector ⃗ Λ (5) = ⃗ Λ n+1 is computed as follows:…”

A Layer‐Averaged Nonhydrostatic Dynamical Framework on an Unstructured Mesh for Global and Regional Atmospheric Modeling: Model Description, Baseline Evaluation, and Sensitivity Exploration

“…Figure 14 shows the results from the RK3 and RK2 tests. The model generates expected climatological patterns, which have been previously examined by some hydrostatic and nonhydrostatic models (e.g., Dubos et al, 2015;Gassmann, 2013;Lin, 2004;Ringler et al, 2000;Tolstykh et al, 2017;Tomita & Satoh, 2004;Wan et al, 2013;Wedi et al, 2009;Zhang et al, 2012;http://www-personal. umich.edu/~cjablono/dycore_test_suite.html ).…”

An Energy Consistent Discretization of the Nonhydrostatic Equations in Primitive Variables

“…The third, forth, seventh, and eight terms cancel in the continuum but rely on additional properties that are not obeyed by general mimetic discretizations. They are responsible for a small lack of conservation in Dubos et al (, section 4.4). These terms will cancel via special integral properties satisfied by the SB81 discretization (Simmons & Burridge, ; Taylor, ).…”