A Multiscale Nonhydrostatic Atmospheric Model Using Centroidal Voronoi Tesselations and C-Grid Staggering

AbstractThe formulation of a fully compressible nonhydrostatic atmospheric model called the Model for Prediction Across Scales–Atmosphere (MPAS-A) is described. The solver is discretized using centroidal Voronoi meshes and a C-grid staggering of the prognostic variables, and it incorporates a split-explicit time-integration technique used in many existing nonhydrostatic meso- and cloud-scale models. MPAS can be applied to the globe, over limited areas of the globe, and on Cartesian planes. The Voronoi meshes are unstructured grids that permit variable horizontal resolution. These meshes allow for applications beyond uniform-resolution NWP and climate prediction, in particular allowing embedded high-resolution regions to be used for regional NWP and regional climate applications. The rationales for aspects of this formulation are discussed, and results from tests for nonhydrostatic flows on Cartesian planes and for large-scale flow on the sphere are presented. The results indicate that the solver is as acc...

[1]  William C. Skamarock,et al.  A unified approach to energy conservation and potential vorticity dynamics for arbitrarily-structured C-grids , 2010, J. Comput. Phys..

[2]  Claude Basdevant,et al.  Parameterization of Subgrid Scale Barotropic and Baroclinic Eddies in Quasi-geostrophic Models: Anticipated Potential Vorticity Method , 1985 .

[3]  R. Sadourny The Dynamics of Finite-Difference Models of the Shallow-Water Equations , 1975 .

[4]  Armin Iske,et al.  Hamburger Beiträge zur Angewandten Mathematik Kernel-Based Vector Field Reconstruction in Computational Fluid Dynamic Models , 2009 .

[5]  Todd D. Ringler,et al.  Exploring a Multiresolution Modeling Approach within the Shallow-Water Equations , 2011 .

[6]  William C. Skamarock,et al.  A time-split nonhydrostatic atmospheric model for weather research and forecasting applications , 2008, J. Comput. Phys..

[7]  D. Williamson,et al.  A baroclinic instability test case for atmospheric model dynamical cores , 2006 .

[8]  Jimy Dudhia,et al.  Conservative Split-Explicit Time Integration Methods for the Compressible Nonhydrostatic Equations , 2007 .

[9]  Jean Côté,et al.  The CMC-MRB Global Environmental Multiscale (GEM) Model. Part III: Nonhydrostatic Formulation , 2002 .

[10]  D. Lüthi,et al.  A new terrain-following vertical coordinate formulation for atmospheric prediction models , 2002 .

[11]  Uang,et al.  The NCEP Climate Forecast System Reanalysis , 2010 .

[12]  Christiane Jablonowski,et al.  Rotated Versions of the Jablonowski Steady‐State and Baroclinic Wave Test Cases: A Dynamical Core Intercomparison , 2010 .

[13]  D. Williamson The Evolution of Dynamical Cores for Global Atmospheric Models(125th Anniversary Issue of the Meteorological Society of Japan) , 2007 .

[14]  Masaki Satoh,et al.  Nonhydrostatic icosahedral atmospheric model (NICAM) for global cloud resolving simulations , 2008, J. Comput. Phys..

[15]  Joseph B. Klemp,et al.  The Dependence of Numerically Simulated Convective Storms on Vertical Wind Shear and Buoyancy , 1982 .

[16]  A. Arakawa,et al.  A Potential Enstrophy and Energy Conserving Scheme for the Shallow Water Equations , 1981 .

[17]  K. Droegemeier,et al.  The Advanced Regional Prediction System (ARPS) – A multi-scale nonhydrostatic atmospheric simulation and prediction model. Part I: Model dynamics and verification , 2000 .

[18]  Oliver Fuhrer,et al.  Numerical consistency of metric terms in terrain-following coordinates , 2003 .

[19]  J. Smagorinsky,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS , 1963 .

[20]  Tom Henderson,et al.  A general method for modeling on irregular grids , 2011, Int. J. High Perform. Comput. Appl..

[21]  Christiane Jablonowski,et al.  A baroclinic wave test case for dynamical cores of general circulation models: Model intercomparisons , 2006 .

[22]  Todd D. Ringler,et al.  A multiresolution method for climate system modeling: application of spherical centroidal Voronoi tessellations , 2008 .

[23]  William C. Skamarock,et al.  Numerical representation of geostrophic modes on arbitrarily structured C-grids , 2009, J. Comput. Phys..

[24]  R. A. Bromley The Ceaseless Wind: An Introduction to the Theory of Atmospheric Motion , 1988 .

[25]  Louis J. Wicker,et al.  Time-Splitting Methods for Elastic Models Using Forward Time Schemes , 2002 .

[26]  William C. Skamarock,et al.  Conservative Transport Schemes for Spherical Geodesic Grids: High-Order Flux Operators for ODE-Based Time Integration , 2011 .

[27]  Roni Avissar,et al.  The Ocean-Land-Atmosphere Model (OLAM). Part I: Shallow-Water Tests , 2008 .

[28]  Joseph B. Klemp,et al.  A Terrain-Following Coordinate with Smoothed Coordinate Surfaces , 2011 .

[29]  David A. Randall,et al.  Geostrophic Adjustment and the Finite-Difference Shallow-Water Equations , 1994 .

[30]  Hirofumi Tomita,et al.  A Stretched Icosahedral Grid by a New Grid Transformation , 2008 .

[31]  Slobodan Nickovic,et al.  Geostrophic Adjustment on Hexagonal Grids , 2002 .

[32]  Louis J. Wicker,et al.  Numerical solutions of a non‐linear density current: A benchmark solution and comparisons , 1993 .

[33]  J. Thuburn Numerical wave propagation on the hexagonal C-grid , 2008, J. Comput. Phys..

[34]  A. Hollingsworth,et al.  An internal symmetric computational instability , 1983 .