DCMIP2016: A Review of Non-hydrostatic Dynamical Core Design and Intercomparison of Participating Models

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 Navier–Stokes 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.

[1]  V. Starr,et al.  A QUASI-LAGRANGIAN SYSTEM OF HYDRODYNAMICAL EQUATIONS , 1945 .

[2]  N. Phillips,et al.  NUMERICAL INTEGRATION OF THE QUASI-GEOSTROPHIC EQUATIONS FOR BAROTROPIC AND SIMPLE BAROCLINIC FLOWS , 1953 .

[3]  E. Lorenz Energy and Numerical Weather Prediction , 1960 .

[4]  N. Phillips,et al.  Scale Analysis of Deep and Shallow Convection in the Atmosphere , 1962 .

[5]  Caskey,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS I . THE BASIC EXPERIMENT , 1962 .

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

[7]  Norman A. Phillips,et al.  The Equations of Motion for a Shallow Rotating Atmosphere and the “Traditional Approximation” , 1966 .

[8]  R. Sadourny Conservative Finite-Difference Approximations of the Primitive Equations on Quasi-Uniform Spherical Grids , 1972 .

[9]  A. Kasahara Various Vertical Coordinate Systems Used for Numerical Weather Prediction , 1974 .

[10]  Richard C. J. Somerville,et al.  Numerical solution of the navier-stokes equations with topography , 1975 .

[11]  Akio Arakawa,et al.  Computational Design of the Basic Dynamical Processes of the UCLA General Circulation Model , 1977 .

[12]  Tatsushi Tokioka,et al.  Some Considerations on Vertical Differencing , 1978 .

[13]  I. Orlanski The Quasi-Hydrostatic Approximation , 1981 .

[14]  A. Simmons,et al.  An Energy and Angular-Momentum Conserving Vertical Finite-Difference Scheme and Hybrid Vertical Coordinates , 1981 .

[15]  S. P. Lloyd,et al.  Least squares quantization in PCM , 1982, IEEE Trans. Inf. Theory.

[16]  P. Woodward,et al.  The Piecewise Parabolic Method (PPM) for Gas Dynamical Simulations , 1984 .

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

[18]  Akio Arakawa,et al.  Baroclinic Instability in Vertically Discrete Systems. , 1988 .

[19]  D. Durran Improving the Anelastic Approximation , 1989 .

[20]  Adrian Simmons,et al.  Use of Reduced Gaussian Grids in Spectral Models , 1991 .

[21]  René Laprise,et al.  The Euler Equations of Motion with Hydrostatic Pressure as an Independent Variable , 1992 .

[22]  Atsuyuki Okabe,et al.  Spatial Tessellations: Concepts and Applications of Voronoi Diagrams , 1992, Wiley Series in Probability and Mathematical Statistics.

[23]  W. Skamarock,et al.  The stability of time-split numerical methods for the hydrostatic and the nonhydrostatic elastic equations , 1992 .

[24]  Rodolfo Bermejo,et al.  The Conversion of Semi-Lagrangian Advection Schemes to Quasi-Monotone Schemes , 1992 .

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

[26]  R. Heikes,et al.  Numerical Integration of the Shallow-Water Equations on a Twisted Icosahedral Grid , 1995 .

[27]  P. Paolucci,et al.  The “Cubed Sphere” , 1996 .

[28]  Shian-Jiann Lin,et al.  An explicit flux‐form semi‐lagrangian shallow‐water model on the sphere , 1997 .

[29]  Georgiy L. Stenchikov,et al.  A Finite-Difference GCM Dynamical Core with a Variable-Resolution Stretched Grid , 1997 .

[30]  Shian-Jiann Lin,et al.  A finite‐volume integration method for computing pressure gradient force in general vertical coordinates , 1997 .

[31]  Steven J. Ruuth,et al.  Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations , 1997 .

[32]  J. Thuburn A PV-Based Shallow-Water Model on a Hexagonal-Icosahedral Grid , 1997 .

[33]  B. Perot Conservation Properties of Unstructured Staggered Mesh Schemes , 2000 .

[34]  B. Stevens,et al.  Efficient computation of vapor and heat diffusion between hydrometeors in a numerical model , 2000 .

[35]  Hirofumi Tomita,et al.  Shallow water model on a modified icosahedral geodesic grid by using spring dynamics , 2001 .

[36]  Masaki Satoh,et al.  Conservative scheme for the compressible nonhydrostatic models with the horizontally explicit and vertically implicit time integration scheme , 2002 .

[37]  R. Bermejo,et al.  A Conservative Quasi-Monotone Semi-Lagrangian Scheme , 2002 .

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

[39]  Hirofumi Tomita,et al.  An optimization of the Icosahedral grid modified by spring dynamics , 2002 .

[40]  Todd D. Ringler,et al.  The ZM Grid: An Alternative to the Z Grid , 2002 .

[41]  R. Bermejo,et al.  NOTES AND CORRESPONDENCE A Conservative Quasi-Monotone Semi-Lagrangian Scheme , 2002 .

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

[43]  Qiang Du,et al.  Constrained Centroidal Voronoi Tessellations for Surfaces , 2002, SIAM J. Sci. Comput..

[44]  Masaki Satoh Conservative Scheme for a Compressible Nonhydrostatic Model with Moist Processes , 2003 .

[45]  W. Skamarock Evaluating Mesoscale NWP Models Using Kinetic Energy Spectra , 2004 .

[46]  A. Kageyama,et al.  ``Yin-Yang grid'': An overset grid in spherical geometry , 2004, physics/0403123.

[47]  Hirofumi Tomita,et al.  A new dynamical framework of nonhydrostatic global model using the icosahedral grid , 2004 .

[48]  Shian‐Jiann Lin A “Vertically Lagrangian” Finite-Volume Dynamical Core for Global Models , 2004 .

[49]  John Thuburn,et al.  Vertical discretizations for compressible Euler equation atmospheric models giving optimal representation of normal modes , 2005 .

[50]  A. Staniforth,et al.  A new dynamical core for the Met Office's global and regional modelling of the atmosphere , 2005 .

[51]  J. Szmelter,et al.  MPDATA: An edge-based unstructured-grid formulation , 2005 .

[52]  Ulrike Wacker,et al.  Evaporation and Precipitation Surface Effects in Local Mass Continuity Laws of Moist Air , 2006 .

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

[54]  Shian-Jiann Lin,et al.  Finite-volume transport on various cubed-sphere grids , 2007, J. Comput. Phys..

[55]  H. Miura An Upwind-Biased Conservative Advection Scheme for Spherical Hexagonal–Pentagonal Grids , 2007 .

[56]  Roni Avissar,et al.  The Ocean-Land-Atmosphere Model (OLAM). Part II: Formulation and Tests of the Nonhydrostatic Dynamic Core , 2008 .

[57]  Martin J. Gander,et al.  shallow-water equations: preliminary results , 2022 .

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

[59]  Christiane Jablonowski Idealized test cases for the dynamical cores of Atmospheric General Circulation Models : A proposal for the NCAR ASP 2008 summer colloquium , 2008 .

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

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

[62]  Jimy Dudhia,et al.  An Upper Gravity-Wave Absorbing Layer for NWP Applications , 2008 .

[63]  J. Prusa,et al.  EULAG, a computational model for multiscale flows , 2008 .

[64]  Almut Gassmann,et al.  Towards a consistent numerical compressible non‐hydrostatic model using generalized Hamiltonian tools , 2008 .

[65]  John Thuburn,et al.  Some conservation issues for the dynamical cores of NWP and climate models , 2008, J. Comput. Phys..

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

[67]  H. Tufo,et al.  Computational aspects of a scalable high-order discontinuous Galerkin atmospheric dynamical core , 2009 .

[68]  A. Arakawa,et al.  Unification of the Anelastic and Quasi-Hydrostatic Systems of Equations , 2009 .

[69]  Y. Baba,et al.  Dynamical Core of an Atmospheric General Circulation Model on a Yin-Yang Grid , 2010 .

[70]  Mark A. Taylor,et al.  A compatible and conservative spectral element method on unstructured grids , 2010, J. Comput. Phys..

[71]  Ramaswamy,et al.  The dynamical core, physical parameterizations, and basic simulation characteristics of the atmospheric component AM3 of the GFDL global coupled model CM3 , 2011 .

[72]  Joanna Szmelter,et al.  An edge-based unstructured mesh discretisation in geospherical framework , 2010, J. Comput. Phys..

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

[74]  J. Szmelter,et al.  A nonhydrostatic unstructured-mesh soundproof model for simulation of internal gravity waves , 2011 .

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

[76]  Vivian Lee,et al.  The Canadian Global Environmental Multiscale model on the Yin‐Yang grid system , 2011 .

[77]  Roni Avissar,et al.  A Direct Method for Constructing Refined Regions in Unstructured Conforming Triangular–Hexagonal Computational Grids: Application to OLAM , 2011 .

[78]  Ryoichi Imasu,et al.  A Three-Dimensional Icosahedral Grid Advection Scheme Preserving Monotonicity and Consistency with C , 2011 .

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

[80]  Christiane Jablonowski,et al.  The pros and cons of diffusion, filters and fixers in Atmospheric General Circulation Models , 2011 .

[81]  Christiane Jablonowski,et al.  Operator-Split Runge-Kutta-Rosenbrock Methods for Nonhydrostatic Atmospheric Models , 2012 .

[82]  Mark A. Taylor,et al.  CAM-SE: A scalable spectral element dynamical core for the Community Atmosphere Model , 2012, Int. J. High Perform. Comput. Appl..

[83]  Christian Kühnlein,et al.  Modelling atmospheric flows with adaptive moving meshes , 2012, J. Comput. Phys..

[84]  Todd D. Ringler,et al.  A Multiscale Nonhydrostatic Atmospheric Model Using Centroidal Voronoi Tesselations and C-Grid Staggering , 2012 .

[85]  Colin J. Cotter,et al.  Mixed finite elements for numerical weather prediction , 2011, J. Comput. Phys..

[86]  Colin J. Cotter,et al.  Computational Modes and Grid Imprinting on Five Quasi-Uniform Spherical C Grids , 2012 .

[87]  Hilary Weller,et al.  Controlling the Computational Modes of the Arbitrarily Structured C Grid , 2012 .

[88]  Sarah-Jane Lock,et al.  Demonstration of a Cut-Cell Representation of 3D Orography for Studies of Atmospheric Flows over Very Steep Hills , 2012 .

[89]  Marsha J. Berger,et al.  A Simplified h-box Method for Embedded Boundary Grids , 2012, SIAM J. Sci. Comput..

[90]  John Thuburn,et al.  Horizontal grids for global weather and climate prediction models: a review , 2012 .

[91]  James Kent,et al.  Dynamical Core Model Intercomparison Project ( DCMIP ) Test Case Document , 2012 .

[92]  Christiane Jablonowski,et al.  MCore: A non-hydrostatic atmospheric dynamical core utilizing high-order finite-volume methods , 2012, J. Comput. Phys..

[93]  Eigil Kaas,et al.  A mass-conserving and multi-tracer efficient transport scheme in the online integrated Enviro-HIRLAM model , 2012 .

[94]  Almut Gassmann,et al.  A global hexagonal C‐grid non‐hydrostatic dynamical core (ICON‐IAP) designed for energetic consistency , 2013 .

[95]  David A. Randall,et al.  Optimized Icosahedral Grids: Performance of Finite-Difference Operators and Multigrid Solver , 2013 .

[96]  Emil M. Constantinescu,et al.  Implicit-Explicit Formulations of a Three-Dimensional Nonhydrostatic Unified Model of the Atmosphere (NUMA) , 2013, SIAM J. Sci. Comput..

[97]  Nigel Wood,et al.  Runge-Kutta IMEX schemes for the Horizontally Explicit/Vertically Implicit (HEVI) solution of wave equations , 2013, J. Comput. Phys..

[98]  Shian-Jiann Lin,et al.  A Two-Way Nested Global-Regional Dynamical Core on the Cubed-Sphere Grid , 2013 .

[99]  N. Wood,et al.  Comparison of Lorenz and Charney–Phillips vertical discretisations for dynamics–boundary layer coupling. Part II: Transients , 2013 .

[100]  Paul A. Ullrich,et al.  Understanding the treatment of waves in atmospheric models. Part 1: The shortest resolved waves of the 1D linearized shallow‐water equations , 2014 .

[101]  Mark A. Taylor,et al.  Optimization-based limiters for the spectral element method , 2014, J. Comput. Phys..

[102]  Paul A. Ullrich A global finite-element shallow-water model supporting continuous and discontinuous elements , 2014 .

[103]  M. Diamantakis,et al.  An inherently mass‐conserving semi‐implicit semi‐Lagrangian discretization of the deep‐atmosphere global non‐hydrostatic equations , 2014 .

[104]  Jean Côté,et al.  Staggered Vertical Discretization of the Canadian Environmental Multiscale (GEM) Model Using a Coordinate of the Log-Hydrostatic-Pressure Type , 2014 .

[105]  Thomas Dubos,et al.  Equations of Atmospheric Motion in Non-Eulerian Vertical Coordinates: Vector-Invariant Form and Quasi-Hamiltonian Formulation , 2014 .

[106]  Christian Kühnlein,et al.  A consistent framework for discrete integrations of soundproof and compressible PDEs of atmospheric dynamics , 2014, J. Comput. Phys..

[107]  Piotr K. Smolarkiewicz,et al.  Anelastic and Compressible Simulation of Moist Deep Convection , 2014 .

[108]  Frédéric Hourdin,et al.  On the inter-comparison of two tracer transport schemes on icosahedral grids , 2015 .

[109]  G. Zängl,et al.  The ICON (ICOsahedral Non‐hydrostatic) modelling framework of DWD and MPI‐M: Description of the non‐hydrostatic dynamical core , 2015 .

[110]  Thomas Dubos,et al.  DYNAMICO-1.0, an icosahedral hydrostatic dynamical core designed for consistency and versatility , 2015 .

[111]  James D Doyle A Next Generation Atmospheric Prediction System for the Navy , 2015 .

[112]  Günther Zängl,et al.  Large eddy simulation using the general circulation model ICON , 2015 .

[113]  C. McLinden,et al.  Semi-Lagrangian Advection of Stratospheric Ozone on a Yin–Yang Grid System , 2016 .

[114]  Paul A. Ullrich,et al.  A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models , 2016 .

[115]  Mats Hamrud,et al.  A new grid for the IFS , 2016 .

[116]  Mats Hamrud,et al.  A finite-volume module for simulating global all-scale atmospheric flows , 2016, J. Comput. Phys..

[117]  Shian‐Jiann Lin,et al.  High-Resolution Climate Simulations Using GFDL HiRAM with a Stretched Global Grid , 2016 .

[118]  Christian Kühnlein,et al.  An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics , 2017, J. Comput. Phys..

[119]  Peter Bauer,et al.  Atlas : A library for numerical weather prediction and climate modelling , 2017, Comput. Phys. Commun..

[120]  Carol S. Woodward,et al.  Implicit–explicit (IMEX) Runge–Kutta methods for non-hydrostatic atmospheric models , 2017 .

[121]  Christian Kühnlein,et al.  A finite-volume module for cloud-resolving simulations of global atmospheric flows , 2017, J. Comput. Phys..