A new dynamical framework of nonhydrostatic global model using the icosahedral grid

For a nonhydrostatic global model that is run efficiently at super-high resolution, we propose the use of an icosahedral grid, which is one of the quasi-homogeneous grid systems. In this paper, we concentrate mainly on the description of the numerical scheme of a new dynamical framework using the icosahedral grid. The numerical method guarantees conservations of mass and total energy. To reduce the computational cost, the time-splitting scheme is employed and the set of equations is solved explicitly in the horizontal directions and implicitly in the vertical direction. This scheme only requires solving a one-dimensional Helmholtz equation for the vertical momentum. With the combination of this conservative nonhydrostatic scheme and the icosahedral grid, it is expected that the new model will efficiently run for super-high resolution simulations.For the first assessment of the performance of the new dynamical core, we performed fundamental wave propagation tests; acoustic waves, gravity waves, mountain waves, equatorial waves, and planetary waves. In order to check the performance as a climate model, we also performed the Held-Suarez Test Case as a statistical test. As a result, our model result has good correspondence with that of other established models.

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

[2]  Hyeong-Bin Cheong,et al.  Double Fourier Series on a Sphere , 2000 .

[3]  Todd D. Ringler,et al.  Modeling the Atmospheric General Circulation Using a Spherical Geodesic Grid: A New Class of Dynamical Cores , 2000 .

[4]  J. Dudhia.  A Nonhydrostatic Version of the Penn State–NCAR Mesoscale Model: Validation Tests and Simulation of an Atlantic Cyclone and Cold Front , 1993 .

[5]  Jimy Dudhia,et al.  A Global Version of the PSU/NCAR Mesoscale Model , 2002 .

[6]  G. R. Stuhne,et al.  Vortex Erosion and Amalgamation in a New Model of Large Scale Flow on the Sphere , 1996 .

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

[8]  David L. Williamson,et al.  Integration of the barotropic vorticity equation on a spherical geodesic grid , 1968 .

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

[10]  William C. Skamarock,et al.  Efficiency and Accuracy of the Klemp-Wilhelmson Time-Splitting Technique , 1994 .

[11]  Application of double Fourier series to the shallow-water equations on a sphere , 2000 .

[12]  David A. Randall.  General circulation model development , 2000 .

[13]  M. Taylor.  The Spectral Element Method for the Shallow Water Equations on the Sphere , 1997 .

[14]  Kazuo Saito,et al.  3-D Mountain Waves by the Lokal-Modell of DWD and the MRI Mesoscale Nonhydrostatic Model. , 1998 .

[15]  Reiji Suda,et al.  A fast spherical harmonics transform algorithm , 2002, Math. Comput..

[16]  David A. Randall,et al.  Global Atmospheric Modeling Using a Geodesic Grid with an Isentropic Vertical Coordinate , 2000 .

[17]  Akio Arakawa,et al.  Integration of the Nondivergent Barotropic Vorticity Equation with AN Icosahedral-Hexagonal Grid for the SPHERE1 , 1968 .

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

[19]  Fedor Mesinger.  Chapter 13 - Numerical Methods: The Arakawa Approach, Horizontal Grid, Global, and Limited-Area Modeling , 2000 .

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

[21]  M. J. P. Cullen,et al.  Forecasting and general circulation results from finite element models , 1979 .

[22]  P. Swarztrauber,et al.  A standard test set for numerical approximations to the shallow water equations in spherical geometry , 1992 .

[23]  B. Hoskins,et al.  The initial value problem for tropical perturbations to a baroclinic atmosphere , 1991 .

[24]  Jeffrey S. Scroggs,et al.  A global nonhydrostatic semi-Lagrangian atmospheric model without orography , 1995 .

[25]  Brian J. Hoskins,et al.  The Steady Linear Response of a Spherical Atmosphere to Thermal and Orographic Forcing , 1981 .

[26]  A. Staniforth,et al.  The Operational CMC–MRB Global Environmental Multiscale (GEM) Model. Part I: Design Considerations and Formulation , 1998 .

[27]  Masaki Satoh,et al.  Computational Performance of the Dynamical Part of a Next Generation Climate Model using an Icosahedral Grid on the Earth Simulator , 2003 .

[28]  D. Randall,et al.  A Potential Enstrophy and Energy Conserving Numerical Scheme for Solution of the Shallow-Water Equations on a Geodesic Grid , 2002 .

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

[30]  Trevor Davies,et al.  An Overview of Numerical Methods for the Next Generation U.K. NWP and Climate Model , 1997 .

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

[32]  Brian J. Hoskins,et al.  On the Influence of Orography on Large-Scale Atmospheric Flow. , 1979 .

[33]  Michael Buchhold,et al.  The Operational Global Icosahedral-Hexagonal Gridpoint Model GME: Description and High-Resolution Tests , 2002 .

[34]  Yoshio Kurihara,et al.  Numerical Integration of the Primitive Equations on a Spherical Grid , 1965 .

[35]  G. R. Stuhne,et al.  New icosahedral grid-point discretization of the shallow water equation on the sphere , 1999 .

[36]  L. Margolin,et al.  Forward-in-time differencing for fluids: Nonhydrostatic modeling of fluid motions on a sphere , 1998 .

[37]  Koji Goto,et al.  A Comparison Study of Computational Performace between a Spectral Transform Model and a Gridpoint Model , 2004 .

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

[39]  M. Suárez,et al.  A proposal for the intercomparison of the dynamical cores of atmospheric general circulation models , 1994 .

[40]  M. J. P. Cullen,et al.  Integrations of the primitive equations on a sphere using the finite element method , 1974 .

[41]  B. Hoskins,et al.  The Direct Response to Tropical Heating in a Baroclinic Atmosphere , 1995 .

[42]  David A. Randall,et al.  Numerical Integration of the Shallow-Water Equations on a Twisted Icosahedral Grid. Part II. A Detailed Description of the Grid and an Analysis of Numerical Accuracy , 1995 .

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

[44]  Nigel Wood,et al.  The deep-atmosphere Euler equations in a generalized vertical coordinate , 2003 .

[45]  J. Klemp,et al.  The Simulation of Three-Dimensional Convective Storm Dynamics , 1978 .

[46]  Yoshinobu Masuda,et al.  An Integration Scheme of the Primitive Equation Model with an Icosahedral-Hexagonal Grid System and its Application to the Shallow Water Equations , 1986 .

[47]  David L. Williamson,et al.  INTEGRATION OF THE PRIMITIVE BAROTROPIC MODEL OVER A SPHERICAL GEODESIC GRID , 1970 .

[48]  Louis J. Wicker,et al.  A Time-Splitting Scheme for the Elastic Equations Incorporating Second-Order Runge–Kutta Time Differencing , 1998 .

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

[50]  A. Staniforth,et al.  The Operational CMC–MRB Global Environmental Multiscale (GEM) Model. Part II: Results , 1998 .

[51]  B. Hoskins,et al.  Two paradigms of baroclinic‐wave life‐cycle behaviour , 1993 .

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