Aspects of the dynamical core of a nonhydrostatic, deep-atmosphere, unified weather and climate-prediction model

The dynamical core, which governs the evolution of resolved fluid-dynamical processes, is a critical element of any atmospheric model. Its governing equations must include all relevant dynamical terms, and the numerical formulae used to approximate them must be accurate, stable and efficient. This is particularly so in a unified modeling environment in which the same dynamical core is used for both operational weather prediction and long term climate simulations. Recent research at the Met Office on unified dynamical core issues is reviewed. Aspects covered include: properties of various equation sets; vertical coordinates; semi-Lagrangian advection and conservation; trajectory computation and dynamical equivalence; horizontal and vertical discretization; and coupling of physical parameterizations to a dynamical core.

[1]  Nigel Wood,et al.  The deep‐atmosphere Euler equations with a mass‐based vertical coordinate , 2003 .

[2]  Nigel Wood,et al.  Analysis of the response to orographic forcing of a time‐staggered semi‐Lagrangian discretization of the rotating shallow‐water equations , 2006 .

[3]  A. Robert.  A Semi-Lagrangian and Semi-Implicit Numerical Integration Scheme for the Primitive Meteorological Equations , 1982 .

[4]  André Robert,et al.  Spurious Resonant Response of Semi-Lagrangian Discretizations to Orographic Forcing: Diagnosis and Solution , 1994 .

[5]  Nigel Wood,et al.  An improved regularization for time‐staggered discretization and its link to the semi‐implicit method , 2006 .

[6]  Terry Davies,et al.  An improved implicit predictor–corrector scheme for boundary layer vertical diffusion , 2006 .

[7]  A. Kasahara,et al.  On the Nonhydrostatic Atmospheric Models with Inclusion of the Horizontal Component of the Earth’s Angular Velocity , 2003 .

[8]  Sebastian Reich,et al.  Linearly implicit time stepping methods for numerical weather prediction , 2006 .

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

[10]  Andrew Staniforth,et al.  Application of the parabolic spline method (PSM) to a multi-dimensional conservative semi-Lagrangian transport scheme (SLICE) , 2007, J. Comput. Phys..

[11]  Clive Temperton,et al.  A two‐time‐level semi‐Lagrangian global spectral model , 2001 .

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

[13]  Nigel Wood,et al.  A monotonic and positive–definite filter for a Semi‐Lagrangian Inherently Conserving and Efficient (SLICE) scheme , 2005 .

[14]  Nigel Wood,et al.  Mixed Parallel–Sequential-Split Schemes for Time-Stepping Multiple Physical Parameterizations , 2005 .

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

[16]  Dale R. Durran,et al.  Comments on “The Roles of the Horizontal Component of the Earth's Angular Velocity in Nonhydrostatic Linear Models” , 2004 .

[17]  A. Kasahara,et al.  The Roles of the Horizontal Component of the Earth's Angular Velocity in Nonhydrostatic Linear Models , 2003 .

[18]  Nigel Wood,et al.  A Simple Comparison of Four Physics–Dynamics Coupling Schemes , 2002 .

[19]  Nigel Wood,et al.  Some numerical properties of approaches to physics–dynamics coupling for NWP , 2006 .

[20]  A. White,et al.  Dynamical equivalence and the departure‐point equation in semi‐Lagrangian numerical models , 2003 .

[21]  Knoch.  Deutsche Meteorologische Gesellschaft , 2005, Naturwissenschaften.

[22]  Andrew Staniforth,et al.  André Robert (1929–1993): His Pioneering Contributions to Numerical Modelling , 1997 .

[23]  M. J. P. Cullen,et al.  The unified forecast/climate model , 1993 .

[24]  Nigel Wood,et al.  Analysis of the numerics of physics–dynamics coupling , 2002 .

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

[26]  M. J. P. Cullen,et al.  On the use of a predictor–corrector scheme to couple the dynamics with the physical parametrizations in the ECMWF model , 2003 .

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

[28]  Nigel Wood,et al.  Energy and energy‐like invariants for deep non‐hydrostatic atmospheres , 2003 .

[29]  Jean Côté,et al.  Variable resolution general circulation models: Stretched‐grid model intercomparison project (SGMIP) , 2006 .

[30]  A. Staniforth,et al.  Semi-Lagrangian integration schemes for atmospheric models - A review , 1991 .

[31]  A. Kasahara,et al.  Reply [to Comments on "The roles of the horizontal components of the Earth's angular velocity in nonhydrostatic linear models" , 2004 .

[32]  A. Staniforth,et al.  Regional modeling: A theoretical discussion , 1997 .

[33]  M. J. P. Cullen,et al.  Alternative implementations of the semi‐Lagrangian semi‐implicit schemes in the ECMWF model , 2001 .

[34]  Nigel Wood,et al.  Analysis of Parallel versus Sequential Splittings for Time-Stepping Physical Parameterizations , 2004 .

[35]  Nigel Wood,et al.  Analysis of semi-Lagrangian trajectory computations , 2003 .

[36]  B. Hoskins,et al.  Consistent approximate models of the global atmosphere: shallow, deep, hydrostatic, quasi‐hydrostatic and non‐hydrostatic , 2005 .

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

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

[39]  John Thuburn,et al.  Vertical discretizations giving optimal representation of normal modes: Sensitivity to the form of the pressure‐gradient term , 2006 .

[40]  Martin Köhler,et al.  The numerics of physical parametrization , 2004 .

[41]  Piotr K. Smolarkiewicz,et al.  Two-Time-Level Semi-Lagrangian Modeling of Precipitating Clouds , 1996 .

[42]  Eugenia Kalnay,et al.  Time Schemes for Strongly Nonlinear Damping Equations , 1988 .

[43]  Monique Tanguay,et al.  A Semi-implicit Send-Lagrangian Fully Compressible Regional Forecast Model , 1990 .

[44]  Mariano Hortal,et al.  A finite‐element scheme for the vertical discretization of the semi‐Lagrangian version of the ECMWF forecast model , 2004 .

[45]  Claude Girard,et al.  Stable Schemes for Nonlinear Vertical Diffusion in Atmospheric Circulation Models , 1990 .

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

[47]  André Robert,et al.  A stable numerical integration scheme for the primitive meteorological equations , 1981 .

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

[49]  René Laprise,et al.  Consequences of Using the Splitting Method for Implementing Physical Forcings in a Semi-Implicit Semi-Lagrangian Model , 1998 .

[50]  Terry Davies,et al.  Validity of anelastic and other equation sets as inferred from normal‐mode analysis , 2003 .

[51]  M. Zerroukat.  A three-dimensional conservative semi-Lagrangian scheme (SLICE-3D) for transport problems∗ , 2006 .

[52]  Nigel Wood,et al.  SLICE: A Semi‐Lagrangian Inherently Conserving and Efficient scheme for transport problems , 2002 .

[53]  David L. Williamson,et al.  Time-Split versus Process-Split Coupling of Parameterizations and Dynamical Core , 2002 .

[54]  Nigel Wood,et al.  Normal modes of deep atmospheres. I: Spherical geometry , 2002 .

[55]  Nigel Wood,et al.  Normal modes of deep atmospheres. II: f–F‐plane geometry , 2002 .

[56]  Nigel Wood,et al.  An Unsuspected Boundary-Induced Temporal Computational Mode in a Two-Time-Level Discretization , 2005 .

[57]  Nigel Wood,et al.  The Parabolic Spline Method (PSM) for conservative transport problems , 2006 .

[58]  Nigel Wood,et al.  Analysis of a regularized, time‐staggered discretization applied to a vertical slice model , 2006 .

[59]  Nigel Wood,et al.  Comments on ‘A finite‐element scheme for the vertical discretization in the semi‐Lagrangian version of the ECMWF forecast model’ by A. Untch and M. Hortal (April B, 2004, 130, 1505–1530) , 2005 .

[60]  Lance M. Leslie,et al.  An Efficient Interpolation Procedure for High-Order Three-Dimensional Semi-Lagrangian Models , 1991 .

[61]  Nigel Wood,et al.  A time-staggered semi-Lagrangian discretization of the rotating shallow-water equations , 2006 .

[62]  John Thuburn,et al.  Conservation and Linear Rossby-Mode Dispersion on the Spherical C Grid , 2004 .

[63]  Nigel Wood,et al.  SLICE‐S: A Semi‐Lagrangian Inherently Conserving and Efficient scheme for transport problems on the Sphere , 2004 .

[64]  Nigel Wood,et al.  Impact of semi‐Lagrangian trajectories on the discrete normal modes of a non‐hydrostatic vertical‐column model , 2005 .

[65]  Jason Frank,et al.  Analysis of a regularized, time‐staggered discretization method and its link to the semi‐implicit method , 2005 .

[66]  M. Déqué,et al.  Variable-Resolution GCMs for Regional Climate Modeling: Stretched-Grid Model Intercomparison Project (SGMIP) , 2006 .