An inherently mass‐conserving iterative semi‐implicit semi‐Lagrangian discretization of the non‐hydrostatic vertical‐slice equations

Recently an inherently mass-conserving semi-Lagrangian transport scheme has been successfully coupled to an iterative semi-implicit scheme in a global shallow-water-equation (SWE) model. Here that methodology is extended and applied to an iterative semi-implicit semi-Lagrangian (SISL) compressible, non-hydrostatic vertical-slice model, in which the constant reference state of the SWE model is now replaced by a vertically varying reference state. An advantage of this approach is that it preserves the same basic structure as the interpolating, non-mass-conserving, iterative SISL model. The resulting mass-conserving model is applied to a standard set of test problems for such models and compared with results from both the literature and the interpolating, iterative SISL version of the model. © Crown Copyright 2010. Reproduced with the permission of HMSO. Published by John Wiley & Sons, Ltd.

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

[2]  S. Reich,et al.  Hamiltonian particle‐mesh simulations for a non‐hydrostatic vertical slice model , 2009 .

[3]  Ronald B. Smith.  The Influence of Mountains on the Atmosphere , 1979 .

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

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

[6]  Semi‐implicit methods, nonlinear balance, and regularized equations , 2007 .

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

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

[9]  Nigel Wood,et al.  Determining near-boundary departure points in semi-Lagrangian models , 2009 .

[10]  D. Durran,et al.  An Upper Boundary Condition Permitting Internal Gravity Wave Radiation in Numerical Mesoscale Models , 1983 .

[11]  Roger Temam,et al.  Open Boundary Conditions for the Primitive and Boussinesq Equations , 2003 .

[12]  Peter H. Lauritzen,et al.  Finite-Volume Methods in Meteorology , 2009 .

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

[14]  Sebastian Reich,et al.  A regularization approach for a vertical‐slice model and semi‐Lagrangian Störmer–Verlet time stepping , 2007 .

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

[16]  Michel Desgagné,et al.  Finescale Topography and the MC2 Dynamics Kernel , 2005 .

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

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

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

[20]  Peter H. Lauritzen,et al.  A mass-conservative version of the semi-implicit semi-Lagrangian HIRLAM , 2008 .

[21]  S. Diebels,et al.  Effects of the horizontal component of the Earth's rotation on wave propagation on an f-plane , 1994 .

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

[23]  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..

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

[25]  E. Kaas.  A simple and efficient locally mass conserving semi-Lagrangian transport scheme , 2008 .

[26]  Nigel Wood,et al.  An inherently mass‐conserving semi‐implicit semi‐Lagrangian discretisation of the shallow‐water equations on the sphere , 2009 .

[27]  Peter H. Lauritzen,et al.  A Mass-Conservative Semi-Implicit Semi-Lagrangian Limited-Area Shallow-Water Model on the Sphere , 2006 .

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

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