An Overview of Numerical Methods for the Next Generation U.K. NWP and Climate Model

ABSTRACT The U.K. Meteorological Office now uses a single model for atmospheric simulation and forecasting from all scales from mesoscale to climate. The constraints which numerical methods for such a model have to satisfy are described. A new version of the model is being developed with the aims of improving its accuracy by better treatment of the ‘balanced’ part of the flow, and increasing its applicability by including non-hydrostatic effects. Unusual features of this version are the use of the Charney-Phillips grid in the vertical, to improve the geostrophic adjustment properties, and the method of constructing the semi-implicit algorithm for solving the fully compressible equations. Idealized tests of these two aspects of the scheme are presented, showing that the Charney-Phillips grid reduces spurious gravity wave generation without compromising the treatment of the atmospheric boundary layer, and that the semi-implicit integration scheme can give stable solutions without the need for added temporal...

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

[2]  M. Cullen.  Implicit finite difference methods for modelling discontinuous atmospheric flows , 1989 .

[3]  Noboru Nakamura,et al.  Nonlinear Equilibration of Two-Dimensional Eady Waves , 1989 .

[4]  M. J. P. Cullen,et al.  A conservative split‐explicit integration scheme with fourth‐order horizontal advection , 1991 .

[5]  George L. Mellor,et al.  A Simulation of the Wangara Atmospheric Boundary Layer Data , 1975 .

[6]  Wayne H. Schubert,et al.  Multigrid methods for elliptic problems: a review , 1986 .

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

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

[9]  Noboru Nakamura.  Nonlinear Equilibration of Two-Dimensional Eady Waves: Simulations with Viscous Geostrophic Momentum Equations , 1994 .

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

[11]  A. J. Gadd.  A split explicit integration scheme for numerical weather prediction , 1978 .

[12]  A. Priestley.  A Quasi-Conservative Version of the Semi-Lagrangian Advection Scheme , 1993 .

[13]  A. White,et al.  Dynamically consistent, quasi-hydrostatic equations for global models with a complete representation of the Coriolis force , 1995 .

[14]  B. W. Golding.  A Study of the Influence of Terrain on Fog Development , 1993 .

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

[16]  David L. Williamson,et al.  Climate Simulations with a Semi-Lagrangian Version of the NCAR Community Climate Model , 1994 .

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

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

[19]  L. Leslie,et al.  A comparative study of the performance of various vertical discretization schemes , 1992 .

[20]  Philippe Courtier,et al.  A global numerical weather prediction model with variable resolution: Application to the shallow‐water equations , 1988 .

[21]  R. T. Williams.  Quasi-Geostrophic versus Non-Geostrophic Frontogenesis , 1972 .

[22]  K. Morton.  A comparison of flux limited difference methods and characteristic Galerkin methods for shock modelling , 1987 .

[23]  R. T. Williams,et al.  Atmospheric Frontogenesis: A Numerical Experiment. , 1967 .

[24]  B. Golding.  An efficient non-hydrostatic forecast model , 1992 .

[25]  Saulo R. M. Barros,et al.  Integration of the shallow water equations on the sphere using a vector semi-Lagrangian scheme with a multigrid solver , 1990 .

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