Treatment of the Coriolis Terms in Semi-Lagrangian Spectral Models

ABSTRACT In a conventional three-time-level semi-Lagrangian scheme, the Coriolis terms are treated in an explicit centred fashion. This option is not available in a two-time-level scheme, and an alternative treatment must be sought. Two possible alternatives are tested here in the framework of a three-time-level scheme. Both are stable and accurate, but only one generalizes easily to a rotated coordinate system; this alternative is based on absorbing the Coriolis terms into the semi-Lagrangian advection.

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

[2]  Jean Côté,et al.  A Two-Time-Level Semi-Lagrangian Semi-implicit Scheme for Spectral Models , 1988 .

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

[4]  Roberto Buizza,et al.  Computation of optimal unstable structures for a numerical weather prediction model , 1993 .

[5]  A. Simmons,et al.  Implementation of the Semi-Lagrangian Method in a High-Resolution Version of the ECMWF Forecast Model , 1995 .

[6]  William Bourke,et al.  An Efficient, One-Level, Primitive-Equation Spectral Model , 1972 .

[7]  P. Courtier,et al.  Four-dimensional variational data assimilation using the adjoint of a multilevel primitive-equation model , 1991 .

[8]  Achi Brandt,et al.  A global shallow‐water numerical model based on the semi‐lagrangian advection of potential vorticity , 1995 .

[9]  Harold Ritchie,et al.  Application of the Semi-Lagrangian Method to a Spectral Model of the Shallow Water Equations , 1988 .

[10]  Philippe Courtier,et al.  Use of cloud‐cleared radiances in three/four‐dimensional variational data assimilation , 1994 .

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

[12]  Harold Ritchie,et al.  Approximations and Sensitivity Experiments with a Baroclinic Semi-Lagrangian Spectral Model , 1994 .

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