Stability and accuracy of the physics—dynamics coupling in spectral models

Abstract

AbstractThis article first reviews the existing spectral time‐step organizations of the Integrated Forecast System (IFS) of the ECMWF and the ARPEGE/ALADIN/AROME models of Météo‐France and the ALADIN partners. They are characterized according to four choices concerning the physics—dynamics coupling: (1) the order in which the physics parametrization and the dynamics are called and coupled inside the time‐step computation, (2) the space‐time location of the physics coupling on the semi‐Lagrangian trajectory, (3) parallel or sequential time stepping of the different physics parametrizations and (4) parallel or sequential physics—dynamics coupling. It is found that according to this classification, IFS on the one hand and the ARPEGE/ALADIN/AROME models on the other hand exhibit two distinct structures.In the models, the dynamical cores of the semi‐implicit semi‐Lagrangian two‐time‐level schemes are linearized around a stationary reference state. This state differs from the real atmospheric state (i.e. the exact solution of the equations). This article generalizes the framework introduced by Staniforth, Wood and Côté to study the relation between the coupled physics parametrization and such reference and atmospheric states. Subsequently, the two above‐mentioned time‐step organizations are translated into this simplified frame. Extra degrees of freedom are added to allow for obvious improvements of the existing spectral time‐step organizations. In order to deal with the complexity of the emerging structures and to avoid tedious algebraic manipulations, a numerical methodology is proposed to characterize their properties. This framework is then used to make a comparative study of the numerical stability and the accuracy of the physics—dynamics coupling within the two above‐mentioned time‐step organizations. Potential improvements are briefly discussed. Copyright © 2007 Royal Meteorological Society