A Numerical Analysis of Six Physics‐Dynamics Coupling Schemes for Atmospheric Models.

Six strategies to couple the dynamical core with physical parameterizations in atmospheric models are analyzed from a numerical perspective. Thanks to a suitably designed theoretical framework featuring a high level of abstraction, the truncation error analysis and the linear stability study are carried out under weak assumptions. Indeed, second‐order conditions are derived which are not influenced either by the specific formulation of the governing equations, nor by the number of parameterizations, nor by the structural design and implementation details of the time‐stepping methods. The theoretical findings are verified on two idealized test beds. Particularly, a hydrostatic model in isentropic coordinates is used for vertical slice simulations of a moist airflow past an isolated mountain. Self‐convergence tests show that the sensitivity of the prognostic variables to the coupling scheme may vary. For those variables (e.g., momentum) whose evolution is mainly driven by the dry dynamics, the truncation error associated with the dynamical core dominates and hides the error due to the coupling. In contrast, the coupling error of moist variables (e.g., the precipitation rate) emerges gradually as the spatio‐temporal resolution increases. Eventually, each coupling scheme tends toward the formal order of accuracy, upon a careful treatment of the grid cell condensation. Indeed, the well‐established saturation adjustment may cap the convergence rate to first order. A prognostic formulation of the condensation and evaporation process is derived from first principles. This solution is shown effective to alleviate the convergence issues in our experiments. Potential implications for a complete forecasting system are discussed. Plain Language Summary: The Earth science community has achieved tremendous progresses in the comprehension, modeling and discretization of the phenomena which occur in the atmosphere. On the other hand, the interactions between the explicitly represented dynamics and the parameterized processes are still less understood, and as a result processes are typically coupled in a low‐accurate fashion in weather and climate numerical models. This work examines six coupling strategies and establishes the conditions in order that the error decays quadratically in the time‐step size. It is found that only two methods do not impose any requirement either on the nature of the problem, nor on the process ordering. Numerical evidence of these theoretical results is grasped via self‐convergence studies conducted on two representative sets of equations. Not all model variables show the same degree of sensitivity to the choice of the coupling though. Plus, the higher‐accurate schemes turn out to be the most computational expensive. Yet, their employment may be well justified at fine grid resolutions where the coupling error dominates on the truncation error associated with the individual processes. Key Points: Accuracy and stability properties of several physics‐dynamics coupling schemes are analyzed from theoretical and practical perspectivesAccuracy of schemes is derived analytically under relaxed assumptions and validated numerically on two idealized modelsA prognostic approach to grid cell condensation is shown beneficial for the numerical convergence in comparison to the saturation adjustment [ABSTRACT FROM AUTHOR]

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