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

Abstract 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 stud...

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Autores principales:	Stefano Ubbiali, Christoph Schär, Linda Schlemmer, Thomas C. Schulthess
Formato:	article
Lenguaje:	EN
Publicado:	American Geophysical Union (AGU) 2021
Materias:	physics‐dynamics coupling time‐step convergence numerical analysis Physical geography GB3-5030 Oceanography GC1-1581
Acceso en línea:	https://doaj.org/article/8d64b0e2e3e14cb3aab20a0fda14a83c
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spelling	oai:doaj.org-article:8d64b0e2e3e14cb3aab20a0fda14a83c2021-11-30T08:40:32ZA Numerical Analysis of Six Physics‐Dynamics Coupling Schemes for Atmospheric Models1942-246610.1029/2020MS002377https://doaj.org/article/8d64b0e2e3e14cb3aab20a0fda14a83c2021-11-01T00:00:00Zhttps://doi.org/10.1029/2020MS002377https://doaj.org/toc/1942-2466Abstract 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.Stefano UbbialiChristoph SchärLinda SchlemmerThomas C. SchulthessAmerican Geophysical Union (AGU)articlephysics‐dynamics couplingtime‐step convergencenumerical analysisPhysical geographyGB3-5030OceanographyGC1-1581ENJournal of Advances in Modeling Earth Systems, Vol 13, Iss 11, Pp n/a-n/a (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	physics‐dynamics coupling time‐step convergence numerical analysis Physical geography GB3-5030 Oceanography GC1-1581
spellingShingle	physics‐dynamics coupling time‐step convergence numerical analysis Physical geography GB3-5030 Oceanography GC1-1581 Stefano Ubbiali Christoph Schär Linda Schlemmer Thomas C. Schulthess A Numerical Analysis of Six Physics‐Dynamics Coupling Schemes for Atmospheric Models
description	Abstract 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.
format	article
author	Stefano Ubbiali Christoph Schär Linda Schlemmer Thomas C. Schulthess
author_facet	Stefano Ubbiali Christoph Schär Linda Schlemmer Thomas C. Schulthess
author_sort	Stefano Ubbiali
title	A Numerical Analysis of Six Physics‐Dynamics Coupling Schemes for Atmospheric Models
title_short	A Numerical Analysis of Six Physics‐Dynamics Coupling Schemes for Atmospheric Models
title_full	A Numerical Analysis of Six Physics‐Dynamics Coupling Schemes for Atmospheric Models
title_fullStr	A Numerical Analysis of Six Physics‐Dynamics Coupling Schemes for Atmospheric Models
title_full_unstemmed	A Numerical Analysis of Six Physics‐Dynamics Coupling Schemes for Atmospheric Models
title_sort	numerical analysis of six physics‐dynamics coupling schemes for atmospheric models
publisher	American Geophysical Union (AGU)
publishDate	2021
url	https://doaj.org/article/8d64b0e2e3e14cb3aab20a0fda14a83c
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A Numerical Analysis of Six Physics‐Dynamics Coupling Schemes for Atmospheric Models

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