Climate Dynamics

, Volume 50, Issue 7–8, pp 2673–2686 | Cite as

Three-pattern decomposition of global atmospheric circulation: part II—dynamical equations of horizontal, meridional and zonal circulations

  • Shujuan Hu
  • Jianbo Cheng
  • Ming Xu
  • Jifan Chou


The three-pattern decomposition of global atmospheric circulation (TPDGAC) partitions three-dimensional (3D) atmospheric circulation into horizontal, meridional and zonal components to study the 3D structures of global atmospheric circulation. This paper incorporates the three-pattern decomposition model (TPDM) into primitive equations of atmospheric dynamics and establishes a new set of dynamical equations of the horizontal, meridional and zonal circulations in which the operator properties are studied and energy conservation laws are preserved, as in the primitive equations. The physical significance of the newly established equations is demonstrated. Our findings reveal that the new equations are essentially the 3D vorticity equations of atmosphere and that the time evolution rules of the horizontal, meridional and zonal circulations can be described from the perspective of 3D vorticity evolution. The new set of dynamical equations includes decomposed expressions that can be used to explore the source terms of large-scale atmospheric circulation variations. A simplified model is presented to demonstrate the potential applications of the new equations for studying the dynamics of the Rossby, Hadley and Walker circulations. The model shows that the horizontal air temperature anomaly gradient (ATAG) induces changes in meridional and zonal circulations and promotes the baroclinic evolution of the horizontal circulation. The simplified model also indicates that the absolute vorticity of the horizontal circulation is not conserved, and its changes can be described by changes in the vertical vorticities of the meridional and zonal circulations. Moreover, the thermodynamic equation shows that the induced meridional and zonal circulations and advection transport by the horizontal circulation in turn cause a redistribution of the air temperature. The simplified model reveals the fundamental rules between the evolution of the air temperature and the horizontal, meridional and zonal components of global atmospheric circulation.


Three-pattern decomposition of global atmospheric circulation New dynamical equations of horizontal, meridional and zonal circulations Three-dimensional vorticity equations Simplified dynamical equations 



This work was supported by the National Natural Science Foundation of China (41475068, 41475064, 41530531 and 41630421) and the Foundation of Key Laboratory for Semi-Arid Climate Change of the Ministry of Education in Lanzhou University. All of the authors express thank to the editor and anonymous reviewers for their useful suggestions and comments.

Supplementary material

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Supplementary material 1 (PDF 433 KB)


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Key Laboratory for Semi-Arid Climate Change of the Ministry of Education, College of Atmospheric SciencesLanzhou UniversityLanzhouChina
  2. 2.Shanghai Typhoon InstituteShanghaiChina

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