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Numerical Techniques for Global Atmospheric Models pp 357–380Cite as

Conservation of Mass and Energy for the Moist Atmospheric Primitive Equations on Unstructured Grids

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 80))

Abstract

The primitive variable formulation of the moist hydrostatic equations conserves mass and moist total energy due to the property that the divergence and gradient operators are adjoints. Any compatible numerical method, which has a discrete analog of this property will conserve a discrete mass and total energy. We demonstrate this using aqua-planet simulations performed with CAM-HOMME (NCAR’s Community Atmospheric Model with the High-Order Method Modeling Environment dynamical core). CAM-HOMME uses a compatible numerical method on arbitrary unstructured quadrilateral grid. The equations described here are the full set of dynamical equations used by CAM. Aqua-planet simulations use the full suite of physics parametrizations as well. The only simplification is the use of idealized surface conditions. We report on the magnitude of the total energy budget in the dynamical core including estimates for the non-adiabatic processes. The practice of fixing dry total energy as opposed to the conserved total moist energy is shown to generate a forcing of − 0. 56 W/m2.

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Acknowledgements

We thank the reviewers for many useful and detailed comments and P.H. Lauritzen for the vertical coordinate figure. This work supported by DOE/BER grant 06-13194.

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Authors and Affiliations

  1. Sandia National Laboratories, Albuquerque, NM, 87185, USA

    Mark A. Taylor

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  1. Mark A. Taylor
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Correspondence to Mark A. Taylor .

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Editors and Affiliations

  1. Atmospheric Research, Dept. Climate/Global Dyn., National Center for, Boulder, Colorado, USA

    Peter Lauritzen

  2. Dept. Atmospheric, Oceanic &, Space Sciences, University of Michigan, Hayward St. 2455, Ann Arbor, 48109, Michigan, USA

    Christiane Jablonowski

  3. Organization 1433, MS-0370, Sandia National Laboratories, Albuquerque, New Mexico, USA

    Mark Taylor

  4. (NCAR), Inst. for Mathematics Applied to, National Center for Atmospheric Research, Boulder, Colorado, USA

    Ramachandran Nair

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Taylor, M.A. (2011). Conservation of Mass and Energy for the Moist Atmospheric Primitive Equations on Unstructured Grids. In: Lauritzen, P., Jablonowski, C., Taylor, M., Nair, R. (eds) Numerical Techniques for Global Atmospheric Models. Lecture Notes in Computational Science and Engineering, vol 80. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11640-7_12

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