Abstract
The conservation properties of the continuous, adiabatic and frictionless equations governing atmospheric flow are summarized. It is often considered desirable for atmospheric models to possess analogues of these conservation properties; some of the techniques for obtaining such analogues are noted. However, there is no widespread agreement in the literature on which conservation properties are most important and why. Here we suggest some ways of thinking about these questions, taking into account the atmospheric flow regimes that global numerical models are intended to represent.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arakawa A (1966) Computational design for long-term numerical integration of the equations of fluid motion: Two-dimensional incompressible flow. J Comput Phys 1:119–143
Arakawa A, Lamb VR (1977) Computational design and the basic dynamical processes of the UCLA general circulation model. Methods in Computational Physics 17:172–265
Gassmann A, Herzog HJ (2008) Towards a consistent numerical compressible non-hydrostatic model using generalized Hamiltonian tools. Q J R Meteorol Soc 134:1597–1613
Grinstein FF, Margolin LG, Rider WJ (eds) (2007) Implicit Large Eddy Simulation: Computing turbulent fluid dynamics. Cambridge University Press
Johnson DR, Lenzen AJ, Zapotocny TH, Schaak TK (2000) Numerical uncertainties in the simulation of reversible isentropic processes and entropy conservation. J Clim 13:3860–3884
Koshyk JN, Boer GJ (1995) Parametrization of dynamical subgrid-scale processes in a spectral gcm. J Atmos Sci 52:965–976
Peixoto JP, Oort M (1992) Physics of Climate. American Institute of Physics
Sadourny R (1975) The dynamics of finite-difference models of the shallow-water equations. J Atmos Sci 32:680–989
Sadourny R, Basdevant C (1985) Parameterization of subgrid scale barotropic and baroclinic eddies in quasi-geostrophic models: Anticipated potential vorticity method. J Atmos Sci 42:1353–1363
Salmon R (2004) Poisson-bracket approach to the construction of energy- and potential-enstrophy-conserving algorithms for the shallow-water equations. J Atmos Sci 61:2016–2036
Shutts G (2005) A kinetic energy backscatter algorithm for use in ensemble prediction systems. Quart J Roy Meteorol Soc 131:3079–3102
Simmons AJ, Burridge DM (1981) An energy and angular-momentum conserving vertical finite-difference scheme and hybrid vertical coordinates. Mon Wea Rev 109(4):758–766
Smagorinsky J (1963) General circulation experiments with the primitive equations: I. the basic experiment. Mon Wea Rev 101:99–164
Thuburn J (2008) Some conservation issues for the dynamical cores of NWP and climate models. J Comput Phys 227:3715 – 3730
Thuburn J, Tan DGH (1997) A parameterization of mixdown time for atmospheric chemicals. J Geophys Res 102:13,037–13,049
White AA, Hoskins BJ, Roulstone I, Staniforth A (2005) Consistent approximate models of the global atmosphere: Shallow, deep, hydrostatic, quasi-hydrostatic and non-hydrostatic. Quart J Roy Meteorol Soc 131:2081–2107
Williamson DL, Olson J (1994) Climate simulations with a semi-Lagrangian version of the NCAR Community Climate Model. Mon Wea Rev 122(7):1594–1610
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Thuburn, J. (2011). Conservation in Dynamical Cores: What, How and Why?. 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_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-11640-7_11
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11639-1
Online ISBN: 978-3-642-11640-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)