Abstract
This chapter will introduce some key ideas in the construction of horizontal discretizations for atmospheric models. One important topic is the ability of different schemes to capture wave propagation accurately. The von Neumann method for analysing numerical wave propagation is presented and applied to some simple schemes to demonstrate the advantages of staggered grids in finite difference models. Another important topic is whether the discretization respects the conservation properties of the differential equations being solved. An introduction to the topic is given, using energy conservation as an illustrative example.
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References
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
Arakawa A, Lamb VR (1981) A potential enstrophy and energy conserving scheme for the shallow water equations. Mon Wea Rev 109:18–36
Holton JR (2004) An Introduction to Dynamic Meteorology, fourth edn. Elsevier Academic Press, Amsterdam
Leslie LM, Purser RJ (1991) High-order numerics in an unstaggered 3-dimensional time-split semi-Lagrangian forecast model. Mon Wea Rev 119:1612–1623
McGregor JL (2005) Geostrophic adjustment for reversibly staggered grids. Mon Wea Rev 133:1119–1128
Ničković S, Gavrilov MB, Tosić IA (2002) Geostrophic adjustment on hexagonal grids. Mon Wea Rev 130:668–683
Randall DA (1994) Geostrophic adjustment and the finite-difference shallow-water equations. Mon Wea Rev 122:1371–1377
Thuburn J (2007) Rossby wave propagation on the c-grid. Atmos Sci Lett 8:37–42
Thuburn J (2008) Numerical wave propagation on the hexagonal c-grid. J Comput Phys 227:5836–5858
Thuburn J, Staniforth A (2004) Conservation and linear Rossby-mode dispersion on the spherical C grid. Mon Wea Rev 132:641–653
Williamson DL, Laprise R (2000) Numerical Modeling of the Global Atmosphere in the Climate System, Kluwer, chap Numerical approximations for global atmospheric GCMs., pp 127–219
Winninghoff FJ (1968) On the adjustment toward a geostrophic balance in a simple primitive equation model with application to the problems of initialization and objective analysis. PhD thesis, Department of Meteorology, UCLA
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© 2011 Springer-Verlag Berlin Heidelberg
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Thuburn, J. (2011). Horizontal Discretizations: Some Basic Ideas. 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_3
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DOI: https://doi.org/10.1007/978-3-642-11640-7_3
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