Abstract
This chapter introduces some key ideas in the design of vertical discretizations for atmospheric models. Various choices of vertical coordinate are possible, and the most widely used ones are introduced. The requirement to retain certain conservation properties can constrain or determine aspects of the discretization: this is illustrated using the Simmons and Burridge angular momentum and energy conserving scheme for hydrostatic models. Another important set of issues surrounds the ability to capture hydrostatic balance and wave dispersion accurately and to avoid computational modes: some implications for the vertical discretization are discussed.
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References
Adcroft A, Hill C, Marshall J (1997) Representation of topography by shaved cells in a height coordinate ocean. Mon Wea Rev 125:2293–2315
Arakawa A, Moorthi S (1988) Baroclinic instability in vertically discrete systems. J Atmos Sci 45:1688–1707
Charney JG, Phillips NA (1953) Numerical integration of the quasi-geostrophic equations for barotropic and simple baroclinic flow. J Meteorol 10:71–99
Durran DD (1999) Numerical Methods for Wave Equations in Geophysical Fluid Dynamics. Springer-Verlag
Gal-Chen T, Somerville RC (1975) On the use of a coordinate transformation for the solution of navier-stokes equations. J Comput Phys 17:209–228
Hsu YJG, Arakawa A (1990) Numerical modeling of the atmosphere with an isentropic vertical coordinate. Mon Wea Rev 118:1933–1959
Kasahara A (1974) Various vertical coordinate systems used for numerical weather prediction. Mon Wea Rev 102(7):509–522
Konor CS, Arakawa A (1997) Design of an atmospheric model based on a generalized vertical coordinate. Mon Wea Rev 125(7):1649–1673
Lin SJ (2004) A ‘vertically Lagrangian’ finite-volume dynamical core for global models. Mon Wea Rev 132:2293–2307
Lorenz EN (1960) Energy and numerical weather prediction. Tellus 12:364–373
Phillips NA (1957) A coordinate system having some special advantage for numerical forecasting. J Meteor 14:184–185
Schneider EK (1987) An inconsistency in vertical discretization in some atmospheric models. Mon Wea Rev 115:2166–2169
Shaw TA, Shepherd TG (2007) Angular momentum conservation and gravity wave drag para- metrization: Implications for climate models. J Atmos Sci 64:190–203
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
Staniforth A, Wood N (2003) The deep-atmosphere Euler equations in a generalized vertical coordinate. Mon Wea Rev 131:1931–1938
Starr VP (1945) A quasi-Lagrangian system of hydrodynamical equations. J Atmos Sci 2:227–237
Thuburn J (2006) Vertical discretizations giving optimal representation of normal modes: Sensitivity to the form of the pressure gradient term. Quart J Roy Meteorol Soc 132:2809–2825
Thuburn J, Woollings TJ (2005) Vertical discretizations for compressible Euler equation atmospheric models giving optimal representation of normal modes. J Comput Phys 203:386–404
Tokioka T (1978) Some considerations on vertical differencing. J Meteorol Soc Japan 56:98–111
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© 2011 Springer-Verlag Berlin Heidelberg
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Thuburn, J. (2011). Vertical 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_4
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DOI: https://doi.org/10.1007/978-3-642-11640-7_4
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