Advertisement

Generalized Vertical Coordinates

  • Lars Petter RøedEmail author
Chapter
  • 681 Downloads
Part of the Springer Textbooks in Earth Sciences, Geography and Environment book series (STEGE)

Abstract

So far, we have only used the Cartesian geopotential coordinate system consisting of three orthogonal spatial coordinates xyz. Relaxing the orthogonality between the vertical coordinate z and the two horizontal coordinates xy can make it much easier to analyze phenomena in atmospheres and oceans, and devise compelling models of them. The development of such non-orthogonal coordinate systems remains at the forefront of research in numerical modeling. The purpose of this chapter is, therefore, to present the salient issues relating to these generalized vertical coordinates.

Keywords

Vertical Coordinate System Montgomery Potential Individual Derivatives Hybrid Coordinate Model Terrain-following Coordinates 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Black TL (1994) The new NMC mesoscale Eta model: description and forecast examples. Weather Forecast 9(2):265–278.  https://doi.org/10.1175/1520-0434(1994)009<0265:TNNMEM>2.0.CO;2
  2. Bleck R (1973) Numerical forecasting experiments based on conservation of potential vorticity on isentropic surfaces. J Appl Meteorol 12:737–752CrossRefGoogle Scholar
  3. Bleck R (2002) An oceanic general circulation model framed in hybrid isopycnic-Cartesian coordinates. Ocean Model. 4(1):55–88CrossRefGoogle Scholar
  4. Bleck R, Smith L (1990) A wind-driven isopycnic coordinate model of the north and equatorial Atlantic ocean. 1. Model development and supporting experiments. J Geophys Res 95C:3273–3285CrossRefGoogle Scholar
  5. Blumberg A, Mellor G (1987) A description of a three-dimensional coastal ocean circulation model. Three-dimensional coastal ocean models. In: Heaps N (ed) Coastal and estuarine sciences, vol 4. American Geophysical Union, Washington, pp 1–16Google Scholar
  6. Bourke W (1974) A multilevel spectral model. I. Formulation and hemispheric integrations. Mon Weather Rev 102:687–701CrossRefGoogle Scholar
  7. Charney JG, Phillips NA (1953) Numerical integration of the quasi-geostrophic equations for barotropic and simple baroclinic flows. J Meteorol 10:71–99CrossRefGoogle Scholar
  8. Eliassen A (1949) The quasi-static equations of motion with pressure as independent variable. Geofys Publ 17(3):44 ppGoogle Scholar
  9. Eliassen A, Raustein E (1968) A numerical integration experiment with a model atmosphere based on isentropic coordinates. Meteorol Ann 5:45–63Google Scholar
  10. Eliassen A, Raustein E (1970) A numerical integration experiment with a six-level atmospheric model with isentropic information surface. Meteorol Ann 5:429–449Google Scholar
  11. Engedahl H (1995) Use of the flow relaxation scheme in a three-dimensional baroclinic ocean model with realistic topography. Tellus 47A:365–382CrossRefGoogle Scholar
  12. Griffies SM (2004) Fundamentals of ocean climate models. Princeton University Press, Princeton. ISBN 0-691-11892-2Google Scholar
  13. Haidvogel DB, Arango H, Budgell PW, Cornuelle BD, Curchitser E, Lorenzo ED, Fennel K, Geyer WR, Hermann AJ, Lanerolle L, Levin J, McWilliams JC, Miller AJ, Moore AM, Powell TM, Shchepetkin AF, Sherwood CR, Signell RP, Warner JC, Wilkin J (2008) Ocean forecasting in terrain-following coordinates: formulation and skill assessment of the regional ocean modeling system. J Comput Phys 227(7):3595–3624.  https://doi.org/10.1016/j.jcp.2007.06.016CrossRefGoogle Scholar
  14. Kasahara A (1974) Various vertical coordinate systems used for numerical weather prediction. Mon Weather Rev 102:509–522CrossRefGoogle Scholar
  15. Phillips NA (1957) A coordinate system having some special advantages for numerical forecasting. J Meteorol 14:184–185CrossRefGoogle Scholar
  16. Satoh M, Matsuno T, Tomita H, Miura H, Nasuno T, Iga S (2008) Nonhydrostatic icosahedral atmospheric model (NICAM) for global cloud resolving simulations. J Comput Phys 227:3486–3514Google Scholar
  17. Shapiro MA (1974) The use of isentropic coordinates in the formulation of objective analysis and numerical prediction models. Atmosphere 12:10–17Google Scholar
  18. Shchepetkin AF, McWilliams JC (2005) The regional ocean modeling system (ROMS): a split-explicit, free-surface, topography-following coordinate ocean model. Ocean Model 9:347–404CrossRefGoogle Scholar
  19. Sutcliffe RC (1947) A contribution to the problem of development. Q J R Meteorol Soc 73:370–383CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of GeosciencesUniversity of OsloOsloNorway
  2. 2.Norwegian Meteorological InstituteOsloNorway

Personalised recommendations