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

Abstract

The purpose of this chapter is to use the knowledge acquired in the previous chapters to learn about some slightly more advanced topics. For instance, we sketch ways to construct schemes of higher order accuracy, and ways to solve problems when advection and diffusion are equally important. Furthermore, we consider ways to treat nonlinearities numerically, and ask whether they harbor implications for instability. Since two-way nesting is becoming more and more popular, we also say a few words about smoothing and filtering, and give a detailed presentation of two-way nesting itself. Since the spectral method mentioned in the preface is rather common in global atmospheric models, the chapter ends with a brief description of a one-dimensional application of this method.

Keywords

Child Domain Child Grid Equation Grid-point Shapiro Filter Child Solution 
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.
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References

  1. Biastoch A, Böning C, Lutjeharms J (2008) Agulhas leakage dynamics affects decadal variability in Atlantic overturning circulation. Nature 456:489–492CrossRefGoogle Scholar
  2. Clancy RM (1981) On wind-driven quasi-geostrophic water movement at fast ice edges. Mon Weather Rev 109:1807–1809CrossRefGoogle Scholar
  3. Cushman-Roisin B (1984) Analytic, linear stability criteria for the leap-frog, Dufort-Frankel method. J Comput Phys 53:227–239CrossRefGoogle Scholar
  4. Debreu L, Blayo E (2008) Two-way embedding algorithms: a review. Ocean Dyn 58:415–428.  https://doi.org/10.1007/s10236-008-0150-9CrossRefGoogle Scholar
  5. Debreu L, Marchesiello P, Penven P, Cambon G (2012) Two-way nesting in split-explicit ocean models: algorithms, implementation and validation. Ocean Model 49–50:1–21CrossRefGoogle Scholar
  6. Haltiner GJ, Williams RT (1980) Numerical prediction and dynamic meteorology, 2nd edn. Wiley, New York, 477 ppGoogle Scholar
  7. Marchesiello P, Capet X, Menkes C, Kennan SC (2011) Submesoscale dynamics in tropical instability waves. Ocean Model 39:31–46.  https://doi.org/10.1016/j.ocemod.2011.04.011CrossRefGoogle Scholar
  8. Phillips NA (1959) An example of non-linear computational instability. In: Bolin B (ed) The atmosphere and the sea in motion. Rockefeller Institute Press, New York, pp 501–504Google Scholar
  9. Richtmyer RD (1963) A survey of difference methods for non-steady fluid dynamics. Technical Note 63-2, National Center for Atmospheric Research (NCAR)Google Scholar
  10. Robert AJ, Shuman FG, Gerrity JP (1970) On partial difference equations in mathematical physics. Mon Weather Rev 98.  https://doi.org/10.1175/1520-0493(1970)0982.3.CO;2
  11. Sannino G, Herrmann M, Carillo A, Rupolo V, Ruggiero V, Artale V, Heimbach P (2009) An eddy-permitting model of the Mediterranean Sea with a two-way grid refinement at the Strait of Gibraltar. Ocean Model 30:56–72CrossRefGoogle Scholar
  12. Shapiro R (1970) Smoothing, filtering, and boundary effects. Rev Geophys Space Phys 8:359–387CrossRefGoogle Scholar
  13. Shapiro R (1975) Linear filtering. Math Comput 29:1094–1097CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

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

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