Abstract
In this chapter, we describe an icosahedral grid method for spherical grid discretization of global atmospheric models. An icosahedral grid is applied to a shallow-water model in this chapter, and application to a global three-dimensional model will be shown in the next chapter.
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 and suggested reading
Adcroft, A., Campin, J.-M., Hill, C., and Marshall, J., 2004: Implementation of an atmosphere-ocean general circulation model on the expanded spherical cube. Mon. Wea. Rev., 132, 2845–2863.
Baba, Y., Takahashi, K., Sugimura, T., and Goto, K., 2010: Dynamical core of an atmospheric general circulation model on a Yin-Yang grid. Mon. Wea. Rev., 138, 3988–4005.
Baumgardner, J. R. and Frederickson, P. O., 1985: Icosahedral discretization of the two-sphere. SIAM J. Numer. Anal., 22, 1107–1115.
Blackburn, M., Williamson, D. L, Nakajima, K., Ohfuchi, W., Takahashi, Y.O., Hayashi, Y.-Y., Nakamura, H., Ishiwatari, M., McGregor, J., Borth, H., Wirth, V., Frank, H., Bechtold, P., Wedi, N.P., Tomita, H., Satoh, M., Zhao,
M., Held, I. M., Suarez, M. J., Lee, M.-I., Watanabe, M., Kimoto, M., Liu, Y., Wang, Z., Molod, A., Rajendran, K., Kitoh A., and Stratton R., 2012: The Aqua Planet Experiment (APE): Control SST Simulation. J. Meteor. Soc. Japan, 91A, in press, doi:10.2151/jmsj.2013-A02.
Cooley, J.W. and Turkey, J.W., 1965: An algorithm for the machine computation of complex Fourier series. Math. Comput., 19, 297–301.
Côté, J., 1988: A Lagrange multiplier approach for the metric terms of semi- Lagrangian models on the sphere. Q. J. R. Meteorol. Soc., 114, 1347–1352.
Cullen, M. J.P., 1974: Integration of the primitive equations on a sphere using the finite element method. Q. J. R. Meteorol. Soc., 100, 555–562.
Cullen, M. J.P. and Hall, C.D., 1979: Forecasting and general circulation results from finite element models. Q. J. R. Meteorol. Soc., 105, 571–591.
Dudhia, J. and Bresch, J. F., 2002: A global version of PSU-NCAR mesoscale model. Mon. Wea. Rev., 130, 2989–3007.
Gassmann, A., 2011: Inspection of hexagonal and triangular C-grid discretizations of the shallow water equations. J. Comp. Phys., 230, 2706–2721.
Heikes, R.H. and Randall, D.A., 1995a: Numerical integration of the shallowwater equations on a twisted icosahedral grid. Part I: Basic design and results of tests. Mon. Wea. Rev., 123, 1862–1880.
Heikes, R.H. and Randall, D.A., 1995b: Numerical integration of the shallowwater equations on a twisted icosahedral grid. Part II: A detailed description of the grid and analysis of numerical accuracy. Mon. Wea. Rev., 123, 1881– 1887.
Lin, S.-J., 2004: A “vertically Lagrangian” finite-volume dynamical core for global models. Mon. Wea. Rev., 132, 2293–2307.
Masuda, Y. and Ohnishi, H., 1986: An integration scheme of the primitive equation model with an icosahedral-hexagonal grid system and its application to the shallow water equations, Short- and Medium-Range Numerical Weather Prediction. Collection of Papers Presented at the WMO/IUGG NWP Symposium, Tokyo, Aug. 4–8 1986, Japan Meteorological Society, 317–326.
Majewski, D., Liermann, D., Prohl, P., Ritter, B., Buchhold, M., Hanisch, T., Paul, G., and Wergen, W., 2002: The operational global icosahedralhexagonal gridpoint model GME: description and high-resolution tests. Mon. Wea. Rev., 130, 319–338.
McGregor, J. L., 1996: Semi-Lagrangian advection on conformal-cubic grids, Mon. Wea. Rev., 124, 1311–1322.
Mesinger, D., 2000: Numerical methods: The Arakawa approach, horizontal grid, global, and limited-area modeling. In General Circulation Model Development, edited by D. A. Randall. Academic Press, 373–419.
Miura, H. and Kimoto, M., 2005: A comparison of grid quality of optimized spherical hexagonal-pentagonal geodesic grids. Mon. Wea. Rev., 133, 2817– 2833.
Phillips, N.A., 1959: Numerical integration of the primitive equation on the hemisphere. Mon. Wea. Rev., 87, 333–345.
Purser, R. J. and Rancic, M., 1998: Smooth quasi-homogeneous gridding of the sphere. Q. J. R. Meteor. Soc., 124, 637–652.
Rancic, M., Purser, R. J., and Mesinger, F.,1996: A global shallow-water model using an expanded spherical cube: Gnomonic versus conformal coordinates. Q. J. R. Met. Soc., 122, 959–982.
Randall, D.A., 1994: Geostrophic adjustment and finite-difference shallow water equations. Mon. Wea. Rev., 122, 1371–1377.
Ringler, T.D., Heikes, R.H. and Randall, D.A., 2000: Modeling the atmospheric general circulation using a spherical geodesic grid: A new class of dynamical cores. Mon. Wea. Rev., 128, 2471–2490.
Ringler, T.D. and Randall, D.A., 2002a: A potential enstrophy and energy conserving numerical scheme for solution of the shallow-water equations on a geodesic grid, Mon. Wea. Rev., 130, 1397–1410.
Ringler, T.D. and Randall, D.A., 2002b: The ZM-grid: an alternative to the Z-grid. Mon. Wea. Rev., 130, 1411–1422.
Ringler, T.D., Thuburn, J., Klemp, J., and Skamarock, W.C., 2010: A unified approach to energy conservation and potential vorticity dynamics for arbitrarilystructured C-grids. J. Comp. Phys., 229, 2065–2090.
Sadourny, R., Arakawa, A., and Mintz, Y., 1968: Integration of the nondivergent barotropic vorticity equation with an icosahedral hexagonal grid for the sphere. Mon. Wea. Rev., 96, 351–356.
Sadourny, R., 1969: Numerical integration of the primitive equations on a spherical grid with hexagonal cells. Proceedings of the WMO/IUGG Symposium on Numerical Weather Prediction in Tokyo, Tech. Rep. of JMA, VII45 – VII52.
Satoh, M., Tomita, H., Miura, H., Iga, S., and Nasuno, T., 2005: Development of a global cloud resolving model – a multi-scale structure of tropical convections. J. Earth Simulator, 3. 11–19.
Skamarock,W. C., Klemp, J.B., Duda, M.G., Fowler, L.D., and Park, S.-H., 2012: A multi-scale nonhydrostatic atmospheric model using centroid Vornoi tesselations and C-grid staggering. Mon. Wea. Rev., 140, 3090-3105.
Staniforth, A. and Thuburn, J, 2012; Horizontal grids for global weather and climate prediction models: a review. Q. J. R. Meteorol. Soc., 138, 1–26.
Stuhne, G.R. and Peltier, W. R., 1996: Vortex erosion and amalgamation in a new model of large scale flow on the sphere. J. Comput. Phys., 128, 58–81.
Stuhne, G.R. and Peltier, W. R., 1999: New icosahedral grid-point discretizations of the shallow water equations on the sphere. J. Comput. Phys., 148, 23–58.
Swinbank, R., and Purser, R. J., 2006: Fibonacci grid: A novel approach to global modelling. Q. J. Roy. Met. Soc., 132, 1769–1793.
Thuburn, J., 1997: A PV-based shallow-water model on a hexagonal-icosahedral grid. Mon. Wea. Rev., 125, 2328–2347.
Thuburn, J., Ringler,W.C., Skamarock,W. C., and Klemp, J.B., 2009: Numerical representation of geostrophic modes on arbitrarily structured C-grids. J. Comp. Phys., 228, 8321–8335.
Tomita, H., Tsugawa, M., Satoh, M., and Goto, K., 2001: Shallow water model on a modified icosahedral geodesic grid by using spring dynamics. J. Comp. Phys., 174, 579–613.
Tomita, H., Satoh, M., and Goto, K., 2002: An optimization of icosahedral grid modified by spring dynamics. J. Comp. Phys., 183, 307–331.
Tomita, H. and Satoh, M., 2004: A new dynamical framework of nonhydrostatic global model using the icosahedral grid. Fluid Dyn. Res., 34, 357–400.
Tomita, H., Goto, K., and Satoh, M., 2008: A new approach of atmospheric general circulation model - Global cloud resolving model NICAM and its computational performance -. SIAM J. Sci. Comput., 30, 2755–2776.
Williamson, D. L., 1968: Integration of the barotropic vorticity equation on a spherical geodesic grid. Tellus, 20, 642–653.
Williamson, D. L., 1970: Integration of the primitive barotropic model over a spherical geodesic grid. Mon. Wea. Rev., 98, 512–520.
Williamson, D. L., Drake, J. B., Hack, J. J., Jacob, R., and Swarztrauber, P. N., 1992: A standard test set for numerical approximations to the shallow water equations in spherical geometry. J. Comput. Phys., 102, 211–224.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Satoh, M. (2014). Icosahedral grids. In: Atmospheric Circulation Dynamics and General Circulation Models. Springer Praxis Books(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13574-3_25
Download citation
DOI: https://doi.org/10.1007/978-3-642-13574-3_25
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13573-6
Online ISBN: 978-3-642-13574-3
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)