A Simple Method to Find a Neighboring Grid Point on the Cubed-sphere

  • Ki-Hwan Kim
  • Pyoung-Seop Shim
  • Seoleun ShinEmail author
  • Junghan Kim


Recently, there has been increasing interest in the use of cubed-sphere geometry in the geoscientific modeling community. For diverse numerical operations such as remapping and parallel communications, the search of neighbor elements or points is required. Here, we propose a novel and simple method to find a neighboring element or point on the cubed-sphere. This new method can be universally used for any types of cubed-sphere, for example, equi-angular, conformal, uniform-jacobian cubed-sphere etc. Key points to simplify the search algorithm are the definition of rotation counts of panels neighboring the centered panel, and the use of operations to obtain integer quotient and remainder given an index interval from the source point. Along with the introduction of the methodology, some examples using this method is described in this article.

Key words

Cubed sphere remapping dynamical core parallel computation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Choblet, G., 2005: Modelling thermal convection with large viscosity gradients in one block of the ‘cubed sphere’. J. Comput. Phys., 205, 269-291.CrossRefGoogle Scholar
  2. Fragile, P. C., C. C. Lindner, P. Anninos, and J. D. Salmonson, 2009: Applications of the cubed-sphere grid to tilted black hole accretion disks. Astrophys. J., 691, 482-494.CrossRefGoogle Scholar
  3. Harris, L. M., and S.-J. Lin, 2013: A two-way nested global-regional dynamical core on the cubed-sphere. Mon. Wea. Rev., 141, 283-306, doi:10.1175/MWR-D-11-00201.1.CrossRefGoogle Scholar
  4. Kang, H.-G., and H.-B. Cheong, 2017: An efficient implementation of a high-order filter for a cubed-sphere spectral element model. J. Comput. Phys., 332, 66-82, doi:10.1016/ Scholar
  5. Koldoba, A. V., M. M. Romanova, G. V. Ustyugova, and R. V. E. Lovelace, 2002: Three-dimensional magnetohydrodynamic simulations of accretion to an inclined rotator: The “cubed sphere” method. Astrophys. J., 576, 53-56.CrossRefGoogle Scholar
  6. Komatitsch, D., and J. Tromp, 2002: Spectral-element simulations of global seismic wave propagation—II. Three-dimensional models, oceans, rotation and self-gravitation. Geophys. J. Int., 150, 303-318.Google Scholar
  7. Purser, R. J., and M. Rani, 1998: Smooth quasi-homogeneous gridding of the sphere. Quart. J. Roy. Meteor. Soc., 124, 637-647.CrossRefGoogle Scholar
  8. Rani, M., R. J. Purser, D. Jovi, R. Vasic, and T. Black, 2017: A nonhydrostatic multiscale model on the uniform jacobian cubed sphere. Mon. Wea. Rev., 145, 1083-1105, doi:10.1175/MWR-D-16-0178.1.CrossRefGoogle Scholar
  9. Ro ca, D., and G. Plonka, 2011: Uniform spherical grids via equal area projection from the cube to the sphere. J. Comput. Appl. Math., 236, 1033-1041, doi:10.1016/ Scholar
  10. Ronchi, C., R. Iacono, and P. S. Paolucci, 1996: The “Cubed Sphere”: A New Method for the Solution of Partial Differential Equations in Spherical Geometry. J. Comput. Phys., 124, 93-114.CrossRefGoogle Scholar
  11. Sadourny, R., 1972: Conservative finite-difference approximations of the primitive equations on quasi-uniform spherical grids. Mon. Wea. Rev., 100, 136-144.CrossRefGoogle Scholar
  12. Taylor, M. A. and A. Fournier, 2010: A compatible and conservative spectral element method on unstructured grids. J. Comput. Physics, 229, 5879-5895.CrossRefGoogle Scholar

Copyright information

© Korean Meteorological Society and Springer Nature B.V. 2018

Authors and Affiliations

  • Ki-Hwan Kim
    • 1
  • Pyoung-Seop Shim
    • 1
  • Seoleun Shin
    • 1
    • 2
    Email author
  • Junghan Kim
    • 1
  1. 1.Korea Institute of Atmospheric Prediction Systems (KIAPS)SeoulKorea
  2. 2.Korea Institute of Atmospheric Prediction Systems (KIAPS)SeoulKorea

Personalised recommendations