EGU21-7990
https://doi.org/10.5194/egusphere-egu21-7990
EGU General Assembly 2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

Interpolating data on the Cubed Sphere with Spherical Harmonics

Jean-Pierre Croisille1, Jean-Baptiste Bellet2, and Matthieu Brachet3
Jean-Pierre Croisille et al.
  • 1Institut Elie Cartan de Lorraine, CNRS, UMR 7502, Univ. Lorraine, 57000 Metz, France (jean-pierre.croisille@univ-lorraine.fr)
  • 2Institut Elie Cartan de Lorraine, CNRS, UMR 7502, Univ. Lorraine, 57000 Metz, France (jean-baptiste.bellet@univ-lorraine.fr)
  • 3Labo. Maths & App.,CNRS, UMR 7348, Univ. Poitiers, F86073 Poitiers, France (matthieu.brachet@math.univ-poitiers.fr)

The Cubed Sphere is a grid commonly used in numerical simulation in climatology. In this talk we present recent progress
on the algebraic and geometrical properties of this highly symmetrical grid.
First, an analysis of the symmetry group of the Cubed Sphere will be presented: this group 
is identified as the group of the Cube, [1]. Furthermore, we show how to construct a discrete Spherical Harmonics (SH) basis associated to 
the Cubed Sphere. This basis displays a truncation scheme relating the zonal and longitudinal 
mode numbers reminiscent of the rhomboidal truncation on the Lon-Lat grid.
The new analysis allows to derive new quadrature rules of  interest for applications in any kind of spherical modelling. In addition,
we will comment on applications in mathematical climatology and meteorology, [2].

[1] J.-B. Bellet, Symmetry group of the equiangular Cubed Sphere, preprint, IECL, Univ. Lorraine, 2020, submitted

[2] J.-B. Bellet, M. Brachet and J.-P. Croisille, Spherical Harmonics on The Cubed Sphere, IECL, Univ. Lorraine, 2021, Preprint.

How to cite: Croisille, J.-P., Bellet, J.-B., and Brachet, M.: Interpolating data on the Cubed Sphere with Spherical Harmonics, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-7990, https://doi.org/10.5194/egusphere-egu21-7990, 2021.

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