Remarks

• 2D case on the plan

  • In polar coordinates: (x,y) ® (r,q)
  • 1D Hankel transform
    (c.f. Daley (1991), ch.4, sect. 4.3 and Appendix G)
    
    expansion in terms of Bessel functions

• 2D case on the sphere

  • Spherical representation is now based on spherical harmonics
  • Correlation functions are represented in terms of only the zonal components (Boer (1983); Gauthier et al. (1993))
  • Gauthier et al. (1998): homogeneous and isotropic correlation model on the sphere (used in the3D-Var of CMC)

• Covariance model with a compact representation (e.g., 2N coefficients instead of N(N+1)/2

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