Adding robust vector-field interpolation functionality (current PR and further work).

[odlomax]

Atlas PR #163 adds functionality to accurately interpolate vector field defined in lol-lat space on the unit-sphere. Here, we've added an interpolation::method::SphericalVector class. Doxygen given below:

  /// @brief   Interpolation post-processor for vector field interpolation
  ///
  /// @details Takes a base interpolation config keyed to "scheme" and creates
  ///          A set of complex intepolation weights which rotate source vector
  ///          elements into the target elements' individual frame of reference.
  ///          Method works by creating a great-circle arc between the source
  ///          and target locations; the amount of rotation is determined by the
  ///          difference the in the great-cricle course (relative to north) at
  ///          the source and target location.
  ///          Both source and target fields require the "type" metadata to be
  ///          set to "vector" for this method to be invoked. Otherwise, the
  ///          base scalar interpolation method is invoked.
  ///          Note: This method only works with matrix-based interpolation
  ///          schemes.

Currently, the code additions test the following.

• Interpolation from a cubedsphere mesh to a gaussian mesh
• Interpolation from a gaussian mesh to a cubedsphere mesh

Suggested further tests and functionality:

Code coverage

• Tests needed for a vector interpolation on a horizontal field
• Tests needed for 3d vectors fields with levels > 1
• Tests needed for "meaningful" 3-vector fields.

Functionality

• Implementation of adjoint methods (and relevant tests)

Scientific validation

• Comparison with vector interpolation methods used with StructuredColumns functionspace.
• Low-to-high resolution comparions.

@wdeconinck @pmaciel do you agree with the above points. Please feel free to add/delete change.

Are there any of the above that need to go into PR #163. I would personally prefer follow-up PRs for the three groups, but I'm completely open to alternatives.

@mo-lormi and myself are well positioned to address the code coverage and adjoint work.

[odlomax]

Hi @fmahebert, @ytremolet,

Just bringing this issue and associated PR(s) to your attention. It's a generic method to interpolate vector fields in Atlas.