[MITgcm-support] possible bug in Rancic et al conformal mapping coefficients

[Chris Hill]

Stephane,

  Thanks for this info, we do still use this code for some
  configurations so we will take a look.

  If I recall we actually "hard-code" a lot of the symmetry.
  That is we generally only use the conformal mapping generated
  coordinates from one quadrant of a cube face and then rotate
  and translate this around the sphere. In principle I think
  this should flag errors because grid cell coordinates would not
  coincide. I also recall, I think, that I could get the same grid
  from an iterative conformal mapping solver approach based
  on a paper by David C. Ives and Robert M. Zacharias from
  the 80s. Again we only generate one quadrant and then use
  symmetry.

  Anyhow we will definitely take a look.

Thanks,

Chris

On Tue, May 8, 2012 at 8:13 PM, Stephane Popinet <s.popinet at gmail.com> wrote:
> Dear MIT developers,
>
> If this file is still in use:
>
> http://mitgcm.org/viewvc/*checkout*/MITgcm/MITgcm_contrib/high_res_cube/matlab-grid-generator/map_xy2xyz.m
>
> I am almost certain it contains an incorrect Taylor expansion
> coefficient. The change is commented in the code as:
>
> %aja changed  -0.00895884801823 to -0.01895884801823 (coeff #4)
>
> but the correct coefficient is -0.00895884801823 not the new value. I
> checked carefully and the resulting expansion (using the incorrect new
> coefficient) does not respect the group of symmetries of the cube.
> Using the old value does. This is important as this will results in
> step discontinuities at the boundaries between cubed sphere tiles.
> Discretising high-order operators such as the Laplacian will then
> amplify these errors to significant levels.
>
> cheers
>
> Stephane
>
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