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

[Stephane Popinet]

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