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Hey Edmund,
In the COSMO (and EXTPAR ) source code inside
utilities.f90
(andmo_utilities_extpar.f90
) there is a subroutineuvrot2uv
which uses the formula you cited, but(!) with the longitude-swapping-correction you already noticed.I copied and used this part of the code a little while ago and tested the rotations, and everything seemed fine, so I think you are correct.
best
Rolf