So there are an infinite number of ways to decompose a 3-D orientation into
three orthogonal rotations. Specifying the projection in terms of the final
location of the north pole and an optional rotation around that point means
that CF is actually agnostic about exactly how you get there.
That said, given that it's being specified in that way, the decomposition that
maps most straightforwardly to those parameters is a Z-Y-X rotation sequence
using an extrinsic (space-fixed) coordinate system:
First rotate by angle phi around the north pole in space-fixed coordinates.
Then rotate by angle theta around 0N 90E in space-fixed coordinates.
Finally, rotate by angle psi around 0N 0E in space-fixed coordinates.
The location of the grid's north pole in the original lat-lon coordinate system
is now at longitude = phi, colatitude = minus theta.
(I'm not sure how psi relates to north_pole_grid_longitude mathematically; it
defaults to zero and I've never seen it in use, so I think it's included mostly
for completeness. I agree that we may well want to change it to something more
obvious like an azimuth angle.)
Switching to the GRIB2 convention where you use the south pole instead of the
north should be just a matter of adding 180 degrees to phi and negating theta.
Cheers,
--Seth
On Wed, 6 Mar 2013 18:29:47 +0000
David Hassell <d.c.hassell at reading.ac.uk> wrote:
>Hello,
>
>It is a bit of mess! As I understand it, the full rotation described
>is a sequence of rotations about three different axes:
>
> Z = 90S - 90N
> Y' = 90W' - 90E'
> X" = 0E" - 180E"
>
>where it is understood that the definitions of the N-S and W-E axes
>change after each rotation (hence the primes and double
>primes). Therefore the order in which they are done matters.
>
>I suspect that the usual and assumed order is Z, Y', X"?
>
>>From the GRIB-2 stuff John posted the north_pole_grid_longitude gives
>the rotation about the X" axis.
>
>Something like John's "Angle of rotation" seems right to me.
>
>The apparent lack of consistency between the parameter names irks
>me. Perhaps one solution could be to:
>
>i) Add some text to the conventions state the order (Z, Y', X", say)
> and direction of rotations.
>
>ii) add three new, consistent, self-describing parameters (e.g.)
>
>angle_of_rotation_z
>angle_of_rotation_y
>angle_of_rotation_x
>
>iii) allow aliases for backwards compatibility
>
>grid_north_pole_longitude <=> angle_of_rotation_z
>grid_north_pole_latitude <=> angle_of_rotation_y
>north_pole_grid_longitude <=> angle_of_rotation_x
>
>Or would that just obfuscate things even more?
>
>All the best,
>
>David
>
>P.S. If you have a copy available, there are some nice descriptions in
> "Coordinate Systems and Map Projections" by D. H. Maling
>
>--
>David Hassell
>National Centre for Atmospheric Science (NCAS)
>Department of Meteorology, University of Reading,
>Earley Gate, PO Box 243,
>Reading RG6 6BB, U.K.
>
>Tel : 0118 3785613
>Fax : 0118 3788316
>E-mail: d.c.hassell at reading.ac.uk
>_______________________________________________
>CF-metadata mailing list
>CF-metadata at cgd.ucar.edu
>http://mailman.cgd.ucar.edu/mailman/listinfo/cf-metadata
Received on Wed Mar 06 2013 - 13:17:34 GMT
