Hi Seth: Thanks for the description, its really helpful.
Im just wondering how we document this in the CF convention, so that implementers have something to check against. Is there a "reference implementation" we can use ?
John On 3/6/2013 1:17 PM, Seth McGinnis wrote:
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.hass...@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.hass...@reading.ac.uk _______________________________________________ CF-metadata mailing list CF-metadata@cgd.ucar.edu http://mailman.cgd.ucar.edu/mailman/listinfo/cf-metadata
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