Hello Brendan
I feel like I have added to the confusion here, I am sorry.
I think you are correct, that there is a Pi missing from my rotation description (although I don't agree with your correction, the sign is wrong)
I think my text should read:
For a spherical geometry, this is equivalent to 3 rotation transforms of the basis (theta,phi) (ordered operation):
- rotate in the theta-hat direction by:
- Pi + grid_north_pole_longitude
- rotate in the phi-hat direction by:
- grid_north_pole_latitude - Pi/2
- rotate in the theta-hat direction by:
- north_pole_grid_longitude | 0
mark
________________________________
From: CF-metadata [cf-metadata-bounces at cgd.ucar.edu] on behalf of DeTracey, Brendan [Brendan.DeTracey at dfo-mpo.gc.ca]
Sent: 20 October 2014 12:53
To: cf-metadata at cgd.ucar.edu
Subject: Re: [CF-metadata] Rotated pole definition
Thanks for the replies. Shouldn?t the second rotation angle be pi/2-grid_north_pole_latitude?
To visualize I was holding a water bottle and imagining the rotations to get the north pole at 0N,-90E. First rotation 90 about the north pole(z). Second rotation has to be 90 degrees(not 0) about the new east-west(y?) axis (perpendicular to the new prime meridian).
The euler angle convention matches the fourth case(intrinsic) on the euler angle Wikipedia page: (
http://en.wikipedia.org/wiki/Euler_angles#Conventions)
i.e. 4. z-y?-z? (intrinsic rotations)
with the angles ordered pi + grid_north_pole_longitude, pi/2 - grid_north_pole_latitude, north_pole_grid_longitude
If so, this really needs to be more clearly stated in the reference. I came here because I could not get a clear answer for these same parameters for the Climate Data Operators, and then assumed they were taken from CF.
Thanks again,
Brendan
------------------------------------------
Brendan DeTracey
brendan.detracey at dfo-mpo.gc.ca<mailto:brendan.detracey at dfo-mpo.gc.ca>
(902)426-9727 3-30 VS
Marine Ecosystem Section / Section de l'?cosyst?me marin
From: Hedley, Mark [mailto:mark.hedley at metoffice.gov.uk]
Sent: October-17-14 8:14 AM
To: DeTracey, Brendan; cf-metadata at cgd.ucar.edu
Subject: RE: Rotated pole definition
Hello Brendan
I believe the intent of the rotated pole grid mapping definition is to describe a polar coordinate reference system, based on the earth, but with a different axis of rotation.
To do this, a new north pole location is specified in the earth polar coordinate reference system by
- grid_north_pole_latitude
- grid_north_pole_longitude
This defines a point on the surface of the non-rotated system. A new rotational axis is defined through this location and the centre of the body.
A further rotation is then applied about this new axis, as defined by:
- north_pole_grid_longitude (optional, default 0).
For a spherical geometry, this is equivalent to 3 rotation transforms of the basis (theta,phi) (ordered operation):
- rotate in the theta-hat direction by:
- Pi + grid_north_pole_longitude
- rotate in the phi-hat direction by:
- grid_north_pole_latitude
- rotate in the theta-hat direction by:
- north_pole_grid_longitude | 0
This provides a new basis which coordinates may be defined with respect to.
I keep an inflatable globe on my desk to help me with this. I have not found a clear diagram on line which illustrates this unambiguously, or managed to draw one for myself; I would like to.
I hope this information is correct and useful.
mark
________________________________
From: CF-metadata [cf-metadata-bounces at cgd.ucar.edu] on behalf of DeTracey, Brendan [Brendan.DeTracey at dfo-mpo.gc.ca]
Sent: 16 October 2014 12:49
To: cf-metadata at cgd.ucar.edu<mailto:cf-metadata at cgd.ucar.edu>
Subject: [CF-metadata] Rotated pole definition
Hi,
I am looking for clarification on the rotated pole definition. Is the globe rotated such that the north pole traces a great circle from its original to its new position? And then rotated counter clockwise about the new pole by north_pole_grid_longitude degrees? There is not enough detail in the CF document describing this.
Brendan
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