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 [[email protected]] on behalf of DeTracey, Brendan [[email protected]] Sent: 20 October 2014 12:53 To: [email protected] 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 [email protected]<mailto:[email protected]> (902)426-9727 3-30 VS Marine Ecosystem Section / Section de l'écosystème marin From: Hedley, Mark [mailto:[email protected]] Sent: October-17-14 8:14 AM To: DeTracey, Brendan; [email protected] 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 [[email protected]] on behalf of DeTracey, Brendan [[email protected]] Sent: 16 October 2014 12:49 To: [email protected]<mailto:[email protected]> 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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