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I have a geographic spatial reference system (i.e., latitude and longitude) which has a north pole that is not the usual north pole: it's the magnetic north pole at approximately 70.30 degrees north, 109 degrees west.

Is it possible to write a PROJ.4 string or a WKT spatial reference string describing this coordinate system? If so, what would that string be?

At the level of precision of my data, the specific ellipsoid does not matter much. Even a spherical Earth would be fine.

(Related: How can I convert geomagnetic coordinates to geographic coordinates without doing the math myself?.)

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The use of a rotated pole has been discussed several times on the PROJ.4 mailing list. In this thread, Hermann Peifer suggested:

+proj=ob_tran +o_proj=latlon +o_lon_p=-162 +o_lat_p=39.25 +lon_0=180 -m 57.2957795130823

so in your case you would use:

+proj=ob_tran +o_proj=latlon +o_lon_p=-109 +o_lat_p=70.5 +lon_0=180 -m 57.2957795130823

This isn't a definition per se, but instead what you would use to get data back to "regular" latitude and longitude values.

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