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I want to translate this wkt version of the SR-ORG:8399 code reference system, to its corresponding proj4 format, so I can use it in QGIS. The exact characteristics of the system are the following: http://spatialreference.org/ref/sr-org/8399/prettywkt/

I have tried to translate to proj4 writing the following format,

+proj=longlat +lat_0=40 +lon_0=-170 +k=1.0 +x_0=0.0 +y_0=0.0 +units=m +no_defs 

but QGIS Custom CRS gives a "This projection definition is not valid" message.

Can you help me correct it?

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I'm afraid you are lost with your task, since PROJECTION["Rotated_Latitude_Longitude"] is not implemented in GDAL. In Proj.4, there is a substitute named +proj=ob_tran, but it is not imlemented in GDAL (and based on it QGIS as well).

You can follow https://trac.osgeo.org/gdal/ticket/4285 and http://lists.maptools.org/pipermail/proj/2010-June/005234.html on the discussions about that. See also How to use PROJ4 to reproject a file

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