I have a set of files that are stored in Tom Patterson's Natural Earth Projection, and I would like to convert them to WGS1984 (or anything that would be more versatile). This will require a transformation, but I can't locate one and don't know where to start with building one, if that's the route this needs to go.
Any help with methods for reprojecting would be appreciated - thanks!
To avoid any confusion, this is NOT the same projection that the Natural Earth data comes in (see the link above for disambiguation).
The .prj string for Natural Earth Projection is:
PROJCS["Sphere_Natural_Earth",GEOGCS["GCS_Sphere_GRS_1980_Mean_Radius",DATUM["D_Sphere_GRS_1980_Mean_Radius",SPHEROID["Sphere_GRS_1980_Mean_Radius",6371008.7714,0.0]],PRIMEM["Greenwich",0.0],UNIT["Degree",0.0174532925199433]],PROJECTION["Natural_Earth"],PARAMETER["False_Easting",90.0],PARAMETER["False_Northing",90.0],PARAMETER["Central_Meridian",180.0],UNIT["Meter",1.0]]
I am not aware of any data being stored in GCS Sphere GRS 1980 Mean Radius except this one. In your case, I assume data was created the same way; originally WGS 1984 data was being projected to Natural Earth projection using GRS 1980 Mean Radius Sphere with no particular transformation.
In case, this is just one time thing, I suggest you first unproject your data to
GEOGCS["GCS_Sphere_GRS_1980_Mean_Radius",DATUM["D_Sphere_GRS_1980_Mean_Radius",SPHEROID["Sphere_GRS_1980_Mean_Radius",6371008.7714,0.0]],PRIMEM["Greenwich",0.0],UNIT["Degree",0.0174532925199433]]
and then use Define Projection tool to assign GCS WGS 1984 to it.
If you have a lot of such data, then you can also Create Custom Geographic Transformation between WGS 1984 and GRS 1980 Mean Radius Sphere using null method. This transformation will consider both models to be the same and directly unproject and move your data back to WGS 1984.