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I have a shapefile of a boundary (polygon) that has the following projection:

NAD_1927_UTM_Zone_11N Projection: Transverse_Mercator False_Easting: 500000.00000000 False_Northing: 0.00000000 Central_Meridian: -117.00000000 Scale_Factor: 0.99960000 Latitude_Of_Origin: 0.00000000 Linear Unit: Meter

Geographic Coordinate System: GCS_North_American_1927 Datum: D_North_American_1927 Prime Meridian: Greenwich Angular Unit: Degree

I need to pull climate data (in netcdf files) that is within this boundary. That data is in x y coordinates and has the following information:

XLAT
Size: 219x285 Dimensions: londim,latdim Datatype: single Attributes: units = 'deg' XLONG
Size: 219x285 Dimensions: londim,latdim Datatype: single Attributes: units = 'deg'

There's no other metadata, so in order to align these files, I need to convert the shapefile to decimal degrees. I tried using the Project tool, selecting the same coordinate system, but I don't see decimal degrees in the drop-down.

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You could try to Project to this geographic coordinate system.

Coordinate System>Geographic Coordinate System>North America>NAD 27.prj

GCS_North_American_1927

Angular Unit: Degree (0.017453292519943295) Prime Meridian: Greenwich (0.000000000000000000) Datum: D_North_American_1927 Spheroid: Clarke_1866 Semimajor Axis: 6378206.400000000400000000 Semiminor Axis: 6356583.799998980900000000 Inverse Flattening: 294.978698200000000000

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