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I recently discovered the raster library in R. With that library one can define a raster's coordinate reference system (crs) or projection. For example, to set the projection as NAD83 UTM 10N:

crs(raster) <- CRS(+init=EPSG:26910')

I wrote that raster to file and imported into ArcMap, but Arc said that the file was missing a spatial reference system.

In general, is it possible for an ASCII file to contain/define its CRS or projection? If so, can that be done with R's raster library or with ArcMap?

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There's no provision for coordinate system information in the ESRI ASCII raster file format:

http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#/ESRI_ASCII_raster_format/009t0000000z000000/

You might get the coordinate system info in a metadata file accompanying an ESRII ASCII grid file, but there's no standard for it as far as I know.

Use another format whenever possible, such as geoTIFF. Most GIS will happily read geoTIFF files and set the coordinate system correctly from the embedded metadata.

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