arcgis desktop - Manually adding spatial reference information for FEWS rainfall data in ArcMap?

I am trying to match rainfall data from USGS/FEWS to coordinate locations of survey households in Uganda, so I will need to be able to project the rainfall data. So far, I downloaded the dekadal RFE 2.0 files for East Africa (bulk by year), and for each dekad, there are five files: .bil, .blw, .clr, .hdr, and .stx. When I add the data (the .bil file) to ArcMap 10.2.2, I get the warning: "The following data sources you added are missing spatial reference information. This data can be drawn in ArcMap, but cannot be projected."

Can anyone advise on how to manually add the spatial reference for the data?

For reference, I downloaded the data files from: http://earlywarning.usgs.gov/fews/downloads/index.php?regionID=af&productID=3&periodID=6

The data documentation page http://earlywarning.usgs.gov/fews/africa/web/readme.php?symbol=rf, offers the following:

Dekadal RFE data characteristics:

Source: NOAA-CPC Time step: 10-day (dekadal) Resolution: 8km Projection: Albers equal area conic File Format: Windisp image, byte (8 bit); Generic BIL, "Integer" (16 bit).

Africa Continental Details:

 Coordinates for corners:


 Lower left lat : -42.243 deg
 Lower left lon : -23.490 deg
 Upper left lat : 43.711 deg
 Upper left lon : -24.600 deg
 Lower right lat : -42.242 deg
 Lower right lon : 63.414 deg
 Upper right lat : 43.712 deg
 Upper right lon : 64.523 deg

 Image size : 1152 rows x 1152 cols

 Center lat,lon : 1.000000, 20.000000
 Pixel size h x w : 8.000000 km x 8.000000 km
 Origin of latitudes : 1.000000 deg
 Central meridian : 20.000000 deg
 First std parallel : -19.000000 deg
 Second std parallel : 21.000000 deg
 Projection = ALBERS Conical Equal-area projection uses the clarke 1866 spheroid

I am happy to download the files for all of Africa instead of East Africa in case this somehow makes it easier to matching the documentation to the coordinates.

Answer

One way is to use the Define Projection Tool in ArcToolbox (or the raster's property page in ArcCatalog). I would pick a related projected coordinate system as a start point.

1. Browse to Projected Coordinate Systems, Continental, Africa and choose Africa Albers Equal Area Conic.


2. Right-click and choose Copy and Modify


3. I would change the PCS name.


4. Update the parameters (central meridian, latitude of origin, standard parallels).


5. Optionally update the geographic coordinate system. Because the data is so coarse (8km2), the GCS really doesn't matter. If you want to match the given information, change it to Spheroid-based, Clarke 1866. Note: there won't be any geographic/datum transformations for Clarke 1866 to anything else.