Environment Canada helpfully provides recent captures of all national weather radar stations at http://dd.meteo.gc.ca/radar/PRECIPET/GIF/ at ten minute intervals. These are the same GIF images as those posted on their weather website (e.g. http://weather.gc.ca/radar/index_e.html?id=xsm) and inserted below.
This question usefully describes how to download current weather radar data in KML formats from Environment Canada. However, I need to automate the processing of a deep archive of GIF images captured at ten minute intervals.
I understand, too, that raw radar data in spatial formats is available from Environment Canada at cost recovery pricing that will have much higher thematic and spatial resolution than is possible from these GIF rasters. However, such precision is unimportant for this application.
The challenge then is to define the coordinate system of these GIFs in a known projection. The location of the radar at the centre of the map ("+") is known and published (51.0246, -113.3981 for the radar station in the above image). I have also determined through inquiries to Environment Canada that these radar images are in an azimuthal equidistant projection.
How would one form a PROJ4 string, or define a projection in ArcGIS, that would describe these GIF images in their untransformed state, and so take advantage of this free resource.
ArcGIS supports spheres or ellipsoids (spheroids) with the azimuthal equidistant projection.
Here's a sample prj (wkt) string for "World_Azimuthal_Equidistant" based on WGS 1984.
PROJCS["World_Azimuthal_Equidistant", GEOGCS["GCS_WGS_1984", DATUM["D_WGS_1984", SPHEROID["WGS_1984",6378137.0,298.257223563]], PRIMEM["Greenwich",0.0], UNIT["Degree",0.0174532925199433]], PROJECTION["Azimuthal_Equidistant"], PARAMETER["False_Easting",0.0], PARAMETER["False_Northing",0.0], PARAMETER["Central_Meridian",0.0], PARAMETER["Latitude_Of_Origin",0.0], UNIT["Meter",1.0]]
To specify a sphere, you would set the second numerical parameter in the SPHEROID keyword to 0 (zero). As AndreJ added in comments, you would change the central meridian and latitude of origin parameter values to match a particular radar site.
If the gifs all represent the same area in azimuthal equidistant, the corner coordinates (which you'll need to georeference the gifs) will all be the same, no matter what the center point's coordinates are.
You have to specify the projection on a sphere, because proj seems to only support the spherical formulas of this projection:
+proj=aeqd +R=6371000 +lat_0=51.0246 +lon_0=-113.3981
For some example plots, see Manipulating Azimuthal Equidistant Projections in QGIS