ArcMAP / R: Convert raster pixels to Long and Lat

Question

I have downloaded a raster, which has the following information.

Item    Data
Date    2015-01-03 00:00:00
Product cold partial sst
Satellite   NOAA-18
Direction   Unknown
Dimension   1596 x 1617
BPP 8
Latitude range  47 — 62.999108
Longditude range    -15 — 13
Real → DN   dn = (rw - -3) / 0.1
DN → real   rw = 0.1 * dn + -3
DN range    0 — 255
Pixel dimensions    1.100149 x 1.100149

On Arcmap it shows the pixel X/Y co-ordinates. How can I convert this to Long and Lat?

From the FAQ of the site that I downloaded the raster from the following information is provided. link

How do I convert image coordinates to latitude/longitude? For converting from x/y pixel co-ordinates on a Mercator projection image to latitude/longitude (lat/lon) positions use:

rows - number of rows in image
cols - number of columns in image
minlon/maxlon - minimum/maximum longitude of image (in decimal degrees)
minlat/maxlat - minimum/maximum latitude of image (in decimal degrees) 
Note that these are the coordinates of the CENTRE of the corner pixels.
DEGTORAD - conversion from degrees to radians (PI/180.0)
RADTODEG - conversion from radians to degrees to radians
ln - natural log
Calculate longitude.

lonfract = x / (cols - 1)
lon = minlon + (lonfract * (maxlon - minlon))
Calculate latitude.

latfract = 1.0 - (y / (rows - 1))
Ymin = ln (tan (DEGTORAD * (45.0 + (minlat / 2.0))))
Ymax = ln (tan (DEGTORAD * (45.0 + (maxlat / 2.0))))
Yint = Ymin + (latfract * (Ymax - Ymin))
lat = 2.0 * (RADTODEG * (arctan (exp (Yint))) - 45.0)

The maximum/minimum latitude/longitude values and sizes are given when the images are viewed.

Would it possible to run the above code in ArcMAP or R (raster package)?

Answer 1

The image metadata (and the linked page) suggest the image is in the Web Mercator Projection.

Hopefully, you also got the world file (.tfw, .jgw or a similar extension) containing five numbers specifying the image dimensions in that projection. If so, it should be easy to convert (project) the image to a different projection using ArcMap as follows:

• Use the Define Projection tool to define the projections of the image. Use WGS 1984 Web Mercator (auxiliary sphere) as the coordinate system.
• Use the Project Raster tool to project the image into WGS-84 coordinates (lat/lon). For that, specify the Output Coordinate System to be WGS 1984.

If you do not have the world file, you can create it with the equations you provided and the specification at Wikipedia.