Define projection and reprojecting raster

[louise_acou]

I have a netcdf file which I have imported to ArcMap as a raster. I set the projection using 'define projection', this is the projection I received from the person who sent me the netcdf file, WGS_1984_Mercator_41. Even though I get a green tick when the operation is completed, the XY coordinate system in Layer Properties isn't updated and is Unknown. So, I tried exporting the data to a .tif, I can then set the projection as desired and it updates correctly. But, then when I try to project the raster to desired CRS WGS 1984 60S, I get error 999999. 

Can anyone help? I am guessing it is because the units on the map are unknown but I don't know how to resolve that. 

[DanPatterson]

would this be it?

WGS 84 / Mercator 41 - EPSG:3994

looks like meters

[louise_acou]

I think the issue might actually be that the netcdf file is read incorrectly. The lat and lon values in the raw data do not match the values in the displayed raster file. What could be going on here, it seems that the process to read the netcdf is straightforward and I assigned the lat/lon correctly.

[DanPatterson]

They look like Eastings (X's) and Northings (Y's) to me as used by the defined coordinate system.