I am trying to do some analysis with Level 3 Standard Mapped MODIS NetCDF files, obtained from the Ocean Color Web level 3 data browser (https://oceancolor.gsfc.nasa.gov/cgi/l3), and I want to project them into a projected coordinate system and do some analysis. When making a NetCDF raster layer in ArcMap (using, predictably, the Make NetCDF Raster Layer tool) the Spatial Reference shows up as GCS_WGS_1984.

However, the map projection associated with the NetCDF file, upon inspection with the NetCDF4 Python package, is "Equidistant Cylindrical".

The documentation seems to agree, and says that the projection should be Plate Carree (which fits into the equidistant cylindrical category, as I understand). (from https://oceancolor.gsfc.nasa.gov/docs/format/#3M)

If the file is in a Plate Carree projection, then why is it not showing up in ArcMap as such? Furthermore, attempting to define the projection as Plate Carree (with, predictably, the Define Projection tool) yields a warning that there is already a projection associated with the layer, and whenever I try to reproject it I get a warning about inconsistent extent (it looks like this)

I have tried my best to understand what is going on but I do not feel confident in what I am doing. Can someone explain my confusion here- why is the raster not showing up with the projection I would expect it to?

I am using ArcGIS 10.3.1

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