Access to several options, including FTP and the Composite Browser, is available via http://www.oceancolour.org/
The data can be directly downloaded from: ftp://oc-cci-data:ELaiWai8ae@oceancolour.org/
FTP server: oceancolour.org
Support is available from firstname.lastname@example.org
Some people have reported that the Mac FTP client has trouble with files bigger than 4GB. If you look at the monthly composites directory and the files there appear to be around 500-600MB rather than ~4.5GB, you're affected by this problem. If you attempt to download, you'll get ~500MB corrupt files. So you'll need to use an alternative FTP client or the terminal.
If you’re interested in downloading a subset of the dataset then THREDDS provides several options. As an example, the NetCDF subset service allows for a spatial and / or temporal subset to be extracted.
From https://rsg.pml.ac.uk/thredds/catalog-cci.html first choose the temporal composites required (daily, 8day or monthly) and then access Option 5, which is NetcdfSubset. Now choose the products, Latitude / Longitude subset and time subset options. Then press Submit at the bottom of the page.
If you receive an error message then it’s likely you’re trying to download too much data in one block – files cannot be larger than 4GB. The Stride parameter can be set to a value greater than 1 if you only want every nth value.
The output is a single NetCDF file and so this method will become unwieldy for large areas / time periods.If you’d prefer binary or ASCII data then choose Option 1, which is OPeNDAP.
To browse the data in an interactive viewer then the Web GIS Portal (http://www.oceancolour.org/portal/) is an option that can produce plots / graphics of the data as well as also exporting layers. First select the product(s) that you’re interested in, then select ‘Analysis’ that should be in the top right hand corner and choose what you’d like to do.