The raw material is real and the calendar is not. Medieval Irish grammatical and scholarly tracts record the letters of the ogham alphabet together with glosses, and among the several kinds of gloss are lists that attach a tree or a plant to each letter. Those lists are word lore: mnemonic kennings for the letters, of the same type as the lists that attach birds, colours, fortresses and occupations to them. They are not a division of time and no medieval text uses them as one.
Robert Graves took the tree glosses, selected thirteen of them, assigned each a lunar month and built a calendar. He was writing a book of poetic argument rather than of scholarship, said so, and reached his conclusions by association and intuition, which he defended as the proper method for the subject. The arithmetic does not survive contact with the alphabet either. Ogham has twenty letters in its basic form, arranged in four groups of five, with further characters added later, so producing thirteen months requires deciding which letters to use, which to leave out and in what order to run them. Every one of those decisions is Graves's, and none of them is reported from a source. The atlas records the medieval tree glosses as genuine material of a genuine tradition, and the calendar built from them as a twentieth century composition by a named author whose method is on the record.