Opinions differ as to whether this taxon is a distinct species or a subspecies of Narcissus bulbocodium, i.e., Narcissus bulbocodium L. subsp. obesus (Salisb.) Maire. I'm opting for the former, but you may need to use the latter if you are searching for more information. There are several broad horticultural groupings of daffodils, so perhaps some of the confusion can be found there; even if treated as a separate species scientifically, the general resemblance to Narcissus bulbocodium results in Narcissus obesus being known horticulturally as one of the bulbocodium daffodils.

The horticultural groupings are based, at least in part, on the morphology of the flowers. Though he doesn't name the groupings (you'll have to visit Wikipedia: Popular culture for those), Ian Young's Bulb Log entry for April 26, 2006 has a photograph of a comparative display of various flower types in Narcissus. He also provides a photograph of Narcissus obesus on that page, or you can visit the Pacific Bulb Society for two other images.

Hoop-petticoat daffodil is a native of west and central Portugal.