Halliday & Matthiessen (2014: 326):
This category construes the meanings of ‘be’ and ‘become’ circumstantially; the Rôle corresponds to the Attribute or Value of an ‘intensive relational’ clause. Rôle includes the subcategories of Guise (‘be’) and Product (‘become’). … A circumstance of Rôle usually relates to a participant in the clause — more specifically, to the Medium; but we also find circumstances of Rôle that do not.