Halliday & Matthiessen (2014: 419):
The adverbial group serves as Adjunct in the modal structure of the clause — either circumstantial Adjunct or modal Adjunct (mood or comment). Examples:
(1) circumstantial AdjunctYou’ve coped beautifully tonight; you’ve coped so well compared to how I would have coped.
(2a) interpersonal Adjunct, mood
I actually didn’t have a lot of chicken; I had probably more vegetables.
(2b) interpersonal Adjunct, comment
Apparently he’s got a wife and a couple of kids.