  We introduce a tropical enumerative invariant depending on a variable y which
generalizes the tropical refined Severi degree. We show that this refined
broccoli invariant is indeed independent of the point configuration, and that
it specializes to a tropical descendant Gromov-Witten invariant for y=1 and to
the corresponding broccoli invariant for y=-1. Furthermore, we define tropical
refined descendant Gromov-Witten invariants which equal the corresponding
refined broccoli invariants giving a new insight to the nature of broccoli
invariants. We discuss various possible generalizations, e.g. to refinements of
bridge curves and Welschinger curves.
