  A time-dependent determining wavenumber was introduced in [5] to estimate the
number of determining modes for the surface quasi-geostrophic (SQG) equation.
In this paper we continue this investigation focusing on the subcritical case
and study trajectories inside an absorbing set bounded in $L^\infty$. Utilizing
this bound we find a time-independent determining wavenumber that improves the
estimate obtained in [5]. This classical approach is more direct, but it is
contingent on the existence of the $L^\infty$ absorbing set.
