  An extension is proposed to the internal symmetry transformations associated
with mass, entropy and other Clebsch-related conservation in geophysical fluid
dynamics. Those symmetry transformations were previously parameterized with an
arbitrary function $\cal F$ of materially conserved Clebsch potentials. The
extension consists in adding potential vorticity $q$ to the list of fields on
which a new arbitrary function $\cal G$ depends. If ${\cal G}=q{\cal A}(s)$,
where ${\cal A}(s)$ is an arbitrary function of specific entropy $s$, then the
symmetry is trivial and gives rise to a trivial conservation law. Otherwise,
the symmetry is non-trivial and an associated non-trivial conservation law
exists. Moreover, the notions of trivial and non-trivial Casimir invariants are
defined. All non-trivial symmetries that become hidden following a reduction of
phase space are associated with non-trivial Casimir invariants of a
non-canonical Hamiltonian formulation for fluids, while all trivial
conservation laws are associated with trivial Casimir invariants.
