  We discuss, for a two-dimensional Dirac Hamiltonian with random scalar
potential, the presence of a $Z_2$ topological term in the non-linear sigma
model encoding the physics of Anderson localization in the symplectic symmetry
class. The $Z_2$ topological term realizes the sign of the Pfaffian of a family
of Dirac operators. We compute the corresponding global anomaly, i.e., the
change in the sign of the Pfaffian by studying a spectral flow numerically.
This $Z_2$ topological effect can be relevant to graphene when the impurity
potential is long-ranged and, also, to the two-dimensional boundaries of a
three-dimensional lattice model of $Z_2$ topological insulators in the
symplectic symmetry class.
