  A Dirac operator on the plane with constant (positive) mass is a Chern
insulator, sitting in class D of the Kitaev table. Despite its simplicity, this
system is topologically ill-behaved: the non-compact Brillouin zone prevents
definition of a bulk invariant, and naively placing the model on a manifold
with boundary results in violations of the bulk-edge correspondence (BEC). We
overcome both issues by letting the mass spatially vary in the vertical
direction, interpolating between the original model and its negative-mass
counterpart. Proper bulk and edge indices can now be defined. They are shown to
coincide, thereby embodying BEC. The shallow-water model exhibits the same
illnesses as the 2D massive Dirac. Identical problems suggest identical
solutions, and indeed extending the approach above to this setting yields
proper indices and another instance of BEC.
