  In a previous article a characteristic discontinuous Galerkin (CDG) advection
scheme was presented for tracer transport. The scheme is conservative,
unconditionally stable with respect to time step and scales sub-linearly with
the number of tracers being advected. Here we present the implementation of the
CDG advection scheme for tracer transport within MPAS-Ocean, a Boussinesque
unstructured grid ocean model with an arbitrary Lagrangian Eulerian vertical
coordinate. The scheme is implemented in both the vertical and horizontal
dimensions, and special care is taken to ensure that the scheme remains
conservative in the context of moving vertical layers. Consistency is ensured
with respect to the dynamics by a renormalization of the fluxes with respect to
the volume fluxes derived from the continuity equation. For spherical
implementations, the intersection of the flux swept regions and the Eulerian
grid are determined for great circle arcs, and the fluxes and element assembly
are performed on the plane via a length preserving projection. Solutions are
presented for a suite of test cases and comparisons made to the existing flux
corrected transport scheme in MPAS-Ocean.
