HAMOCC

HAMOCC simulates the oceanic cycles of carbon and other biogeochemical elements. It has been initially developed to study the role of oceanic transport and storage of carbon in the climate system.Additionally it has been expanded with biogeochemical tracers (nitrogen, DMS), a sediment module and also models fluxes between sediment, water and air-sea interface. HAMOCC is developed by the Max Planck Institute for Meteorology in Hamburg.

The software is open-source under BSD-3C License.

More information about HAMOCC in this paper and more about the underlying processes in this presentation. 
This submodel is still being used. It is, however, not being further developed at MPI-M, which is now fully focused on the joint development of ICON.

If you want to get started, get in touch with the former developers at MPI-M.