Tracer Conservation with an Explicit Free Surface Method for z-Coordinate Ocean Models

This paper details a free surface method using an explicit time stepping scheme for use in z-coordinate ocean models. One key property that makes the method especially suitable for climate simulations is its very stable numerical time stepping scheme, which allows for the use of a long density time step, as commonly employed with coarse-resolution rigid-lid models. Additionally, the effects of the undulating free surface height are directly incorporated into the baroclinic momentum and tracer equations. The novel issues related to local and global tracer conservation when allowing for the top cell to undulate are the focus of this work. The method presented here is quasi-conservative locally and globally of tracer when the baroclinic and tracer time steps are equal. Important issues relevant for using this method in regional as well as large-scale climate models are discussed and illustrated, and examples of scaling achieved on parallel computers provided.