Application of a third-order upwind scheme in the NCAR ocean model

The National Center for Atmospheric Research (NCAR) Ocean Model has been developed for use in NCAR's Climate System Modeling project, a comprehensive development of a coupled ocean-atmosphere-sea ice-land surface model of the global climate system. As part of this development, new parameterizations of diffusive mixing by unresolved processes have been implemented for the tracer equations in the model. Because the strength of the mixing depends upon the density structure under these parameterizations, it is possible that local explicit mixing may be quite small in selected locations, in contrast to the constant diffusivity model generally used. When a spatially centered advection scheme is used in the standard model configuration, local overshooting of tracer values occurs, leading to unphysical maxima and minima in the fields. While the immediate problem is a local Gibbs's phenomenon, there is the possibility that such local tracer anomalies might propagate by advection and diffusion far from the source, causing inaccuracies in the tracer fields globally. Because of these issues, a third-order upwind scheme was implemented for the advection of tracers. Numerical experiments show that this scheme is computationally efficient compared to alternatives (such as the flux-corrected transport scheme) and that it works well with other aspects of the model, such as acceleration (important for spinup efficiency) and the new mixing parameterizations. The scheme minimizes overshooting effects while keeping the dissipative aspect of the advective operator reasonably small. The net effect is to produce solutions in which the large-scale fields are affected very little while local extrema are nearly (but not completely) removed, leading to physically much more realistic tracer patterns.