A CONSIDERATION OF TRACER ADVECTION SCHEMES IN A PRIMITIVE EQUATION OCEAN MODEL

We consider several tracer advection schemes in the context of a simpl e sector configuration of a Bryan-Cox-Semtner type ocean model. The sc hemes are centered-in-time centered-in-space, donor cell upwind differ encing, flux corrected transport (FCT), QUICKEST and MPDATA. While we discuss the transport of temperature and salinity, and apply alternati ve schemes to this transport within our model, we concentrate primaril y on a problem which involves passive tracer advection in which vertic al gradients are high and concentrations asymptote to zero near the se a surface, as is the case in biogeochemical ocean modeling. We find th at flux correction (available optionally with the MPDATA scheme, as we ll as the FCT scheme) is required in order to produce acceptable resul ts on this challenging problem. A method of supercycling of passive tr acers relative to dynamic variables, whereby the time step for passive tracers is larger that that used for the other prognostic variables o f the model, is introduced in order to apply these more expensive flux limited schemes efficiently. We also present a general method for the second-order accurate application of one-dimensional forward-in-time advection schemes in three dimensions.