UPWIND-WEIGHTED ADVECTION SCHEMES FOR OCEAN TRACER TRANSPORT - AN EVALUATION IN A PASSIVE TRACER CONTEXT

Centered-in-space, centered-in-time integration has generally been use d for the advection of scalars in ocean models. An assessment is made of the implications of centered leapfrog integration in the context of two-dimensional passive tracer advection within a Stommel (1948) gyre . Nonphysical ripples in the tracer field grow to alarming levels in p urely advective integrations. Diffusive parameterizations of eddy mixi ng moderate these ripples, but it is found that Laplacian diffusion gr eatly reduces the peak amplitude of the tracer field, while biharmonic or weaker Laplacian diffusion allows ripples of large amplitude. Seve ral forward-in-time, upwind-weighted schemes are found to provide bett er solutions. Smolarkiewicz's (1984) Multi-Dimensional Positive-Defini te Advection and Transport Algorithm (MPDATA) scheme is slightly super ior for an integration at moderate resolution within which the western boundary current is poorly resolved in typical fashion. Third-order, upwind-based schemes exhibit little sensitivity to the details of mult idimensional treatment for this problem of passive tracer advection, w ith results nearly as good as for MPDATA.