Cautionary tales of persistent accumulation of numerical error: Dispersive centered advection

We identify a potentially severe source of spurious cooling within and below the thermocline. The effect involves an interplay between tracer advection scheme and eddy parameterization: a dispersive advection scheme generates spurious warm and cold extrema, and then the tracer mixing scheme is relied upon to moderate those extrema. Noise suppression is less robust when the eddy parameterization consists of the more physically based use of eddy-induced transport and isopycnal tracer mixing. Convection occurs in response to the spurious warm and cold extrema generated by the dispersive advection scheme, driving a persistent cooling below the thermocline. When choosing an advection scheme for ocean climate modelling this effect should be considered as a significant concern associated with the use of dispersive centered advection.