Comparison of two classical advection schemes in a general circulation model

The authors compare two classical advection schemes, the centered differenc e and weighted upcurrent, for coarse-resolution OGCMs. using an idealized o cean basin and a realistic World Ocean topography. For the idealized basin, three experiments are run, one with 12 vertical levels and the centered di fference scheme, one with 12 levels and the weighted upcurrent scheme, and the other with 800 levels and the centered scheme. The last experiment perf ectly satisfies the grid Peclet number stability criterion and is regarded as the "true solution." Comparison of the coarse vertical resolution experi ments with the true solution indicates 1) that with the centered scheme, wh en strong vertical motion crosses a strong stratification, false density va lues are created in the coarse resolution model and this leads to false con vective adjustment, which transports those false density values downward; a nd 2) that because of computational diffusion, the weighted upcurrent schem e leads to a less dense deep water with a stronger stratification than thos e of the true solution. These characteristics also apply even to the World Ocean model with relatively small grid Peclet numbers (moderately high vert ical resolution and relatively large vertical diffusivity): the centered sc heme leads to artificial convective adjustment near the surface in the equa torial Pacific, creating an artificial circulation, and the weighted upcurr ent scheme leads to a warmer deep water and more diffuse thermocline. Deep equatorial "stacked jets" are found in all idealized-basin experiments, in particular, in the super-high vertical resolution case. Horizontal diffusio n is found to dominate the density balance at the bottom jet in the super-h igh-resolution model, as previously found in an OGCM with a moderately high vertical resolution. This is consistent with the hypothesis that the jets exist owing to diapycnal mixing.