Comparison of Two Classical Advection Schemes in a General Circulation Model

Yasuhiro Yamanaka Center for Climate System Research, University of Tokyo, Tokyo, Japan

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Ryo Furue Center for Climate System Research, University of Tokyo, Tokyo, Japan

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Hiroyasu Hasumi Center for Climate System Research, University of Tokyo, Tokyo, Japan

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Nobuo Suginohara Center for Climate System Research, University of Tokyo, Tokyo, Japan

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Abstract

The authors compare two classical advection schemes, the centered difference and weighted upcurrent, for coarse-resolution OGCMs, using an idealized ocean basin and a realistic World Ocean topography. For the idealized basin, three experiments are run, one with 12 vertical levels and the centered difference scheme, one with 12 levels and the weighted upcurrent scheme, and the other with 800 levels and the centered scheme. The last experiment perfectly satisfies the grid Péclet number stability criterion and is regarded as the “true solution.” Comparison of the coarse vertical resolution experiments with the true solution indicates 1) that with the centered scheme, when strong vertical motion crosses a strong stratification, false density values are created in the coarse resolution model and this leads to false convective adjustment, which transports those false density values downward; and 2) that because of computational diffusion, the weighted upcurrent scheme leads to a less dense deep water with a stronger stratification than those of the true solution. These characteristics also apply even to the World Ocean model with relatively small grid Péclet numbers (moderately high vertical resolution and relatively large vertical diffusivity): the centered scheme leads to artificial convective adjustment near the surface in the equatorial Pacific, creating an artificial circulation, and the weighted upcurrent 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 diffusion is found to dominate the density balance at the bottom jet in the super-high-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.

* Current affiliation: Graduate School of Environmental Earth Science, Hokkaido University, Sapporo, Japan.

Corresponding author address: Dr. Ryo Furue, Center for Climate System Research, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8904, Japan.

Email: furufuru@ccsr.u-tokyo.ac.jpz

Abstract

The authors compare two classical advection schemes, the centered difference and weighted upcurrent, for coarse-resolution OGCMs, using an idealized ocean basin and a realistic World Ocean topography. For the idealized basin, three experiments are run, one with 12 vertical levels and the centered difference scheme, one with 12 levels and the weighted upcurrent scheme, and the other with 800 levels and the centered scheme. The last experiment perfectly satisfies the grid Péclet number stability criterion and is regarded as the “true solution.” Comparison of the coarse vertical resolution experiments with the true solution indicates 1) that with the centered scheme, when strong vertical motion crosses a strong stratification, false density values are created in the coarse resolution model and this leads to false convective adjustment, which transports those false density values downward; and 2) that because of computational diffusion, the weighted upcurrent scheme leads to a less dense deep water with a stronger stratification than those of the true solution. These characteristics also apply even to the World Ocean model with relatively small grid Péclet numbers (moderately high vertical resolution and relatively large vertical diffusivity): the centered scheme leads to artificial convective adjustment near the surface in the equatorial Pacific, creating an artificial circulation, and the weighted upcurrent 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 diffusion is found to dominate the density balance at the bottom jet in the super-high-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.

* Current affiliation: Graduate School of Environmental Earth Science, Hokkaido University, Sapporo, Japan.

Corresponding author address: Dr. Ryo Furue, Center for Climate System Research, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8904, Japan.

Email: furufuru@ccsr.u-tokyo.ac.jpz

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