Accuracy and stability analysis of horizontal discretizations used in unstructured grid ocean models
One important tool at our disposal to evaluate the robustness of Global Circulation Models (GCMs) is to understand the horizontal discretization of the dynamical core under a shallow water approximation. Here, we evaluate the accuracy and stability of different methods used in, or adequate for, unst...
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Veröffentlicht in: | Ocean modelling (Oxford) 2024-06, Vol.189, p.102335, Article 102335 |
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Zusammenfassung: | One important tool at our disposal to evaluate the robustness of Global Circulation Models (GCMs) is to understand the horizontal discretization of the dynamical core under a shallow water approximation. Here, we evaluate the accuracy and stability of different methods used in, or adequate for, unstructured ocean models considering shallow water models. Our results show that the schemes have different accuracy capabilities, with the A- (NICAM) and B-grid (FeSOM 2.0) schemes providing at least 1st order accuracy in most operators and time integrated variables, while the two C-grid (ICON and MPAS) schemes display more difficulty in adequately approximating the horizontal dynamics. Moreover, the theory of the inertia-gravity wave representation on regular grids can be extended for our unstructured based schemes, where from least to most accurate we have: A-, B, and C-grid, respectively. Considering only C-grid schemes, the MPAS scheme has shown a more accurate representation of inertia-gravity waves than ICON. In terms of stability, we see that both A- and C-grid MPAS scheme display the best stability properties, but the A-grid scheme relies on artificial diffusion, while the C-grid scheme does not. Alongside, the B-grid and C-grid ICON schemes are within the least stable. Finally, in an effort to understand the effects of potential instabilities in ICON, we note that the full 3D model without a filtering term does not destabilize as it is integrated in time. However, spurious oscillations are responsible for decreasing the kinetic energy of the oceanic currents. Furthermore, an additional decrease of the currents’ turbulent kinetic energy is also observed, creating a spurious mixing, which also plays a role in the strength decrease of these oceanic currents.
•Shallow water analysis performed for NICAM, FeSOM 2.0, MPAS, and ICON-O.•NICAM and FeSOM show 1st order accuracy, but MPAS and ICON-O may display 0th order.•MPAS and ICON display most accurate representation of energy spectrum.•Thin layer stability analysis performed, where MPAS had the highest stability.•3D ICON-O stable without filter, but susceptible to spurious numerical oscillations. |
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ISSN: | 1463-5003 1463-5011 |
DOI: | 10.1016/j.ocemod.2024.102335 |