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.

中文翻译：

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非结构化网格海洋模型中水平离散化的精度和稳定性分析

我们评估全球环流模型（GCM）稳健性的一个重要工具是了解浅水近似下动力核心的水平离散化。在这里，我们评估了考虑浅水模型的非结构化海洋模型中使用的或足够的不同方法的准确性和稳定性。我们的结果表明，这些方案具有不同的精度能力，A-（NICAM）和 B-网格（FeSOM 2.0）方案在大多数算子和时间积分变量中提供至少一阶精度，而两个 C-网格（ICON 和MPAS）方案在充分近似水平动态方面表现出更大的困难。此外，规则网格上的惯性重力波表示理论可以扩展到我们的基于非结构化的方案，其中从最不准确到最准确，我们分别有：A-网格、B-网格和C-网格。仅考虑 C 网格方案，MPAS 方案比 ICON 更准确地表示惯性重力波。在稳定性方面，我们看到A网格和C网格MPAS方案都显示出最好的稳定性特性，但A网格方案依赖于人工扩散，而C网格方案则不依赖人工扩散。此外，B 网格和 C 网格 ICON 方案的稳定性也最差。最后，为了了解 ICON 中潜在不稳定性的影响，我们注意到，没有过滤项的完整 3D 模型不会不稳定，因为它是及时积分的。然而，寄生振荡是导致洋流动能降低的原因。此外，还观察到洋流的湍流动能进一步减少，从而产生虚假混合，这也在这些洋流强度的减弱中发挥了作用。