There is a growing interest in tidal effects on the global wind-driven oceanic circulation. Tidal models used in such investigations have been verified by comparison with satellite and tide gauge data, but synthetic tests have not been published. In this paper we present three numerical tests in spherical geometry, which are suitable for testing the tidal component of global ocean models. The first test is a tsunami-like propagation of an initial Gaussian depression with no external forcing. The other two tests examine the tidal response of an ocean with an undulating bottom with four Gaussian ridges and an ocean with a flat bottom with a realistic land mask. We provide the results from six model configurations, which differ in the time-stepping scheme and computational grid used. Most of them are implemented in present-day global ocean models. Although the proposed numerical tests are simple compared to realistic simulations, their analytic solutions are not available. We thus check the conservation of time invariants to ensure that the solutions are physically meaningful. We also compare the time evolution of certain physical quantities and the differences in sea surface heights at particular time instants with respect to a reference solution. All tested time stepping schemes are suitable for tidal studies except for the Euler implicit time stepping scheme. Model configurations based on the Arakawa grids B/E use smoothing to suppress the grid-scale noise which results in an energy leakage of around 5%. The B/E-grid energy leakage is probably acceptable if we consider that tuned diffusive terms are used in real-world configurations. The C-grid and B/E-grid solutions differ in the vicinity of solid boundaries as a consequence of different boundary conditions. The B-grid and E-grid solutions are similar, unless the shape of the solid boundaries is complex due to the different shapes of the respective grid cells.

潮汐对全球风力驱动的海洋环流的影响越来越引起人们的关注。通过与卫星和潮汐仪数据进行比较，已验证了在此类调查中使用的潮汐模型，但尚未发布综合测试。在本文中，我们提出了三个球形几何数值测试，适用于测试全球海洋模型的潮汐分量。第一个测试是初始高斯抑郁的海啸状传播，没有外部强迫。其他两个测试检查了波浪起伏的海底和四个高斯脊之间的潮汐响应，以及平坦的海底和真实的陆地面具的海潮响应。我们提供了六个模型配置的结果，它们在时间步调方案和所使用的计算网格上有所不同。其中大多数是在当今的全球海洋模型中实施的。尽管所提出的数值测试与实际模拟相比很简单，但是它们的解析解却不可用。因此，我们检查时间不变性的守恒性，以确保解在物理上有意义。我们还比较了某些物理量的时间演化和相对于参考解决方案在特定时刻的海平面高度的差异。除Euler隐式时间步进方案外，所有经过测试的时间步进方案均适用于潮汐研究。基于Arakawa网格B / E的模型配置使用平滑来抑制网格规模的噪声，从而导致大约5％的能量泄漏。如果我们考虑在实际配置中使用经过调整的扩散项，则B / E电网的能量泄漏可能是可以接受的。由于不同的边界条件，C网格和B / E网格解决方案在实体边界附近有所不同。B网格和E网格解决方案相似，除非由于各个网格单元的形状不同，固体边界的形状复杂。