Abstract Wetting and drying processes in shallow water systems by surges, tides and seiches have important societal, physical and biological impacts. Operational 3D regional models are of sufficient resolution, O(1 km), that the processes of wetting and drying need to be included. Here we describe a flux limiter based approach that allows a numerical ocean model with a flux formulation of tracer advection to wet and dry. The flux limiter approach limits the outflow from a cell whose depth is below a critical value defined by the user. The limiter can be a step function or a smooth function of the water depth, the latter increases model stability and avoids rapid alternation between dry and wet states on long slopes as the critical depth is approached. Furthermore, the user may proportionally limit the baroclinic fluxes as a cell transitions from wet to dry over the course of the large baroclinic time step. The simplicity of the flux limiter approach lends itself to its application within existing numerical models without significant intrusion into the code base. In this paper the vertical coordinate is restricted to pure terrain following coordinates with no z -like steps. We explore the scheme’s effectiveness, sensitivities and limitations within the 3D NEMO ocean model by assessing it using test cases of increasing complexity. It is shown to perform well in classic channel test cases and 2D parabolic test cases with analytic solutions. All test cases with initially uniform temperature and salinity preserve this initial condition throughout the wetting and drying phases. The scheme’s performance against analytical 1D dam break experiments is explored and used to interpret its performance against laboratory measurements of a 2D dam break. It is also shown to run stably for a realistic 3D regional domain of the North West European shelf and to improve some aspects of the model’s performance against tide gauges.

中文翻译：

---

NEMO 中基于通量限制器的润湿和干燥方案的实施和评估

摘要 由潮汐、潮汐和地震引起的浅水系统中的干湿过程具有重要的社会、物理和生物影响。可操作的 3D 区域模型具有足够的分辨率，O(1 km)，需要包括润湿和干燥过程。在这里，我们描述了一种基于通量限制器的方法，该方法允许使用示踪平流到湿和干的通量公式的数值海洋模型。通量限制器方法限制了深度低于用户定义的临界值的单元的流出。限制器可以是水深的阶跃函数或平滑函数，后者增加模型稳定性并避免在接近临界深度时长斜坡上干湿状态之间的快速交替。此外，当细胞在大的斜压时间步长过程中从湿过渡到干时，用户可以按比例限制斜压通量。通量限制器方法的简单性使其适用于现有数值模型中，而不会显着侵入代码库。在本文中，垂直坐标仅限于纯地形跟随坐标，没有类似 z 的步骤。我们通过使用越来越复杂的测试案例对其进行评估，从而探索该方案在 3D NEMO 海洋模型中的有效性、敏感性和局限性。它在具有解析解的经典通道测试用例和二维抛物线测试用例中表现良好。所有初始温度和盐度均一的测试案例在整个润湿和干燥阶段都保持这种初始条件。该方案针对分析一维溃坝实验的性能进行了探索，并用于解释其对二维溃坝实验室测量的性能。它还被证明可以在西北欧大陆架的真实 3D 区域域中稳定运行，并改善模型在某些方面的测潮仪性能。