Abstract The isopycnal tracer diffusion scheme is commonly used in a coarse-resolution global ocean model to parameterize the diffusive effect of mesoscale eddy stirring. This scheme implemented in a depth-coordinate model often accompanies a fail-safe system to prevent numerical instability caused by large isopycnal diffusion around steeply sloped isopycnal surfaces. Its practical implementation artificially induces spurious diapycnal mixing across an isopycnal surface whose slope exceeds a prescribed slope maximum. This slope maximum widely ranges from 1/1000 to 3/10 in a recent global ocean model intercomparison project of Coordinated Ocean-ice Reference Experiments phase II. This study quantitatively investigates the effects of isopycnal tracer diffusion on meridional overturning circulation by calculating water mass transformation rate due to isopycnal diffusion with the use of Walin’s (1982) methodology. We focus on the following three effects of isopycnal diffusion in a depth-coordinate model: densification induced by nonlinearity of the equation of state, spurious diapycnal mixing in the interior ocean induced by practical implementation of the isopycnal diffusion scheme, and diapycnal mixing in the surface diabatic layer. It is revealed that a slope maximum that is too small (1/1000) leads to large spurious diapycnal mixing in the interior ocean. This diapycnal mixing supplies much buoyancy to the bottom water around Antarctica and makes it locally upwell within the Southern Ocean. It results in less northward export of bottom waters from the Southern Ocean into the Atlantic and the Indo-Pacific oceans and weakening of the bottom cell of meridional overturning circulation. This spurious diapycnal mixing is significantly suppressed if we use the slope maximum of more than 1/100 or tapering isopycnal diffusivity around steep isopycnal slopes. This study also shows that these changes in the implementation of the isopycnal diffusion scheme also affect the various aspects of the simulated Southern Ocean. The experiment tapering isopycnal diffusivity suppresses unrealistic open ocean deep convections and polynyas in the Weddell Sea by both diminishing spurious diapycnal mixing in the interior ocean and applying the strong diapycnal mixing in the surface boundary layer associated with the isopycnal diffusion scheme. It results in the smallest biases of the potential temperature distribution, the winter sea ice concentration and mixed layer depth in the Weddell Sea and the ACC transport in our coarse resolution model.

中文翻译：

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等密度示踪剂扩散方案的实际实施引起的深度坐标模型对双密度混合的敏感性

摘要 等密度示踪剂扩散方案通常用于粗分辨率全球海洋模型，以参数化中尺度涡旋搅拌的扩散效应。这种在深度坐标模型中实施的方案通常伴随着一个故障安全系统，以防止由陡峭倾斜等密面周围的大等密扩散引起的数值不稳定。其实际实施人为地在斜率超过规定斜率最大值的等密度表面上引起虚假的双密度混合。在最近的协调海冰参考实验第二阶段的全球海洋模型比对项目中，该斜率最大值的范围很广，从 1/1000 到 3/10。本研究通过使用 Walin (1982) 的方法计算等密度扩散引起的水质量转化率，定量研究等密度示踪剂扩散对经向翻转环流的影响。我们关注深度坐标模型中等密度扩散的以下三个影响：由状态方程的非线性引起的致密化、由等密度扩散方案的实际实施引起的内部海洋中的虚假双密度混合以及表面的双密度混合绝热层。结果表明，太小（1/1000）的最大斜率会导致内部海洋中大量的假渗流混合。这种透心混合为南极洲周围的底水提供了很大的浮力，并使其在南大洋内局部上升。这导致南大洋底水向大西洋和印度太平洋的北出口减少，经向翻转环流的底细胞减弱。如果我们使用大于 1/100 的最大斜率或在陡峭的等密斜率周围逐渐变细的等密扩散率，则这种虚假的双密度混合会被显着抑制。这项研究还表明，等密度扩散方案实施中的这些变化也会影响模拟南大洋的各个方面。通过减少内部海洋中的虚假渗流混合和在与等密度扩散方案相关的表面边界层中应用强渗流混合，逐渐减小等密度扩散率的实验抑制了威德尔海中不切实际的开阔海洋深层对流和冰间湖。