Numerical mixing, defined here as the physically spurious tracer diffusion due to the numerical discretization of advection, is known to contribute to biases in ocean models. However, quantifying numerical mixing is nontrivial, with most studies utilizing targeted experiments in idealized settings. Here, we present a water mass transformation-based method for quantifying numerical mixing that can be applied to any conserved variable in general circulation models. Furthermore, the method can be applied within individual fluid columns to provide spatial information. We apply the method to a suite of global ocean model simulations with differing grid spacings and subgrid-scale parameterizations. In all configurations numerical mixing drives diathermal heat transport of comparable magnitude to that associated with explicit parameterizations. Numerical mixing is prominent in the tropical thermocline, where it is sensitive to the vertical diffusivity and resolution. At colder temperatures numerical mixing is sensitive to the presence of explicit neutral diffusion, suggesting that it may act as a proxy for neutral diffusion when it is explicitly absent. Comparison of otherwise equivalent 1/4° and 1/10° configurations with grid-scale dependent horizontal viscosity shows only a modest enhancement in numerical mixing at 1/4°. However, if the lateral viscosity is maintained while resolution is increased then numerical mixing is reduced by almost 35%. This result suggests that the common practice of reducing viscosity in order to maximize permitted variability must be considered carefully. Our results provide a detailed view of numerical mixing in ocean models and pave the way for improvements in parameter choices and numerical methods.

中文翻译：

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一套全球海洋模型中数值混合的地理学

数值混合，这里定义为由于对流数值离散而产生的物理虚假示踪剂扩散，已知会导致海洋模型中的偏差。然而，量化数值混合并非易事，大多数研究都在理想化环境中利用目标实验。在这里，我们提出了一种基于水质量变换的量化数值混合的方法，该方法可以应用于一般循环模型中的任何守恒变量。此外，该方法可以应用于单个流体柱以提供空间信息。我们将该方法应用于具有不同网格间距和亚网格尺度参数化的一套全球海洋模型模拟。在所有配置中，数值混合驱动的热传递与显式参数化相关的数值相当。数值混合在热带温跃层中很突出，它对垂直扩散率和分辨率很敏感。在较冷的温度下，数值混合对显式中性扩散的存在很敏感，这表明当它显式不存在时，它可以作为中性扩散的代理。其他等效的 1/4° 和 1/10° 配置与网格尺度相关的水平粘度的比较显示在 1/4° 处的数值混合仅适度增强。然而，如果在增加分辨率的同时保持横向粘度，那么数值混合会减少近 35 表明当它明确不存在时，它可以作为中性扩散的代理。其他等效的 1/4° 和 1/10° 配置与网格尺度相关的水平粘度的比较显示在 1/4° 处的数值混合仅适度增强。然而，如果在增加分辨率的同时保持横向粘度，那么数值混合会减少近 35 表明当它明确不存在时，它可以作为中性扩散的代理。其他等效的 1/4° 和 1/10° 配置与网格尺度相关的水平粘度的比较显示在 1/4° 处的数值混合仅适度增强。然而，如果在增加分辨率的同时保持横向粘度，那么数值混合会减少近 35% . 该结果表明，必须仔细考虑降低粘度以最大化允许可变性的常见做法。我们的结果提供了海洋模型中数值混合的详细视图，并为改进参数选择和数值方法铺平了道路。