Here, we present the first attempt to fully represent three‐dimensional turbulence fluxes in the “Terra Incognita” or the gray zone in other words. In order to derive partitioning functions, representing the partitioning between subgrid and total fluxes, we make use of high‐resolution large‐eddy simulations (LES), which are performed with the Weather Research and Forecasting (WRF) model. LES computations are performed for various levels of convective instability, ranging from pure buoyant to strongly sheared convection. Then, the resulting reference‐LES fields are successively coarse grained from its original microscale grid spacing (  m) up to typical mesoscale grid spacings (  km). The given process is applied by means of an advanced filter, that is, the Butterworth filter. It enables a clear scale‐specific filtering that results in a more controlled energy transition from lower to higher wavenumbers, unlike the drawbacks of current filters in use. Finally, we parameterize the subgrid scale (SGS) partitioning functions of 10 SGS turbulence quantities: momentum fluxes (τ_ij, six terms), heat fluxes (q_j, three terms), and turbulence kinetic energy (k). Turbulence partitioning relations are parameterized in a scale‐aware, stability‐dependent, and height‐dependent form, using the sigmoidal Gompertz function. Thus, the new gray zone model provides a framework that bridges the mesoscale and microscale limits and that is suitable for the development of next generation three‐dimensional, multiscale turbulence parameterization methods or planetary boundary layer schemes.

中文翻译：

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对流大气边界层中灰区划分函数和湍流通量参数化

在这里，我们提出了首次尝试完全表示“ Terra Incognita”或灰色区域中的三维湍流的方法。为了导出表示子网格和总通量之间的分区的分区函数，我们使用了高分辨率大涡模拟（LES），该模拟是通过天气研究和预报（WRF）模型执行的。LES计算是针对各种级别的对流不稳定性进行的，从纯浮力到强剪切对流不等。然后，从原始的微尺度网格间距（  m）到典型的中尺度网格间距（  公里）。给定的过程通过高级过滤器（即Butterworth过滤器）应用。与使用中的电流滤波器的缺点不同，它可以实现特定比例的清晰滤波，从而可以更好地控制从低波数到高波数的能量转换。最后，我们参数化亚格（SGS）的10 SGS湍流量划分功能：动量通量（τ_我Ĵ，六个方面），热通量（q _Ĵ，三个方面），和湍流动能（ķ）。使用S型Gompertz函数，以比例感知，依赖于稳定性和依赖于高度的形式对湍流分配关系进行参数化。因此，新的灰色地带模型提供了一个桥接中尺度和微尺度极限的框架，适用于开发下一代三维，多尺度湍流参数化方法或行星边界层方案。