Assumed‐PDF (probability density function) higher‐order turbulence closures (APHOCs) are now widely used for parameterizing boundary layer turbulence and shallow convection in Earth system models (ESMs). A better understanding of the resolution‐dependent behavior of APHOCs is essential for improving the performance of next‐generation ESMs with intended horizontal resolutions finer than 10 km. In this study, we evaluate the PDF family of Analytic double‐Gaussian 1 implemented in Cloud Layers Unified By Binormals (CLUBB) over a range of spatial scales (Dx) from 2 to 100 km. A 120‐km‐wide large eddy simulation (LES) for a continental convection case during 2016 Holistic Interactions of Shallow Clouds, Aerosols, and Land‐Ecosystems (HI‐SCALE) field campaign serves as benchmark to evaluate the PDF closure using an off‐line approach. We find during the shallow convection period, the CLUBB PDF closure tends to produce positive biases of cloud properties and liquid water flux near cloud base for all scales of analysis. It produces negative biases for these variables near cloud top that are more severe for Dx larger than 25 km. Results show that replacing the CLUBB‐parameterized moisture and temperature skewnesses with LES‐derived ones can fix most of the biases if clipping of input moments is allowed to prevent the occurrence of unrealizable solutions. Overall, the performance of the PDF closure is better for smaller Dx = 2–5 km than for larger Dx = 50–100 km; for a given grid spacing, it is better when the convective clouds become deeper in the late afternoon. Likely causes for the resolution dependence and implications for improving the PDF closure are discussed.

中文翻译：

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在多个空间尺度上评估大陆浅到深对流过渡案例的CLUBB PDF封闭假设

假定PDF（概率密度函数）的高阶湍流闭塞（APHOC）现在被广泛用于参数化地球系统模型（ESM）中的边界层湍流和浅对流。更好地了解APHOC的分辨率相关行为对于改善预期水平分辨率小于10 km的下一代ESM的性能至关重要。在这项研究中，我们评估了在一系列空间尺度（D x）上由双归一化统一的云层（CLUBB）中实现的解析双高斯1 PDF系列）从2到100公里。在2016年浅云，气溶胶和陆地生态系统的整体相互作用（HI-SCALE）野外活动期间，对一个大陆对流案例进行了120公里宽的大涡模拟（LES），以此作为基准来评估PDF封闭度。行方法。我们发现，在浅对流期间，对于所有规模的分析，CLUBB PDF封闭趋于在云基附近产生云特性和液态水通量的正偏差。它对云顶附近的这些变量产生负偏差，对于D x更为严重大于25公里。结果表明，如果允许削减输入力矩以防止出现无法实现的解决方案，则用LES衍生的参数替换CLUBB参数化的水分和温度偏度可以解决大多数偏差。总的来说，对于较小的D x  = 2-5 km ，PDF封闭的性能要优于较大的D x  = 50-100 km。对于给定的网格间距，最好是下午晚些时候对流云变深。讨论了分辨率依赖性的可能原因以及改进PDF封闭效果的含义。