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Abstract 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 ( D x ) 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 D x 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 D x = 2–5 km than for larger D x = 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.
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