Limitations of bin and bulk microphysics in reproducing the observed spatial structure of light precipitation

Coarse-gridded atmospheric models often account for subgrid-scale variability by specifying probability distribution functions (PDFs) of process rate inputs such as cloud and rain water mixing ratios ($q_c$ and $q_r$, respectively). PDF parameters can be obtained from numerous sources: in situ observations, ground- or space-based remote sensing, or fine-scale modeling such as large eddy simulation (LES). LES is appealing to constrain PDFs because it generates large sample sizes, can simulate a variety of cloud regimes/case studies, and is not subject to the ambiguities of observations. However, despite the appeal of using model output for parameterization development, it has not been demonstrated that LES satisfactorily reproduces the observed spatial structure of microphysical fields. In this study, the structure of observed and modeled microphysical fields are compared by applying bifractal analysis, an approach that quantifies variability across spatial scales, to simulations of a drizzling stratocumulus field that span a range of domain sizes, drop concentrations (a proxy for mesoscale organization), and microphysics schemes (bulk and bin). Simulated $q_c$ closely matches observed estimates of bifractal parameters that measure smoothness and intermittency. There are major discrepancies between observed and simulated $q_r$ properties, though, with bulk simulated $q_r$ consistently displaying the bifractal properties of observed clouds (smooth, minimally intermittent) rather than rain while bin simulations produce $q_r$ that is appropriately intermittent but too smooth. These results suggest fundamental limitations of bulk and bin schemes to realistically represent higher-order statistics of the observed rain structure.

粗网格大气模式通常通过指定过程速率输入量的概率分布函数（Probability Distribution Function，PDF）来表征次网格尺度变率，这类输入量包括云水混合比（$q_c$）与雨水混合比（$q_r$）。概率分布函数参数可通过多种途径获取：现场观测、地基或星基遥感，以及大涡模拟（Large Eddy Simulation，LES）这类精细尺度模拟。大涡模拟在约束概率分布函数参数时颇具优势：它可生成大量样本，能够模拟多种云型/个例研究场景，且不受观测歧义的影响。然而，尽管利用模式输出开展参数化开发颇具吸引力，但目前尚未有研究证明大涡模拟能够准确再现观测到的微物理场空间结构。本研究通过将双分形分析——一种量化空间尺度间变率的方法——应用于多组毛毛雨层积云场模拟实验，对比观测与模拟得到的微物理场结构；这些模拟实验涵盖了不同区域尺寸、滴数浓度（作为中尺度组织的代用指标）以及微物理方案（整体方案与分档方案）。模拟得到的云水混合比$q_c$与观测得到的表征平滑性和间歇性的双分形参数估算值高度吻合。但观测与模拟得到的雨水混合比$q_r$特征存在显著差异：整体方案模拟的$q_r$始终表现出观测云的双分形特征（平滑且间歇性极弱），而非降雨的特征；而分档方案模拟的$q_r$虽具备合适的间歇性，但平滑度过高。上述结果表明，整体方案与分档方案在真实再现观测到的降雨结构高阶统计特征方面存在根本性局限。