Abstract
The process of entrainment-mixing between cumulus clouds and the ambient air is important for the development of cumulus clouds. Accurately obtaining the entrainment rate (λ) is particularly important for its parameterization within the overall cumulus parameterization scheme. In this study, an improved bulk-plume method is proposed by solving the equations of two conserved variables simultaneously to calculate λ of cumulus clouds in a large-eddy simulation. The results demonstrate that the improved bulk-plume method is more reliable than the traditional bulk-plume method, because λ, as calculated from the improved method, falls within the range of λ values obtained from the traditional method using different conserved variables. The probability density functions of λ for all data, different times, and different heights can be well-fitted by a log-normal distribution, which supports the assumed stochastic entrainment process in previous studies. Further analysis demonstrate that the relationship between λ and the vertical velocity is better than other thermodynamic/dynamical properties; thus, the vertical velocity is recommended as the primary influencing factor for the parameterization of λ in the future. The results of this study enhance the theoretical understanding of λ and its influencing factors and shed new light on the development of λ parameterization.
摘 要
积云与环境空气之间的夹卷混合过程对于积云的发展非常重要. 准确获得夹卷率对于积云参数化方案中夹卷率的参数化尤为重要. 本研究提出了一种改进的积云气柱法, 通过同时求解两个守恒量的方程来计算大涡模拟中积云的夹卷率. 结果表明, 改进的积云气柱法比传统方法更可靠, 因为根据改进方法计算得出的夹卷率处于使用不同守恒量的传统方法所得到的夹卷率范围内. 对于所有数据、 不同时间和不同高度, 夹卷率的概率密度函数可以很好地拟合为对数正态分布, 这支撑了以往研究中假设的随机夹卷过程. 进一步的分析表明, 夹卷率与垂直速度的关系优于其他热力学/动力学性质, 因此在未来的夹卷率参数化中, 建议将垂直速度作为首要影响因子. 本研究的结果增强了对夹卷率及其影响因子的理论认识, 并为夹卷率参数化的发展提供了参考.
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Data availability The large-scale forcing data used in this study can be downloaded from the Atmospheric Radiation Measurement (ARM) user facility (https://doi.org/10.5439/1647300 (Tao and Xie, 2004); https://doi.org/10.5439/1647174 (Tao and Xie, 2012)). LASSO data can be downloaded from https://doi.org/10.5439/1342961 (Gustafson et al., 2017).
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Acknowledgements
The authors would like to thank Jianfeng GU at Nanjing University for the helpful discussions. This research is supported by the National Natural Science Foundation of China (Grant Nos. 42175099, 42027804, 42075073) and the Innovative Project of Postgraduates in Jiangsu Province in 2023 (Grant No. KYCX23_1319). Shi LUO is supported by the National Natural Science Foundation of China (Grant No. 42205080), the Natural Science Foundation of Sichuan (Grant No. 2023YFS0442), and the Research Fund of Civil Aviation Flight University of China (Grant No. J2022-037). This research is also supported by the National Key Scientific and Technological Infrastructure project “Earth System Science Numerical Simulator Facility” (EarthLab). The numerical calculations in this paper were conducted on the supercomputing system in the Supercomputing Center of Nanjing University of Information Science & Technology.
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Article Highlights
• An improved bulk-plume method is proposed to calculate the entrainment rate.
• Probability density functions of entrainment rates are well-fitted by a log-normal distribution.
• The entrainment rate has the strongest relationship with the vertical velocity among the other thermodynamic/dynamical properties.
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The Probability Density Function Related to Shallow Cumulus Entrainment Rate and Its Influencing Factors in a Large-Eddy Simulation
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Zhu, L., Lu, C., Xu, X. et al. The Probability Density Function Related to Shallow Cumulus Entrainment Rate and Its Influencing Factors in a Large-Eddy Simulation. Adv. Atmos. Sci. 41, 173–187 (2024). https://doi.org/10.1007/s00376-023-2357-6
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DOI: https://doi.org/10.1007/s00376-023-2357-6
Key words
- large-eddy simulation
- cumulus clouds
- entrainment rate
- probability density functions
- spatial and temporal distribution