Cloud Modeling and Probability Density Functions

大气的大尺度数值模式包括微物理和辐射过程的参数化。这种参数化需要以网格分解场的形式进行精确输入，如液态水含量、冰水含量和液滴数浓度。这些场是由主模型方程产生的。一些中尺度模式预测液态水的假设是，在小于网格大小的尺度上没有热力学变率。这一假设与预测亚网格尺度云分数或任何其他热力学亚网格变异性的云方案不相容。在这项研究中，首席研究员试图改进驱动微物理和辐射参数化的液体、冰和液滴数量的宿主模型方程的公式和准确性。为了改进它们，他将研究子网格变异性的影响。研究的一个主要对象是相关量的概率密度函数（PDF），例如总含水量。具体来说，PI将(1)利用相关PDF的数学性质严格推导液态水含量、冰水含量和液滴数浓度的大规模方程；(2)对飞机数据进行分析，确定液冰联合pdf的形状，利用pdf闭合主模型方程；(3)在理想的一维云参数化中实现主机模型方程。该研究具有双重的学术价值：(1)提高了对混合相云的认识；(2)改进大气数值模式中云的表征。如果成功，该研究可能最终对云参数化产生影响，范围从简单的整体微物理方案到bin微物理方案，以及从一般环流模式到云解析模式的模式。这项研究将产生两个更广泛的影响：它将有助于培养一名博士后研究助理，它的结果将通过期刊出版物和互联网广泛地提供给科学界。

Large-scale numerical models of the atmosphere include parameterizations of microphysical and radiative processes. Such parameterizations require accurate input in the form of grid-resolved fields such as liquid water content, ice water content, and droplet number concentration. These fields are produced by host model equations. Some mesoscale models prognose liquid water using the assumption that there is no thermodynamic variability on scales smaller than the grid box size. This assumption is incompatible with cloud schemes that predict subgrid-scale cloud fraction or any other thermodynamic subgrid variability.In this research, the Principal Investigator seeks to improve the formulation and accuracy of host model equations for liquid, ice, and droplet number that drive microphysics and radiative parameterizations. To improve them, he will investigate the effects of subgrid variability.A principal object of study is the probability density function (PDF) of relevant quantities, such as total water content. Specifically, the PI will (1) use mathematical properties of the relevant PDF to rigorously derive large-scale equations for liquid water content, ice water content, and droplet number concentration; (2) analyze aircraft data to ascertain the shapes of joint PDFs of liquid and ice, and then use the PDFs to close the host model equations; and (3) implement the host model equations in an idealized one-dimensional cloud parameterization.The intellectual merit is twofold: (1) to improve understanding of mixed-phase clouds; and (2) to improve representation of clouds in atmospheric numerical models. If successful, the research may ultimately have implications for cloud parameterizations ranging from simple bulk microphysics schemes to bin microphysics schemes, and for models ranging from general circulation models to cloud resolving models.The research will have two broader impacts: it will help train a postdoctoral research associate, and its results will be made widely available to the scientific community through journal publications and the internet.