Detailed microphysics in a Lagrangian cloud model

云的湍流行为造成了天气和气候模型中的许多不确定性，特别是在降水的时间和强度方面。天气和气候模式过于粗糙，无法解决云与其环境之间相互作用的细节，而且对微物理过程的描述也过于简化，例如云滴的生长和雨、雪和冰的形成。这种过程可以在所谓的大涡模式中进行大量详细的研究，其中云与其环境之间的相互作用在很大程度上得到了解决（网格间距小于100米）。大涡模型对于理解云中的湍流非常有用，但是当涉及到微物理过程时，它们通常仍然依赖于简单的描述。例如，这样的描述可能只知道模型网格单元中的液态水的数量，并且需要对如何将其划分为小滴和大滴做出许多假设。为了解决这个问题，有可能使用所谓的bin微物理方案，其中与不同大小类别的液滴相关的冷凝水量被预测。这种方法已经在英国气象局的大涡模型中成功实现，但是对于许多需要高分辨率的应用来说，计算成本太高。此外，传统的大涡模型是在欧拉框架下制定的（它们在网格细胞上执行簿记），受到虚假混合的影响，这使得结果对分辨率非常敏感。这里的一个基本问题是微物理过程本质上是拉格朗日的：它们沿着流动的轨迹（对于小颗粒）或沿着下降的轨迹（对于大颗粒，受周围风的影响）发生。我们最近开发了一个新的代码，MPIC（细胞中的湿包），它在本质上是拉格朗日框架中处理云的动力学，即通过流体的平流包（Christiansen 1973, Dritschel et al. 2016）。该代码不受杂散混合的影响，并已证明与传统的大涡模型相比效果良好。当使用相同的分辨率时，MPIC还降低了计算成本，我们预计这些计算优势在垃圾箱微物理方案中会更大。一种简单的思考方法是这样的：我们移动一个包裹，它包含一个桶大小的分布，只需要在平流过程中改变包裹的位置，而不是单独移动对应于50-100个液滴大小类别的液态水。同样，当包裹混合和分割时，可以通过简单的求和和分割来完成。该学生将通过改变其热力学公式并将bin微物理方案集成到模型中，使新的MPIC模型适合于现实大气云的研究。这项工作将与圣安德鲁斯大学的David Dritschel合作完成，MPIC的大部分开发都是在那里进行的。我们将首先研究随着流动而移动的云滴的生长，但稍后也想考虑雨的形成。我们希望这项工作能发表一些文章，告诉我们更多关于大云滴形成的细节，这对降雨的形成很重要。特别是，我们对这种下降的轨迹感兴趣，这可以在MPIC框架中以一致的方式确定。

The turbulent behaviour of clouds is responsible for many of the uncertainties in weather and climate models, in particular when it comes to the timing and intensity of precipitation. Weather and climate models are too coarse to resolve the details of the interactions between clouds and their environment and also have a much simplified representation of microphysical processes, such as the growth of cloud drops and the formation of rain, snow and ice. Such processes can be studied in a great amount of detail in so-called Large Eddy Models, where the interaction between clouds and their environment is largely resolved (grid spacing is less than 100 m). Large Eddy Models have been very useful for understanding turbulence in clouds, but when it comes to microphysical processes they are often still reliant on simple descriptions. For example, such a description may only know about the amount of liquid water in a model grid cell, and needs to make many assumptions about how this is divided between smaller and bigger drops.In order to address this problem, it is possible to use so-called bin microphysics schemes, where the amount of condensate associated with drops of different size categories is prognosed. This approach has been successfully implemented in the Met Office Large Eddy Model, but is too computationally expensive for many applications where a high resolution is needed. Moreover, traditional Large Eddy Models, which are formulated in a Eulerian framework (they perform bookkeeping on grid cells), suffer from spurious mixing, which makes results very sensitive to resolution. One of the fundamental problems here is that microphysical processes are essentially Lagrangian: they happen along trajectories of the flow (for small particles) or along fall trajectories (for bigger particles, influenced by the ambient wind). We have recently developed a new code, MPIC (moist parcel in cell), which deals with the dynamics of clouds in an essentially Lagrangian framework, i.e. by advecting parcels of fluid (Christiansen 1973, Dritschel et al. 2016). This code does not suffer from spurious mixing, and has been shown to compare well to traditional Large Eddy Models. MPIC also reduces computational cost when the same resolution is used, and we expect these computational advantages to be even bigger for a bin microphysics scheme. A simple way to think about it is this: rather than separately moving around liquid water corresponding to 50-100 droplet size categories from grid cell to grid cell, we move one parcel which contains a bin size distribution and only need to change the parcel's location during the advection process. Similarly, when parcels mix and split this can be done by simple summations and divisions.The student will make the new MPIC model suitable for studies of realistic atmospheric clouds by changing its thermodynamical formulation and integrating a bin microphysics scheme into the model. This work will be done in collaboration with David Dritschel at the University of St Andrews, where much of the development of MPIC took place. We will first look into the growth of cloud droplets that move along with the flow, but would later also like to consider the formation of rain. We expect this work to lead to the publication of a number of articles that will tell us more about the details of the formation of large cloud drops, which are important for rain formation. In particular, we are interested in the trajectories of such drops, which can be determined in a consistent way in the MPIC framework.