Mathematical Modelling of Atmospheric Convection for better Regional Climate Change Prediction

云和降水的模拟是天气和气候模式中最薄弱的方面之一，并且已知会导致在预测气候变化的区域影响时出现错误。云和降水受大气对流控制，而大气对流通常发生在比网格尺度小的空间尺度上，因此必须用参数化来表示。在对流参数化中提出了一些有问题的假设，例如忽略对流的质量传递。对流参数化的一种新的理论方法是使用条件平均来计算每个大气网格框的动量、温度和密度的两个值：一个用于流动的对流稳定部分，一个用于对流活跃部分。这种方法将使质量通过对流传输成为可能。然而，所得方程的数值解可能有严格的时间步长限制。这个项目将涉及设计一种数值技术来求解条件平均方程来表示对流，这将不需要非常小的时间步长。支持学生在OpenFOAM中实现他们的数值方法，这是一个用于求解微分方程的c++工具箱。该项目是雷丁大学“对流参数化革命”项目的一部分，该项目是英国国家能源研究中心/英国气象局项目“理解和代表跨尺度大气对流”的一部分。因此，该学生将成为全国网络的一部分。这是一个促进模型开发的机会，将直接用于天气和气候预报。

The simulation of clouds and precipitation is one of the weakest aspects of weather and climate models and is known to contribute to errors in predicting the regional impacts of climate change. Clouds and precipitation are controlled by atmospheric convection which usually occurs on spatial scales smaller than the grid scale and consequently must be represented by a parameterisation. Questionable assumptions are made in convection parameterisations such as neglecting mass transport by convection.A new theoretical approach to convection parameterisation uses conditional averaging to calculate two values of momentum, temperature and density per atmospheric grid box: one for the convectively stable part of the flow and one for the convectively active part. This approach will enable transport of mass by convection. However, numerical solution of the resulting equations could have severe time-step restrictions. This project will involve designing a numerical technique for solving the conditionally averaged equations for representing convection that will not require a very small time-step. Support will be provided for the student to implement their numerical method in OpenFOAM, a C++ toolbox for solving differential equations.This project is part of the ``Revolutionizing Convective Parameterization'' project at Reading which is part of the NERC/Met Office programme ``Understanding and Representing Atmospheric Convection across Scales''. The student will therefore be part of a national network. This is an opportunity to contribute to model development that will directly feed in to weather and climate forecasting.