Adaptive Mesh Modelling of the Global Atmosphere

当前的天气和气候预报模型使用固定的、统一的分辨率，因此所有地区都使用相同的网格间距表示。这使得有效、有价值的预报成为可能，但也有可能通过根据当地天气条件改变网格间距来改善大气的表示，即自适应网格建模。这可以改善例如强降水或山脉的表现。本研究的首要主题是试图使自适应网格建模足够准确和有效地用于操作使用，并对这是否可能进行现实的评估。首先提出研究垂直离散化；山脉周围的大气垂直层的分裂。目前的气候模型使用的是像毯子一样覆盖在山脉上的地层图，这些地层图在峰顶被压扁，在山谷中被分隔开。这对于气候模式中使用的粗分辨率是准确的，因为这些层从来都不是很陡。一旦分辨率增加，就会模拟更陡的斜坡，从而降低精度。因此，在一些小尺度模型中使用了切割细胞，即山脉突破了平坦的层。切割细胞有不同的精度妥协。地形跟随层和切割细胞之间的新型混合将被创建，以最大限度地减少误差来源，并与不使用层的离散相比较。如果计算网格能够与流动对齐，在条件变化小的方向上网格间距大，在条件变化快的方向上网格间距小，则可以在代价最小的情况下实现精度最大化。这些各向异性网格的创建首先需要各向异性的细化标准，然后需要一种算法来生成具有所需属性的网格。这两个问题都将得到解决。为了使用最少的额外计算资源（即网格细化标准）来提高大气模拟的分辨率，在哪里做的工作很少。这是一个具有挑战性的话题，因为不同地区的天气之间存在复杂的相互依赖关系，即使使用自适应网格划分，也不可能在单个全球模型中解决所有问题。将开发一种新的预期网格细化技术，包括对需要分辨率的地方进行粗分辨率预测，然后进行适应的网格模拟。因此，细化网格将在小尺度特征出现之前到位，提高精度。成本将降低，因为昂贵的网格自适应只需要很少地进行。云和降水是大气环流的重要方面，可以影响数千公里以外的天气。然而，在气候模式中，它们通常预测得很差，在高分辨率天气预报模式中有一些改进。如果自适应网格可以用于解析与深对流相关的最深云，那么大气模拟可能会得到改进。然而，事先确定对流在哪些地方需要高分辨率的标准以前还没有被创造出来。在气候模式中，深层对流无法解决，因此已经开发了一些方案来估计哪些网格框可能发生亚网格尺度的对流。在这个项目中，计划使用现有对流方案中的准则，以便在深层对流爆发之前进行细化。不管是自适应网格还是静态网格，垂直离散化的工作对于提高山周围的水平分辨率是必要的。其他工作包括为自适应建模创建最佳网格，具有最佳单元形状和方向，网格细化频率和标准以及在深层对流爆发之前解决深层对流的新策略。这些成果将大大提高全球大气自适应网格建模的保真度和竞争力。

Current weather and climate forecasting models use fixed, uniform resolution, so that all regions are represented using the same grid spacing. This has enabled efficient, valuable forecasts, but it may be possible to improve the representation of the atmosphere by varying the grid spacing depending on the local weather conditions, that is, adaptive mesh modelling. This could improve the representation of, for example, heavy precipitation or mountain ranges. The overarching themes of this research are to try to make adaptive mesh modelling sufficiently accurate and efficient for operational use and give a realistic assessment of whether this is possible. It is first proposed to study vertical discretisation; the splitting of the atmosphere vertical layers around mountains. Climate models currently use terrain following layers which are draped over mountains like blankets, becoming squashed at summits and spaced out in valleys. This is accurate for the coarse resolution used in climate models since the layers are never very steep. Once resolution increases, steeper slopes are simulated and accuracy can be compromised. Therefore cut cells have been used in some small scale models, whereby the mountains break through flat layers. Cut cells have different accuracy compromises. Novel hybrids between terrain following layers and cut cells will be created in order to minimise both sources of error and compared with discretisations which do not use layers. If the computational mesh can be aligned with the flow, with wide mesh spacing in directions in which conditions change little and fine spacing in directions in which conditions change rapidly, then accuracy can be maximised for the cost. The creation of these anisotropic meshes first requires anisotropic refinement criteria and then an algorithm to generate a mesh with the desired properties. Both of these will be addressed. There has been little work done on where to increase resolution in order to improve atmospheric simulation using the minimum extra computing resources, ie mesh refinement criteria. This is a challenging topic due to the complex inter-dependencies between the weather in different regions and the impossibility of resolving everything in a single global model, even with adaptive meshing. A new anticipative mesh refinement technique will be developed, involving a coarse resolution prediction of where resolution will be needed followed by the adapted mesh simulation. The refined mesh will therefore be in place before small scale features appear, improving accuracy. Cost will be reduced since the expensive mesh adaptation needs only to be done infrequently. Clouds and precipitation are crucial aspects of atmospheric circulation and can be influential on the weather thousands of kilometres away. However they are usually predicted poorly in climate models, with some improvement in higher resolution weather forecasting models. If adaptive meshes can be used to resolve the deepest clouds associated with deep convection, then atmospheric simulation may be improved. However criteria to identify in advance where convection will need high resolution have not before been created. In climate models, deep convection cannot be resolved so schemes have been developed which estimate in which grid boxes sub-grid scale convection may occur. In this project it is planned to use criteria from existing convection schemes in order to enable refinement of deep convection before it breaks out. The work on vertical discretisation is necessary for higher horizontal resolution around mountains with either adaptive meshes or static grids. The other work involves creating optimal meshes for adaptive modelling, with optimal cell shapes and orientations, mesh refinement frequency and criteria and novel strategies for resolving deep convection before it breaks out. These achievements could greatly improve the fidelity and competitiveness of adaptive mesh modelling of the global atmosphere.