Adaptive Mesh Modelling of the Global Atmosphere

目前的天气和气候预测模型使用固定的统一分辨率，因此所有区域都使用相同的网格间距表示。这使得能够进行有效和有价值的预报，但也有可能通过根据当地天气条件改变网格间距，即自适应网格建模，来改进大气层的表示。这可以改善例如强降水或山脉的代表性。这项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的业务使用，并给出一个现实的评估，这是否是可能的。首次提出研究垂直离散化，分裂的大气垂直层周围的山脉。气候模型目前使用的是像毯子一样覆盖在山脉上的地形层，在山顶被压扁，在山谷中被隔开。这对于气候模型中使用的粗分辨率来说是准确的，因为图层从来都不是很陡。一旦分辨率增加，则模拟更陡的斜率，并且精度可能会受到影响。因此，在一些小比例模型中使用了切割单元，从而使山脉突破平坦的地层。切割单元具有不同的精度折衷。为了最大限度地减少两种误差源，并与不使用层的离散化进行比较，将创建地形跟随层和切割单元之间的新混合体。如果计算网格可以与流动对齐，在条件变化不大的方向上具有宽网格间距，在条件变化迅速的方向上具有细间距，则可以将精度最大化以降低成本。这些各向异性网格的创建首先需要各向异性细化标准，然后是生成具有所需属性的网格的算法。这两个问题都将得到解决。在哪里增加分辨率，以提高大气模拟使用最少的额外计算资源，即网格细化标准的工作做得很少。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，并且即使使用自适应网格，也不可能在单个全局模型中解决所有问题。一个新的预期网格细化技术将被开发，涉及一个粗分辨率预测的分辨率将需要随后的适应网格模拟。因此，在小尺度特征出现之前，细化的网格将就位，从而提高精度。成本将降低，因为昂贵的网格适应只需要很少做。云和降水是大气环流的重要方面，可以影响数千公里外的天气。然而，它们通常在气候模式中预测得很差，在更高分辨率的天气预报模式中有一些改进。如果自适应网格可以用来解决与深对流相关的最深的云，那么大气模拟可能会得到改善。然而，标准，以确定在对流将需要高分辨率事先尚未创建。在气候模式中，深层对流无法解决，因此已经开发了估计可能发生次网格尺度对流的网格框的方案。在这个项目中，计划使用现有对流方案的标准，以便在爆发前对深对流进行改进。垂直离散化的工作是必要的，以提高水平分辨率周围的山脉，无论是自适应网格或静态网格。其他工作涉及创建自适应建模的最佳网格，最佳单元形状和方向，网格细化频率和标准以及在爆发前解决深对流的新策略。这些成就可大大提高全球大气自适应网格建模的逼真度和竞争力。

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.