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，因此所有区域都使用相同的网格间距来表示。这使得有效、有价值的预报成为可能，但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。例如，这可以改善对强降水或山脉的表示。这项研究的主要主题是试图使自适应网格建模足够准确和有效，以供操作使用，并对这是否可能做出现实的评估。它首先被提出研究垂直离散化，即山脉周围大气垂直层的分裂。气候模型目前使用的是地形，这些地形像毯子一样覆盖在山脉上，在山顶变得挤压，并在山谷中隔开。这对于气候模型中使用的粗略分辨率来说是准确的，因为层永远不会非常陡峭。一旦分辨率提高，就会模拟更陡峭的坡度，精度可能会受到影响。因此，切割细胞已被用于一些小比例模型，借此山脉突破平坦的层。切割的单元格有不同的精度折衷。将创建地形跟踪层和切割单元之间的新型混合，以最大限度地减少误差来源，并与不使用层的离散化进行比较。如果计算网格可以与流动对齐，在条件变化很小的方向上具有宽的网格间距，在条件变化迅速的方向上具有细间距，则可以最大限度地提高精度。这些各向异性网格的创建首先需要各向异性细化标准，然后需要一个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。在如何提高分辨率以使用最少的额外计算资源(即网格细化标准)来改进大气模拟方面，几乎没有做过什么工作。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，而且不可能在一个全球模式中解决所有问题，即使是在自适应网格划分的情况下也是如此。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，然后进行自适应网格模拟。因此，精细化的网格将在小比例特征出现之前到位，从而提高精度。由于仅需要不频繁地进行昂贵的网状自适应，因此成本将会降低。云和降水是大气环流的重要方面，可能对数千公里以外的天气产生影响。然而，它们在气候模式中的预测通常很差，在更高分辨率的天气预报模式中有所改进。如果自适应网格可以用来分解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，以前还没有制定标准来预先确定哪里的对流将需要高分辨率。在气候模式中，深层对流是无法解决的，因此已经开发了一些方案来估计哪些网格箱中可能发生亚网格尺度的对流。在该项目中，计划使用现有对流方案中的标准，以便能够在深层对流爆发之前对其进行改进。无论是采用自适应网格还是静态网格，为了提高山脉周围的水平分辨率，垂直离散化工作是必要的。另一项工作包括创建自适应建模的最佳网格，具有最佳的单元形状和方向、网格细化频率和标准以及在深对流爆发之前解决深对流的新策略。这些成果可以极大地提高全球大气自适应网格模型的保真度和竞争力。

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.