A new approach to guaranteeing physical wave propagation on triangular meshes for numerical weather prediction

数值天气预报（NWP）是一门建立大气计算机模型，并利用它们与来自地球仪的测量数据相结合来预测天气和气候的科学。在NWP预报模式中，地球表面被划分成网格。当网格变得更细时，预测模型可以变得更真实，但需要更大的计算机。为了获得足够真实的预测，有必要使用许多并行工作的计算机处理器（芯片）。在理想的情况下，随着您添加更多的处理器，模型运行得更快。然而，对于大多数已建立的业务预报中心（包括英国气象局）使用的网格类型，增加更多的处理器并不能使模型运行得更快。这是因为网格是经纬度网格（就像地图中使用的网格系统），这意味着在北极和南极，所有的经度线都会聚在一起。这些线表示处理器之间的连接太多，这会降低计算速度。为了避免这个问题，许多人建议使用三角形或六边形网格（而不是经纬度网格中使用的四边形），它们可以更均匀地覆盖球体。英国气象局拒绝采用这些网格，因为三角形和六边形可以支持真实的大气中不存在的大气波类型;四边形没有这个问题。在这个项目中，我们将研究一个非常简单的解决方案：通过将每个三角形细分为三个四边形，可以将在球体上具有相等覆盖范围的三角形网格变成四边形网格。这个项目的目的是对使用这个想法的NWP模式的准确性进行一些非常初步的调查。如果这些研究表明该方法足够准确，这将导致该方法的更大发展，并有可能在具有大量处理器的计算机上进行准确的天气预报和气候模拟，从而导致更准确的天气和气候预测。

Numerical weather prediction (NWP) is the science of building computer models of the atmosphere and using them, in combination with measurements from around the globe, to predict the weather and climate. In an NWP forecast model, the surface of the Earth is divided up into a grid. When the grid is made finer, the forecast model can get more realistic, but requires bigger computers. To get sufficiently realistic forecasts, it is becoming necessary to use many computer processors (chips) working together in parallel. In the ideal case, as you add more processors, the model runs faster. However, for the type of grids used by most established operational forecast centre (including the UK Met Office), there becomes a point where adding more processors does not make the model run faster. This is because the grids are latitude-longitude grids (like the grid systems used in maps) which means that at the North and South pole, all of the lines of longitude converge. These lines represent too many connections between processors, which slow down the computation. To avoid this problem, many people have proposed using triangle or hexagon grids (rather than the quadrilaterals used in the latitude-longitude grid) which can cover the sphere more uniformly. The UK Met Office has resisted adopting these grids because the triangles and hexagons can support types of atmospheric waves which do not exist in the real atmosphere; the quadrilaterals do not have this problem. In this project, we will investigate a very simple solution: a triangular grid with equal coverage over the sphere can be turned into a quadrilateral grid by subdividing each triangle into three quadrilaterals. The aim of this project is to make some very preliminary investigations of the accuracy of NWP models that use this idea. If these investigations show that the method is accurate enough, this will lead to more substantial developments of the method and the potential to allow accurate weather forecasts and climate simulations on computers with enormous numbers of processors, leading to more accurate weather and climate predictions.