Multiscale wavelet modelling of turbulent flows in the atmosphere and oceans

数值天气预报帮助加拿大人管理他们的日常生活和业务，气候建模帮助加拿大规划未来。风暴、洪水和干旱等极端天气事件的影响是可以减轻的，但前提是必须提前足够长的时间进行准确预测。业务模式使用静态计算网格，无法适应快速发展的风暴或粗化，需要较低的精度。这意味着计算资源没有得到有效利用，并且所产生的误差在空间和时间上是不均匀的。 在需要更高精度的情况下，例如在人口稠密地区或环境敏感的栖息地，也很难提高分辨率。这项研究的目标是开发一个实验性的大气和海洋模型，该模型将使用创新的小波技术来动态地修改网格分辨率，以保持所需的精度水平，或最佳地利用现有的计算资源。还可以静态调整分辨率，以改进对特别感兴趣领域的预测。这个项目的第一阶段是开发一个计算机代码，自适应地解决旋转的浅水方程的球。第二阶段是将二维浅水模式扩展到三维多层静力模式。在这一点上，计算机代码将形成一个所谓的“动力核心”，在这个核心上可以添加更多的物理效应（例如辐射、云、地形的影响、植被），以建立一个真正的气候模型。该项目的最后阶段将是将多尺度计算模型扩展到多尺度多物理模型，以考虑重要的次网格尺度物理效应，如云的形成。该提案是国际上开发下一代天气和气候模型的努力的一部分，这些模型将使用动态适应性和多尺度建模来提高计算效率和预测准确性。加拿大在数值天气预报和气候建模方面一直处于世界领先地位，在这一研究项目中获得的知识将使加拿大在开发新模型以应对新出现的挑战方面保持领先地位。

Numerical weather forecasting helps Canadians manage their lives and businesses day-to-day, and climate modelling helps Canada plan for the future. The effects of extreme weather events, such as storms, floods and droughts, can be mitigated, but only if they are accurately predicted far enough in advance. Operational models use static computational grids, which are not able to adapt to resolve rapidly developing storms or coarsen where less accuracy is needed. This means that computational resources are not used efficiently and that the resulting error is not uniform in space and time. It is also difficult to increase resolution where more accuracy is needed, for example over densely populated areas, or over environmentally sensitive habitats. The goal of this proposed research is to develop an experimental atmosphere and ocean model that will use innovative wavelet techniques to dynamically modify the grid resolution to maintain the desired level of accuracy, or to make optimal use of the available computational resources. The resolution could also be adapted statically to improve predictions in areas of special interest. The first stage of this project is to develop a computer code that adaptively solves the rotating shallow water equations on the sphere. The second stage is to extend the two-dimensional shallow water model to a three-dimensional multilayer hydrostatic model. At this point the computer code will form a so-called "dynamical core" on which more physical effects (e.g. radiation, clouds, the effect of topography, vegetation) can be added to build a true climate model. The final stage of this project will be to extend the multiscale computational model to a multiscale multi-physics model to account for important subgrid scale physical effects, such as cloud formation. This proposal is part of an international effort to develop the next generation of weather and climate models that will use dynamic adaptivity and multiscale modelling to improve computational efficiency and prediction accuracy. Canada has been a world leader in numerical weather prediction and climate modelling, and the knowledge gained in this research project will keep Canada at the forefront as new models are developed to deal with emerging challenges.