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日常生活和业务，气候模型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可以减轻，但前提是必须提前足够准确地进行预测。业务模式使用静态计算网格，不能适应快速发展的风暴或对精度要求较低的粗化。这意味着计算资源没有得到有效利用，由此产生的误差在空间和时间上并不一致。在需要更高精度的地方，例如在人口稠密的地区或环境敏感的生境上，也很难提高分辨率。这项拟议研究的目标是开发一个实验大气和海洋模型，该模型将使用创新的小波技术来动态修改网格分辨率，以保持所需的精度水平，或最佳利用现有的计算资源。该决议还可以进行静态调整，以改进对特别感兴趣领域的预测。该项目的第一阶段是开发一种自适应地求解球面上旋转的浅水方程的计算机代码。第二阶段是将二维浅水模型推广到三维多层静水模型。在这一点上，计算机代码将形成一个所谓的“动力核心”，在其上可以添加更多的物理效应(如辐射、云、地形、植被的影响)，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，以考虑重要的亚网格尺度的物理效应，如云的形成。这项提议是开发下一代天气和气候模型的国际努力的一部分，该模型将使用动态自适应和多尺度建模来提高计算效率和预测精度。加拿大在数值天气预报和气候模型方面一直处于世界领先地位，在这项研究项目中获得的知识将使加拿大保持领先地位，因为新的模型正在开发以应对新出现的挑战。

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.