A Coupled Atmosphere-Ocean-Sea-Ice Model: Mathematical Analysis, Numerics and Computations

大气-海洋-海冰耦合模型：数学分析、数值和计算

• 批准号: 520497983
• 负责人: Professor Dr.-Ing. Rupert Klein
• 金额: --
• 依托单位: Max-Planck-Institut für Meteorologie (MPI-M)
• 依托单位国家: 德国
• 项目类别: Research Units
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/520497983?language=en
• 关键词: Coupled; Atmosphere; Ocean; Sea; Ice

Numerical weather prediction and climate projection are relevant application areas of the geophysical fluid dynamical models that form the subject of this Research Unit. A feature that distinguishes weather and climate forecasting from classical geophysical fluid dynamics is the use of ``coupled'' models in which mass, matter and energy are exchanged between components of a coupled model through a permeable boundary such as, for example, between the atmosphere and the ocean or between the ocean and sea-ice. This research field has been initiated by the Nobel-prize awarded work of S. Manabe and K. Hasselmann and is now continued in operational centres for climate and weather forecasting. The characteristics of the interfaces separating different compartments, such as the atmosphere-ocean interface, are not well understood and subject to heuristic physical assumptions and subgridscale closures. The trend in weather and climate modelling towards higher spatio-temporal resolutions does question many of these assumptions and provides the general background to this project. Accordingly, the goals of this project are to 1. construct a coupled atmosphere--ocean--sea-ice model following mathematical principles, 2. investigate the mathematical underpinnings of coupled atmosphere-ocean-sea-ice equations, 3. develop numerical methods that reflect this mathematical analysis 4. evaluate the resulting codes in simulations of the atmosphere-ocean-sea-ice systems. One mathematical principle to be adhered to is that the coupled model should provably admit local or global existence of weak/strong solutions in suitable function spaces. These function spaces incorporate boundary conditions that couple the components of the coupled system and therefore differ substantially from the solution spaces usually assumed for the individual components. A second principle is consistency with the first and second law of thermodynamics. This constitutes non-trivial tasks already for the atmosphere, due to the presence of moist air and phase changes, and for the ocean, due to the current lack of a realistic analytical equation of state. With consistent thermodynamics established for the individual components, we aim to also demonstrate thermodynamic consistency for the full coupled model. Building upon structure-preserving numerical methods, this modelling and analytical framework will be translated into a finite-dimensional approximation that retains key properties of the continuous coupled system. The preservation of discrete versions of continuous conservation properties plays a pivotal role in computing physically sound solutions and in pursuing our goal to show that these discrete solutions, too, satisfy the first and second law of thermodynamics. Finally, we will carry out numerical experiments of the discrete coupled equations and compare the solutions to solutions of other coupled models.

数值天气预报和气候预测是地球物理流体动力学模型的相关应用领域，构成本研究单元的主题。天气和气候预报与经典地球物理流体动力学的一个区别是使用"耦合“模型，在这种模型中，质量、物质和能量在耦合模型的各组成部分之间通过可渗透的边界，例如在大气和海洋之间或在海洋和海冰之间进行交换。这一研究领域是由诺贝尔奖获得者S。Manabe和K.哈塞尔曼，现在继续在业务中心的气候和天气预报。分隔不同区域的界面，例如大气-海洋界面的特征，还没有得到很好的理解，并受到启发性物理假设和次网格尺度闭合的影响。天气和气候建模朝着更高的时空分辨率发展的趋势确实对其中许多假设提出了质疑，并为这一项目提供了一般背景。因此，该项目的目标是1。根据数学原理建立一个大气-海洋-海冰耦合模式; 2.研究大气-海洋-海冰耦合方程的数学基础，3.发展反映这种数学分析的数值方法4.评估大气-海洋-海冰系统模拟中产生的代码。要坚持的一个数学原则是，耦合模型应可证明地承认在适当的函数空间中局部或整体存在弱/强解。这些函数空间包含耦合系统的组件的边界条件，因此与通常为单个组件假设的解空间有很大不同。第二个原则是与热力学第一和第二定律的一致性。这对大气层和海洋来说都是非常重要的任务，因为大气层中存在着潮湿的空气和相变，而海洋目前还没有一个现实的状态方程。与一致的热力学建立的各个组件，我们的目标是也证明热力学的一致性，完全耦合模型。在结构保持数值方法的基础上，这种建模和分析框架将被转化为有限维近似，保留了连续耦合系统的关键特性。连续守恒性质的离散形式的保持在计算物理上合理的解和追求我们的目标，以表明这些离散的解决方案，也满足热力学第一和第二定律中起着关键作用。最后，我们将进行离散耦合方程的数值实验，并将其解与其他耦合模型的解进行比较。