Collaborative Research: Fast Spin Up of Ocean General Circulation Models Using Newton-Krylov Methods

合作研究：使用牛顿-克雷洛夫方法快速旋转海洋环流模型

• 批准号: 0824783
• 负责人: Carl Wunsch
• 金额: $ 10.82万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-01 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0824783&HistoricalAwards=false
• 关键词: Collaborative; Research; Fast; Spin; Up

Numerical models of the climate system play an important role in efforts to understand past climate variability and predict future climate changes. In many studies, climate models are driven by forcing fields that are either time-independent or that vary periodically (seasonally) and it is often highly desirable to obtain equilibrium solutions of the model. Existing methods, based on the simple expedient of integrating the model until the transients have died out, are too expensive to use routinely because the deep ocean takes several thousand years to equilibrate. The principal objective of this project is to develop a practical and efficient method for computing equilibrium solutions of periodically forced ocean general circulation models (OGCMs). The general approach will be to formulate the problem as a large system of nonlinear algebraic equations to be solved with a class of methods known as matrix-free Newton-Krylov, a combination of Newton-type methods for superlinearly convergent solution of nonlinear equations, and Krylov subspace methods for solving the Newton correction equations. To render this approach practical for global models with order (107) degrees of freedom, novel matrix free preconditioning strategies will be developed. The "matrix-free" nature of the proposed approach makes it extremely flexible, allowing its use with any ocean or climate model. The method can be applied to models forced at any period, including those driven by time-independent forcing, although the main focus here is the seasonal cycle. Preliminary results suggest that this scheme can accelerate the spin up of seasonally forced OGCMs by over two orders of magnitude over current practice. The convergence properties of this technique will be analyzed, and its efficiency assessed against traditional "acceleration" methods. While the primary target is ocean climate models with a nominal resolution of one , the method will also be applied to the next generation of higher resolution models, including eddy permitting ones. The technique will be applied to obtain equilibrium solutions for various forcing estimates for both present day climate from ocean reanalysis products, and that of the Last Glacial Maximum. Intellectual merit: The slow dynamical adjustment timescale of the deep ocean is one of the principal obstacles to our ability to make more effective use of climate models. The proposed study will address this fundamental problem in climate simulation by developing practical algorithms for efficiently computing equilibrium solutions of seasonally forced OGCMs. A direct outcome of this research will be improved estimates of the circulation of both the modern ocean, and that of the Last Glacial Maximum. Broader Impacts: By greatly reducing the computational cost of obtaining equilibrium solutions of climate models, this research will allow scientists to address questions of scientific and societal relevance that are currently unfeasible. These questions include systematic parameter sensitivity studies and simulations of paleoclimate, areas that are especially important for characterizing uncertainties in climate change simulations. A key advantage of the proposed approach is that it makes few assumptions about the underlying ocean or climate model code thus ensuring that the results of this research can be used by the widest possible group of researchers. This work is directly relevant to ongoing work in the areas of ocean circulation, paleoceanography, and ocean biogeochemistry. More broadly, while the specific objective is to address the ocean spin up problem, the computation of periodic solutions and limit cycles of systems modeled by partial differential equations is a very general one, and the proposed method is likely to have broad applicability in other disciplines. This research will contribute to the training and education of a graduate student. Numerical code developed as part of this research will be made freely available to the research community. Findings of this study will be published in journal articles and presented at conference meetings.

气候系统的数值模型在了解过去的气候变化和预测未来的气候变化方面发挥着重要作用。在许多研究中，气候模型是由强迫场驱动的，这些场要么是时间无关的，要么是周期性(季节性)变化的，而且通常非常希望获得模型的均衡解。现有的方法，基于简单的权宜之计，整合模型，直到瞬变消失，太昂贵的常规使用，因为深海需要数千年才能达到平衡。本项目的主要目标是发展一种实用而有效的方法来计算周期性强迫海洋环流模式(OGCM)的平衡解。一般的方法是将问题描述为一个大的非线性代数方程组，用一类称为无矩阵的牛顿-克里洛夫方法来求解，该方法是非线性方程组的超线性收敛的牛顿型方法和求解牛顿校正方程的克里洛夫子空间方法的组合。为了使这种方法适用于阶数为(107)个自由度的全局模型，将开发新的无矩阵预处理策略。拟议方法的“无矩阵”性质使其非常灵活，允许它用于任何海洋或气候模型。这种方法可以应用于任何时间段的强迫模式，包括那些由时间无关的强迫所驱动的模式，尽管这里主要关注的是季节性循环。初步结果表明，该方案可以将季节性强迫的OGCM的自转速度比目前的做法加快两个数量级以上。分析了该技术的收敛特性，并与传统的“加速”方法进行了比较。虽然主要目标是名义分辨率为1的海洋气候模式，但该方法也将应用于下一代更高分辨率的模式，包括允许涡流的模式。这项技术将被应用于从海洋再分析产品中获得各种强迫估计的平衡解，包括从海洋再分析产品和最后一次冰盛期的气候估计。智力优势：深海缓慢的动态调整时间尺度是我们更有效地利用气候模型的能力的主要障碍之一。这项拟议的研究将通过开发实用的算法来解决气候模拟中的这一基本问题，以有效地计算季节性强迫的OGCM的平衡解。这项研究的一个直接结果将是改进对现代海洋和最后一次冰川盛期的环流的估计。更广泛的影响：通过大幅降低获得气候模型均衡解的计算成本，这项研究将使科学家能够解决目前不可行的具有科学和社会相关性的问题。这些问题包括系统的参数敏感性研究和古气候模拟，这些领域对于描述气候变化模拟中的不确定性特别重要。拟议办法的一个主要优点是，它对基本海洋或气候模型代码几乎没有做任何假设，从而确保这项研究的结果能够被尽可能广泛的研究人员使用。这项工作与海洋环流、古海洋学和海洋生物地球化学领域正在进行的工作直接相关。更广泛地说，虽然该方法的具体目标是解决海洋自转问题，但由偏微分方程组模拟的系统的周期解和极限环的计算是非常普遍的，所提出的方法可能在其他学科中具有广泛的适用性。本研究将对研究生的培养和教育有所帮助。作为这项研究的一部分开发的数字代码将免费提供给研究界。这项研究的结果将发表在期刊文章上，并在会议上发表。