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: 0824635
• 负责人: Samar Khatiwala
• 金额: $ 36.18万
• 依托单位: Columbia University
• 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 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0824635&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，气候模型是由与时间无关或周期性（季节性）变化的强迫场驱动的，并且通常非常希望获得模型的平衡解。现有的方法基于对模型进行积分直至瞬变消失的简单权宜之计，但由于深海需要数千年才能达到平衡，因此常规使用成本太高。该项目的主要目标是开发一种实用且有效的方法来计算周期性强制海洋环流模型（OGCM）的平衡解。一般方法是将问题表述为一个大型非线性代数方程组，并用一类称为无矩阵牛顿-克雷洛夫的方法来求解，该方法是非线性方程超线性收敛解的牛顿型方法的组合，以及用于求解牛顿校正方程的克雷洛夫子空间方法。为了使这种方法适用于具有阶 (107) 自由度的全局模型，将开发新颖的无矩阵预处理策略。所提出的方法的“无矩阵”性质使其极其灵活，允许其与任何海洋或气候模型一起使用。该方法可以应用于任何时期的强迫模型，包括那些由与时间无关的强迫驱动的模型，尽管这里的主要焦点是季节周期。初步结果表明，该方案可以将季节性强制 OGCM 的启动速度比当前做法加快两个数量级以上。将分析该技术的收敛特性，并根据传统的“加速”方法评估其效率。虽然主要目标是标称分辨率为 1 的海洋气候模型，但该方法也将应用于下一代更高分辨率的模型，包括允许涡流的模型。该技术将用于从海洋再分析产品和末次盛冰期的产品中获得当今气候的各种强迫估计的平衡解。智力价值：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主要障碍之一。拟议的研究将通过开发有效计算季节性强迫 OGCM 平衡解的实用算法来解决气候模拟中的这一基本问题。这项研究的直接成果将是改进对现代海洋环流和末次盛冰期环流的估计。更广泛的影响：通过大大降低获得气候模型平衡解的计算成本，这项研究将使科学家能够解决目前不可行的科学和社会相关问题。这些问题包括系统参数敏感性研究和古气候模拟，这些领域对于表征气候变化模拟中的不确定性尤其重要。所提出方法的一个关键优点是，它对底层海洋或气候模型代码做出了很少的假设，从而确保了这项研究的结果可以被最广泛的研究人员群体使用。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，虽然具体目标是解决海洋旋转问题，但由偏微分方程建模的系统的周期解和极限环的计算是非常通用的，并且所提出的方法可能在其他学科中具有广泛的适用性。这项研究将有助于研究生的培训和教育。作为本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中并在会议上介绍。