Accelerated Dynamical Spin Up of Ocean General Circulation Models

[449703]深海缓慢的动力调整给海洋环流模式造成了计算瓶颈。特别是，将海洋gcm整合到平衡状态仍然非常昂贵，限制了我们的能力，例如，模拟不同（古）边界条件下的气候，系统地探索对参数和亚网格尺度物理表示的敏感性，或使用天然放射性碳等示踪剂研究海洋通风。提出的研究目标是利用最近开发的海洋模型中有效的示踪剂模拟方法来加速海洋模型的动态自旋。该方案被称为“矩阵法”，使得无需显式时间积分即可直接获得示踪方程的平衡解成为可能。矩阵法对于被动示踪剂是线性且精确的，通过将非线性自旋向上问题嵌入到迭代算法中，使其“射向”平衡循环，从而适应非线性自旋向上问题。拟议的研究将广泛利用科学计算和数值分析方面的最新发展，特别是“雅可比-自由牛顿-克雷洛夫”类方法。所提出的研究是探索性的和高风险的，因为线性示踪模型将扩展到非线性自旋问题。该方法的精度和数值效率在开发出来之前很难预测。更广泛的影响：这项研究的一个重要成果将是开发准确有效的示踪剂模拟和GCM自旋上升方法。这些工具对古气候研究特别有用。所提出的算法将在广泛使用的MOM海洋GCM中实现，以确保其可被广泛的研究人员使用。然而，这些技术可以应用于任何现有的GCM，并且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。

0449703The slow dynamical adjustment of the deep ocean creates a computational bottleneck for models of the ocean circulation. In particular, integrating ocean GCMs to equilibrium remains prohibitively expensive, limiting our ability, for example, to simulate climate under different (paleo) boundary conditions, systematically explore sensitivity to parameters and representations of sub-grid scale physics, or to study the ventilation of the ocean using tracers such as natural radiocarbon. The goal of the proposed study accelerating the dynamical spin up of ocean models with a recently developed method for efficient tracer simulation in ocean models. This scheme, known as the "matrix method", makes it feasible to directly obtain equilibrium solutions to the tracer equations without explicit time integration. The matrix method, which is linear and exact for passive tracers, will be adapted to the nonlinear spin up problem by embedding it into an iterative algorithm to "shoot" toward an equilibrium circulation. The proposed study will make extensive use of recent developments in scientific computing and numerical analysis, in particular, the "Jacobian-Free Newton-Krylov" class of methods.The proposed study is exploratory and high-risk because the linear tracer model will be extended to the non-linear spin-up problem. The accuracy and numerical efficiency of the method is hard to predict until after it is developed.Broader impacts: An important outcome of this research will be the development of accurate and efficient methods for tracer simulation and GCM spin up. These tools will be especially useful for paleoclimate studies. The proposed algorithms will be implemented in the widely used MOM ocean GCM to ensure its accesibility to a broad group of researchers. However, the techniques can be applied to any existing GCM, and numerical code developed as part of this research will be made freely available to the research community.