CMG COLLABORATIVE RESEARCH: Enabling ice sheet sensitivity and stability analysis with a large-scale higher-order ice sheet model?s adjoint to support sea level change assessment.

CMG 合作研究：利用大规模高阶冰盖模型的伴随物进行冰盖敏感性和稳定性分析，以支持海平面变化评估。

• 批准号: 0934404
• 负责人: Patrick Heimbach
• 金额: $ 46.74万
• 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: 2009
• 资助国家: 美国
• 起止时间: 2009-09-15 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0934404&HistoricalAwards=false
• 关键词: CMG; COLLABORATIVE; RESEARCH; Enabling; ice

Heimbach 0934404MITFunds are provided to enable applications of powerful mathematical concepts and computational tools for rigorous sensitivity analysis, pseudo-spectra and generalized stability theory, and advanced state estimation in the context of large-scale ice sheet modeling. At the center of the proposal is the generation and application of adjoint model (ADM) and tangent linear model (TLM) components of the new Community Ice Sheet Model (CISM). The goal will be achieved through rigorous use of automatic differentiation (AD) to ensure synchronicity between the ongoing model development and improvement in terms of better representation of higher-order stress terms (which account for crucial fast flow regimes) of the nonlinear forward model (NLM) code and the derivative codes. The adjoint enables extremely efficient computation of gradients of scalar-valued functions in very high-dimensional control spaces. A hierarchy of applications is envisioned:(1) sensitivity calculations in support of the Intergovernmental Panel on Climate Change (IPCC) in order to determine to which control variables the polar ice sheet volumes are most sensitive; based on adjoint sensitivity maps, to establish quantitative estimates of ice sheet volume changes for relevant forcing scenarios; and to assess how sensitivities change when including higher-order stress terms;(2) coupling of the ADM and TLM to calculate pseudo-spectra or singular vectors (SV?s) of relevant ice sheet norms; SV?s provide perturbation patterns which lead to non-normal growth, optimally amplifying norm kernels over finite times; among the many applications of SV?s are optimal initialization of ensembles to assess uncertainties; SV?s are calculated through matrix-free iterative solution of a generalized eigenvalue problem via Lanczos or Arnoldi implicit restart algorithms;(3) a long-term goal is the development of an ice sheet state estimation system based on the adjoint or Lagrange Multiplier Method (LMM) in order to synthesize, in a formal manner, the increasing number and heterogeneous types of observations with a three-dimensional, state-of-the-art ice sheet model; an important requirement is that the adjoint incorporate new schemes that are being developed for CISM to capture crucial, but as yet unrepresented physical processes.

Heimbach 0934404MITFunds 的提供是为了能够应用强大的数学概念和计算工具来进行严格的灵敏度分析、伪谱和广义稳定性理论以及大规模冰盖建模背景下的高级状态估计。该提案的核心是新社区冰盖模型（CISM）的伴随模型（ADM）和切线模型（TLM）组件的生成和应用。该目标将通过严格使用自动微分（AD）来实现，以确保正在进行的模型开发和改进之间的同步性，以更好地表示非线性正演模型的高阶应力项（它解释了关键的快速流动状态）（ NLM）代码和派生代码。该伴随函数能够在极高维控制空间中极其有效地计算标量值函数的梯度。设想了一个应用层次结构：（1）支持政府间气候变化专门委员会（IPCC）的敏感性计算，以确定极地冰盖体积对哪些控制变量最敏感；基于伴随敏感性图，建立相关强迫情景的冰盖体积变化的定量估计；并评估当包括高阶应力项时敏感性如何变化；(2) ADM 和 TLM 的耦合以计算相关冰盖规范的伪谱或奇异向量 (SV?s)； SV 提供了导致非正态增长的扰动模式，在有限的时间内最优地放大了范数核； SV 的众多应用包括集成的最优初始化以评估不确定性； SV 是通过 Lanczos 或 Arnoldi 隐式重启算法对广义特征值问题进行无矩阵迭代求解来计算的；(3) 长期目标是开发基于伴随或拉格朗日乘子法的冰盖状态估计系统（LMM）以便以正式的方式综合日益增多的数量和异质类型的观测结果以及三维、最先进的冰盖模型；一个重要的要求是，伴随物纳入了 CISM 正在开发的新方案，以捕获关键但尚未表征的物理过程。