CMG Collaborative Research: Enabling ice sheet sensitivity and stability analysis with a large-scale higher-order ice sheet models adjoint to support sea level change assessment

CMG 合作研究：通过大规模高阶冰盖模型辅助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: 0934742
• 负责人: Paul Hovland
• 金额: $ 16万
• 依托单位: University of Chicago
• 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 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0934742&HistoricalAwards=false
• 关键词: CMG; Collaborative; Research; Enabling; ice

Hovland 0934742University of ChicagoFunds 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.

Hovland 0934742芝加哥大学提供资金，使强大的数学概念和计算工具的应用程序，严格的灵敏度分析，伪谱和广义稳定性理论，并在大规模冰盖建模的背景下先进的状态估计。在该建议的中心是新的社区冰盖模式（CISM）的伴随模式（ADM）和切线线性模式（TLM）组件的生成和应用。这一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，以便更好地表示非线性正演模型（NLM）代码和导数代码的高阶应力项（这是关键的快速流动状态）。伴随使得在非常高维的控制空间中标量值函数的梯度的计算非常有效。设想了一个应用层次：（1）支持政府间气候变化专门委员会（气专委）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;根据伴随的敏感性图，为相关的强迫情景建立冰盖体积变化的定量估计;评估在包括高阶应力项时敏感性如何变化;（2）耦合ADM和TLM计算伪谱或奇异向量（SV？s）的相关冰盖规范; SV？s提供扰动模式，导致非正常增长，最佳放大规范内核在有限的时间;在许多应用SV？s是评估不确定性的集合的最佳初始化; SV？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;（3）长期目标是开发基于伴随或拉格朗日乘子方法（LMM）的冰盖状态估计系统，以便以正式的方式综合具有三维、国家的最先进的冰盖模型;一个重要的要求是，伴随纳入新的计划，正在开发的CISM捕捉关键，但尚未代表的物理过程。