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.

提供了强大的数学概念和计算工具，用于严格的灵敏度分析，伪光谱和广义稳定性理论，以及大尺度冰盖建模背景下的高级状态估计。该提案的核心是新群落冰盖模型（CISM）的伴随模型（ADM）和切线模型（TLM）分量的生成和应用。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（NLM）代码和导数代码的高阶应力项（其解释了关键的快速流动状态）。伴随矩阵可以在非常高维的控制空间中非常高效地计算标量值函数的梯度。设想了应用层次结构：(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，建立相关强迫情景下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)耦合ADM和TLM计算伪光谱或奇异向量(SV？S)相关冰盖规范；SV吗?S提供导致非正常增长的扰动模式，在有限时间内最佳地放大范数核；在SV的众多应用中？S是用于评估不确定性的最优初始化系统；SV吗?通过Lanczos或Arnoldi隐式重启算法求解广义特征值问题的无矩阵迭代解；(3)长期目标是开发基于伴随或拉格朗日乘数法（LMM）的冰盖状态估计系统，以正式的方式将数量不断增加且类型各异的观测数据与最先进的三维冰盖模型综合起来；一个重要的要求是，伴随体必须包含正在为CISM开发的新方案，以捕获关键的、但尚未被表示的物理过程。

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.