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.

Heimbach 0934404MITFunds用于在大规模冰盖建模环境中应用强大的数学概念和计算工具，用于严格的灵敏度分析、伪谱和广义稳定性理论以及高级状态估计。该提案的核心是生成和应用新的社区冰盖模式(CISM)的伴随模式(ADM)和切线模式(TLM)组件。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，从而更好地表示非线性正向模型(NLM)代码和派生代码的高阶应力项(这是关键的快速流型)。这种伴随使得在超高维控制空间中计算标量值函数的梯度变得非常有效。设想了一个应用层次：(1)支持政府间气候变化专门委员会(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，为相关强迫情景建立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耦合计算相关冰盖规范的伪谱或奇异向量(SV？S)；SV？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？S的众多应用中，包括集合的最优初始化以评估不确定性；SV？S通过Lanczos或Arnoldi隐式重启算法通过广义特征值问题的无矩阵迭代求解来计算；(3)长期目标是基于伴随或拉格朗日乘子法(LMM)开发一个冰盖状态估计系统，以便以正式的方式用三维最先进的冰盖模式综合越来越多和不同类型的观测；一个重要的要求是伴随着正在开发的新的方案，这些新的方案正在开发中，以捕捉关键的，但尚未代表的物理过程。

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.