Funds 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.
