CISM Adjoint Project Summary

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Our goal is to enable applications of powerful mathematical concepts and computational tools for rigorous sensitivity analysis, pseudo-spectra and generalized stability the- ory, 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 ongo- ing 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): determine to which control variables the polar ice sheet volumes are most sensitive to; based on adjoint sensitivity maps, establish quantitative estimates of ice sheet volume changes for relevant forcing scenarios; 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, op- timally 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 in- creasing 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.

The proposed approach is analogous to the one successfully pursued for the global ocean circulation by the ”Estimating the Circulation and Climate of the Ocean” (ECCO) consortium. It differs from existing ice sheet studies in a variety of important ways:

  • The use of AD permits efficient generation and updating of adjoint code of an ice sheet model. The primary tool of choice is OpenAD which has been developed as part of two NSF-ITR pro jects.
  • We explore the wealth of information contained in dual-space variables and singular vectors.
  • The underlying time-dependent model will be extended to capture fast processes such as longitudinal shear stresses and glacial hydrology, essential for resolving ”short” time-scales.
  • We seek to increase the control space to a much wider range of uncertain variables, including model parameters, forcings, initial and basal boundary conditions.
  • One project outcome is to make available an adjoint-based estimation system that enables the use of heterogeneous satellite observations to achieve simultaneous fit of the model to all the data.