2014/03/10 by Nathan Martin, Martin, Nathan, Jérôme Monnier +1
Earth and Planetary Sciences · Environmental Science · Medicine · #Classical Physics (physics.class-ph) #Climate change and permafrost #Cryospheric studies and observations #FOS: Mathematics #FOS: Physical sciences #Landslides and related hazards #Optimization and Control (math.OC) #Winter Sports Injuries and Performance
paper · pdf · doi:10.48550/arxiv.1403.2148
openalex publication_date 2014/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work focuses on the numerical assessment of the accuracy of an\nadjoint-based gradient in the perspective of variational data assimilation and\nparameter identification in glaciology. Using noisy synthetic data, we quantify\nthe ability to identify the friction coefficient for such methods with a\nnon-linear friction law. The exact adjoint problem is solved, based on second\norder numerical schemes, and a comparison with the so called "self-adjoint"\napproximation, neglecting the viscosity dependency to the velocity (leading to\nan incorrect gradient), common in glaciology, is carried out. For data with a\nnoise of 1 %, a lower bound of identifiable wavelengths of 10 ice\nthicknesses in the friction coefficient is established, when using the exact\nadjoint method, while the "self-adjoint" method is limited, even for lower\nnoise, to a minimum of 20 ice thicknesses wavelengths. The second order exact\ngradient method therefore provides robustness and reliability for the parameter\nidentification process. In other respect, the derivation of the adjoint model\nusing algorithmic differentiation leads to formulate a generalization of the\n"self-adjoint" approximation towards an incomplete adjoint method, adjustable\nin precision and computational burden.\n