Adjoint accuracy for the full-Stokes ice flow model: limits to the transmission of basal friction variability to the surface

• Published in: The Cryosphere
• Main Authors: Martin, Nathan, Monnier, Jerome
• Other Authors: Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA), Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)
• Format: Article in Journal/Newspaper
• Language: English
• Published: HAL CCSD 2014
• Subjects: adjoint method; fourier analysis; friction identification; [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph]; [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph]; [SDU.STU.GL]Sciences of the Universe [physics]/Earth Sciences/Glaciology; [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]; The Cryosphere
• Online Access: https://hal.archives-ouvertes.fr/hal-00957142; https://hal.archives-ouvertes.fr/hal-00957142v2/document; https://hal.archives-ouvertes.fr/hal-00957142v2/file/tc-2013-120.pdf; https://doi.org/10.5194/tc-8-721-2014

International audience This work focuses on the numerical assessment of the accuracy of an adjoint-based gradient in the perspective of variational data assimilation and parameter identification in glaciology. Using noisy synthetic data, we quantify the ability to identify the friction coefficient for such methods with a non-linear friction law. The exact adjoint problem is solved, based on second order numerical schemes, and a comparison with the so called ''self-adjoint'' approximation, neglecting the viscosity dependency to the velocity (leading to an incorrect gradient), common in glaciology, is carried out. For data with a noise of $1\%$, a lower bound of identifiable wavelengths of $10$ ice thicknesses in the friction coefficient is established, when using the exact adjoint method, while the ''self-adjoint'' method is limited, even for lower noise, to a minimum of $20$ ice thicknesses wavelengths. The second order exact gradient method therefore provides robustness and reliability for the parameter identification process. In other respect, the derivation of the adjoint model using algorithmic differentiation leads to formulate a generalization of the ''self-adjoint'' approximation towards an incomplete adjoint method, adjustable in precision and computational burden.