Physically-constrained data-driven inversions to infer the bed topography beneath glaciers flows. Application to East Antarctica

• Main Authors: Monnier, Jerome, Zhu, Jiamin
• Other Authors: Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)
• Format: Report
• Language: English
• Published: HAL CCSD 2021
• Subjects: Data assimilation; reduced flow model; surface data; bed inference; Antarctica; Variational data assimilation; deep learning; inference; topography; glaciers; [INFO.INFO-MS]Computer Science [cs]/Mathematical Software [cs.MS]; [INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA]; [INFO.INFO-NE]Computer Science [cs]/Neural and Evolutionary Computing [cs.NE]; [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]; [SDU.STU.GL]Sciences of the Universe [physics]/Earth Sciences/Glaciology; East Antarctica; Antarc*; Ice Sheet
• Online Access: https://hal.archives-ouvertes.fr/hal-01926620; https://hal.archives-ouvertes.fr/hal-01926620v3/document; https://hal.archives-ouvertes.fr/hal-01926620v3/file/MonnierZhu-ComputSc.pdf

A method to infer the bed elevation from glaciers surface measurements (eleva-tion, velocity) and sparse in-situ thickness values is developed and assessed. This inversion method relies on: a statistical model (Deep Neural Network) based on the in-situ thickness measurements, the dedicated RU-SIA flow model (RU for Reduced Uncertainty) natively integrating the surface measurements (altimetry, InSAR) and advanced Variational Data Assimilation processes. The RU-SIA model takes into account basal slipperiness and non uniform vertical profiles (including thermal gradients) via an unique dimensionless parameter. The inversion method is robust; it may be applied to very poorly covered and uncovered areas during airborne campaigns as soon as flows are moderately sheared. Numerical inversions are performed for some large East Antarctica Ice Sheet areas presenting surface velocities ranging from ∼ 5 to 80 m/y. Estimations are provided in uncovered areas during airborne campaigns hence presenting up to now highly uncertain bed elevation values. The estimations are valid for wave lengths greater than ∼ 10 ¯ h due to the considered shallow flow assumption, with a resolution at ∼ ¯ h (¯ h a characteristic thickness value). Detailed analysis and comparisons with the bed topography BedMap2 are presented.