Modeling Glacier and Ice-shelf Flow and Fracture Processes using Computation, Data, and Machine Learning
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Ravindra Duddu The-do
Associate Professor
Department of Civil and Environmental Engineering
Department of Mechanical Engineering
Department of Earth and Environmental Sciences
Vanderbilt University, Nashville, TN, USA
USACM Earth & Energy Systems Webinar
January 22, 2024
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Outline
Acknowledgement
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Grads
Undergrads
High-school
Postdocs
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References
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Glaciers and Ice Sheets Are a Key Part of the Climate and Earth System
Alters the solid earth
Storage of freshwater around the world
Fixture of ecosystems and habitats
Affects ocean circulation
Courtesy: Meghana Raganathan, Georgia Tech.
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Antarctic Ice Sheet Fracture and Sea Level Rise
Antarctic ice sheet bedrock elevation map
(Source: BEDMAP 2 British Antarctic Survey)
27 million km3 of ice, with a sea level
equivalent of ~ 58 m [Fretwell et al., 2013]
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Consequences of Sea Level Rise in the Coming Centuries
Landmarks around the world under two different global warming scenarios
Energy and environmental choices in this decade could set the destination, but the timing of rise is more difficult to project using models.
Sea levels may take hundreds of years to be fully realized.
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Bassis, J.N., Crawford, A., Kachuck, S. B., Benn, D. I., Walker, C., Millstein, J., Duddu, R., Åström, J., Fricker, H., Luckman, A. Annual Review of Earth and Planetary Sciences 2024 52:1
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Rifts – horizontal fractures
(Larsen C ice shelf, Antarctic Peninsula)
Crevasses – vertical fractures
(Ross ice shelf, West Antarctica)
Classification of Fractures in Glaciers and Ice Shelves
Objective: To understand fracture propagation in relation to viscous creep deformation, material state and damage evolution.
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Fracture-mechanics-based Crevasse Models
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Outline
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Stress-based Poro-Damage Phase Field Model
Surface crevasse
Basal crevasse
Viscoplastic (Glen’s law)
Elastic (Hooke’s law)
Inertia is negligible if quasi-static
Sun, X., Duddu, R., and Hirshikesh (2021) Extreme Mechanics Letters
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Strain-energy-based Poro-Damage Phase Field Model
Sun, X., Duddu, R., and Hirshikesh (2021) Extreme Mechanics Letters
Viscous regularization
Compressible elastic,
Tension-compression asymmetry,
Quasi-static hydrofracture
Plane strain [Lo et al., 2019]
Handles compressive states due to self weight
If
then
elseif
then
else
[Angelillo et al., 2010]
(III)
(II)
(II)
(I)
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Stress-based Poro-Damage Phase Field Model
Clayton, T., Duddu R., Siegert, M., and Martínez-Pañeda, E. (2022) Engrg. Frac. Mech.
Positive principal stress
Rankine-type failure
Damage irreversibility
Incompressibility
Tension-compression asymmetry
Viscous Stokes flow
Quasi-static hydrofracture
No viscous term
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Evaluation of Stress Intensity Factor in LEFM Models
Jimenez and Duddu, Journal of Glaciology, 64(247): 759-770, 2018
Superposition of linear elastic stress fields
Central through crack
Double edge crack
Single edge crack
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Single Surface Crevasse in a Grounded Glacier
Free slip at the base, isothermal conditions
A prior adaptive finite element mesh with bilinear quadrilateral, 8 elements within damage length scale
LEFM
Phase-field
Clayton, T., Duddu R., Siegert, M., and Martínez-Pañeda, E. (2022) Engrg. Frac. Mech.
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Multiple Surface Crevasses in a Grounded Glacier
Free slip at the base, isothermal conditions
A prior adaptive finite element mesh with bilinear quadrilateral, 8 elements within damage length scale
Zero stress
Phase-field
Clayton, T., Duddu R., Siegert, M., and Martínez-Pañeda, E. (2022) Engrg. Frac. Mech.
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Two Surface Crevasses in a Grounded Glacier
Crevasses propagate both vertically and horizontally, first move away from each other and then coalesce
Clayton, T., Duddu R., Siegert, M., and Martínez-Pañeda, E. (2022) Engrg. Frac. Mech.
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A poro-damage cohesive zone model for hydrofracture
Gao, Y., Ghosh, G., Jimenez, S., & Duddu, R., Computing in Science and Engineering, 2023
Mixed mode fracture
Creep deformation
Hydrofracture
Depth dependent material properties
Traction-separation law
Water pressure in crevasses
Data extracted from ice core specimens from the Ronne ice shelf by Rist et al. (2002)
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Calving outcomes can be altered due to ice density variations
Depth varying density and temperature promote surface crevasse propagation
Ice sheet models must appropriately parameterize the effects of variable ice density, in addition to temperature.
Water-filled surface crevasses in ice shelves
Gao, Y., Ghosh, G., Jimenez, S., & Duddu, R., Computing in Science and Engineering, 2023
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Outline
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Model Assumptions
Hageman, T., Mejia, J.Z., Duddu, R., and Martínez-Pañeda, E. (to be submitted)
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Two-scale Model Formulation
Glacier-scale governing equations
Fracture-scale governing equations
Momentum balance
Stress-strain relation
Viscous strain rate
(Glen’s law)
Mass balance
Fracture aperture relation
Thermal equilibrium
Fracture aperture relation
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Cohesive fracture model
Decoupled solution strategy
Solid stress related to fluid pressure
Exponential traction-separation law for mode I fracture
Two-scale Model Formulation
A rapid lake drainage event in Greenland (Das, 2008)
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Geometric parameters:
Parameters used for comparison with observations:
Out-of-plane width
Glacier thickness
Glacier length
Mesh size
Surface area of lake
Depth varying temperature, viscosity and strength
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The temperature profile is obtained from borehole measurements of Ryser et al. (2014)
Glen’s Law creep coefficient:
Tensile strength (Litwin et al., 2012):
Temperature also directly included in freezing/melting process
Effect of rheology on hydraulic fracture propagation
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Vertical fracture filled with water propagates faster with linear-elastic rheology, although water is transferred more effectively with visco-plastic rheology.
The vertical fracture closes due to the bending moment in the linear elastic case, as ice penetrates the bedrock (about 0.2 m)
Displacements magnified by x1000
Linear-elastic rheology
Linear-elastic visco-plastic rheology
Crack opening and Vertical Displacement
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Linear-elastic rheology
Linear-elastic visco-plastic rheology
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Outline
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Modeling Antarctic Glacier and Ice-shelf Calving and Stability (MAGICS)
Challenge: How can we model the fracture of viscous fluid-like material on long time scales?
Common framework needs to:
Updated Lagrangian or Material Point Method
Jimenez, S., Duddu, R., & Bassis, J. N., Computer. Methods in Applied. Mechanics. and Engineering, 2017
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The Generalized Interpolation Material Point Method (GI-MPM)
The GI-MPM with SSA formulation can track grounding line, ice front, and thickness
Huth, A. (2020) A generalized interpolation material point method and anisotropic creep damage model for shallow ice shelves Ph. D. Thesis, University of Washington.
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Simulation of Marine Ice Sheet Fracture with the GI-MPM
Anisotropic damage models predict more realistic rift propagation paths in ice shelves
MISMIP+
Pine Island Glacier
Huth, A., Duddu, R., & Smith, B. E., Journal of Advances in Modeling Earth Systems, 2021, Part I
Huth, A., Duddu, R., & Smith, B. E., Journal of Advances in Modeling Earth Systems, 2021, Part II
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Inverse Modeling and Data Assimilation for Larsen C Ice Shelf Calving
Variable | Source |
Velocity | 2015 Landsat-8 mosaic (Pope, 2016)/ NASA Measures (Rignot et al., 2017) |
Ice shelf thickness | Cryosat-2, swath processed (Smith et al. 2017) |
Bed elevation, grounded ice thickness | Bedmap2 (Fretwell et al., 2013) |
Surface temperature | RACMO2.3 (Van Wessam et al., 2015) |
Surface mass balance | RACMO2.3 (Van Wessam et al., 2015) |
Geothermal heat flow | Satellite magnetic data (Fox-Maule et al., 2005) |
Huth, A., Duddu, R., Smith, B., and Sergienko, O. (2023), Journal of Glaciology.
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Simulation of Larsen C Ice-shelf Fracture with the GI-MPM
Initialization of ice shelf viscosity and damage is key to simulating rift propagation
November 2017, four months after calving of iceberg A-68
Larsen C ice shelf on December 3, 2017, before rift propagation
Huth, A., Duddu, R., Smith, B., and Sergienko, O. (2023), Journal of Glaciology.
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Rift path is sensitive to mélange and rift wall contact assumptions
Rift is fully closed
No residual ice strength
Rift is partially closed
Some residual ice strength
Huth, A., Duddu, R., Smith, B., and Sergienko, O. (2023), Journal of Glaciology.
Processes controlling ice shelf rift paths
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Outline
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Summary
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Community Ice Sheet Model – Community Earth System Model
Modeling Antarctic Ice Sheet Evolution Over Long Timescales
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Machine Learning for Crevasse Identification and Inverse Estimation
U-Net architecture (Lai et al. (2020)
Crop
Opportunity: spatio-temporal maps of crevasses and rifts across Antarctica
Challenge: training data set generation, accuracy, advection of crevasses/rifts, depth of crevasses, rift boundary conditions
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An Adaptive FEM for Phase Field Fracture in FEniCS
We developed open-source FEniCS programs adhering to FAIR principles
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Collaborative Research: GEO OSE Track 1: Advanced cloud-based Data- and Visualization-Integrated Simulation EnviRonment (ADVISER) to Advance Computational Glaciology
To democratize the power of cloud computing and share its benefits with those who have little or no expertise in the cloud.
FEniCS/Firedrake workshop and ADVISER Hackathon to be announced later this year.
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References