Calving relation for tidewater glaciers based on detailed stress field
analysis

Mercenier, Rémy; Lüthi, Martin P.; Vieli, Andreas

doi:10.5194/tc-2017-183

Cited by 8 publications

(23 citation statements)

References 18 publications

(33 reference statements)

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“…Our model permits the use of arbitrary linear combinations, and results from a selection are shown in the following. Here we list the commonly used stress criteria in glaciological studies (see Table for a summary of the stress measures and their notations): The Hayhurst criterion σ H is the most widely used stress criterion in glaciological studies for damage evolution (Duddu & Waisman, , ; Duddu et al, ; Jiménez et al, ; Mercenier et al, ; Mobasher et al, ; Pralong & Funk, ; Pralong et al, ). This criterion (Hayhurst, ) uses a linear combination of the maximum principal stress σ 1 , the first stress invariant

I_{1} = σ_{m} = \frac{1}{3} σ_{i i}

, and the von Mises stress

J_{2} = σ_{e} = \sqrt{\frac{3}{2} σ_{i j}^{'} σ_{i j}^{'}} = \sqrt{3} A^{- \frac{1}{n}} {\overset{ε}{true}}_{e}^{\frac{1}{n}}

as stress measure χ :

\begin{matrix} right & left σ_{H} = α σ_{1} + β σ_{e} + γ σ_{m}, & right \\ right & left 0 \leq α, β, γ \leq 1 . \end{matrix}

The Hayhurst stress is generally used as a criterion for ductile and brittle materials that allows for damage under uniaxial compression (Krug et al, ; Pralong & Funk, ). The maximum principal stress σ 1 has been used as a stress measure χ in combination with LEFM to simulate calving (Krug et al, ).…”

Section: Methodsmentioning

confidence: 99%

“…The local geometry of the terminus controls the stress field and therefore the fracture and failure process (Hanson & Hooke, ; Mercenier et al, ). Further processes can contribute to iceberg calving.…”

Section: Introductionmentioning

confidence: 99%

“…This dynamic approach for calving allowed for successful reproduction of calving front variations of ocean‐terminating glaciers in Greenland and Antarctica (Cook et al, ; Otero et al, , ; Nick et al, , ; Todd et al, ). Although the crevasse‐depth model can be calibrated to observations (Lea et al, ), the validation of the related processes with field observations is limited and is based on a snapshot of the stress balance, neglecting the preexistence of cracks and their effect on the stress state of the glacier (Krug et al, ; Mercenier et al, ). The earlier studies applying this model were limited to one or two dimensions and did not permit the model domain to evolve through time.…”

Section: Introductionmentioning

confidence: 99%

“…Pralong et al () first proposed an Eulerian damage mechanics description combining Stokes flow and continuum damage mechanics and were able to successfully predict lamella break‐off from hanging glaciers (Pralong & Funk, ). Further glaciological studies used the combination of continuum damage mechanics with ice flow models (Borstad et al, ; Duddu & Waisman, , ; Duddu et al, ; Jiménez et al, ; Jouvet et al, ; Krug et al, , ; Mercenier et al, ; Mobasher et al, ; Pralong & Funk, ). Applying this technique in an Eulerian reference frame facilitates the description of the physics of ice flow and fracture; however, the implementation of damage advection with flow is affected by artificial diffusion, and the numerical accuracy is mesh dependent (Jiménez et al, ).…”

Section: Introductionmentioning

confidence: 99%

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A Transient Coupled Ice Flow‐Damage Model to Simulate Iceberg Calving From Tidewater Outlet Glaciers

Mercenier

Lüthi

Vieli

2019

J Adv Model Earth Syst

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Iceberg calving, the detachment of an ice block at the glacier front, is the main process responsible for the dynamic mass loss from the ice sheets to the ocean. Understanding this process is essential to accurately predict ice sheet response to the future climate. We present a transient multiphysics finite-element model to simulate iceberg break-off and geometry evolution of a marine-terminating glacier. The model solves the coupled equations of ice flow, damage mechanics, oceanic melt, and geometry evolution on the same Lagrangian computational grid. A modeling sensitivity analysis shows that the choice of stress measure used for damage evolution strongly influences the resulting calving front geometries. Our analysis suggests that the von Mises stress measures produce the most realistic calving front geometry evolutions for tidewater glaciers. Submarine frontal melt is shown to have a strong impact on the calving front geometry. The presented multiphysics model includes all processes thus far shown to be relevant for the evolution of tidewater glaciers and can be readily adapted for 3-D and arbitrary bedrock geometries.

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I_{1} = σ_{m} = \frac{1}{3} σ_{i i}

, and the von Mises stress

J_{2} = σ_{e} = \sqrt{\frac{3}{2} σ_{i j}^{'} σ_{i j}^{'}} = \sqrt{3} A^{- \frac{1}{n}} {\overset{ε}{true}}_{e}^{\frac{1}{n}}

as stress measure χ :

\begin{matrix} right & left σ_{H} = α σ_{1} + β σ_{e} + γ σ_{m}, & right \\ right & left 0 \leq α, β, γ \leq 1 . \end{matrix}

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Transient Coupled Ice Flow‐Damage Model to Simulate Iceberg Calving From Tidewater Outlet Glaciers

Mercenier

Lüthi

Vieli

2019

J Adv Model Earth Syst

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“…Krug et al [29] modelled tidewater glacier calving by combining a damage parameterization and a linear elastic fracture mechanics method of calculating crevasse depth. Most recently, Mercenier et al [101] developed a calving rate law based on a stress threshold and a damage evolution function, tuned to fit data from Arctic glaciers.…”

Section: 'Calving Laws'mentioning

confidence: 99%

Calving glaciers and ice shelves

Benn

Åström

2018

Advances in Physics: X

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Calving, or the release of icebergs from glaciers and floating ice shelves, is an important process transferring mass into the world's oceans. Calving glaciers and ice sheets make a large contribution to sea-level rise, but large uncertainty remains about future ice sheet response to alternative carbon scenarios. In this review, we summarize recent progress in understanding calving processes and representing them in the models needed to predict future ice sheet evolution and sea-level rise. We focus on two main types of calving models: (1) discrete element models that represent ice as assemblages of particles linked by breakable bonds, which can explicitly simulate fracture and calving processes; and (2) continuum models, in which calving processes are parameterized using simple calving laws. With a series of examples using both synthetic and real-world ice geometries, we show how explicit models are yielding a detailed, process-based understanding of system physics that can be translated into predictive capability via improved calving laws.

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Recent ice dynamics and mass balance of Jorge Montt Glacier, Southern Patagonia Icefield

et al. 2019

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The Southern Patagonia Icefield (SPI) withdrawal in recent decades shows contrasting behaviours between adjacent basins. One of the basins with highest volumetric losses is located at northernmost SPI. We refer to Jorge Montt tidewater glacier (48° 30′S/73° 30′W, 445 km2 in 2018), which retreated 2.7 km between 2011 and 2018 and thinned at rates of up to 21 m a−1 over this period. Based on the retreat record, remote-sensing imagery, field data, a mass-balance model and a calving parameterisation, we attempted to differentiate climatic-induced changes (i.e. surface mass balance) and dynamic responses (i.e. calving fluxes). The surface mass balance reached −4.15 km3 w.e. a−1 between 2012 and 2017. When frontal ablation is included, the net mass balance is −17.79 km3 w.e. a−1. This represents a change of trend compared with modelling estimations of positive surface mass balance prior to 2010. This shift is attributed to higher ablation rates given that accumulation is known to have increased between 1980 and 2015. The available evidence, therefore, indicates that frontal ablation is the main factor, supported by observed rates at Jorge Montt as high as 3.81 km3 w.e. a−1 in 2015, with ice velocities peaking at 11 km a−1.

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Calving relation for tidewater glaciers based on detailed stress field analysis

Cited by 8 publications

References 18 publications

A Transient Coupled Ice Flow‐Damage Model to Simulate Iceberg Calving From Tidewater Outlet Glaciers

A Transient Coupled Ice Flow‐Damage Model to Simulate Iceberg Calving From Tidewater Outlet Glaciers

Calving glaciers and ice shelves

Recent ice dynamics and mass balance of Jorge Montt Glacier, Southern Patagonia Icefield

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