Corrigendum to “A two-dimensional, higher-order, enthalpy-based thermomechanical ice flow model for mountain glaciers and its benchmark experiments” [Comput. Geosci. 141 (2020) 104526]

AbstractIn this paper, a higher-order numerical flowline model is presented which is numerically stable and fast and can cope with very small horizontal grid sizes (<10 m). The model is compared with the results from Blatter and others (1998) on Haut Glacier d’Arolla, Switzerland, and with the European Ice-Sheet Modelling Initiative benchmarks (Huybrechts and others, 1996). Results demonstrate that the significant difference between calculated basal-drag and driving-stress profiles in a fixed geometry disappears when the glacier profile is allowed to react to the surface mass-balance conditions and reaches a steady state. Dynamic experiments show that the mass transfer in higher-order models occurs at a different speed in the accumulation and ablation areas and that the front position is more sensitive to migration compared to the shallow-ice approximation.

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A two-dimensional shallow ice-flow model of Glacier de Saint-Sorlin, France

Journal of Glaciology ◽

10.3189/172756503781830421 ◽

2003 ◽

Vol 49 (167) ◽

pp. 527-538 ◽

Cited By ~ 45

Author(s):

Emmanuel Le Meur ◽

Christian Vincent

Keyword(s):

Steady State ◽

20Th Century ◽

Flow Rate ◽

Flow Model ◽

Parameter Study ◽

Two Dimensional ◽

Zeroth Order ◽

Ice Flow ◽

Glacier Changes ◽

Bedrock Surface

AbstractA two-dimensional ice-flow model based on the shallow-ice approximation (SIA) is used to investigate the dynamics of Glacier de Saint-Sorlin, France. This glacier is well suited for this kind of study. First, the particular geometry of the glacier itself as well as that of the bedrock surface allows for correct applicability of the SIA (zeroth-order equations), provided that thickness changes and termini positions rather than short-scale dynamics are considered. Secondly, the wealth of available data for the glacier including mass-balance series and records of glacier changes provides a reliable forcing and a powerful constraining set for the model. Steady-state simulations show realistic results and the capabilities of the model in reproducing the glacier extent at the beginning of the 20th century. An extensive parameter study of ice rheology and sliding intensity is also carried out and the results are checked against the thickness changes as well as the glacier termini positions since 1905. It is possible to find a parameter combination that best matches these two types of data with an ice-flow rate factor of 2 × 10−24 Pa−3 s−1 and a Weertman-type sliding factor of 5 × 10−14 m8 N−3 a−1 which both appear to be in agreement with similar inferences from recent modelling attempts.

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PoLIM: an open source 2D higher-order thermomechanically coupled mountain glacier flow model

10.5194/egusphere-egu2020-21050 ◽

2020 ◽

Author(s):

Yuzhe Wang ◽

Tong Zhang

Keyword(s):

Flow Model ◽

Order Approximation ◽

Water Pressure ◽

Computational Cost ◽

Higher Order ◽

Thermomechanical Coupling ◽

High Mountain ◽

Climate Data ◽

Mountain Glacier ◽

Ice Flow

<p>The worldwide glacier is retreating and is expected to continue shrinking in a warming climate. Understanding the dynamics of glaciers is essential for the knowledge of sea-level rise, water resources in high mountain and arid regions, and the potential glacier hazards. Over the past decades, various 3D higher-order and full-Stokes ice flow models including thermomechanical coupling have been developed, and some have opened their source codes. However, such 3D modeling requires detailed datasets about surface and bedrock topography, variable climatic conditions, and high computational cost. Due to difficulties in measuring glacier thickness, only a small minority of glaciers around the globe have ice thickness observations. It is also a challenge to downscale the climate data (e.g., air temperature, precipitation) to the glacier surface, particularly, in rugged high-mountain terrains. In contrast to 3D models, flowline models only require inputs along the longitudinal profile and are thus computationally efficient. They continue to be useful tools for simulating the evolution of glaciers and studying the particular phenomena related to glacier dynamics. In this study, we present a two-dimensional thermomechanically coupled ice flow model named PoLIM (Polythermal Land Ice Model). The velocity solver of PoLIM is developed based on the higher-order approximation (Blatter-Pattyn type). It includes three critical features for simulating the dynamics of mountain glaciers: 1) an enthalpy-based thermal model to describe the heat transfer, which is particularly convenient to simulate the polythermal structures; 2) a drainage model to simulate the water transport in the temperate ice layer driven by gravity; 3) a subglacial hydrology model to simulate the subglacial water pressure for the coupling with the basal sliding law. We verify PoLIM with several standard benchmark experiments (e.g., ISMIP-HOM, enthalpy, SHMIP) in the glacier modeling community. PoLIM shows a good performance and agrees well with these benchmark results, indicating its reliable and robust capability of simulating the thermomechanical behaviors of glaciers.</p>

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The zero-ice ice-flow problem

10.5194/egusphere-egu2020-10613 ◽

2020 ◽

Author(s):

G. Hilmar Gudmundsson

Keyword(s):

Lagrange Multipliers ◽

Flow Model ◽

Unsolved Problem ◽

Flow Problem ◽

Higher Order ◽

Ice Thickness ◽

Active Set ◽

Ice Flow ◽

Active Set Method ◽

Constrained Optimisation

<p>When modelling ice flow, one often encounters the situation where melt is applied over ice-free areas. For example, determining the terminus position of a glacier involves finding the locations where applied surface melt and ice flow produces areas of zero ice thickness. How to best deal numerically this situation without producing negative ice thickness is an open and unsolved problem. One approach is to impose positive ice-thickness constraints and reformulating the problem as a constrained optimisation problem using the active-set method. This approach is, for example, used in the ice flow model &#218;a. &#160;I&#8217;ll provide an overview over the approach used in the model and explain some difficulties, and how these have been addressed, associated with the use of higher order elements where the sign of the Lagrange multipliers can not be used to identify the active set.</p>

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Supplementary material to "Upstream flow effects revealed in the EastGRIP ice core using a Monte Carlo inversion of a two-dimensional ice-flow model"

10.5194/tc-2021-63-supplement ◽

2021 ◽

Author(s):

Tamara Annina Gerber ◽

Christine Schøtt Hvidberg ◽

Sune Olander Rasmussen ◽

Steven Franke ◽

Giulia Sinnl ◽

...

Keyword(s):

Monte Carlo ◽

Flow Model ◽

Ice Core ◽

Two Dimensional ◽

Ice Flow ◽

Supplementary Material ◽

Flow Effects ◽

Upstream Flow

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Seasonal-scale abrasion and quarrying patterns from a two-dimensional ice-flow model coupled to distributed and channelized subglacial drainage

Geomorphology ◽

10.1016/j.geomorph.2014.04.036 ◽

2014 ◽

Vol 219 ◽

pp. 176-191 ◽

Cited By ~ 18

Author(s):

Flavien Beaud ◽

Gwenn E. Flowers ◽

Sam Pimentel

Keyword(s):

Flow Model ◽

Two Dimensional ◽

Ice Flow ◽

Seasonal Scale ◽

Subglacial Drainage

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An investigation of the thermo-mechanical features of Laohugou Glacier No. 12 in Mt. Qilian Shan, western China, using a two-dimensional first-order flow-band ice flow model

10.5194/tc-2016-38 ◽

2016 ◽

Cited By ~ 2

Author(s):

Yuzhe Wang ◽

Tong Zhang ◽

Jiawen Ren ◽

Xiang Qin ◽

Yushuo Liu ◽

...

Keyword(s):

Flow Model ◽

Thermal Conditions ◽

Western China ◽

Two Dimensional ◽

Ice Flow ◽

Near Surface ◽

Ablation Area ◽

Ice Surface ◽

Surface Ice

Abstract. En-glacial thermal conditions are very important for controlling ice rheology. By combining in situ measurements and a two-dimensional thermo-mechanically coupled ice flow model, we investigate the present thermal status of the largest valley glacier (Laohugou No. 12; LHG12) in Mt. Qilian Shan in the arid region of western China. Our model results suggest that LHG12, previously considered as fully cold, is probably polythermal, with a lower temperate ice layer (approximately 5.4 km long) overlain by an upper layer of cold ice over a large region of the ablation area. Generally, modelled ice surface velocities match in situ observations in the east branch (mainstream) well but clearly underestimate the ice surface velocities near the glacier terminus because the convergent flow of the west branch is ignored. The modelled ice temperatures agree closely with the in situ measurements (with biases less than 0.5 K) from a deep borehole (110 m) in the upper ablation area. The model results were highly sensitive to surface thermal boundary conditions, for example, surface air temperature and near-surface ice temperature. In this study, we suggest using a combination of surface air temperatures and near-surface ice temperatures (following the work of Wohlleben et al., 2009) as Dirichlet surface thermal conditions to include the contributions of the latent heat released during refreezing of surface melt-water in the accumulation zone. Like many other alpine glaciers, strain heating is the most important parameter controlling the en-glacial thermal structure in LHG12.

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An investigation of the thermomechanical features of Laohugou Glacier No. 12 on Qilian Shan, western China, using a two-dimensional first-order flow-band ice flow model

The Cryosphere ◽

10.5194/tc-12-851-2018 ◽

2018 ◽

Vol 12 (3) ◽

pp. 851-866 ◽

Cited By ~ 3

Author(s):

Yuzhe Wang ◽

Tong Zhang ◽

Jiawen Ren ◽

Xiang Qin ◽

Yushuo Liu ◽

...

Keyword(s):

Flow Model ◽

In Situ Measurements ◽

Western China ◽

Two Dimensional ◽

Ice Flow ◽

Near Surface ◽

Ablation Area ◽

Glacier Terminus ◽

Air Temperatures

Abstract. By combining in situ measurements and a two-dimensional thermomechanically coupled ice flow model, we investigate the thermomechanical features of the largest valley glacier (Laohugou Glacier No. 12; LHG12) on Qilian Shan located in the arid region of western China. Our model results suggest that LHG12, previously considered as fully cold, is probably polythermal, with a lower temperate ice layer overlain by an upper layer of cold ice over a large region of the ablation area. Modelled ice surface velocities match well with the in situ observations in the east branch (main branch) but clearly underestimate those near the glacier terminus, possibly because the convergent flow is ignored and the basal sliding beneath the confluence area is underestimated. The modelled ice temperatures are in very good agreement with the in situ measurements from a deep borehole (110 m deep) in the upper ablation area. The model results are sensitive to surface thermal boundary conditions, for example surface air temperature and near-surface ice temperature. In this study, we use a Dirichlet surface thermal condition constrained by 20 m borehole temperatures and annual surface air temperatures. Like many other alpine glaciers, strain heating is important in controlling the englacial thermal structure of LHG12. Our transient simulations indicate that the accumulation zone becomes colder during the last two decades as a response to the elevated equilibrium line altitude and the rising summer air temperatures. We suggest that the extent of accumulation basin (the amount of refreezing latent heat from meltwater) of LHG12 has a considerable impact on the englacial thermal status.

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