Modelling a paleo valley glacier network using a hybrid model: an assessment with a Stokes ice flow model

AbstractModelling paleo-glacier networks in mountain ranges on the millennial timescales requires ice flow approximations. Hybrid models calculating ice flow by combining vertical shearing (shallow ice approximation) and longitudinal stretching (shallow shelf approximation) have been applied to model paleo-glacier networks on steep terrain, yet their validity has not yet been assessed quantitatively. Moreover, hybrid models consistently yield higher ice thicknesses than Last Glacial Maximum geomorphological reconstructions in the European Alps. Here, we compare results based on the hybrid Parallel Ice Sheet Model (PISM) and the Stokes model Elmer/Ice on the Rhine Glacier, a catchment of the former European Alpine Icefield. For PISM, we also test two magnitudes of flux limitation in a scheme that reduces shearing velocities. We find that the flux limitation typically used in PISM yields significantly reduced shearing speeds and increases ice thicknesses by up to 500 m, partly explaining previous overestimations. However, reducing the ice flux limitation allows the hybrid model to minimize this mismatch and captures sliding speeds, ice thicknesses, ice extent and basal temperatures in close agreement with those obtained with the Stokes model.

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A comparison of different methods of evaluating glacier response characteristics: application to glacier AX010, Nepal Himalaya

The Cryosphere Discussions ◽

10.5194/tcd-3-765-2009 ◽

2009 ◽

Vol 3 (3) ◽

pp. 765-804 ◽

Cited By ~ 2

Author(s):

S. Adhikari ◽

S. J. Marshall ◽

P. Huybrechts

Keyword(s):

Response Time ◽

Flow Model ◽

Ice Flow ◽

Nepal Himalaya ◽

Response Characteristics ◽

Response Behaviour ◽

Himalayan Glaciers ◽

Valley Glacier ◽

Volume Response ◽

Small Valley

Abstract. Himalayan glaciers are considered to be amongst the most sensitive glaciers to climate change. However, the response behaviour of these glaciers is not well understood. Here we use several approaches to estimate characteristic timescales of glacier AX010, a small valley glacier in the Nepal Himalaya, as a measure of glacier sensitivity. Assuming that temperature solely defines the mass budget, glacier AX010 waits for about 8 yr (reaction time) to exhibit its initial terminus response to changing climate. On the other hand, it takes between 29–56 yr (volume response time) and 37–70 yr (length response time) to adjust its volume and length following the changes in mass balance conditions, respectively. A numerical ice-flow model, the only method that yields both length and volume response time, confirms that a glacier takes longer to adjust its length than its volume.

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Data assimilation using a hybrid ice flow model

The Cryosphere ◽

10.5194/tc-5-315-2011 ◽

2011 ◽

Vol 5 (2) ◽

pp. 315-327 ◽

Cited By ~ 45

Author(s):

D. N. Goldberg ◽

O. V. Sergienko

Keyword(s):

Flow Model ◽

Control Method ◽

Ice Flow ◽

Inverse Control ◽

Flow Models ◽

Wide Range ◽

Inversion Procedure ◽

Order Stress ◽

The Cost ◽

Vertical Shearing

Abstract. Hybrid models, or depth-integrated flow models that include the effect of both longitudinal stresses and vertical shearing, are becoming more prevalent in dynamical ice modeling. Under a wide range of conditions they closely approximate the well-known First Order stress balance, yet are of computationally lower dimension, and thus require less intensive resources. Concomitant with the development and use of these models is the need to perform inversions of observed data. Here, an inverse control method is extended to use a hybrid flow model as a forward model. We derive an adjoint of a hybrid model and use it for inversion of ice-stream basal traction from observed surface velocities. A novel aspect of the adjoint derivation is a retention of non-linearities in Glen's flow law. Experiments show that in some cases, including those nonlinearities is advantageous in minimization of the cost function, yielding a more efficient inversion procedure.

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Data assimilation using a hybrid ice flow model

The Cryosphere Discussions ◽

10.5194/tcd-4-2201-2010 ◽

2010 ◽

Vol 4 (4) ◽

pp. 2201-2231 ◽

Cited By ~ 2

Author(s):

D. N. Goldberg ◽

O. V. Sergienko

Keyword(s):

Flow Model ◽

Control Method ◽

Ice Flow ◽

Inverse Control ◽

Flow Models ◽

Wide Range ◽

Inversion Procedure ◽

Order Stress ◽

The Cost ◽

Vertical Shearing

Abstract. Hybrid models, or depth-integrated flow models that include the effect of both longitudinal stresses and vertical shearing, are becoming more prevalent in dynamical ice modeling. Under a wide range of conditions they closely approximate the well-known First Order stress balance, yet are of computationally lower dimension, and thus require less intensive resources. Concomitant with the development and use of these models is the need to perform inversions of observed data. Here, an inverse control method is extended to use a hybrid flow model as a forward model. We derive an adjoint of a hybrid model and use it for inversion of ice-stream basal traction from observed surface velocities. A novel aspect of the adjoint derivation is a retention of non-linearities in Glen's flow law. Experiments show that including those nonlinearities is advantageous in minimization of the cost function, yielding a more efficient inversion procedure.

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Dilation of subglacial sediment governs incipient surge motion in glaciers with deformable beds

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2020.0033 ◽

2020 ◽

Vol 476 (2238) ◽

pp. 20200033 ◽

Cited By ~ 1

Author(s):

B. M. Minchew ◽

C. R. Meyer

Keyword(s):

Pore Water ◽

Flow Model ◽

Pore Water Pressure ◽

Water Pressure ◽

Slip Rate ◽

Effective Pressure ◽

Ice Flow ◽

History Of ◽

Glacier Surges ◽

Geographical Clustering

Glacier surges are quasi-periodic episodes of rapid ice flow that arise from increases in slip rate at the ice–bed interface. The mechanisms that trigger and sustain surges are not well understood. Here, we develop a new model of incipient surge motion for glaciers underlain by sediments to explore how surges may arise from slip instabilities within a thin layer of saturated, deforming subglacial till. Our model represents the evolution of internal friction, porosity and pore water pressure within the till as functions of the rate and history of shear deformation, and couples the till mechanics to a simple ice-flow model. Changes in pore water pressure govern incipient surge motion, with less permeable till facilitating surging because dilation-driven reductions in pore water pressure slow the rate at which till tends towards a new steady state, thereby allowing time for the glacier to thin dynamically. The reduction of overburden (and thus effective) pressure at the bed caused by dynamic thinning of the glacier sustains surge acceleration in our model. The need for changes in both the hydromechanical properties of the till and the thickness of the glacier creates restrictive conditions for surge motion that are consistent with the rarity of surge-type glaciers and their geographical clustering.

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Ice thickness estimates of Lemon Creek Glacier, Alaska, from active-source seismic imaging

Journal of Glaciology ◽

10.1017/jog.2021.32 ◽

2021 ◽

pp. 1-9

Author(s):

Stephen A. Veitch ◽

Marianne Karplus ◽

Galen Kaip ◽

Lucia F. Gonzalez ◽

Jason M. Amundson ◽

...

Keyword(s):

Ice Thickness ◽

Equilibrium Line Altitude ◽

Seismic Line ◽

Ice Flow ◽

Southeast Alaska ◽

Velocity Modeling ◽

Active Source ◽

Valley Glacier ◽

Subglacial Topography ◽

The Impact

Abstract Lemon Creek Glacier, a temperate valley glacier in the Juneau Icefield of Southeast Alaska, is the site of long running (>60 years) glaciological studies. However, the most recent published estimates of its thickness and subglacial topography come from two ~50 years old sources that are not in agreement and do not account for the effects of years of negative mass balance. We collected a 1-km long active-source seismic line on the upper section of the glacier parallel and near to the centerline of the glacier, roughly straddling the equilibrium-line altitude. We used these data to perform joint reflection-refraction velocity modeling and reflection imaging of the glacier bed. We find that this upper section of Lemon Creek Glacier is as much as 150 m (~65%) thicker than previously suggested with a large overdeepening in an area previously believed to have a uniform thickness. Our results lead us to reinterpret the impact of basal motion on ice flow and have a significant impact on expectations of subglacial hydrology. We suggest that further efforts to develop a whole-glacier model of subglacial topography are necessary to support studies that require accurate models of ice thickness and subglacial topography.

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Volcanic synchronization of Dome Fuji and Dome C Antarctic deep ice cores over the past 216 kyr

Climate of the Past ◽

10.5194/cp-11-1395-2015 ◽

2015 ◽

Vol 11 (10) ◽

pp. 1395-1416 ◽

Cited By ~ 13

Author(s):

S. Fujita ◽

F. Parrenin ◽

M. Severi ◽

H. Motoyama ◽

E. W. Wolff

Keyword(s):

Age Differences ◽

Flow Model ◽

Ice Cores ◽

Ice Flow ◽

Surface Mass ◽

The Past ◽

The One ◽

Mis 5E ◽

Age Constraints ◽

Mis 5

Abstract. Two deep ice cores, Dome Fuji (DF) and EPICA Dome C (EDC), drilled at remote dome summits in Antarctica, were volcanically synchronized to improve our understanding of their chronologies. Within the past 216 kyr, 1401 volcanic tie points have been identified. DFO2006 is the chronology for the DF core that strictly follows O2 / N2 age constraints with interpolation using an ice flow model. AICC2012 is the chronology for five cores, including the EDC core, and is characterized by glaciological approaches combining ice flow modelling with various age markers. A precise comparison between the two chronologies was performed. The age differences between them are within 2 kyr, except at Marine Isotope Stage (MIS) 5. DFO2006 gives ages older than AICC2012, with peak values of 4.5 and 3.1 kyr at MIS 5d and MIS 5b, respectively. Accordingly, the ratios of duration (AICC2012 / DFO2006) range between 1.4 at MIS 5e and 0.7 at MIS 5a. When making a comparison with accurately dated speleothem records, the age of DFO2006 agrees well at MIS 5d, while the age of AICC2012 agrees well at MIS 5b, supporting their accuracy at these stages. In addition, we found that glaciological approaches tend to give chronologies with younger ages and with longer durations than age markers suggest at MIS 5d–6. Therefore, we hypothesize that the causes of the DFO2006–AICC2012 age differences at MIS 5 are (i) overestimation in surface mass balance at around MIS 5d–6 in the glaciological approach and (ii) an error in one of the O2 / N2 age constraints by ~ 3 kyr at MIS 5b. Overall, we improved our knowledge of the timing and duration of climatic stages at MIS 5. This new understanding will be incorporated into the production of the next common age scale. Additionally, we found that the deuterium signals of ice, δDice, at DF tends to lead the one at EDC, with the DF lead being more pronounced during cold periods. The lead of DF is by +710 years (maximum) at MIS 5d, −230 years (minimum) at MIS 7a and +60 to +126 years on average.

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At what depth is the Eemian layer expected to be found at NEEM?

Annals of Glaciology ◽

10.3189/172756408784700617 ◽

2008 ◽

Vol 48 ◽

pp. 100-102 ◽

Cited By ~ 7

Author(s):

Susanne L. Buchardt ◽

Dorthe Dahl-Jensen

Keyword(s):

Flow Model ◽

Accumulation Rate ◽

Ice Core ◽

Monte Carlo Analysis ◽

Interglacial Period ◽

Ice Flow ◽

North West ◽

Flow Parameters ◽

Drill Site ◽

Radio Echo Sounding

AbstractNo continuous record from Greenland of the Eemian interglacial period (130–115 ka BP) currently exists. However, a new ice-core drill site has been suggested at 77.449˚ N, 51.056˚Win north-west Greenland (North Eemian or NEEM). Radio-echo sounding images and flow model investigations indicate that an undisturbed Eemian record may be obtained at NEEM. In this work, a two-dimensional ice flow model with time-dependent accumulation rate and ice thickness is used to estimate the location of the Eemian layer at the new drill site. The model is used to simulate the ice flow along the ice ridge leading to the drill site. Unknown flow parameters are found through a Monte Carlo analysis of the flow model constrained by observed isochrones in the ice. The results indicate that the Eemian layer is approximately 60m thick and that its base is located approximately 100m above bedrock.

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Sensitivity of Greenland Ice Sheet Projections to Model Formulations

Journal of Glaciology ◽

10.3189/2013jog12j182 ◽

2013 ◽

Vol 59 (216) ◽

pp. 733-749 ◽

Cited By ~ 87

Author(s):

H. Goelzer ◽

P. Huybrechts ◽

J.J. Fürst ◽

F.M. Nick ◽

M.L. Andersen ◽

...

Keyword(s):

Regional Climate Model ◽

Sea Level ◽

Flow Model ◽

Climate Model ◽

Regional Climate ◽

Ice Sheet ◽

Greenland Ice Sheet ◽

Ice Flow ◽

Outlet Glacier ◽

Glacier Dynamics

AbstractPhysically based projections of the Greenland ice sheet contribution to future sea-level change are subject to uncertainties of the atmospheric and oceanic climatic forcing and to the formulations within the ice flow model itself. Here a higher-order, three-dimensional thermomechanical ice flow model is used, initialized to the present-day geometry. The forcing comes from a high-resolution regional climate model and from a flowline model applied to four individual marine-terminated glaciers, and results are subsequently extended to the entire ice sheet. The experiments span the next 200 years and consider climate scenario SRES A1B. The surface mass-balance (SMB) scheme is taken either from a regional climate model or from a positive-degree-day (PDD) model using temperature and precipitation anomalies from the underlying climate models. Our model results show that outlet glacier dynamics only account for 6–18% of the sea-level contribution after 200 years, confirming earlier findings that stress the dominant effect of SMB changes. Furthermore, interaction between SMB and ice discharge limits the importance of outlet glacier dynamics with increasing atmospheric forcing. Forcing from the regional climate model produces a 14–31 % higher sea-level contribution compared to a PDD model run with the same parameters as for IPCC AR4.

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On the substantial influence of the treatment of friction at the grounding line

The Cryosphere Discussions ◽

10.5194/tcd-9-3475-2015 ◽

2015 ◽

Vol 9 (3) ◽

pp. 3475-3501 ◽

Cited By ~ 1

Author(s):

O. Gagliardini ◽

J. Brondex ◽

F. Gillet-Chaulet ◽

L. Tavard ◽

V. Peyaud ◽

...

Keyword(s):

Flow Model ◽

Ice Sheets ◽

Velocity Fields ◽

Practical Implementation ◽

Total Force ◽

Model Intercomparison ◽

Fe Method ◽

Ice Flow ◽

Grounding Line ◽

Diagnostic Experiment

Abstract. The dynamical contribution of marine ice sheets to sea level rise is largely controlled by grounding line (GL) dynamics. Seroussi et al. (2014) emphasised the sensitivity of numerical ice flow model results to the practical implementation of the friction of the ice on its bed in the very close vicinity of the GL. Elmer/Ice is a reference finite element (FE) ice flow model used in recent marine ice sheet model intercomparison (MISMIP) exercises. In the model, the GL is defined as the nodes where the ice is in contact with the bedrock but belong to both grounded and floating elements. Inherently to the FE method, computing the contribution of the friction by element requires evaluating the friction at the integration points. In Elmer/Ice, this is done by interpolating the values of the friction parameter C prescribed at the nodes. In this brief communication, we discuss and compare three alternative ways to prescribe the friction at the GL: (i) C is prescribed and non null at the GL nodes, (ii) C is set to zero at the GL nodes, and (iii) C is discontinuous at the GL nodes (i.e. is prescribed and non null for grounded elements and otherwise null). So far, all published results using Elmer/Ice were obtained with the first method. Using the MISMIP3d diagnostic experiment, we first show that, although the change in the total force at the base is insignificant, the three methods lead to significantly different velocity fields. We then show that these methods also lead to different steady state GL positions and different transient behaviours. Such model sensitivity to the methods discussed here is certainly specific to the high friction prescribed in the MISMIP experiments and should be smaller in real setups where friction in the vicinity of the GL would be expected to be lower. Results obtained with the three methods are available as Supplement for future comparisons.

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A Global Sensitivity Analysis Framework for Hybrid Simulation with Stochastic Substructures

Frontiers in Built Environment ◽

10.3389/fbuil.2021.778716 ◽

2021 ◽

Vol 7 ◽

Author(s):

Nikolaos Tsokanas ◽

Xujia Zhu ◽

Giuseppe Abbiati ◽

Stefano Marelli ◽

Bruno Sudret ◽

...

Keyword(s):

Sensitivity Analysis ◽

Hybrid Model ◽

Surrogate Model ◽

Global Sensitivity Analysis ◽

Hybrid Simulation ◽

Hybrid Models ◽

Analysis Framework ◽

Global Sensitivity ◽

Sensitivity Indices ◽

Realistic Situation

Hybrid simulation is an experimental method used to investigate the dynamic response of a reference prototype structure by decomposing it to physically-tested and numerically-simulated substructures. The latter substructures interact with each other in a real-time feedback loop and their coupling forms the hybrid model. In this study, we extend our previous work on metamodel-based sensitivity analysis of deterministic hybrid models to the practically more relevant case of stochastic hybrid models. The aim is to cover a more realistic situation where the physical substructure response is not deterministic, as nominally identical specimens are, in practice, never actually identical. A generalized lambda surrogate model recently developed by some of the authors is proposed to surrogate the hybrid model response, and Sobol’ sensitivity indices are computed for substructure quantity of interest response quantiles. Normally, several repetitions of every single sample of the inputs parameters would be required to replicate the response of a stochastic hybrid model. In this regard, a great advantage of the proposed framework is that the generalized lambda surrogate model does not require repeated evaluations of the same sample. The effectiveness of the proposed hybrid simulation global sensitivity analysis framework is demonstrated using an experiment.

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