Glacier Ice Flow Research Articles

Universal differential equations for glacier ice flow modelling

Abstract. Geoscientific models are facing increasing challenges to exploit growing datasets coming from remote sensing. Universal differential equations (UDEs), aided by differentiable programming, provide a new scientific modelling paradigm enabling both complex functional inversions to potentially discover new physical laws and data assimilation from heterogeneous and sparse observations. We demonstrate an application of UDEs as a proof of concept to learn the creep component of ice flow, i.e. a nonlinear diffusivity differential equation, of a glacier evolution model. By combining a mechanistic model based on a two-dimensional shallow-ice approximation partial differential equation with an embedded neural network, i.e. a UDE, we can learn parts of an equation as nonlinear functions that then can be translated into mathematical expressions. We implemented this modelling framework as ODINN.jl, a package in the Julia programming language, providing high performance, source-to-source automatic differentiation (AD) and seamless integration with tools and global datasets from the Open Global Glacier Model in Python. We demonstrate this concept for 17 different glaciers around the world, for which we successfully recover a prescribed artificial law describing ice creep variability by solving ∼ 500 000 ordinary differential equations in parallel. Furthermore, we investigate which are the best tools in the scientific machine learning ecosystem in Julia to differentiate and optimize large nonlinear diffusivity UDEs. This study represents a proof of concept for a new modelling framework aiming at discovering empirical laws for large-scale glacier processes, such as the variability in ice creep and basal sliding for ice flow, and new hybrid surface mass balance models.

The Twannberg iron meteorite strewn field in the Swiss Jura mountains: insights for Quaternary environmental conditions

The ~ 10 km2 strewn field of the Twannberg type IIG iron meteorite is located in the Swiss Jura Mountains, 30 km northwest of Bern. The strewn field has been mapped by a group of citizen scientists since 2006, yielding more than 2000 meteorite fragments with a total mass of 152.7 kg until the end of 2022. With a terrestrial age of 176 ± 19 ka and a minimum pre-atmospheric mass of ~ 250 t, the Twannberg meteorite is a local time marker in an area with a poorly-known paleoenvironmental history. The Twannberg strewn field is located just outside of the maximum extent of ice during the Last Glacial Maximum (LGM). On the Mont Sujet, meteorites are size-sorted in a 6-km long section of the primary strewn field (altitude 945–1370 m a.s.l.), indicating a fall direction from east-northeast to west-southwest (azimuth approximately 250°). On the Twannberg plateau and in the Twannbach gorge, meteorites are not size-sorted and occur in a ~ 5.7-km long area associated with till and recent stream sediments (altitude 430–1075 m a.s.l.). The mass distribution of meteorites on the Twannberg plateau demonstrate that these meteorites were not found where they fell but that they must have been transported up to several km by glacier ice flow after the fall. The distribution of meteorites and of glacially transported Alpine clasts on the Mont Sujet and on the Chasseral chain indicates the presence of local ice caps and of an approximately 200-m higher Alpine ice surface with respect to the LGM at the time of fall. This high ice level during MIS 6 (Marine Isotopic Stage 6, 191–130 ka) indicated by the meteorite distribution is consistent with surface exposure ages of 50–144 ka from nearby resting erratic boulders at altitudes of up to 1290 m a.s.l., including the newly dated Jobert boulder (63 ka). These boulders indicate an ice level ~ 400 m higher than during LGM at a time not later than MIS 6. Post-LGM luminescence ages of loess-containing meteorites on the Mont Sujet and 14C ages of materials associated with meteorite finds indicate relatively young pedoturbation and increased oxidation of meteorites since ~ 7300 cal BP, possibly correlated with deforestation and enhanced erosion resulting from increased human activities since the Neolithic. This study shows that Twannberg meteorites in their palaeoenvironmental context provide valuable information about ice levels and transport directions during MIS 6 and about their interaction with the post-LGM environmental conditions. The unique Twannberg strewn field has the potential to reveal more valuable information.

Seasonal ice flow velocity variations of Polar Record Glacier, East Antarctica during 2016–2019 using Sentinel-1 data

Remote sensing-based investigation of ice flow dynamics of Polar Record Glacier (PRG) during December–April of 2016–2019 has been conducted in this work. Using offset tracking method on the Sentinel-1 Synthetic Aperture Radar (SAR) images, we estimated the glacier ice flow velocity. Ice flow velocity near the glacier terminus indicated higher velocity during January and subsequently showed lower values in December during 2016–2019. The maximum and minimum velocity of the glacier was found to be ∼2.54 and 0.03 m/d for 2016–2017, ∼2.49 and 0.03 m/d for 2017–2018, and ∼2.47 and 0.03 m/d for 2018–2019. Results indicate that the maximum velocity occurred at the terminus of the glacier and minimum flow was detected on the ice sheet portion of the glacier. The average ice front position receded from ∼900 m in 2016–2017 to ∼650 m in 2017–2018 to ∼200 m in 2018–2019. A slowdown near the glacier terminus is observed for the period 2018–2019, while the total glacier advancement was observed to be 28 km2 from 877 km2 to 905 km2 during the period of 2016–2019. The enhanced velocity at the terminus in the early winter (March and April) was attributed to ice-free water surrounding the PRG terminus which eliminated the buttressing effect.

Quantitative analysis of Arctic ice flow acceleration with increasing temperature

This study explores the ice flow acceleration (21.1%) of Pedersenbreen during 2016–2017 after the extremely warm winter throughout the whole Arctic in 2015/2016 using in situ data and quantitatively analyses the factors contributing to this acceleration. Several data sets, including 2008–2018 air temperature data from Ny-Alesund, ten-year in situ GPS measurements and Elmer/Ice ice flow modelling under different ice temperature scenarios, suggest that the following factors contributed to the ice flow acceleration: the softened glacier ice caused by an increase in the air temperature (1.5°C) contributed 2.7%–30.5%, while basal lubrication contributed 69.5%–97.3%. The enhanced basal sliding was mostly due to the increased surface meltwater penetrating to the bedrock under the rising air temperature conditions; consequently, the glacier ice flow acceleration was caused mainly by an increase in subglacial water. For Pedersenbreen, there was an approximately one-year time lag between the change in air temperature and the change in glacier ice flow velocity.

Bedrock reconstruction from free surface data for unidirectional glacier flow with basal slip

Glacier ice flow is shaped and defined by several properties, including the bedrock elevation profile and the basal slip distribution. The effect of these two basal properties can present in similar ways in the surface. For bedrock recovery this makes distinguishing between them an interesting and complex problem. The results of this paper show that in some synthetic test cases it is indeed possible to distinguish and recover both bedrock elevation and basal slip given free surface elevation and free surface velocity. The unidirectional shallow ice approximation is used to compute steady state surface data for a number of synthetic cases with different bedrock profiles and basal slip distributions. A simple inversion method based on Newton's method is applied to the known surface data to return the bedrock profile and basal slip distribution. In each synthetic test case, the inversion was successful in recovering both the bedrock elevation profile and the basal slip distribution variables. These results imply that there is a unique bedrock profile and basal slip which give rise to a unique combination of free surface velocity and free surface elevation.

Three-dimensional deformation time series of glacier motion from multiple-aperture DInSAR observation

The previously presented Multidimensional Small Baseline Subset (MSBAS-2D) technique computes two-dimensional (2D), east and vertical, ground deformation time series from two or more ascending and descending Differential Interferometric Synthetic Aperture Radar (DInSAR) data sets by assuming that the contribution of the north deformation component is negligible. DInSAR data sets can be acquired with different temporal and spatial resolutions, viewing geometries and wavelengths. The MSBAS-2D technique has previously been used for mapping deformation due to mining, urban development, carbon sequestration, permafrost aggradation and pingo growth, and volcanic activities. In the case of glacier ice flow, the north deformation component is often too large to be negligible. Historically, the surface-parallel flow (SPF) constraint was used to compute the static three-dimensional (3D) velocity field at various glaciers. A novel MSBAS-3D technique has been developed for computing 3D deformation time series where the SPF constraint is utilized. This technique is used for mapping 3D deformation at the Barnes Ice Cap, Baffin Island, Nunavut, Canada, during January–March 2015, and the MSBAS-2D and MSBAS-3D solutions are compared. The MSBAS-3D technique can be used for studying glacier ice flow at other glaciers and other surface deformation processes with large north deformation component, such as landslides. The software implementation of MSBAS-3D technique can be downloaded from http://insar.ca/.

A Thin Film Viscoplastic Theory for Calving Glaciers: Toward a Bound on the Calving Rate of Glaciers

Projections of the growth and demise of ice sheets and glaciers require physical models of the processes governing flow and fracture of ice. The flow of glacier ice has been treated using increasingly sophisticated models. By contrast, fracture, the process ultimately responsible for half of the mass lost from ice sheets through iceberg calving, is often included using ad hoc parameterizations. In this study we seek to bridge this gap by introducing a model where ice obeys a power law rheology appropriate for intact ice below a yield strength. Above the yield strength, we introduce a separate rheology appropriate for the flow of heavily fractured ice, where ice deformation occurs more readily along faults and fractures. We show that, provided the motion of fractured ice is sufficiently rapid compared to that of intact ice, the behavior of glaciers depends solely on the rheology of intact ice and the yield strength of ice and is insensitive to the precise rheology of fractured ice. Moreover, assuming that glacier ice is unyielded allows us to bound the long‐term average rate of terminus advance, providing a first principles estimate of rates of retreat associated with the marine ice cliff instability. We illustrate model behavior using idealized geometries and climate forcing and show that the model not only exhibits realistic patterns of advance and retreat but also has the potential to exhibit hysteresis. This hysteresis could provide an explanation for the sudden onset of rapid retreat observed in marine‐terminating glaciers.

Heterogeneous water storage and thermal regime of supraglacial ponds on debris‐covered glaciers

AbstractThe water storage and energy transfer roles of supraglacial ponds are poorly constrained, yet they are thought to be important components of debris‐covered glacier ablation budgets. We used an unmanned surface vessel (USV) to collect sonar depth measurements for 24 ponds to derive the first empirical relationship between their area and volume applicable to the size distribution of ponds commonly encountered on debris‐covered glaciers. Additionally, we instrumented nine ponds with thermistors and three with pressure transducers, characterizing their thermal regime and capturing three pond drainage events. The deepest and most irregularly‐shaped ponds were those associated with ice cliffs, which were connected to the surface or englacial hydrology network (maximum depth = 45.6 m), whereas hydrologically‐isolated ponds without ice cliffs were both more circular and shallower (maximum depth = 9.9 m). The englacial drainage of three ponds had the potential to melt ~100 ± 20 × 103 kg to ~470 ± 90 × 103 kg of glacier ice owing to the large volumes of stored water. Our observations of seasonal pond growth and drainage with their associated calculations of stored thermal energy have implications for glacier ice flow, the progressive enlargement and sudden collapse of englacial conduits, and the location of glacier ablation hot‐spots where ponds and ice cliffs interact. Additionally, the evolutionary trajectory of these ponds controls large proglacial lake formation in deglaciating environments. Copyright © 2017 John Wiley & Sons, Ltd.

Glacier studies on the basis of acoustic measurements

The possibility of glacier ice flow studies using the method of acoustic emission (AE) in frequency range from 15 Hz to 20 kHz has been considered. A portable acoustic line system has been developed and a number of methodological issues (mounting of acoustic sensors into glacial ice, their location, reliability of acoustic coupling, etc.) have been solved. Acoustic studies of glacial ice have been performed; rock fall effect, ice cracking and ice movement on bedrock have been simulated. Correspondences of AE parameters to specific sources have been identified. The results of acoustic studies on Aldegondabreen (Spitsbergen), Central Tuyuksu and Molodezhny glaciers (northern Tien Shan) have been summarized. The dependence of the adhesive strength of ice with smooth substrate (serpentenite) on the shear rate has been considered; the effect of tor-shaped obstacle on shear force has been estimated. It is shown that the acoustic effects at cohesive ice failure on obstacles are similar to the observed natural acoustic vibrations generated in glaciers from distant sources. The results might be applied in development of the mobile ice lab and system for remote acoustic monitoring the processes in the bottom layers of glaciers.

Sensitivity Analysis of Pine Island Glacier ice flow using ISSM and DAKOTA

Assessing output errors of ice flow models is a major challenge that needs to be addressed if we are to increase our confidence level in projections of mass balance in Antarctica and Greenland. Major inputs to ice flow models include geometry (ice thickness and surface elevation), constitutive laws and boundary conditions (geothermal flux, basal drag coefficient, surface temperature). These inputs can be either measured, in which case they carry errors due to instruments, or inferred using inverse methods (such as basal drag which is inverted using InSAR surface velocities) in which case they carry additional errors generated by the inversion process itself. In both cases, these input errors will result in uncertainties that propagate throughout a forward model, and that influence output diagnostics. In order to estimate the resulting error margins on diagnostics such as mass flux, we develop a new framework based on the Design Analysis Kit for Optimization and Terascale Applications (DAKOTA), which we interface to the Ice Sheet System Model (ISSM). We present results on the Pine Island Glacier, West Antarctica, for which we evaluate error margins of mass flux across the whole glacier, given currently known error margins on ice thickness, basal friction and ice hardness. Our results suggest errors in these inputs propagate linearly through the ice flow model, providing a way to 1) calibrate measurement requirements for field campaigns collecting data such as bedrock or surface topography 2) quantify uncertainties in projections of mass balance and 3) assess the sensitivity of model outputs to input parameters. This new error propagation model should help quantify confidence levels that we assign to model projections for the mass balance of Antarctica and Greenland, which will ultimately improve our projections of future sea level rise in a warming climate.

Glacial modification of granite tors in the Cairngorms, Scotland

AbstractA range of evidence indicates that many granite tors in the Cairngorms have been modified by the flow of glacier ice during the Pleistocene. Comparisons with SW England and the use of a space–time transformation across 38 tor groups in the Cairngorms allow a model to be developed for progressive glacial modification. Tors with deeply etched surfaces and no, or limited, block removal imply an absence of significant glacial modification. The removal of superstructure and blocks, locally forming boulder trains, and the progressive reduction of tors to stumps and basal slabs represent the more advanced stages of modification. Recognition of some slabs as tor stumps from which glacial erosion has removed all superstructure allows the original distribution of tors to be reconstructed for large areas of the Cairngorms. Unmodified tors require covers of non‐erosive, cold‐based ice during all of the cold stages of the Middle and Late Pleistocene. Deformation beneath cold‐based glacier ice is capable of the removal of blocks but advanced glacial modification requires former wet‐based glacier ice. The depth of glacial erosion at former tor sites remains limited largely to the partial or total elimination of the upstanding tor form. Cosmogenic nuclide exposure ages (Phillips et al., 2006) together with data from weathering pit depths (Hall and Phillips, 2006), from the surfaces of tors and large erratic blocks require that the glacial entrainment of blocks from tors occurred in Marine Isotope Stages (MIS) 4–2, 6 and, probably, at least one earlier phase. The occurrence of glacially modified tors on or close to, the main summits of the Cairngorms requires full ice cover over the mountains during these Stages. Evidence from the Cairngorms indicates that tor morphology can be regarded as an important indicator of former ice cover in many formerly glaciated areas, particularly where other evidence of ice cover is sparse. Recognition of the glacial modification of tors is important for debates about the former existence of nunataks and refugia. Copyright © 2006 John Wiley & Sons, Ltd.

About this title

The flow of glacier ice can produce structures that are striking and beautiful. Associated sediments,too, can develop spectacular deformation structures, and examples are remarkbly well preserved in Quaternary deposits. Although such features have long been recognized, they are now the subject of new attention from glaciologists and glacial geologists. This collection of papers addresses how the methods for unravelling deformation structures evolved in recent years by structural geologists can be used for glacial materials, and the opportunities offered to structural geologists by glacial materials for studying deformation in rocks.

Whole-Field Measurement of Ice Displacement and Strain Rates

The flow of glacier ice is mapped using high-resolution photography and noncoherent light speckle interferometry. Time-lapse, double-exposures of a straining surface yield Young’s fringes when the resulting image is interrogated by a narrow beam of coherent light. Such fringe patterns, when corrected for camera motion, are indicative of the surface displacement occurring between exposures. Results of glacier field experiments are consistent with those garnered by conventional methods at the Nisqually Glacier, Washington. The interferometric method seems amenable to other geophysical applications, such as mapping sea ice flow, using terrestrial or space-based camera platforms.

A Whole-Field Interferometric Scheme for Measuring strain and Flow Rates of Glacier and Other Natural Surfaces

AbstractThe flow of glacier ice is mapped using high-resolution photography and non-coherent-light speckle interferometry. Young’s fringe patterns result when a double-exposed photoplate image of the straining surface is illuminated by a narrow beam of coherent light. Geometry gives a relationship between the ice surface displacement vector and the interference fringe patterns. This displacement vector is corrected for rigid-body (camera) movement and projected onto the ice surface using topological maps. The strain during the time-lapse interval is thus known. Comparison with data acquired by surveying techniques at Nisqually Glacier, Washington, U.S.A., is limited because of small overlap of the surface studied. In the areas for which results can be compared, our experiments yield a flow of 0.6 m/d where conventional methods yield about 0.4 m/d.

A Whole-Field Interferometric Scheme for Measuring strain and Flow Rates of Glacier and Other Natural Surfaces

AbstractThe flow of glacier ice is mapped using high-resolution photography and non-coherent-light speckle interferometry. Young’s fringe patterns result when a double-exposed photoplate image of the straining surface is illuminated by a narrow beam of coherent light. Geometry gives a relationship between the ice surface displacement vector and the interference fringe patterns. This displacement vector is corrected for rigid-body (camera) movement and projected onto the ice surface using topological maps. The strain during the time-lapse interval is thus known. Comparison with data acquired by surveying techniques at Nisqually Glacier, Washington, U.S.A., is limited because of small overlap of the surface studied. In the areas for which results can be compared, our experiments yield a flow of 0.6 m/d where conventional methods yield about 0.4 m/d.

Some Hypotheses on Surging Glaciers

Glacier surges can result when an ice dam, which is above the equilibrium length of the glacier, breaks from the forces of the excess ice that builds up behind the dam. It is shown that the high velocities of flow of surging glaciers cannot be due to the normal pseudo-plastic flow of glacier ice. Rather, the high velocities must result from a combination of sliding on the glacier bed and a fluidized block (or powder) flow resulting from melt water around the ice blocks in the interior and at the base of the ice mass. Various calculations are made to show the feasibility of the mechanisms proposed. The predictions are in line with the available observations on surging glaciers.

Structure and Flow of Glacier Ice: A Review

Structure and Flow of Glacier Ice: A Review

Ice

THE subject of Sir William Bragg's Friday evening discourse at the Royal Institution on March 18 last is one which is of deep interest from a remarkable variety of points of view, among them that of the crystallographer, the physicist, the geologist, the climber, the ski-runner, the plumber, the food purveyor and distributor, and even the very housewife herself. Moreover, it is one which has proved of unusual difficulty, although it concerns natural phenomena of the most familiar kind and one of the most abundant substances in Nature. Indeed, we never seem to get a thorough and complete understanding concerning the extraordinary nature and unusual properties of ice, although they have been investigated and discussed for ages. Only quite recently, an Association for the Study of Snow and Ice has been formed in Great Britain, now numbering about eighty members, the nucleus being the British members of the International Commission of Ice and Snow, which deals with the survey of glaciers and the prevention of catastrophes due to them. One of the latest discussions at the London meeting of the Association concerned "The Structure of Flow of Glacier Ice".

The Flow of Glacier Ice

The Flow of Glacier Ice