Evolution of debris cover on glaciers of the Eastern Alps,Austria, between 1996 and 2015

Debris cover on glaciers is an important component of glacial systems as it influences climate–glacier dynamics and thus the lifespan of glaciers. Increasing air temperatures, permafrost thaw and rock faces freshly exposed by glacier downwasting in accumulation zones result in increased rockfall activity and debris input. In the ablation zone, negative mass balances result in an enhanced melt-out of englacial debris. Glacier debris cover thus represents a clear signal of climate warming in mountain areas. To assess the temporal development of debris on glaciers of the Eastern Alps, Austria, we mapped debris cover on 255 glaciers using Landsat data at three time steps. We applied a ratio-based threshold classification technique and analysed glacier catchment characteristics to understand debris sources better. Across the Austrian Alps, debris cover increased by more than 10% between 1996 and 2015 while glaciers retreated in response to climate warming. Debris cover distribution shows significant regional variability, with some mountain ranges being characterised by mean debris cover on glaciers of up to 75%. We also observed a general rise of the mean elevation of debris cover on glaciers in Austria. The debris cover distribution and dynamics are highly variable due to topographic, lithological and structural settings that determine the amount of debris delivered to and stored in the glacier system. Despite strong variation in debris cover, all glaciers investigated melted at increasing rates. We conclude that the retarding effects of debris cover on the mass balance and melt rate of Austrian glaciers is strongly subdued compared with other mountain areas. The study indicates that, if this trend continues, many glaciers in Austria may become fully debris covered. However, since debris cover seems to have little impact on melt rates, this would not lead to prolonged existence of debris-covered ice compared with clean ice glaciers.     

The origins of Antarctic rock glaciers: periglacial or glacial features?

In extensively glaciarized permafrost areas such as Northern Victoria Land, rock glaciers are quite common and are considered postglacial cryotic landforms. This paper reveals that two rock glaciers in Northern Victoria Land (at Adélie Cove and Strandline) that are located close to the Italian Antarctic Station (Mario Zucchelli Station) should have the same origin, although they were previously mapped as Holocene periglacial landforms and subsequently considered ice‐cored and ice‐cemented rock glaciers, respectively. In fact, by integrating different geophysical investigations and borehole stratigraphy, we show that both landforms have similar internal structures and cores of buried glacier ice. Therefore, this kind of rock glacier is possibly related to the long‐term creep of buried ice rather than to permafrost creep alone. This interpretation can be extended to the larger part of the features mapped as rock glaciers in Antarctica. In addition, a high‐reflective horizon sub‐parallel to the topographic surface was detected in Ground Probing Radar (GPR) data over a large part of the study area. Combining all the available information, we conclude that it cannot be straightforwardly interpreted as the base of the active layer but rather represents the top of a cryo‐lithological unit characterized by ice lenses within sediments that could be interpreted as the transition zone between the active layer and the long‐term permafrost table. More generally, knowledge of the subsurface ice content and, in particular, the occurrence of massive ice and its depth is crucial to make realistic and affordable forecasts regarding thermokarst development and related feedbacks involving GHG emissions, especially in the case of cryosoils rich in carbon content. Copyright © 2017 John Wiley & Sons, Ltd.     

Extensive valley glacier deposits in the northern mid-latitudes of Mars: Evidence for Late Amazonian obliquity-driven climate change

Understanding spin orbital parameter-driven climate change on Mars prior to ∼ 20 Ma ago requires geological evidence because numerical solutions for that period are chaotic and non-unique. We show geological evidence that lineated valley fill at low mid-latitudes in the northern hemisphere of Mars (∼ 37.5° N) originated through regional snow and ice accumulation and underwent glacial-like flow. Breached upland craters and theater-headed valleys reveal features typical of erosion in association with terrestrial glaciers. Parallel, converging and chevron-like lineations in potentially ice-rich deposits on valley floors indicate that flow occurred through constrictions and converged from different directions at different velocities. Together, these Martian deposits and erosional landforms resemble those of intermontaine glacial systems on Earth, particularly in their major morphology, topographic shape, planform and detailed surface features. An inferred Late Amazonian age, combined with predictions of climate models, suggest that the obliquity of Mars exceeded a mean of 45° for a sustained period. During this time, significant transfer of ice occurred from ice-rich regions (e.g., the poles) to mid-latitudes, causing prolonged snow and ice accumulation there and forming an extensive system of valley glaciers.     

Slope failures and erosion rates on a glacierized high‐mountain face under climatic changes

In this study, rapid topographic changes and increased erosion rates caused by massive slope failures in a glacierized and permafrost‐affected high‐mountain face were investigated with respect to the current climatic change. The study was conducted at one of the highest periglacial rock faces in the European Alps, the east face of Monte Rosa, Italy. Pronounced changes in ice cover and repeated rock and ice avalanche events have been documented in this rock wall since around 1990. The performed multi‐temporal comparison of high‐resolution digital terrain models (DTMs) complemented by detailed analyses of repeat photography represents a unique assessment of topographic changes and slope failures over half a century and reveals a total volume loss in bedrock and steep glaciers in the central part of the face of around 25 × 10⁶ m³ between 1988 and 2007. The high rock and ice avalanche activity translates into an increase in erosion rates of about one order of magnitude during recent decades. The study indicates that changes in atmospheric temperatures and connected changes in ice cover can induce slope destabilization in high‐mountain faces. Analyses of temperature data show that the start of the intense mass movement activity coincided with increased mean annual temperatures in the region around 1990. However, once triggered, mass movement activity seems to be able to proceed in a self‐reinforcing cycle, whereby single mass movement events might be strongly influenced by short‐term extreme temperature events. The investigations suggest a strong stability coupling between steep glaciers and underlying bedrock, as most bedrock instabilities are located in areas where surface ice has disappeared recently and the failure zones are frequently spatially correlated and often develop from lower altitudes progressively upwards. Copyright © 2013 John Wiley & Sons, Ltd.     

Stability of supraglacial debris

Rock debris on the surface of ablating glaciers is not static, and is often transported across the ice surface as relief evolves during melt. This supraglacial debris transport has a strong influence on the spatial distribution of melt, and is implicated in the formation of hummocky glacial topography in deglaciated terrain. Furthermore, as ice‐dammed lakes and ice‐cored slopes become increasingly common in deglaciating watersheds, there is rising concern about hazards to humans and infrastructure posed by mass‐wasting of ice‐cored debris. The existing quantitative framework for describing these debris transport processes is limited, making it difficult to account for transport in mass balance, hazard assessment, and landscape development models. This paper develops a theoretical framework for assessing slope stability and gravitational mass transport in a debris‐covered ice setting. Excess water pressure at the interface between ablating ice and lowering debris is computed by combining Darcy's law with a meltwater balance. A limit‐equilibrium slope stability analysis is then applied to hypothetical debris layers with end‐member moisture conditions derived from a downslope meltwater balance that includes production and seepage. The resulting model system constrains maximum stable slope angles and lengths that vary with debris texture, thickness, and the rate of meltwater production. Model predictions are compared with field observations and with digital elevation model (DEM)‐derived terrain metrics from two modern debris‐covered glaciers on Mount Rainier, USA. Copyright © 2017 John Wiley & Sons, Ltd.     

Modelling the hydrological response of debris‐free and debris‐covered glaciers to present climatic conditions in the semiarid Andes of central Chile

We apply the process‐based, distributed TOPKAPI‐ETH glacio‐hydrological model to a glacierized catchment (19% glacierized) in the semiarid Andes of central Chile. The semiarid Andes provides vital freshwater resources to valleys in Chile and Argentina, but only few glacio‐hydrological modelling studies have been conducted, and its dominant hydrological processes remain poorly understood. The catchment contains two debris‐free glaciers reaching down to 3900 m asl (Bello and Yeso glaciers) and one debris‐covered avalanche‐fed glacier reaching to 3200 m asl (Piramide Glacier). Our main objective is to compare the mass balance and runoff contributions of both glacier types under current climatic conditions. We use a unique dataset of field measurements collected over two ablation seasons combined with the distributed TOPKAPI‐ETH model that includes physically oriented parameterizations of snow and ice ablation, gravitational distribution of snow, snow albedo evolution and the ablation of debris‐covered ice. Model outputs indicate that while the mass balance of Bello and Yeso glaciers is mostly explained by temperature gradients, the Piramide Glacier mass balance is governed by debris thickness and avalanches and has a clear non‐linear profile with elevation as a result. Despite the thermal insulation effect of the debris cover, the mass balance and contribution to runoff from debris‐free and debris‐covered glaciers are similar in magnitude, mainly because of elevation differences. However, runoff contributions are distinct in time and seasonality with ice melt starting approximately four weeks earlier from the debris‐covered glacier, what is of relevance for water resources management. At the catchment scale, snowmelt is the dominant contributor to runoff during both years. However, during the driest year of our simulations, ice melt contributes 42 ± 8% and 67 ± 6% of the annual and summer runoff, respectively. Sensitivity analyses show that runoff is most sensitive to temperature and precipitation gradients, melt factors and debris cover thickness. Copyright © 2016 John Wiley & Sons, Ltd.     

Use of terrain variables for mapping gully erosion susceptibility in Lebanon

This paper predicts the geographic distribution and size of gullies across central Lebanon using a geographic information system (GIS) and terrain analysis. Eleven primary (elevation; upslope contributing area; aspect; slope; plan, profile and tangential curvature; flow direction; flow width; flow path length; rate of change of specific catchment area along the direction of flow) and three secondary (steady‐state; quasi‐dynamic topographic wetness; sediment transport capacity) topographic variables were generated and used along with digital data collected from other sources (soil, geology) to statistically explain gully erosion field measurements. Three tree‐based regression models were developed using (1) all variables, (2) primary topographic variables only and (3) different pairs of variables. The best regression tree model combined the steady‐state topographic wetness and sediment transport capacity indices and explained 80% of the variability in field gully measurements. This model proved to be simple, quick, realistic and practical, and it can be applied to other areas of the Mediterranean region with similar environmental conditions, thereby providing a tool to help with the implementation of plans for soil conservation and sustainable management. Copyright © 2007 John Wiley & Sons, Ltd.     

Large ice‐contact slope movements: glacial buttressing,deformation and erosion

Glaciers and slope movements may act simultaneously to erode and modify glaciated slopes. Undercutting by glaciers can destabilize slopes but the extent to which slope failure may progress prior to subsequent glacier withdrawal has not hitherto been considered. The traditional view has been that the buttressing effect of ice prevents slope movement. The problem with this view is that ice is one‐third the density of rock and flows under low applied stress. Consequently, failed slopes may move into the glacier if they exert a stress in excess of the resistance provided by the glacier. Slope movement rate depends on ice rheology and other factors influencing driving and resisting stresses. Simple viscous equations are used to investigate these variables. The equations predict that small (<125 000 m³) ice‐contact rockslides can deform ice at several mm/year, increasing to several m/year for very large (>10⁸ m³) rockslides. To test these estimates, field evidence is presented of slope movements in glaciated valleys of New Zealand; narrowing or squeezing of glaciers adjacent to unstable rock slopes is demonstrated and considered to be the result of slope movement. For one site, geomorphic mapping and slope movement monitoring data show that movement rates are of similar order of magnitude to those predicted by the viscous equations; closer agreement could be achieved with the application of modelling techniques that can more realistically model the complex slope geometries and stability factors encountered, or by obtaining additional empirical data to calibrate the models. This research implies that, while the concept of glacial debuttressing – the reduction of slope support from withdrawal of glaciers – is valid, complete debuttressing is not a prerequisite for the movement of ice‐contact rock slopes. These slope movements may contribute to the erosional processes of glaciers and the evolution of glaciated slopes in a previously unrecognized way. Copyright © 2012 John Wiley & Sons, Ltd.     

Rock-glacier dams in High Asia

Rock glaciers in semiarid mountains contain large amounts of ice and might be important water stores aside from glaciers, lakes, and rivers. Yet whether and how rock glaciers interact with river channels in mountain valleys remains largely unresolved. We examine the potential for rock glaciers to block or disrupt river channels, using a new inventory of more than 2000 intact rock glaciers that we mapped from remotely sensed imagery in the Karakoram (KR), Tien Shan (TS), and Altai (ALT) mountains. We find that between 5% and 14% of the rock glaciers partly buried, blocked, diverted or constricted at least 95 km of mountain rivers in the entire study area. We use a Bayesian robust logistic regression with multiple topographic and climatic inputs to discern those rock glaciers disrupting mountain rivers from those with no obvious impacts. We identify elevation and potential incoming solar radiation (PISR), together with the size of feeder basins, as dominant predictors, so that lower-lying and larger rock glaciers from larger basins are more likely to disrupt river channels. Given that elevation and PISR are key inputs for modelling the regional distribution of mountain permafrost from the positions of rock-glacier toes, we infer that river-blocking rock glaciers may be diagnostic of non-equilibrated permafrost. Principal component analysis adds temperature evenness and wet-season precipitation to the controls that characterise rock glaciers impacting on rivers. Depending on the choice of predictors, the accuracy of our classification is moderate to good with median posterior area-under-the-curve values of 0.71–0.89. Clarifying whether rapidly advancing rock glaciers can physically impound rivers, or fortify existing dams instead, deserves future field investigation. We suspect that rock-glacier dams are conspicuous features that have a polygenetic history and encourage more research on the geomorphic coupling between permafrost lobes, river channels, and the sediment cascades of semiarid mountain belts. © 2018 John Wiley & Sons, Ltd.     

An overview of black carbon deposition in High Asia glaciers and its impacts on radiation balance

Since 2000, 18 High Asia glaciers have been surveyed for black carbon (BC) deposition 22 times, and numerous snow samples and ice cores have been collected by researchers. However, most of the results were interpreted individually in papers. Here, we assemble the data and discuss the distribution of BC deposition and its impacts on the melting of the glaciers through radiative forcing. We find that BC distribution on the surfaces of High Asia glaciers primarily depends upon their elevations (i.e., higher sites have lower concentrations) and then upon regional BC emissions and surface melting conditions. BC concentrations in High Asia glaciers are similar to the Arctic and western American mountains but are significantly less than heavy industrialized areas such as northern China. Although Himalayan glaciers, which are important due to their water resources, are directly facing the strong emissions from South Asia, their mean BC is the lowest due to high elevations. A new finding indicated by ice core records suggested that great valleys in the eastern Himalayan section are effective pathways for BC entering the Tibetan Plateau and make increasing BC trends in the local glaciers. On average, BC deposition causes a mean forcing of ∼6 W m⁻² (roughly estimated 5% of the total forcing) in High Asia glaciers and therefore may not be a major factor impacting the melting of most glaciers.     

The effect of glaciation on the intensity of seismic ground motion

Seismicity is known to contribute to landscape denudation through its role in earthquake‐triggered slope failure; but little is known about how the intensity of seismic ground motions, and therefore triggering of slope failures, may change through time. Topography influences the intensity of seismic shaking – generally steep slopes amplify shaking more than flatter slopes – and because glacial erosion typically steepens and enlarges slopes, glaciation may increase the intensity of seismic shaking of some landforms. However, the effect of this may be limited until after glaciers retreat because valley ice or ice‐caps may damp seismic ground motions. Two‐dimensional numerical models (FLAC 6.0) were used to explore how edifice shape, rock stiffness and various levels of ice inundation affect edifice shaking intensity. The modelling confirmed that earthquake shaking is enhanced with steeper topography and at ridge crests but it showed for the first time that total inundation by ice may reduce shaking intensity at hill crests to about 20–50% of that experienced when no ice is present. The effect is diminished to about 80–95% if glacier ice level reduces to half of the mountain slope height. In general, ice cover reduced shaking most for the steepest‐sided edifices, for wave frequencies higher than 3 Hz, and when ice was thickest and the rock had shear stiffness well in excess of the stiffness of ice. If rock stiffness is low and shear‐wave velocity is similar to that of ice, the presence of ice may amplify the shaking of rock protruding above the ice surface. The modelling supports the idea that topographic amplification of earthquake shaking increases as a result of glacial erosion and deglaciation. It is possible that the effect of this is sufficient to have influenced the distribution of post‐glacial slope failures in glaciated seismically active areas. Copyright © 2012 John Wiley & Sons, Ltd.     

The influence of ground ice distribution on geomorphic dynamics since the Little Ice Age in proglacial areas of two cirque glacier systems

Holocene glaciers have contributed to an abundance of unstable sediments in mountainous environments. In permafrost environments, these sediments can contain ground ice and are subject to rapid geomorphic activity and evolution under condition of a warming climate. To understand the influence of ground ice distribution on this activity since the Little Ice Age (LIA), we have investigated the Pierre Ronde and Rognes proglacial areas, two cirque glacier systems located in the periglacial belt of the Mont Blanc massif. For the first time, electrical resistivity tomography, temperature data loggers and differential global positioning systems (dGPS) are combined with historical documents and glaciological data analysis to produce a complete study of evolution in time and space of these small landsystems since the LIA. This approach allows to explain spatial heterogeneity of current internal structure and dynamics. The studied sites are a complex assemblage of debris‐covered glacier, ice‐rich frozen debris and unfrozen debris. Ground ice distribution is related to former glacier thermal regime, isolating effect of debris cover, water supply to specific zones, and topography. In relation with this internal structure, present dynamics are dominated by rapid ice melt in the debris‐covered upper slopes, slow creep processes in marginal glacigenic rock glaciers, and weak, superficial reworking in deglaciated moraines. Since the LIA, geomorphic activity is mainly spatially restricted within the proglacial areas. Sediment exportation has occurred in a limited part of the former Rognes Glacier and through water pocket outburst flood and debris flows in Pierre Ronde. Both sites contributed little sediment supply to the downslope geomorphic system, rather by episodic events than by constant supply. In that way, during Holocene and even in a paraglacial context as the recent deglaciation, proglacial areas of cirque glaciers act mostly as sediment sinks, when active geomorphic processes are unable to evacuate sediment downslope, especially because of the slope angle weakness. Copyright © 2014 John Wiley & Sons, Ltd.     

Geomorphic influence on small glacier response to post‐Little Ice Age climate warming: Julian Alps,Europe

The evolution of glaciers and ice patches, as well as the equilibrium‐line altitude (ELA) since the Little Ice Age (LIA) maximum were investigated in the Julian Alps (south‐eastern European Alps) including ice masses that were previously unreported. Twenty‐three permanent firn and ice bodies have been recognized in the 1853 km² of this alpine sector, covering a total area in 2012 of 0.385 km², about one‐fifth of the area covered during the LIA (2.350 km²). These features were classified as very small glaciers, glacierets or ice patches, with major contribution to the mass balance from avalanches and wind‐blown snow. Localized snow accumulation is also enhanced in the area due to the irregular karst topography. The ice masses in the region are at the lowest elevations of any glaciers in the Alpine Chain, and are characterized by low dynamics. The ELAs of the two major LIA glaciers (Canin and Triglav) have been established at 2275 ± 10 m and 2486 ± 10 m, respectively, by considering the reconstructed area and digital elevation model (DEM) and using an accumulation area ratio (AAR) of 0.44 ± 0.07, typical of small cirque glaciers. Changes in the ELA and glaciers extension indicate a decoupling from climate. This is most evident in the smallest avalanche‐dominated ice bodies, which are currently controlled mainly by precipitation. The damming effect of moraine ridges and pronival ramparts at the snout of small ice bodies in the Julian Alps represents a further geomorphological control on the evolution of such ice masses, which seem to be resilient to recent climate warming instead of rapidly disappearing as should be expected. Copyright © 2016 John Wiley & Sons, Ltd.     

基于偏移追踪的青藏高原卓琼冰川流速监测及成因分析

冰川作为地球系统中重要的组成部分,是全球气候变化的敏感指示器和调节器.冰川运动的遥感监测也是进行冰川研究的重要内容.本文主要采用偏移追踪的方法,利用2003-2010年期间7对雷达单视复数数据监测了青藏高原珠穆朗玛峰地区的卓琼冰川运动情况.经验证,本研究获得的冰川流速结果可靠.卓琼冰川的流向自西向东,流速自冰川末端向上游积累区逐渐增加,流速大小主要来自距离向的贡献.研究结果显示,卓琼冰川在2003-2005年期间流速较大,最大流速达到45 m·a~(-1),而在2005-2010年期间流速有所降低,最大流速在35~40 m·a~(-1)范围内波动;卓琼冰川年际间流速变化基本一致,冰川中部存在流速突变情况,突变幅度为3~7 m·a~(-1),但该尺度的突变并不会影响卓琼冰川的总体运动趋势.此外,本文还分析了气象以及地理位置因素对卓琼冰川运动的影响.     

Evaluating the effect of snow and ice melt in an Alpine headwater catchment and further downstream in the River Rhine

Abstract

The runoff regime of glacierized headwater catchments in the Alps is essentially characterized by snow and ice melt. High Alpine drainage basins influence distant downstream catchments of the Rhine River basin. In particular, during the summer months, low-flow conditions are probable with strongly reduced snow and ice melt under climate change conditions. This study attempts to quantify present and future contributions from snow and ice melt to summer runoff at different spatial scales. For the small Silvretta catchment (103 km²) in the Swiss Alps, with a glacierization of 7%, the HBV model and the glacio-hydrological model GERM are applied for calculating future runoff based on different regional climate scenarios. We evaluate the importance of snow and ice melt in the runoff regime. Comparison of the models indicates that the HBV model strongly overestimates the future contribution of glacier melt to runoff, as glaciers are considered as static components. Furthermore, we provide estimates of the current meltwater contribution of glaciers for several catchments downstream on the River Rhine during the month of August. Snow and ice melt processes have a significant direct impact on summer runoff, not only for high mountain catchments, but also for large transboundary basins. A future shift in the hydrological regime and the disappearance of glaciers might favour low-flow conditions during summer along the Rhine.

Citation Junghans, N., Cullmann, J. & Huss, M. (2011) Evaluating the effect of snow and ice melt in an Alpine headwater catchment and further downstream in the River Rhine. Hydrol. Sci. J. 56(6), 981–993.     

Seasonal changes in ground‐penetrating radar signature observed at a polythermal glacier,Bylot Island,Canada

In recent years, ground‐penetrating radar (GPR) has been increasingly used for characterization of subglacial and englacial environments at polythermal glaciers. The geophysical method is able to exploit the dielectric difference between water, air, sediment and ice, allowing delineation of subsurface hydrological, thermal and structural conditions. More recent GPR research has endeavoured to examine temporal change in glaciers, in particular the distribution of the cold ice zone at polythermal glaciers. However, the exact nature of temporal change that can be identified using GPR has not been fully examined. This research presents the results of three GPR surveys conducted over the course of a summer ablation season at a polythermal glacier in the Canadian Arctic. A total of approximately 30 km of GPR profiles were collected in 2002 repeatedly covering the lower 2 km of Stagnation Glacier, Bylot Island (72°58′ N 78°22′ W). Comparison between profiles indicated changes in the radar signature, including increased noise, appearance and disappearance of englacial reflections, and signal attenuation in the latter survey. Further, an area of chaotic returns in up‐glacier locations, which was interpreted to be a wet temperate ice zone, showed marked recession over the course of the ablation season. Combining all the temporal changes that were detected by GPR, results indicate that a polythermal glacier may exhibit strongly seasonal changes in hydrological and thermal characteristics throughout the ice body, including the drainage of 17 000 m³ of temporarily stored intra‐glacial meltwater. It is also proposed that the liquid water content in the temperate ice zone of polythermal glaciers can be described as a fraction of a specific retention capacity. Copyright © 2006 John Wiley & Sons, Ltd.     

Using structure‐from‐motion to create glacier DEMs and orthoimagery from historical terrestrial and oblique aerial imagery

Increased resolution and availability of remote sensing products, and advancements in small‐scale aerial drone systems, allows observations of glacial changes at unprecedented levels of detail. Software developments, such as structure‐from‐motion (SfM), now allow users an easy and efficient method to generate three‐dimensional (3D) models and orthoimages from aerial or terrestrial datasets. While these advancements show promise for current and future glacier monitoring, many regions still suffer a lack of observations from earlier time periods. We report on the use of SfM to extract spatial information from various historic imagery sources. We focus on three geographic regions, the European Alps, high Arctic Norway and the Nepal Himalayas. We used terrestrial field photographs from 1896, high oblique aerial photographs from 1936 and aerial handheld photographs from 1978 to generate digital elevation models (DEMs) and orthophotos of the Rhone glacier, Brøggerhalvøya and the lower Khumbu glacier, respectively. Our analysis shows that applying SfM to historic imagery can generate high quality models using only ground control points. Limited camera/orientation information was largely reproduced using self‐calibrated model data. Using these data, we calculated mean ground sampling distances across each site which demonstrates the high potential resolution of resulting models. Vertical errors for our models are ±5.4 m, ±5.2 m and ±3.3 m. Differencing shows similar patterns of thinning at lower Rhone (European Alps) and Brøggerhalvøya (Norway) glaciers, which have mean thinning rates of 0.31 m a^?1 (1896–2010) to 0.86 m a^?1 (1936–2010) respectively. On these clean ice glaciers thinning is highest in the terminus region and decreasing up‐glacier. In contrast to these glaciers, uneven topography, exposed ice‐cliffs and debris cover on the Khumbu glacier create a highly variable spatial distribution of thinning. The mean thinning rate for the Khumbu study area was found to be 0.54 ± 0.9 m a^?1 (1978–2015). Copyright © 2017 John Wiley & Sons, Ltd.     

Simulation and parameterization of superimposed ice formation

In cold Arctic snowpacks, meltwater retention is a significant factor controlling the timing and magnitude of runoff. Meltwater percolates vertically through the snowpack until it reaches an impermeable horizon, whereupon a saturated zone is established. If the underlying media is below the freezing point, accretive ice formation takes place. This process has previously been crudely parameterized or modelled numerically. Such ice is called either superimposed ice on glaciers or basal ice on bare land. Using theory derived from sea‐ice formation, an analytical solution to basal ice growth is proposed. Results are compared against growth rates derived from numerical modelling. In addition, model results are compared to field observations of ice temperatures. The analytical solution is further extended to account for the temperature gradient inside the underlying media and the variable thermal properties of the underlying media. In the analysis, observations and references have predominantly relied on knowledge from glaciers. However, the process of accretive ice growth is equally important in seasonal snow packs with a cold snow‐ground interface and on Arctic sea ice where the ice‐snow interface is well below freezing point. The simplification of this accretive ice growth problem makes the solution attractive for incorporation in large‐scale cryospheric models. Copyright © 2007 John Wiley & Sons, Ltd.     

Representing Grounding Line Dynamics in Numerical Ice Sheet Models: Recent Advances and Outlook

Recent satellite observations of the Antarctic and Greenland ice sheets show accelerated ice flow and associated ice sheet thinning along coastal outlet glaciers in contact with the ocean. Both processes are the result of grounding line retreat due to melting at the grounding line (the grounding line is the contact of the ice sheet with the ocean, where it starts to float and forms an ice shelf or ice tongue). Such rapid ice loss is not yet included in large-scale ice sheet models used for IPCC projections, as most of the complex processes are poorly understood. Here we report on the state-of-the art of grounding line migration in marine ice sheets and address different ways in which grounding line migration can be attributed and represented in ice sheet models. Using one-dimensional ice flow models of the ice sheet/ice shelf system we carried out a number of sensitivity experiments with different spatial resolutions and stress approximations. These are verified with semi-analytical steady state solutions. Results show that, in large-scale finite-difference models, grounding line migration is dependent on the numerical treatment (e.g. staggered/non-staggered grid) and the level of physics involved (e.g. shallow-ice/shallow-shelf approximation).     

A mathematical model of polythermal glaciers and ice sheets

Abstract

A mathematical model of the flow and temperature distribution of polythermal glaciers or ice sheets is deduced. Cold ice is treated as a non-linear viscous heat conducting fluid, while temperate ice is regarded as a binary mixture of ice and water. The simplest mixture concept with two balance laws of mass but only one balance law of momentum and energy is proposed. The field equations for the ice and water content and the boundary conditions which must hold at the free surface, at the ice-water interface, at the cold-temperature transition surface and at the rock-bed are deduced. In particular it is shown that an earlier formulation of polythermal ice due to Fowler and Larson (1978) is inconsistent. No boundary value problems are solved as the emphasis is on the physical motivation and justification of the principles.