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Retreat of calving glaciers worldwide has contributed substantially to sea-level rise in recent decades. Mass loss by calving contributes significantly to the uncertainty of sea-level rise projections. At Bowdoin Glacier, Northwest Greenland, most calving occurs by a few large events resulting from kilometre-scale fractures forming parallel to the calving front. High-resolution terrestrial radar interferometry data of such an event reveal that crevasse opening is fastest at low tide and accelerates during the final 36 h before calving. Using the ice flow model Elmer/Ice, we identify the crevasse water level as a key driver of modelled opening rates. Sea water-level variations in the range of local tidal amplitude (1 m) can reproduce observed opening rate fluctuations, provided crevasse water level is at least 4 m above the low-tide sea level. The accelerated opening rates within the final 36 h before calving can be modelled by additional meltwater input into the crevasse, enhanced ice cliff undercutting by submarine melt, ice damage increase due to tidal cyclic fatigue, crevasse deepening or a combination of these processes. Our results highlight the influence of surface meltwater and tides on crevasse opening leading to major calving events at grounded tidewater glaciers such as Bowdoin., Journal of Glaciology, 66 (255), ISSN:0022-1430, ISSN:1727-5652

The subglacial hydrology of tidewater glaciers is a key but poorly understood component of the complex ice-ocean system, which affects sea level rise. As it is extremely difficult to access the interior of a glacier, our knowledge relies mostly on the observation of input variables such as air temperature, and output variables such as the ice flow velocities reflecting the englacial water pressure, and the dynamics of plumes reflecting the discharge of meltwater into the ocean. In this study we use a cost-effective Vertical Take-Off and Landing (VTOL) Unmanned Aerial Vehicle (UAV) to monitor the daily movements of Bowdoin Glacier, north-west Greenland, and the dynamics of its main plume. Using Structure-from-Motion photogrammetry and feature-tracking techniques, we obtained 22 high-resolution ortho-images and 19 velocity fields at the calving front for 12 days in July 2016. Our results show a two-day-long speed-up event (up to 170%) – caused by an increase in buoyant subglacial forces – with a strong spatial variability revealing that enhanced acceleration is an indication of shallow bedrock. Further, we used the Particle Image Velocimetry (PIV) method to analyze water flow from successive UAV images taken while flying over the main plume of the glacier. We found that PIV successfully captures the area of radially diverging flow of the plume, and provides information on spatial and time variability as no other remote sensing technique can. Most interestingly, the active part of the plume features pulsating water jets at the time scale of seconds, and is 1 to 5 times smaller than its visual footprint defined by the iceberg-free area. Combined with an ice flow model or a non-steady plume model, our approach has the potential to generate a novel set of input data to gather information about the depth of the bedrock, the discharge of meltwater, or the subglacial melting rate of tidewater glaciers.

Measuring the ice flow motion accurately is essential to better understand the time evolution of glaciers and ice sheets, and therefore to better anticipate the future consequence of climate change in terms of sea-level rise. Although there exist a variety of remote sensing methods to fill this task, in-situ measurements are always needed for validation or to capture high temporal resolution movements. Yet glaciers are in general hostile environments where the installation of instruments might be tedious and risky when not impossible. Here we report the first-ever in-situ measurements of ice flow motion using a remotely controlled Unmanned Aerial Vehicle (UAV). We used a multicopter UAV to land on a highly crevassed area of Eqip Sermia Glacier, West Greenland, to measure the displacement of the glacial surface with the aid of an on-board differential GNSS receiver. Despite the unfortunate loss of the UAV, we measured approximately 70 cm of displacement over 4.36 hours without setting foot onto the glacier – a result validated by applying UAV photogrammetry and template matching techniques. Our study demonstrates that UAVs are promising instruments for in-situ monitoring, and have a great potential for capturing short-term ice flow variations in inaccessible glaciers – a task that remote sensing techniques can hardly achieve.

We develop a posteriori ‘mechanical’ error estimators that are able to evaluate the solution discrepancy between two ice flow models. We first reformulate the classical shallow ice flow models by applying simplifications to the weak formulation of the Glen–Stokes model. This approach leads to a unified hierarchical formulation which relates the Glen–Stokes model, the Blatter model, the shallow ice approximation and the shallow shelf approximation. Based on this formulation and on residual techniques commonly used to estimate numerical errors, we derive three a posteriori estimators, each of which compares a pair of models using measures of the velocity field from the simpler (shallower) model. Numerical experiments confirm that these estimators can be used to assess the validity of the shallow ice models that are commonly used in glacier and ice sheet modelling.

In this paper, a multilayer generalisation of the Shallow Shelf Approximation (SSA) is considered. In this recent hybrid ice flow model, the ice thickness is divided into thin layers, which can spread out, contract and slide over each other in such a way that the velocity profile is layer-wise constant. Like the SSA (1-layer model), the multilayer model can be reformulated as a minimisation problem. However, unlike the SSA, the functional to be minimised involves a new penalisation term for the interlayer jumps of the velocity, which represents the vertical shear stresses induced by interlayer sliding. Taking advantage of this reformulation, numerical solvers developed for the SSA can be naturally extended layer-wise or column-wise. Numerical results show that the column-wise extension of a Newton multigrid solver proves to be robust in the sense that its convergence is barely influenced by the number of layers and the type of ice flow. In addition, the multilayer formulation appears to be naturally better conditioned than the one of the first-order approximation to face the anisotropic conditions of the sliding-dominant ice flow of ISMIP-HOM experiments.

During the Last Glacial Maximum (LGM), glaciers in the Alps reached a maximum extent, and broad sections of the foreland were covered by ice. In this study, we simulated the alpine ice cap using a glacier flow model to constrain the prevailing precipitation pattern with a geomorphological reconstruction of ice extent. For this purpose we forced the model using different temperature cooling and precipitation reduction factors. The use of the present-day precipitation pattern led to a systematic overestimation of the ice cover on the northern part of the Alps relative to the southern part. To reproduce the LGM ice cap, a more severe decrease in precipitation in the north than in the south was required. This result supports a southwesterly advection of atmospheric moisture to the Alps, sustained by a southward shift of the North Atlantic storm track during the LGM., Geographica Helvetica, 71 (3), ISSN:0016-7312

A new hybrid model for the dynamics of glaciers, ice sheets and ice shelves is introduced. In this ‘multilayer’ model the domain of ice consists of a pile of thin layers, which can spread out, contract and slide over each other such that the two most relevant types of stresses are accounted for: membrane and vertical shear. Assuming the horizontal velocity field to be vertically piecewise constant in each layer, the model is derived from local depth integrations of the hydrostatic approximation of the Stokes equations. These integrations give rise to interlayer tractions, which can be redefined at zeroth order in the interlayer surface slope by keeping the vertical shear stress components. Furthermore, if the layers are chosen such that they are aligned with the streamlines, then second-order accurate interlayer tractions can replace zeroth-order ones. The final model consists of a tridiagonal system of two-dimensional nonlinear elliptic equations, the size of this system being equal to the number of layers. When running the model for prognostic flowline ISMIP-HOM benchmark experiments, the multilayer solutions show good agreement with the higher-order solutions if no severe depression occurs in the bedrock. As an alternative to three-dimensional models, the multilayer approach offers to glacier and ice sheet modellers a way of upgrading the commonly used shallow shelf approximation model into a mechanically complete but mathematically two-dimensional model.

In this paper, we consider a model for the time evolution of three-dimensional marine ice sheets. This model combines the Shallow Ice Approximation (SIA) for the ice deformation, the Shallow Shelf Approximation (SSA) for the basal sliding, and the mass conservation principle. At each time step, we solve a scalar p-Laplace minimization-type problem with obstacle (SIA), a vectorial p-Laplace minimization-type problem (SSA) and a transport equation (mass conservation). The two minimization problems are solved using a truncated nonsmooth Newton multigrid method while the transport equation is solved using a vertex-centred finite volume method. Our approach is combined to an heuristic mesh adaptive refinement procedure to face the large gradients of the solution that are expected between the ice sheet and the ice shelf. As applications, we present some simulations of the Marine Ice Sheet Model Intercomparison Project MISMIP (2D and 3D) and validate our results against an analytic solution (2D) and other participant model results (3D). Further numerical results show that the convergence of our Newton multigrid method is insensitive to local refinements making our overall adaptive strategy fully efficient.

In this study, a modelling approach was used to investigate the cause of the diversion of erratic boulders from Mont Blanc and southern Valais by the Valais Glacier to the Solothurn lobe during the Last Glacial Maximum (LGM). Using the Parallel Ice Sheet Model, we simulated the ice flow field during the LGM, and analyzed the trajectories taken by erratic boulders from areas with characteristic lithologies. The main difficulty in this exercise laid with the large uncertainties affecting the paleo climate forcing required as input for the surface mass-balance model. In order to mimic the prevailing climate conditions during the LGM, we applied different temperature offsets and regional precipitation corrections to present-day climate data, and selected the parametrizations, which yielded the best match between the modelled ice extent and the geomorphologically-based ice-margin reconstruction. After running a range of simulations with varying parameters, our results showed that only one parametrization allowed boulders to be diverted to the Solothurn lobe during the LGM. This precipitation pattern supports the existing theory of preferential southwesterly advection of moisture to the alps during the LGM, but also indicates strongly enhanced precipitation over the Mont Blanc massif and enhanced cooling over the Jura Mountains., Journal of Glaciology, 63 (239), ISSN:0022-1430, ISSN:1727-5652

Global warming is expected to significantly affect the runoff regime of mountainous catchments. Simple methods for calculating future glacier change in hydrological models are required in order to reliably assess economic impacts of changes in the water cycle over the next decades. Models for temporal and spatial glacier evolution need to describe the climate forcing acting on the glacier, and ice flow dynamics. Flow models, however, demand considerable computational resources and field data input and are moreover not applicable on the regional scale. Here, we propose a simple parameterization for calculating the change in glacier surface elevation and area, which is mass conserving and suited for hydrological modelling. The Δh-parameterization is an empirical glacier-specific function derived from observations in the past that can easily be applied to large samples of glaciers. We compare the Δh-parameterization to results of a 3-D finite-element ice flow model. As case studies, the evolution of two Alpine glaciers of different size over the period 2008–2100 is investigated using regional climate scenarios. The parameterization closely reproduces the distributed ice thickness change, as well as glacier area and length predicted by the ice flow model. This indicates that for the purpose of transient runoff forecasts, future glacier geometry change can be approximated using a simple parameterization instead of complex ice flow modelling. Furthermore, we analyse alpine glacier response to 21st century climate change and consequent shifts in the runoff regime of a highly glacierized catchment using the proposed methods., Hydrology and Earth System Sciences, 14 (5), ISSN:1027-5606, ISSN:1607-7938

Due to climatic change, many Alpine glaciers have significantly retreated during the last century. In this study we perform the numerical simulation of the temporal and spatial change of Rhonegletscher, Swiss Alps, from 1874 to 2007, and from 2007 to 2100. Given the shape of the glacier, the velocity of ice u is obtained by solving a 3D nonlinear Stokes problem with a nonlinear sliding law along the bedrock-ice interface. The shape of the glacier is updated by computing the volume fraction of ice @f, which satisfies a transport equation. The accumulation due to snow fall and the ablation due to melting is accounted by adding a source term to the transport equation. A decoupling algorithm allows the two above problems to be solved using different numerical techniques. The nonlinear Stokes problem is solved on a fixed, unstructured finite element mesh consisting of tetrahedrons. The transport equation is solved using a fixed, structured grid of smaller cells. The numerical simulation, from 1874 to 2007, is validated against measurements. Afterwards, three different climatic scenarios are considered in order to predict the shape of Rhonegletscher until 2100. A dramatic retreat of Rhonegletscher during the 21st century is anticipated. Our results contribute to a better understanding of the impact of climatic change on mountain glaciers.

For more than a century Alpine glaciers have been retreating dramatically, and they are expected to shrink even more quickly over the coming decades. This study addresses the future evolution of Grosser Aletschgletscher, Switzerland, the largest glacier in the European Alps. A three-dimensional combined surface mass-balance and glacier dynamics model was applied. The ice flow was described with the full Stokes equations. The glacier surface evolution was obtained by solving a transport equation for the volume of fluid. Daily surface melt and accumulation were calculated on the basis of climate data. The combined model was validated against several types of measurements made throughout the 20th century. For future climate change, scenarios based on regional climate models in the ENSEMBLES project were used. According to the median climatic evolution, Aletschgletscher was expected to lose 90% of its ice volume by the end of 2100. Even when the model was driven using current climate conditions (the past two decades) the glacier tongue experienced a considerable retreat of 6 km, indicating its strong disequilibrium with the present climate. By including a model for the evolution of supraglacial debris and its effect in reducing glacier melt, we show that this factor can significantly slow future glacier retreat.