MODELLING GLACIER AND RUNOFF CHANGES IN THE ALPS & HIMALAYA

Glacier melt within alpine catchments provides a vital component of runoff that constitutes an important water resource for downstream populations. With future climate changes, it is expected that glacier volume change will be considerable in the coming decades, with associated implications for runoff. Estimation of future changes in glacier volume and catchment runoff is therefore essential for understanding future water resource implications in alpine environments. This thesis focuses on glacier volume and runoff changes predicted using the statistical model GERM (Glacier Evolution and Runoff Model; Huss et al., 2008a) and has three novel aims. Firstly, to provide more robust assessments of the modelling uncertainty associated with predicted glacier and runoff changes from alpine catchments than previous studies, by challenging the model to reproduce historic changes in glacier volume and evolution over 120 year periods, and comparing predicted and measured runoff. Secondly, to use this assessment of uncertainty to contextualise and understand the precision of future (to 2100 AD) runoff projections for alpine catchments under a wide range of possible climate changes scenarios. Thirdly, to develop the model so that it can be applied to a debris-covered, downwasting glacier in the Himalaya. Two further novel aspects of this thesis are the development of a more systematic and robust calibration procedure for GERM, and the application of climate data downscaling techniques that are more sophisticated than have hitherto been applied in glacio-hydrological studies. To achieve aim 1, GERM was used to forward model glacier volume and runoff for the Griesgletscher and Rhonegletscher catchments in the European Alps from 1884-2004. As a statistical model that requires catchment-specific calibration, GERM was first calibrated to each catchment using contemporary glacier volume and catchment runoff measurements (as is standard when using the model for future projections). Digital elevation models were then used to obtain the initial glacier geometry required to begin each model run, and each completed model run was subsequently used to estimate the accumulated uncertainty associated with the predicted glacier volume/runoff changes by comparing modelled with observed glacier volume/runoff change at the end of the simulation. To achieve aim 2, future model runs (2010-2100) were conducted for the same two catchments and the glacier volume/runoff uncertainty calculated from model performance in the past (aim 1) applied to future projections. Future simulations were driven by a wide-range of climate inputs to allow quantification of the uncertainty associated with climate scenarios/models. The combination of these two sources of uncertainty (GERM and climate) provides future II projections with greater awareness and better quantification of uncertainties than previous studies. Finally, to achieve aim 3, GERM was applied to the debris-covered Khumbu Glacier by adjusting the mass redistribution process of GERM (Δh-parameterisation) to reflect the downwasting behaviour of the debris-covered glacier tongue, based on observed thinning rates at Khumbu Glacier. Additionally, to account for the insulating effect of debris on ice, the modelled melt rate was reduced in proportion to debris thickness on a spatially distributed basis (i.e. debris thickness was not uniform) using observations of reduced melt at glaciers close to Khumbu. Improvements to the calibration procedure used when applying GERM were made and applied throughout this thesis by developing an automated calibration which systematically adjusts the parameters, calculates a combined goodness-of-fit statistic that allows comparison to observations of both glacier volume and runoff, and selects the optimal parameter set. Improved downscaling methods were also used and applied to all future volume and runoff change projections made during this thesis. Specifically, state-of-the-art General Circulation Model simulations were dynamically-statistically downscaled using Regional Climate Model simulations and quantile mapping, and were used to drive future model runs at all three sites. Finally, the novel adjustments made to the mass redistribution process and the inclusion of reduced melt beneath debris indicate that GERM can now be applied to debris-covered glaciers. A recommendation for future research is that GERM is further tested on additional debris- covered glaciers and applied to additional catchments in the larger Everest region. The results of the uncertainty analyses (aim 1) show that glacio-hydrological model uncertainty amounts to annual runoff errors of ±0.04 106m3yr-1 (±0.15 % yr-1), and glacier volume errors of ±0.16 % yr-1, over time periods of 120 years at Griesgletscher. At Rhonegletscher, the uncertainty assessment resulted in annual runoff errors of ±0.16 106m3yr-1 (±0.2 % yr-1) and glacier volume errors of ±0.13 % yr-1, over time periods of 120 years. Nonetheless, the key finding is that the main sources of future uncertainty relate to emissions scenarios and GCM-RCM (General Circulation Model - Regional Climate Model), combinations which lead to variations in predicted future runoff in 2100 of ±36 % at Griesgletscher and ±20 % at Rhonegletscher. The results of the future simulations (aims 2 and 3) indicate that all three glaciers that form the focus of this thesis will lose considerable volume. Specifically, by 2100, Griesgletscher is likely to have become an ice-free catchment (87-100 % ice loss); Rhonegletscher will have lost 70-90 % of ice; and Khumbu Glacier will have lost 61-92 % of ice. The results further show that mass losses will cause an initial increase in annual river discharge followed by a decline in discharge levels, such that annual discharge by 2100 will be considerably lower than present, with peak discharge at Griesgletscher occurring in 2020, at Rhonegletscher in 2075, and at Khumbu Glacier in 2045

Modelling the trajectory of the corpses of mountaineers who disappeared in 1926 on Aletschgletscher, Switzerland

In this paper we reconstruct the space–time trajectory beneath the surface of Aletschgletscher, Switzerland, of the corpses of three mountaineers that disappeared in March 1926 and reappeared at the glacier surface in June 2012. Our method integrates the time-dependent velocity field of an existing full-Stokes glacier model, starting at the point where the corpses were found at the glacier surface. Our main result is that we were able to localize the immersion location where the brothers presumably died. As a second result, the upstream end point of the computed trajectory emerges very close to the glacier surface in 1926, giving a new and global validation of the glacier model in space and time. Testing the sensitivity of the immersion location obtained with respect to the model and other uncertainties indicates an area of 0.6% of the entire glacier area where the accident could have occurred. Our result suggests that death was not caused by an avalanche or a fall into a crevasse; instead, it is likely that the mountaineers became disoriented in prolonged severe weather conditions and froze to death

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

Jordan R. Mertes acknowledges funding from Michigan Technological University and The Michigan Technological University 2016 Fall Finishing Fellowship. Lindsey Nicholson is supported by the Austrian Science Fund (FWF) Grant V309-N26.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 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 Himalaya. We used terrestrial field photos from 1896, high oblique aerial photos from 1936 and aerial handheld photos from 1978 to generate 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 upglacier. 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).PostprintPeer reviewe

Modélisation, analyse mathématique et simulation numérique de la dynamique des glaciers

We address the free boundary problem that consists in finding the shape of a three dimensional glacier over a given period and under given climatic conditions. Glacier surface moves by sliding, internal shear and external exchange of mass. Ice is modelled as a non Newtonian fluid. Given the shape of the glacier, the velocity of ice is obtained by solving a stationary non-linear Stokes problem with a sliding law along the bedrock-ice interface. The shape of the glacier is updated by computing a Volume Of Fluid (VOF) function, which satisfies a transport equation. Climatic effects (accumulation and ablation of ice) are taken into account in the source term of this equation. A decoupling algorithm with a two-grid method allows the velocity of ice and the VOF to be computed using different numerical techniques, such that a Finite Element Method (FEM) and a characteristics method. On a theoretical level, we prove the well-posedness of the non-linear Stokes problem. A priori estimates for the convergence of the FEM are established by using a quasi-norm technique. Eventually, convergence of the linearisation schemes, such that a fixed point method and a Newton method, is proved. Several applications demonstrate the potential of the numerical method to simulate the motion of a glacier during a long period. The first one consists in the simulation of Rhone et Aletsch glacier from 1880 to 2100 by using climatic data provided by glaciologists. The glacier reconstructions over the last 120 years are validated against measurements. Afterwards, several different climatic scenarios are investigated in order to predict the shape the glaciers until 2100. A dramatic retreat during the 21st century is anticipated for both glaciers. The second application is an inverse problem. It aims to find a climate parametrization allowing a glacier to fit some of its moraines. Two other aspects of glaciology are also addressed in this thesis. The first one consists in modeling and in simulating ice collapse during the calving process. The previous ice flow model is supplemented by a Damage variable which describes the presence of micro crack in ice. An additional numerical scheme allows the Damage field to be solved and a two dimensional simulation of calving to be performed. The second problem aims to prove the existence of stationary ice sheet when considering shallow ice model and a simplified geometry. Numerical investigation confirms the theoretical result and shows physical properties of the solution

Analysis and finite element approximation of a nonlinear stationary stokes problem arising in glaciology

The aim of this paper is to study a nonlinear stationary Stokes problem with mixed boundary conditions that describes the ice velocity and pressure fields of grounded glaciers under Glen's flow law. Using convex analysis arguments, we prove the existence and the uniqueness of a weak solution. A finite element method is applied with approximation spaces that satisfy the inf-sup condition, and a priori error estimates are established by using a quasinorm technique. Several algorithms (including Newton's method) are proposed to solve the nonlinearity of the Stokes problem and are proved to be convergent. Our results are supported by numerical convergence studies

Deep learning speeds up ice flow modelling by several orders of magnitude

This paper introduces the Instructed Glacier Model (IGM) – a model that simulates ice dynamics, mass balance and its coupling to predict the evolution of glaciers, icefields or ice sheets. The novelty of IGM is that it models the ice flow by a Convolutional Neural Network, which is trained from data generated with hybrid SIA + SSA or Stokes ice flow models. By doing so, the most computationally demanding model component is substituted by a cheap emulator. Once trained with representative data, we demonstrate that IGM permits to model mountain glaciers up to 1000 × faster than Stokes ones on Central Processing Units (CPU) with fidelity levels above 90% in terms of ice flow solutions leading to nearly identical transient thickness evolution. Switching to the GPU often permits additional significant speed-ups, especially when emulating Stokes dynamics or/and modelling at high spatial resolution. IGM is an open-source Python code which deals with two-dimensional (2-D) gridded input and output data. Together with a companion library of trained ice flow emulators, IGM permits user-friendly, highly efficient and mechanically state-of-the-art glacier and icefields simulations

Modelling the future evolution of glaciers in the European Alps under the EURO-CORDEX RCM ensemble

Glaciers in the European Alps play an important role in the hydrological cycle, act as a source for hydroelectricity and have a large touristic importance. The future evolution of these glaciers is driven by surface mass balance and ice flow processes, of which the latter is to date not included explicitly in regional glacier projections for the Alps. Here, we model the future evolution of glaciers in the European Alps with GloGEMflow, an extended version of the Global Glacier Evolution Model (GloGEM), in which both surface mass balance and ice flow are explicitly accounted for. The mass balance model is calibrated with glacier-specific geodetic mass balances and forced with high-resolution regional climate model (RCM) simulations from the EURO-CORDEX ensemble. The evolution of the total glacier volume in the coming decades is relatively similar under the various representative concentrations pathways (RCP2.6, 4.5 and 8.5), with volume losses of about 47&thinsp;%–52&thinsp;% in 2050 with respect to 2017. We find that under RCP2.6, the ice loss in the second part of the 21st century is relatively limited and that about one-third (36.8&thinsp;%&thinsp;±&thinsp;11.1&thinsp;%, multi-model mean ±1σ) of the present-day (2017) ice volume will still be present in 2100. Under a strong warming (RCP8.5) the future evolution of the glaciers is dictated by a substantial increase in surface melt, and glaciers are projected to largely disappear by 2100 (94.4±4.4&thinsp;% volume loss vs. 2017). For a given RCP, differences in future changes are mainly determined by the driving global climate model (GCM), rather than by the RCM, and these differences are larger than those arising from various model parameters (e.g. flow parameters and cross-section parameterisation). We find that under a limited warming, the inclusion of ice dynamics reduces the projected mass loss and that this effect increases with the glacier elevation range, implying that the inclusion of ice dynamics is likely to be important for global glacier evolution projections.</p

Potential climatic transitions with profound impact on Europe

We discuss potential transitions of six climatic subsystems with large-scale impact on Europe, sometimes denoted as tipping elements. These are the ice sheets on Greenland and West Antarctica, the Atlantic thermohaline circulation, Arctic sea ice, Alpine glaciers and northern hemisphere stratospheric ozone. Each system is represented by co-authors actively publishing in the corresponding field. For each subsystem we summarize the mechanism of a potential transition in a warmer climate along with its impact on Europe and assess the likelihood for such a transition based on published scientific literature. As a summary, the ‘tipping’ potential for each system is provided as a function of global mean temperature increase which required some subjective interpretation of scientific facts by the authors and should be considered as a snapshot of our current understanding. <br/

État des lieux des représentations dynamiques des temporalités des territoires

Le temps et ses caractéristiques ont toujours fait l’objet de grandes attentions pour comprendre les dynamiques des territoires. Aujourd’hui, que ce soit à cause des nouvelles capacités d’observation en temps réel, de l’accumulation des séries de données au cours du temps, ou à cause de la multiplication des rythmes, les temporalités à prendre en compte pour comprendre les dynamiques territoriales se multiplient et leurs imbrications se complexifient. Interroger les rythmes, les vitesses, les cycles de ces dynamiques, ou mettre en relation temporelle des phénomènes spatiaux tels que les évènements catastrophiques passés devient plus que jamais un enjeu pour comprendre et décider.Les jeux de méthodes mobilisables aujourd’hui pour représenter les temporalités des territoires sont en plein renouvellement, et imposent désormais bien souvent de franchir les fractures disciplinaires traditionnelles entre échelles, entre outils, entre formalismes. Les domaines d’applications potentiellement concernés, comme celui du développement durable des territoires, sont autant de domaines susceptibles de nourrir les questions associées à l’exploration des temporalités des territoires. Le projet "Représentation dynamique des temporalités des territoires" se veut un état des lieux de différents développements et solutions pour analyser et rendre compte des temporalités des territoires. Cet état des lieux est à entrées multiples, interrogeant à la fois des choix amont (modélisation) et des choix proprement liés à la question de la représentation. Le projet débouche sur un ensemble de résultats dont certains sont mis en ligne sur le site: http://www.map.cnrs.fr/jyb/puca/- Une grille de lecture de la collection d'applications analysée (voir onglet "47 applications"), grille où sont combinés des indicateurs généraux sur par exmeple le type de service rendu ou le type de dynamique spatiale analysée, et des indicateurs plus spécifiques au traitement des dimensions spatiales et temporelles. Cette grille est mise en place sur 47 applications identifiées et analysées,- Des visualisations récapitulatives conçues comme outils d'analyse comparative de la collection,- Une bibliographie structurée en relation avec la grille de lecture