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

Ice-flow model emulator based on physics-informed deep learning

Convolutional neural networks (CNN) trained from high-order ice-flow model realisations have proven to be outstanding emulators in terms of fidelity and computational performance. However, the dependence on an ensemble of realisations of an instructor model renders this strategy difficult to generalise to a variety of ice-flow regimes found in the nature. To overcome this issue, we adopt the approach of physics-informed deep learning, which fuses traditional numerical solutions by finite differences/elements and deep-learning approaches. Here, we train a CNN to minimise the energy associated with high-order ice-flow equations within the time iterations of a glacier evolution model. As a result, our emulator is a promising alternative to traditional solvers thanks to its high computational efficiency (especially on GPU), its high fidelity to the original model, its simplified training (without requiring any data), its capability to handle a variety of ice-flow regimes and memorise previous solutions, and its relatively simple implementation. Embedded into the ‘Instructed Glacier Model’ (IGM) framework, the potential of the emulator is illustrated with three applications including a large-scale high-resolution (2400x4000) forward glacier evolution model, an inverse modelling case for data assimilation, and an ice shelf

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

Future retreat of Great Aletsch Glacier

We model the future evolution of the largest glacier of the European Alps – Great Aletsch Glacier, Switzerland – during the 21st century. For that purpose we use a detailed three-dimensional model, which combines full Stokes ice dynamics and surface mass balance forced with the most recent climate projections (CH2018), as well as with climate data of the last decades. As a result, all CH2018 climate scenarios yield a major glacier retreat: Results range from a loss of 60% of today's ice volume by 2100 for a moderate CO2 emission scenario (RCP2.6) being in line with the Paris agreement to an almost complete wastage of the ice for the most extreme emission scenario (RCP8.5). Our model results also provide evidence that half of the mass loss is already committed under the climate conditions of the last decade

Glacial and erosional contributions to Late Quaternary uplift of the European Alps (GEOLQUEA)

Isostatic adjustments of the Earth’s surface to changes in water, ice, and sediment loading are important contributions to present-day uplift/subsidence rates in many regions on Earth. In the absence of significant horizontal tectonic shortening in the central and western parts of the European Alps, uplift rates larger than 2 mm/yr are difficult to explain by geodynamic processes and have been a matter of debate for many decades. Here we examine the likely contribution of glacial isostatic adjustment in the European Alps in response to changes in ice loading using state of the art ice flow and lithospheric numerical modeling. In contrast to a similar previous approach (Mey et al., 2016), we employ a transient ice sheet model over the last glacial cycle (100 kyr) in combination with a spherical viscoelastic solid earth model. We present ice model results using the Instructed Glacier Model (Jouvet et al., 2021), in which we tested the effect of spatial resolution on the growth and extent of the European ice cap. We found significant differences using a model resolution of 200 m compared to a resolution of 2000 m, which is commonly used in large-scale glacier modeling studies. These differences result in near-steady state volumetric differences at the maximum ice extent of +13% for the high compared to the low-resolution model. In addition, we observed periods of marked ice growth that initiated at significantly different times for the different resolution models. Therefore, we conclude that a realistic ice loading history requires a sufficiently high spatial resolution, which is significantly higher than used in previous models. Based on the modeled ice loading histories, we used the lithosphere and mantle model VILMA (Klemann et al., 2008, J. Geodyn.) to predict the vertical land motion. These estimates are based on a global 60 km thick elastic lithosphere, followed by a 200 km thick viscous layer with a viscosity of 1020 Pa s, which increases to 5 x 1020 Pa s down to 670 km depth, and 3.16 x 1021 Pa s to the core mantle boundary. Preliminary results indicate similar first-order lithospheric responses, with spatiotemporal differences in the magnitude of postglacial response. We hope to present more results based on further ice models that are forced by a more realistic climate history

Detecting of a Patient's Condition From Clinical Narratives Using Natural Language Representation

The rapid progress in clinical data management systems and artificial intelligence approaches enable the era of personalized medicine. Intensive care units (ICUs) are the ideal clinical research environment for such development because they collect many clinical data and are highly computerized environments. We designed a retrospective clinical study on a prospective ICU database using clinical natural language to help in the early diagnosis of heart failure in critically ill children. The methodology consisted of empirical experiments of a learning algorithm to learn the hidden interpretation and presentation of the French clinical note data. This study included 1386 patients' clinical notes with 5444 single lines of notes. There were 1941 positive cases (36 % of total) and 3503 negative cases classified by two independent physicians using a standardized approach. The multilayer perceptron neural network outperforms other discriminative and generative classifiers. Consequently, the proposed framework yields an overall classification performance with 89 % accuracy, 88 % recall, and 89 % precision. Furthermore, a generative autoencoder learning algorithm was proposed to leverage the sparsity reduction that achieved 91% accuracy, 91% recall, and 91% precision. This study successfully applied learning representation and machine learning algorithms to detect heart failure from clinical natural language in a single French institution. Further work is needed to use the same methodology in other institutions and other languages.Comment: Submitting to IEEE Transactions on Biomedical Engineering. arXiv admin note: text overlap with arXiv:2104.0393

Observational constraints on the sensitivity of two calving glaciers to external forcings

Future mass loss projections of the Greenland ice sheet require understanding of the processes at a glacier terminus, especially of iceberg calving. We present detailed and high-rate terrestrial radar interferometer observations of Eqip Sermia and Bowdoin Glacier, two outlet glaciers in Greenland with comparable dimensions and investigate iceberg calving, surface elevation, velocity, strain rates and their links to air temperature, tides and topography. The results reveal that the two glaciers exhibit very different flow and calving behaviour on different timescales. Ice flow driven by a steep surface slope with several topographic steps leads to high velocities, areas of extension and intense crevassing, which triggers frequent but small calving events independent of local velocity gradients. In contrast, ice flow under smooth surface slopes leaves the ice relatively intact, such that sporadic large-scale calving events dominate, which initiate in areas with high shearing. Flow acceleration caused by enhanced meltwater input and tidal velocity variations were observed for terminus sections close to floatation. Firmly grounded terminus sections showed no tidal signal and a weak short-term reaction to air temperature. These results demonstrate reaction timescales to external forcings from hours to months, which are, however, strongly dependent on local terminus geometry

Crystallographic analysis of temperate ice on Rhonegletscher, Swiss Alps

Crystal orientation fabric (COF) analysis provides information about the c-axis orientation of ice grains and the associated anisotropy and microstructural information about deformation and recrystallisation processes within the glacier. This information can be used to introduce modules that fully describe the microstructural anisotropy or at least direction-dependent enhancement factors for glacier modelling. The COF was studied at an ice core that was obtained from the temperate Rhonegletscher, located in the central Swiss Alps. Seven samples, extracted at depths between 2 and 79 m, were analysed with an automatic fabric analyser. The COF analysis revealed conspicuous four-maxima patterns of the c-axis orientations at all depths. Additional data, such as microstructural images, produced during the ice sample preparation process, were considered to interpret these patterns. Furthermore, repeated high-precision global navigation satellite system (GNSS) surveying allowed the local glacier flow direction to be determined. The relative movements of the individual surveying points indicated longitudinal compressive stresses parallel to the glacier flow. Finally, numerical modelling of the ice flow permitted estimation of the local stress distribution. An integrated analysis of all the data sets provided indications and suggestions for the development of the four-maxima patterns. The centroid of the four-maxima patterns of the individual core samples and the coinciding maximum eigenvector approximately align with the compressive stress directions obtained from numerical modelling with an exception for the deepest sample. The clustering of the c axes in four maxima surrounding the predominant compressive stress direction is most likely the result of a fast migration recrystallisation. This interpretation is supported by air bubble analysis of large-area scanning macroscope (LASM) images. Our results indicate that COF studies, which have so far predominantly been performed on cold ice samples from the polar regions, can also provide valuable insights into the stress and strain rate distribution within temperate glaciers