388 research outputs found

    Finite elements numerical solution of a coupled profile–velocity–temperature shallow ice sheet approximation model

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    AbstractThis work deals with the numerical solution of a complex mathematical model arising in theoretical glaciology. The global moving boundary problem governs thermomechanical processes jointly with ice sheet hydrodynamics. One major novelty is the inclusion of the ice velocity field computation in the framework of the shallow ice model so that it can be coupled with profile and temperature equations. Moreover, the proposed basal velocity and shear stress laws allow the integration of basal sliding effects in the global model. Both features were not taking into account in a previous paper (Math. Model. Methods Appl. Sci. 12 (2) (2002) 229) and provide more realistic convective terms and more complete Signorini boundary conditions for the thermal problem. In the proposed numerical algorithm, one- and two-dimensional piecewise linear Lagrange finite elements in space and a semi-implicit upwinding scheme in time are combined with duality and Newton's methods for nonlinearities. A simulation example involving real data issued from Antarctic shows the temperature, profile and velocity qualitative behaviour as well as the free boundaries and basal effects

    The shallow shelf approximation as a "sliding law" in a thermomechanically coupled ice sheet model

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    The shallow shelf approximation is a better ``sliding law'' for ice sheet modeling than those sliding laws in which basal velocity is a function of driving stress. The shallow shelf approximation as formulated by \emph{Schoof} [2006a] is well-suited to this use. Our new thermomechanically coupled sliding scheme is based on a plasticity assumption about the strength of the saturated till underlying the ice sheet in which the till yield stress is given by a Mohr-Coulomb formula using a modeled pore water pressure. Using this scheme, our prognostic whole ice sheet model has convincing ice streams. Driving stress is balanced in part by membrane stresses, the model is computable at high spatial resolution in parallel, it is stable with respect to parameter changes, and it produces surface velocities seen in actual ice streams.Comment: 12 pages of text; 4 tables; 27 figures; submitted to JGR Earth Surfac

    Global-scale modelling of glaciers, ice sheets and permafrost : recommendations for Hydro-JULES

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    This report is part of the Hydro-JULES research programme supported by NERC National Capability funding (grant number: NE/S017380/1) to the UK Centre for Ecology & Hydrology (UKCEH), British Geological Survey (BGS) and National Centre for Atmospheric Science (NCAS). Hydro-JULES will deliver an open-source, three-dimensional community model of the terrestrial water cycle. As part of work package 4, the BGS will develop an enhanced representation of groundwater in Hydro-JULES and link it to land-surface processes, with the aim of implementing the model on a global scale. In cold regions, glaciers, ice sheets and permafrost influence regional groundwater flow and recharge processes. This report aims to facilitate the inclusion of cryosphere–groundwater systems in the Hydro-JULES modelling framework by reviewing potential modelling approaches and then prioritising a set of model developments that should be undertaken as part of the ongoing development of the Hydro-JULES modelling framework. All outputs from the HydroJULES programme (including this report) are open and freely available to ensure transparency and auditability in the development of the scientific approach

    Analysis of Recent Dynamic Changes of Jakobshavn Isbrae, West Greenland, using a Thermomechanical Model

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    Jakobshavn Isbrae is a major marine terminating outlet glacier of the western Greenland Ice Sheet, which has been undergoing widespread acceleration and strong mass loss since the disintegration of its floating ice tongue in the late 1990s. The underlying mechanisms are poorly understood despite a wealth in observational and modelling studies. This doctoral thesis analyses the dynamic changes of Jakobshavn Isbrae using the Ice Sheet System Model (ISSM), a state-of-the-art finite-element ice flow model. Two missing model features for 1) the modelling the polythermal regime of glaciers and ice sheets, and 2) the dynamic evolution of its horizontal calving front position are designed and implemented into ISSM. A three-dimensional, thermodynamically coupled model of Jakobshavn Isbrae is set up and calibrated using modern observational data products. Low basal drag in the trough under the ice stream requires that its high driving stress is balanced by lateral drag in the shear margins, which allows for high flow velocities, as the ice viscosity is strain-rate-dependent. The developed modules are applied to the glacier model, which captures 90% of the observed changes from 1985 to 2015. Analysis of the model results reveals that calving front retreat is able to trigger widespread inland acceleration due to a rheological ice viscosity drop in the shear margins. Thermal feedbacks contribute 5 to 10% to the total acceleration. The study shows that Jakobshavn Isbrae will continue to contribute to eustatic sea level rise for at least the next century due to ongoing geometry adjustment to the new calving front position. Future fields of research include deriving a suitable calving rate parametrisation for large-scale ice flow models, a material law for temperate ice with a microscopic water content larger than 1%, and technical refinements of the modules developed for this thesis

    Effect of a Cold Margin on Ice Flow at the Terminus of Storglaciaren, Sweden: Implications for Sediment Transfer

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    The cold-based termini of polythermal glaciers are usually assumed to adhere strongly to an immobile substrate and thereby supply significant resistance to the flow of warm-based ice upglacier. This compressive environment is commonly thought to uplift basal sediment to the surface of the glacier by folding and thrust faulting. We present model and field evidence from the terminus of Storglaciaren, Sweden, showing that the cold margin provides limited resistance to flow from up-glacier. Ice temperatures indicate that basal freezing occurs in this zone at 10−1 –10−2 ma−1, but model results indicate that basal motion at rates greater than 1ma−1 must, nevertheless, persist there for surface and basal velocities to be consistent with measurements. Estimated longitudinal compressive stresses of 20– 25 kPa within the terminus further indicate that basal resistance offered by the cold-based terminus is small. These results indicate that where polythermal glaciers are underlain by unlithified sediments, ice-flow trajectories and sediment transport pathways may be affected by subglacial topography and hydrology more than by the basal thermal regime

    Present State and Prospects of Ice Sheet and Glacier Modelling

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    Since the late 1970s, numerical modelling has become established as an important technique for the understanding of ice sheet and glacier dynamics, and several models have been developed over the years. Ice sheet models are particularly relevant for predicting the possible response of ice sheets to climate change. Recent observations suggest that ice dynamics could play a crucial role for the contribution of ice sheets to future sea level rise under global warming conditions, and the need for further research into the matter was explicitly stated in the Fourth Assessment Report (AR4) of the United Nations Intergovernmental Panel on Climate Change (IPCC). In this paper, we review the state of the art and current problems of ice sheet and glacier modelling. An outline of the underlying theory is given, and crucial processes (basal sliding, calving, interaction with the solid Earth) are discussed. We summarise recent progress in the development of ice sheet and glacier system models and their coupling to climate models, and point out directions for future wor

    Variational Methods in Ice Sheet Modelling

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    A complete simulation of flowing ice requires knowledge of both the fundamental physical principles that govern the stress and energy balances and a framework for assimilating data into a model to help estimate unknown parameters. Modelling ice is complex, due to the large spatial extent of ice sheets, the multiple scales at which relevant physics operate, and the coupling between heat, stress, and ice rheology. As such, it is usually necessary to make approximations to the equations governing ice flow. At the same time, it is important to have an understanding of the specific assumptions that lead to these approximations. We develop a variational principle for Stokes flow, and neglect certain components in order to obtain the variational principle for the first-order approximation for ice flow. This result is fundamentally the result of assuming bed slopes to be much less than surface slopes, and that vertical resistive stresses are negligible. From a practical standpoint, using automatic differentiation tools on this functional yields a compact model of ice flow that automatically incorporates correct boundary condition. This model is compared to well known benchmark tests. We also present an improved model of ice thermodynamics that operates on enthalpy rather than temperature, avoiding many of the difficulties associated with phase change. We derive a method for inverting the Blatter-Pattyn ice sheet model in order to solve for the rate of basal sliding. This method uses the adjoint equations of the forward model to obtain the gradient of an error functional, and this is minimized using a quasi-Newton method. These methods are applied to an instrumented streamline of the Greenland ice sheet. We perform numerical experiments on this geometry in order to assess the sensitivity of thermal conditions at the ice sheet bed to perturbations in unknown parameters. The basal thermal regime is sensitive to changes in geothermal heat flux, with the location of the transition zone between cold and temperate ice being linear sensitive to changes in it. The temperature field of the ice sheet is insensitive to downstream changes in sliding speed due to the short length scales over which longitudinal coupling acts

    An efficient regional energy-moisture balance model for simulation of the Greenland Ice Sheet response to climate change

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    In order to explore the response of the Greenland ice sheet (GIS) to climate change on long (centennial to multi-millennial) time scales, a regional energy-moisture balance model has been developed. This model simulates seasonal variations of temperature and precipitation over Greenland and explicitly accounts for elevation and albedo feedbacks. From these fields, the annual mean surface temperature and surface mass balance can be determined and used to force an ice sheet model. The melt component of the surface mass balance is computed here using both a positive degree day approach and a more physically-based alternative that includes insolation and albedo explicitly. As a validation of the climate model, we first simulated temperature and precipitation over Greenland for the prescribed, present-day topography. Our simulated climatology compares well to observations and does not differ significantly from that of a simple parameterization used in many previous simulations. Furthermore, the calculated surface mass balance using both melt schemes falls within the range of recent regional climate model results. For a prescribed, ice-free state, the differences in simulated climatology between the regional energy-moisture balance model and the simple parameterization become significant, with our model showing much stronger summer warming. When coupled to a three-dimensional ice sheet model and initialized with present-day conditions, the two melt schemes both allow realistic simulations of the present-day GIS

    Changes in the seawater salinity-oxygen isotope relation between last glacial and present: sediment core data and OGCM modelling

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    The presently available paleotemperature data implies large ice-free areas in the Greenland- Iceland-Norwegian Seas during the Last Glacial Maximum 21 600 yr BP. From these temperatures and the independent measurements of oxygen isotope ratios of fossil foraminiferal shells, glacial sea surface salinities could be computed, if the glacial relation between salinity and water isotope ratio was known. For this study, a three-dimensional numerical ocean circulation model was employed to investigate the possible shape of this still not precisely known relation, and to reconstruct a physically consistent scenario of the northern North Atlantic for the glacial summer. This scenario turned out to be quite similar to modern winter conditions, whereas the required salinity vs. oxygen isotope relation of this time must have been very different from its modern counterpart
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