Finite Element Analysis of Small Scale Continuous Calving

Ice shelves are floating ice masses, which are sensitive to climate changes. The main mechanisms for the mass loss of ice shelves around Antarctica are basal melting and calving. For an understanding of the mechanisms of calving the influence of environmental parameters needs to be investigated. We use a fracture mechanical approach to examine the nature and frequency of calving events. Ice responses to load in two ways: on long time scales ice reacts like a viscous fluid, and on short time scale like an elastic solid. As calving is a representation of the solid nature of ice, the elastic response is important and linear elastic fracture mechanics can be applied. However, gravity remains a long time load and hence, a viscous component needs to be taken into account as well. Therefore, we use a Kelvin-Voigt model for analyzing the transient response of an ice shelf to a calving event. In a simplified 2D-model the ice shelf is treated as a rectangular block, in which the gravity force is the only load in a first analysis. The stresses on the surface in the vicinity of the calving front are computed with the finite element software COMSOL. The boundary conditions are the water pressure at the front and bottom of the ice shelf and a constant displacement at the inflow. A stationary state will reappear until eventually the subsequent calving event occurs, the termination time is around 175days. Based on this time interval and the flow velocity of the ice shelf we estimate the calving rate. Different parameter studies reveal the influence of geometry and material parameters on the stresses for an elastic material model. The literature and measurements at the Ekstroem Ice Shelf, East Antarctica, provides the relevant parameter range. Due to the depth-dependent water pressure at the ice front, a bell shaped distribution of stresses on the surface is found. For this reason the location of the maximal stress denotes the most likely position for a calving event and is arranged in between 0.65H and 0.85H, with H the thickness at the ice front. The results of these studies are compared to the results for two cross-sections of measured geometries of the Ekstroem Ice Shelf

A Law for Small Scale, Continuous Calving

Ice shelves are formed by the viscous flow of inland ice into the ocean, they are floating and loosing mass by iceberg calving. There are two different kinds of calving: large tabular icebergs detach as singular events in time, and small scale calving occuring on a rather continuous time scale. Three visco-elastic approaches are discussed, in order to derive a general law for calving rates applicable to small scale calving. The results are highly dependent on the termination criterium for each approach, hence the computed calving rate has to be adapted and validated with measurements to get the most qualified value

Discussion of Different Model Approaches for the Flow Behavior of Ice

Ice of Antarctic ice shelves is assumed to behave on long-term as an incompressible viscous fluid, which is dominated on short time scales by the elastic response. Hence, a viscoelastic material model is required. The thermodynamic pressure is treated differently in elastic and viscous models. For small deformations, the elastic isometric stress for ν → 0.5 gives similar results to those solving for pressure in an incompressible laminar flow model. A viscous model, in which the thermodynamic pressure is approximated by an elastic isometric stress, can be easily extended to viscoelasticity

Enteignung oder Rückkauf? Wie begriffliche Rahmung politische Meinungen beeinflusst!

Die sprach- und denkpsychologische Forschung hat nachgewiesen, dass die sprachliche Benennung von politischen Ereignissen und Konzepten die allgemeine Meinung dazu beeinflusst (Modell der begrifflichen Rahmung: Framing-Ansatz). In einer aktuellen Online-Studie (10./11.4. 2019 mit 300 TeilnehmerInnen) wurde untersucht, inwieweit das auch für die Benennung als ‚Enteignung’ oder ‚Rückkauf’ für den derzeit diskutierten Vorschlag gilt, dass die Kommunen vor Jahren verkaufte Sozialwohnungen wieder zurückkaufen.Es zeigt sich, dass bei der Benennung als ‚Enteignung’ mit dem Vorschlag häufiger ein (finanzieller) Verlust für die Wohnungsgesellschaften als derzeitige Eigentümer verbunden wird im Vergleich zur begrifflichen Rahmung als ‚Rückkauf’ (und umgekehrt für Nicht-Verlust). Dementsprechend werden (als Hauptergebnis) der Vorschlag und die damit verbundenen Maßnahmen unter der Rahmung ‚Enteignung’ im Vergleich zur Benennung als ‚Rückkauf’ sowohl für weniger sinnvoll als auch für schlechter durchführbar gehalten. Dabei gibt es einen Einfluss der politischen Links-Rechts-Orientierung der Personen: Unabhängig von der begrifflichen Rahmung halten eher links Orientierte die Maßnahme für sinnvoller als eher rechts Orientierte; in Bezug auf die Durchführbarkeit sehen links Orientierte eine bessere Durchführbarkeit bei der Benennung als Rückkauf, für eher rechts Orientierte macht die Benennung hier keinen Unterschied (in ihrer kritischeren Haltung zur vorgeschlagenen Maßnahme). Praktische Konsequenz für die Verfechter der Maßnahme (z.B. Volksbegehren in Berlin): Sie sollten berücksichtigen, dass die Akzeptanz ihres Vorschlags (mit) von der Benennung abhängt. Und die Medien(-Macher) sollten sich ihres Einflusses auf die Meinungsbildung durch die sprachliche Darstellung von politischen Ereignissen und Konzepten bewusst sein

Viscous and viscoelastic stress states at the calving front of Antarctic ice shelves

Calving mechanisms are still poorly understood and stress states in the vicinity of ice-shelf fronts are insufficiently known for the development of physically motivated calving laws that match observations. A calving model requires the knowledge of maximum tensile stresses. These stresses depend on different simulation approaches and material models. Therefore, this study compares results of a two-dimensional (2-D) continuum approach using finite elements with results of a one- dimensional (1-D) beam model elaborated in Reeh (1968). A purely viscous model, as well as a viscoelas- tic Maxwell model, is applied for the 2-D case. The maximum tensile stress usually appears at the top surface of an ice shelf. Its location and magnitude are predominantly influenced by the thickness of the ice shelf and the height of the freeboard, the traction-free part at the ice front. More precisely, doub- ling the thickness leads to twice the stress maximum, while doubling the freeboard, based on changes of the ice density, results in an increase of the stress maximum by 61%. Poisson’s ratio controls the evolu- tion of the maximum stress with time. The viscosity and Young’s modulus define the characteristic time of the Maxwell model and thus the time to reach the maximum principal stress

On the evolution of an ice shelf melt channel at the base of Filchner Ice Shelf, from observations and viscoelastic modeling

Ice shelves play a key role in the stability of the Antarctic Ice Sheet due to their buttressing effect. A loss of buttressing as a result of increased basal melting or ice shelf disintegration will lead to increased ice discharge. Some ice shelves exhibit channels at the base that are not yet fully understood. In this study, we present in situ melt rates of a channel which is up to 330 m high and located in the southern Filchner Ice Shelf. Maximum observed melt rates are 2 m yr−1. Melt rates inside the channel decrease in the direction of ice flow and turn to freezing ∼55 km downstream of the grounding line. While closer to the grounding line melt rates are higher within the channel than outside, this relationship reverses further downstream. Comparing the modeled evolution of this channel under present-day climate conditions over 250 years with its present geometry reveals a mismatch. Melt rates twice as large as the present-day values are required to fit the observed geometry. In contrast, forcing the model with present-day melt rates results in a closure of the channel, which contradicts observations. The ice shelf experiences strong tidal variability in vertical strain rates at the measured site, and discrete pulses of increased melting occurred throughout the measurement period. The type of melt channel in this study diminishes in height with distance from the grounding line and is hence not a destabilizing factor for ice shelves.</p

Polarimetric radar reveals the spatial distribution of ice fabric at domes and divides in East Antarctica

Ice crystals are mechanically and dielectrically anisotropic. They progressively align under cumulative deformation, forming an ice-crystal-orientation fabric that, in turn, impacts ice deformation. However, almost all the observations of ice fabric are from ice core analysis, and its influence on the ice flow is unclear. Here, we present a non-linear inverse approach to process co- and cross-polarized phase-sensitive radar data. We estimate the continuous depth profile of georeferenced ice fabric orientation along with the reflection ratio and horizontal anisotropy of the ice column. Our method approximates the complete second-order orientation tensor and all the ice fabric eigenvalues. As a result, we infer the vertical ice fabric anisotropy, which is an essential factor to better understand ice deformation using anisotropic ice flow models. The approach is validated at two Antarctic ice core sites (EPICA (European Project for Ice Coring in Antarctica) Dome C and EPICA Dronning Maud Land) in contrasting flow regimes. Spatial variability in ice fabric characteristics in the dome-to-flank transition near Dome C is quantified with 20 more sites located along with a 36 km long cross-section. Local horizontal anisotropy increases under the dome summit and decreases away from the dome summit. We suggest that this is a consequence of the non-linear rheology of ice, also known as the Raymond effect. On larger spatial scales, horizontal anisotropy increases with increasing distance from the dome. At most of the sites, the main driver of ice fabric evolution is vertical compression, yet our data show that the horizontal distribution of the ice fabric is consistent with the present horizontal flow. This method uses polarimetric-radar data, which are suitable for profiling radar applications and are able to constrain ice fabric distribution on a spatial scale comparable to ice flow observations and models

Results of the third Marine Ice Sheet Model Intercomparison Project (MISMIP+)

We present the result of the third Marine Ice Sheet Model Intercomparison Project, MISMIP+. MISMIP+ is intended to be a benchmark for ice-flow models which include fast sliding marine ice streams and floating ice shelves and in particular a treatment of viscous stress that is sufficient to model buttressing, where upstream ice flow is restrained by a downstream ice shelf. A set of idealized experiments first tests that models are able to maintain a steady state with the grounding line located on a retrograde slope due to buttressing and then explore scenarios where a reduction in that buttressing causes ice stream acceleration, thinning, and grounding line retreat. The majority of participating models passed the first test and then produced similar responses to the loss of buttressing. We find that the most important distinction between models in this particular type of simulation is in the treatment of sliding at the bed, with other distinctions - notably the difference between the simpler and more complete treatments of englacial stress but also the differences between numerical methods - taking a secondary role. © 2020 Wolters Kluwer Medknow Publications. All rights reserved

Results of the third Marine Ice Sheet Model Intercomparison Project (MISMIP+)

We present the result of the third Marine Ice Sheet Model Intercomparison Project, MISMIP+. MISMIP+ is intended to be a benchmark for ice-flow models which include fast sliding marine ice streams and floating ice shelves and in particular a treatment of viscous stress that is sufficient to model buttressing, where upstream ice flow is restrained by a downstream ice shelf. A set of idealized experiments first tests that models are able to maintain a steady state with the grounding line located on a retrograde slope due to buttressing and then explore scenarios where a reduction in that buttressing causes ice stream acceleration, thinning, and grounding line retreat. The majority of participating models passed the first test and then produced similar responses to the loss of buttressing. We find that the most important distinction between models in this particular type of simulation is in the treatment of sliding at the bed, with other distinctions – notably the difference between the simpler and more complete treatments of englacial stress but also the differences between numerical methods – taking a secondary role