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

Indication of high basal melting at the EastGRIP drill site on the Northeast Greenland Ice Stream

The accelerated ice flow of ice streams that reach far into the interior of the ice sheets is associated with lubrication of the ice sheet base by basal meltwater. However, the amount of basal melting under the large ice streams – such as the Northeast Greenland Ice Stream (NEGIS) – is largely unknown. In situ measurements of basal melt rates are important from various perspectives as they indicate the heat budget, the hydrological regime and the relative importance of sliding in glacier motion. The few previous estimates of basal melt rates in the NEGIS region were 0.1 m/a and more, based on radiostratigraphy methods. These findings raised the question of the heat source, since even an increased geothermal heat flux could not deliver the necessary amount of heat. Here, we present basal melt rates at the recent deep drill site EastGRIP, located in the centre of NEGIS. Within 2 subsequent years, we found basal melt rates of 0.19±0.04 m/a that are based on analysis of repeated phase-sensitive radar measurements. In order to quantify the contribution of processes that contribute to melting, we carried out an assessment of the energy balance at the interface and found the subglacial water system to play a key role in facilitating such high melt rates

A confined-unconfined aquifer model for subglacial hydrology

Modeling the evolution of subglacial channels underneath ice sheets is an urgent need for ice sheet modellers, as channels affect sliding velocities and hence ice discharge. Owing to very limited observations of the subglacial hydraulic system, the development of physical models is quite restricted. Subglacial hydrology models are currently taking two different approaches: either modeling the development of a network of individual channels or modeling an equivalent porous layer where the channels are not resolved individually but modeled as a diffusive process, adjusted to reproduce the characteristic of an efficient system. Here, we use the latter approach, improving it by using a confined-unconfined aquifer model (CUAS), that allows the system to run dry in absence of sufficient water input. This ensures physical values for the water pressure. Channels are represented by adjusting the permeability and storage of the system according to projected locations of channels. The evolution of channel positions is governed by a reduced complexity model that computes channel growths according to simple rules (weighted random walks descending the hydraulic potential). As a proof of concept we present the results of the evolution of the hydrological system over time for a simple artificial glacier geometr

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

Grounding line migration as response to cycles of sliding pertubations and initial geometries in the MISMIP3D experiment

The benchmark experiment MISMIP3D (Pattyn et al., 2013) investigated the response of a artificial ice stream-ice shelf system to a sliding perturbation. We continued this experiment by applying cycles of pertubations at different time scales in order to see the long term response of the grounding line positions to changes in basal sliding. For this purpose we applied the finite-difference full-Stokes model TIM-FD3 on 2.5km and 1.25km using three different initial geometries. We found that our steady-state geometry shows a strong dependency of the grounding line position on the horizontal grid size and the chosen initial geometry. Not all experiments show a neutral equilibrium in subsequent basal sliding perturbation simulations

The Beauty and Complexity of the Brunt Ice Shelf from MOA and ICESat

Beginning in February 2003, NASA's Ice, Cloud, and land Elevation Satellite (ICESat) has determined surface elevations from approx. 86degN to 86degS latitude. To date, altimetry data have been acquired in a series of observation periods in repeated track patterns using all three Geoscience Laser Altimeter System (GLAS) lasers. This paper will focus on ice shelf elevation data that were obtained in 2003 across the Brunt Ice Shelf and the Stancomb-Wills Ice Tongue. Integrating the altimetry with the recently available MODIS Mosaic of Antarctica (MOA), quantifies the relative accuracy and precision of the resulting ice shelf elevations. Furthermore, the elevation data was processed onto an elevation grid, by regional interpolation across the area s complex glacial features only. Ice thickness estimation from the altimetry of the floating ice is discussed. ICESat operates at 40Hz and its elevation data is obtained every 172m along track. These elevations have a relative accuracy of about 14cm based on the standard deviation of low-slope crossover differences and a precision of close to 2cm for the Laser 2a, Release 21, GLA12 data used here

Comparison of ice dynamics using full-Stokes and Blatter–Pattyn approximation: application to the Northeast Greenland Ice Stream

Full-Stokes (FS) ice sheet models provide the most sophisticated formulation of ice sheet flow. However, their applicability is often limited due to the high computational demand and numerical challenges. To balance computational demand and accuracy, the so-called Blatter–Pattyn (BP) stress regime is frequently used. Here, we explore the dynamic consequences of using simplified approaches by solving FS and the BP stress regime applied to the Northeast Greenland Ice Stream. To ensure a consistent comparison, we use one single ice sheet model to run the simulations under identical numerical conditions. A sensitivity study to the horizontal grid resolution (from 12.8 to a resolution of 0.1 km) reveals that velocity differences between the FS and BP solution emerge below ∼ 1 km horizontal resolution and continuously increase with resolution. Over the majority of the modelling domain both models reveal similar surface velocity patterns. At the grounding line of the 79∘ North Glacier the simulations show considerable differences whereby the BP model overestimates ice discharge of up to 50 % compared to FS. A sensitivity study to the friction type reveals that differences are stronger for a power-law friction than a linear friction law. Model differences are attributed to topographic variability and the basal drag, in which neglected stress terms in BP become important

Fracture Mechanical Analysis of Cracks in Ice Shelves using the Finite Element Method and Configurational Forces

Ice shelves are important elements of the climate system and sensitive to climate changes. The disintegration of large Antarctic ice shelves is the focus of this fracture mechanical analysis. Ice is a complex material which, depending on the context, can be seen as a viscous fluid or as an elastic solid. A fracture event usually occurs on a rather short time scale, thus the elastic response is important and linear elastic fracture mechanics can be used. The investigation of the stress intensity factor as a measure of crack tip loading is based on a 2-dimensional analysis of a single crack with a mode-I type load and additional body loads. This investigation is performed using configurational forces. Depth dependent density and temperature profiles are considered. The relevant parameters are obtained by literature, remote sensing data analysis and modeling of the ice dynamics. The criticality of wet surface cracks is investigated

Dynamic changes on the Wilkins Ice Shelf during the 2006–2009 retreat derived from satellite observations

The vast ice shelves around Antarctica provide significant restraint to the outflow from adjacent tributary glaciers. This important buttressing effect became apparent in the last decades, when outlet glaciers accelerated considerably after several ice shelves were lost around the Antarctic Peninsula (AP). The present study aims to assess dynamic changes on the Wilkins Ice Shelf (WIS) during different stages of ice-front retreat and partial collapse between early 2008 and 2009. The total ice-shelf area lost in these events was 2135 ± 75 km2 ( ∼  15 % of the ice-shelf area relative to 2007). Here, we use time series of synthetic aperture radar (SAR) satellite observations (1994–1996, 2006–2010) in order to derive variations in surface-flow speed from intensity-offset tracking. Spatial patterns of horizontal strain-rate, stress and stress-flow angle distributions are determined during different ice-front retreat stages. Prior to the final break up of an ice bridge in 2008, a strong speed up is observed, which is also discernible from other derived quantities. We identify areas that are important for buttressing and areas prone to fracturing using in-flow and first principal strain rates as well as principal stress components. Further propagation of fractures can be explained as the first principal components of strain rates and stresses exceed documented threshold values. Positive second principal stresses are another scale-free indicator for ice-shelf areas, where fractures preferentially open. Second principal strain rates are found to be insensitive to ice-front retreat or fracturing. Changes in stress-flow angles highlight similar areas as the in-flow strain rates but are difficult to interpret. Our study reveals the large potential of modern SAR satellite time series to better understand dynamic and structural changes during ice-shelf retreat but also points to uncertainties introduced by the methods applied