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

A continuum mechanics perspective on the rheology of firn in the context of firn densification

While the complex nonlinear rheology of ice is well known and often discussed, for example in the context of large-scale ice sheet modeling, calving, and isotropy occurring at shear margins, the rheology of firn is often considered to be rather simple. According to Truesdell’s first metaphysical principle, which states that ”all properties of a mixture must be mathematical consequences of properties of the constituents” (Truesdell, C. (1984), Rational Thermodynamics, Springer-Verlag, p. 221), the material behavior of firn should be related to that of ice, since firn is primarily a mixture of ice and air. What distinguishes firn from ice is its microstructure. The field of continuum mechanics provides methods to relate the microstructural properties of a material to its macroscopic material behavior. Here we review a homogenization method developed for the densification of nonlinear creeping metallic powders and first applied to the simulation of firn densification by Gagliardini and Meyssonnier (1997, Annals of Glaciology, 24, pp. 242–248). The method links the rheology of ice to that of firn by describing firn as a porous medium with an ice matrix. The advantage of this approach is that it is formulated in all three spatial dimensions, allowing the inclusion of horizontal divergence due to ice flow without additional parameterization. A large database of dated firn cores allows the determination of the governing model parameters using an optimization approach. We discuss the results, advantages, and limitations of this approach, as well as validation strategies

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