On the role of grain growth, recrystallization and polygonization in a continuum theory for anisotropic ice sheets

AbstractWe outline how to incorporate microscale effects of polycrystalline ice into a continuum description. Actually, analyses of ice cores in Antarctica show that different microstructures generally produce different responses, i.e. a non-uniform distribution of c axes gives rise to anisotropic behaviour. It has been recognized that, to describe certain microstructural processes, like recrystallization or polygonization, we need a parameter able to switch them on (e.g. dislocation density or its associated lattice distortion energy). With this in mind, balance equations for a continuum theory of an anisotropic ice sheet undergoing recrystallization have been recently proposed. In this work, we examine relations for some constitutive quantities, in order to take into account the effects of grain-boundary migration, nucleation and polygonization. We check our assumptions by explicit comparison with the first 1200 m of the Byrd (Antarctica) ice core. Current literature usually gives a relation between normal grain growth and grain boundary migration rate. Here, an equation for normal grain growth which also incorporates the influence of polygonization is suggested. It is based on experimental data from the same core in Antarctica. Polygonization is a microscopic process, but here we present a continuum description of the bending stresses which promote the fragmentation of crystallites in terms of the theory of mixtures with continuous diversity

Data mining techniques contributions to support electrical vehicle demand response

The introduction of Electric Vehicles (EVs) together with the implementation of smart grids will raise new challenges to power system operators. This paper proposes a demand response program for electric vehicle users which provides the network operator with another useful resource that consists in reducing vehicles charging necessities. This demand response program enables vehicle users to get some profit by agreeing to reduce their travel necessities and minimum battery level requirements on a given period. To support network operator actions, the amount of demand response usage can be estimated using data mining techniques applied to a database containing a large set of operation scenarios. The paper includes a case study based on simulated operation scenarios that consider different operation conditions, e.g. available renewable generation, and considering a diversity of distributed resources and electric vehicles with vehicle-to-grid capacity and demand response capacity in a 33 bus distribution network

Continuum-mechanical, Anisotropic Flow model for polar ice masses, based on an anisotropic Flow Enhancement factor

A complete theoretical presentation of the Continuum-mechanical, Anisotropic Flow model, based on an anisotropic Flow Enhancement factor (CAFFE model) is given. The CAFFE model is an application of the theory of mixtures with continuous diversity for the case of large polar ice masses in which induced anisotropy occurs. The anisotropic response of the polycrystalline ice is described by a generalization of Glen's flow law, based on a scalar anisotropic enhancement factor. The enhancement factor depends on the orientation mass density, which is closely related to the orientation distribution function and describes the distribution of grain orientations (fabric). Fabric evolution is governed by the orientation mass balance, which depends on four distinct effects, interpreted as local rigid body rotation, grain rotation, rotation recrystallization (polygonization) and grain boundary migration (migration recrystallization), respectively. It is proven that the flow law of the CAFFE model is truly anisotropic despite the collinearity between the stress deviator and stretching tensors.Comment: 22 pages, 5 figure

Microstructure in the EastGRIP ice core, Greenland

Behavior of Earth’s ice sheets is intensely monitored via surface and remote sensing techniques to improve predictions of sea level evolution. Radio echo sounding along with drilling ice cores are currently used to monitor the Earth’s ice sheets behaviour not only from the surface but in the 3rd dimension. Particularly the ice material properties can only be accessed via ice drilling. These properties control the deformation in general, and particularly strain localization such as observed in ice streams, which supply the major discharges into the oceans. Currently the first ice core on an active ice stream, the North-East Greenland Ice Stream (NEGIS) is being drilled. EastGRIP (East Greenland Ice-Core Project, http://eastgrip.org) drilling started in 2016 and will be ongoing until 2019. This is the first chance to study ice microstructure from a dynamically active region (www.awi.de/en/focus/eisschilde/eis-ist-ein-heisses-material.html), with a deformation regime differing from the usual locations of previous long ice cores. Those were usually placed on domes or on ice divides due to straightforward kinematics and deformation rates which is advantageous for paleo-climate reconstruction from ice core records. We present CPO (c-axes fabric) and the grain size measurements of the uppermost 350m, the depth to which the ice core has been processed for analysis so far (275 thin sections discontinuous with 10m depth resolution). The CPO patterns found in the upper 350m at EastGRIP show (1) a more rapid evolution of c-axes anisotropy with depth compared to other ice cores and (2) partly novel characteristics in the caxes distributions. (Remark: This is an invited poster.

Physical properties of the NEGIS ice core - The upper 1700m in EGRIP

We will present the EGRIP CPO (c-axes fabric) dataset and give preliminary interpretations concerning the processes leading to its evolution. 120 bags were selected, with a minimum depth resolution of 15m. Bags were mostly measured continuously, and in total 778 thin sections were prepared, measured and pre-processed on site. Thus, c-axes distribution CPO data are already available, while other parameters on grain stereology are still to be processed at this stage. The CPO patterns found in the upper 1650m at EGRIP show (1) a rapid evolution of c-axes anisotropy compared to lower dynamics sites and (2) partly novel characteristics in the CPO patterns. (1) Starting the measurements at 118m of depth we find a very broad single maximum distribution. The c-axes align with depth in the upper 400m much more rapidly than seen in ice cores from divides or domes. Down to only 140m depth the almost random CPO develops into a very broad single maximum which is similar to those CPOs found in the shallowest samples of other ice cores. Possible interpretations of these distributions are deformation by vertical compression from overlying layers, or alternatively a temperature-gradient snow metamorphosis. This weak CPO pattern is, however, quickly overprinted in the depth zone below 140m where a progressive evolution towards a vertical girdle distribution is observed. As vertical girdles are produced by extension along flow, the observed distribution indicates that the ice at this depth is deforming rather than just being translated by rigid block movement. From approximately 600m of depth downward we observe crystal orientation anisotropy of a strength comparable to samples from ~1400m of depth at divides (NEEM and EDML). This strong girdle CPO remains rather stable down to approximately 1300m depth, where we reach the ice deposited during the last glacial period. A novel pattern, not observed before in natural ice, is a higher densities of c-axes horizontally oriented within the vertical girdle. (2) The early onset of deformation seems further supported by the observation of a broad “hourglass shaped” girdle, which seems to develop in some depths into a “butterfly shaped” cross girdle. Another characteristic deserves attention: the distribution density within the girdle. In contrast to observations in deep ice cores so far, the highest density seems to deviate from the vertical direction being (sub-)parallel to the horizontal. The origin of this may lay in the main deformation modes, e.g. a combination of along flow extension with additional deformation modes. Especially interesting is the cross girdle, which has not yet been observed in polar ice cores so far. We suggest three possible interpretations for its origin: a) In other materials, such as quartz, cross girdles can be interpreted as activation of multiple dislocation slip systems. b) Alternatively, the CPO pattern may reflect reminiscent features from previous deformation modes, which the ice experienced upstream or possibly even outside of the ice stream. This memory effect would point to a relevance of strain dependence of the CPO. c) The cross- /double-girdle might be caused by the early onset of dynamic migration recrystallization under horizontal uniaxial extension

An analysis of the influence of deformation and recrystallisation on microstructures of the EastGRIP ice core

New and more detailed investigations from the EGRIP physical properties dataset down to 1650m of the ice core will be presented. EGRIP is the first deep ice core through one of our Earth’s ice sheets partly motivated by ice dynamics’ research. It is drilled just downstream of the onset of the largest ice stream in Greenland (North East Greenland Ice Stream). Data processing of the collected ice core physical properties data was done at the Alfred Wegener Institute Helmholtz Centre for Marine and Polar Research. The two main findings regarding CPO (c-axes fabric) pattern, 1) a rapid evolution of c-axes anisotropy and 2) partly novel characteristics, were further, and in more detail, investigated. To gain a better understanding of the dominating deformation mechanisms of NEGIS, different approaches considering different length scales were chosen (1650m versus 0.55m and 0.09m scale), including several case studies. A large-scale statistical analysis of the entire dataset results in new information about the depth-dependent evolution of parameters as for example the strength of c-axes anisotropy and grain-size in the polycrystal. In general, mean grain-size decreases with depth as we drill through the Holocene ice and approach the Glacial material. The grain size variability with fine and coarse grain layers is extreme in the Holocene ice but decreases in the Glacial ice. Microstructure properties were examined, with the aim to investigate the relationship between the remarkable rapid evolution of CPO-pattern and grain properties evolution. Furthermore, the evolution of a grain-size dependent anisotropy, found in the first 350m of the ice core, is investigated and examined also in deeper sections of the core. The large-scale evolution of density distributions of c-axes orientations differ significantly from observations in deep ice cores made so far: A novel "hourglass shaped" girdle was observed, characterized by a high density of horizontally oriented c-axes within the vertical girdle. In some parts of the core, this shape develops into a "butterfly shaped" cross girdle, varying in intensity and strength. It is the first time that this cross girdle was observed in polar ice and by combining approaches considering different length scales, we aimed to verify one of our three hypotheses for its origin: a) activation of multiple dislocation slip systems (in analogy to quartz), b) a memory effect or reminiscent features from older deformation modes, further upstream or even outside of NEGIS or c) horizontal uniaxial extension causing an early onset of dynamic migration recrystallization. Small-scale high-resolution studies were carried out on several selected bags (0.55m long) from different depth regimes and were chosen as case studies to better understand the formation mechanisms of the novel CPO patterns found in the EGRIP ice core. One approach is the examination of thin sections (9 x 7 x 0.03cm) regarding the occurrence of patches of grains with similar orientations, which was observed in several samples from different depths. Small grains with similar orientations seem to cluster around large grains with a different orientation. High-resolution images (5 to 20µm/pix), derived with a Large Area Scan Macroscope (LASM), enable detailed investigations of grain shape, grain boundaries and sub-grain boundaries and therefore the possibility to find distinct features from deformation and recrystallisation in the microstructure. Grains are rarely horizontally aligned and usually show irregular, circular or rectangular shapes rather than elongated shapes. Characteristic for our case studies are also amoeboid grain shapes and sutured grain boundaries, typical features of grain boundary migration. Furthermore, layering, "sandwiched grains" and strong gradients in grain-size over distances of only a few centimetres were observed in several samples. Although still under progress, at the current state of investigation, combining fabric data and microstructure analysis, the novel CPO patterns found in the EGRIP ice core are strongly influenced by dynamic migration recrystallisation