Continuum sea ice rheology determined from subcontinuum mechanics

[1] A method is presented to calculate the continuum-scale sea ice stress as an imposed, continuum-scale strain-rate is varied. The continuum-scale stress is calculated as the area-average of the stresses within the floes and leads in a region (the continuum element). The continuum-scale stress depends upon: the imposed strain rate; the subcontinuum scale, material rheology of sea ice; the chosen configuration of sea ice floes and leads; and a prescribed rule for determining the motion of the floes in response to the continuum-scale strain-rate. We calculated plastic yield curves and flow rules associated with subcontinuum scale, material sea ice rheologies with elliptic, linear and modified Coulombic elliptic plastic yield curves, and with square, diamond and irregular, convex polygon-shaped floes. For the case of a tiling of square floes, only for particular orientations of the leads have the principal axes of strain rate and calculated continuum-scale sea ice stress aligned, and these have been investigated analytically. The ensemble average of calculated sea ice stress for square floes with uniform orientation with respect to the principal axes of strain rate yielded alignment of average stress and strain-rate principal axes and an isotropic, continuum-scale sea ice rheology. We present a lemon-shaped yield curve with normal flow rule, derived from ensemble averages of sea ice stress, suitable for direct inclusion into the current generation of sea ice models. This continuum-scale sea ice rheology directly relates the size (strength) of the continuum-scale yield curve to the material compressive strength

Sea ice and the ocean mixed layer over the Antarctic shelf seas

An ocean mixed-layer model has been incorporated into the Los Alamos sea ice model CICE to investigate regional variations in the surface-driven formation of Antarctic shelf waters. This model captures well the expected sea ice thickness distribution, and produces deep (> 500 m) mixed layers in the Weddell and Ross shelf seas each winter. This results in the complete destratification of the water column in deep southern coastal regions leading to high-salinity shelf water (HSSW) formation, and also in some shallower regions (no HSSW formation) of these seas. Shallower mixed layers are produced in the Amundsen and Bellingshausen seas. By deconstructing the surface processes driving the mixed-layer depth evolution, we show that the net salt flux from sea ice growth/melt dominates the evolution of the mixed layer in all regions, with a smaller contribution from the surface heat flux and a negligible input from wind stress. The Weddell and Ross shelf seas receive an annual surplus of mixing energy at the surface; the Amundsen shelf sea energy input in autumn/winter is balanced by energy extraction in spring/summer; and the Bellingshausen shelf sea experiences an annual surface energy deficit, through both a low energy input in autumn/winter and the highest energy loss in spring/summer. An analysis of the sea ice mass balance demonstrates the contrasting mean ice growth, melt and export in each region. The Weddell and Ross shelf seas have the highest annual ice growth, with a large fraction exported northwards each year, whereas the Bellingshausen shelf sea experiences the highest annual ice melt, driven by the advection of ice from the northeast. A linear regression analysis is performed to determine the link between the autumn/winter mixed-layer deepening and several atmospheric variables. The Weddell and Ross shelf seas show stronger spatial correlations (temporal mean – intra-regional variability) between the autumn/winter mixed-layer deepening and several atmospheric variables compared to the Amundsen and Bellingshausen. In contrast, the Amundsen and Bellingshausen shelf seas show stronger temporal correlations (shelf sea mean – interannual variability) between the autumn/winter mixed-layer deepening and several atmospheric variables

Stress and deformation characteristics of sea ice in a high-resolution, anisotropic sea ice model

The drift and deformation of sea ice floating on the polar oceans is caused by the applied wind and ocean currents. Over ocean basin length scales the internal stresses and boundary conditions of the sea ice pack result in observable deformation patterns. Cracks and leads can be observed in satellite images and within the velocity fields generated from floe tracking. In a climate sea ice model the deformation of sea ice over ocean basin length scales is modelled using a rheology that represents the relationship between stresses and deformation within the sea ice cover. Here we investigate the link between emergent deformation characteristics and the underlying internal sea ice stresses using the Los Alamos numerical sea ice climate model. We have developed an idealized square domain, focusing on the role of sea ice rheologies in producing deformation at spatial resolutions of up to 500 m. We use the elastic anisotropic plastic (EAP) and elastic viscous plastic (EVP) rheologies, comparing their stability, with the EAP rheology producing sharper deformation features than EVP at all space and time resolutions. Sea ice within the domain is forced by idealized winds, allowing for the emergence of five distinct deformation types. Two for a low confinement ratio: convergent and expansive stresses. Two about a critical confinement ratio: isotropic and anisotropic conditions. One for a high confinement ratio and isotropic sea ice. Using the EAP rheology and through the modification of initial conditions and forcing, we show the emergence of the power law of strain rate, in accordance with observations.This article is part of the theme issue 'Modelling of sea-ice phenomena'

Continuum sea ice rheology determined from subcontinuum mechanics

[1] A method is presented to calculate the continuum-scale sea ice stress as an imposed, continuum-scale strain-rate is varied. The continuum-scale stress is calculated as the area-average of the stresses within the floes and leads in a region (the continuum element). The continuum-scale stress depends upon: the imposed strain rate; the subcontinuum scale, material rheology of sea ice; the chosen configuration of sea ice floes and leads; and a prescribed rule for determining the motion of the floes in response to the continuum-scale strain-rate. We calculated plastic yield curves and flow rules associated with subcontinuum scale, material sea ice rheologies with elliptic, linear and modified Coulombic elliptic plastic yield curves, and with square, diamond and irregular, convex polygon-shaped floes. For the case of a tiling of square floes, only for particular orientations of the leads have the principal axes of strain rate and calculated continuum-scale sea ice stress aligned, and these have been investigated analytically. The ensemble average of calculated sea ice stress for square floes with uniform orientation with respect to the principal axes of strain rate yielded alignment of average stress and strain-rate principal axes and an isotropic, continuum-scale sea ice rheology. We present a lemon-shaped yield curve with normal flow rule, derived from ensemble averages of sea ice stress, suitable for direct inclusion into the current generation of sea ice models. This continuum-scale sea ice rheology directly relates the size (strength) of the continuum-scale yield curve to the material compressive strength

Sea ice–ocean feedbacks in the Antarctic shelf seas

Observed changes in Antarctic sea ice are poorly understood, in part due to the complexity of its interactions with the atmosphere and ocean. A highly simplified, coupled sea ice–ocean mixed layer model has been developed to investigate the importance of sea ice–ocean feedbacks on the evolution of sea ice and the ocean mixed layer in two contrasting regions of the Antarctic continental shelf ocean: the Amundsen Sea, which has warm shelf waters, and the Weddell Sea, which has cold and saline shelf waters. Modeling studies where we deny the feedback response to surface air temperature perturbations show the importance of feedbacks on the mixed layer and ice cover in the Weddell Sea to be smaller than the sensitivity to surface atmospheric conditions. In the Amundsen Sea the effect of surface air temperature perturbations on the sea ice are opposed by changes in the entrainment of warm deep waters into the mixed layer. The net impact depends on the relative balance between changes in sea ice growth driven by surface perturbations and basal-driven melting. The changes in the entrainment of warm water in the Amundsen Sea were found to have a much larger impact on the ice volume than perturbations in the surface energy budget. This creates a net negative ice albedo feedback in the Amundsen Sea, reversing the sign of this typically positive feedback mechanism

Disclosing physician ratings: performance effects and the difficulty of altering rating consensus

I examine effects of a health care system's policy to publicly disclose patient ratings of its physicians. I find evidence that this policy leads to performance improvement by the disclosed, subjective ratings and also by undisclosed, objective measures of quality. These effects are consistent with multitasking theory, in that physicians respond to the disclosure by providing more of a shared input—time with patients—that benefits performance by ratings and underlying quality. I also find, as predicted by information cascade theory, that the ratings become jammed to some degree near initially disclosed values. Specifically, raters observe the pattern of initial ratings and follow suit by providing similar ratings. Finally, I find evidence that physicians anticipate rating jamming and so concentrate their effort on earlier performance in order to set a pattern of high ratings that later ratings follow. These results demonstrate that the disclosure of subjective ratings can benefit performance broadly but can also shift effort toward earlier performance

A model for the consolidation of rafted sea ice

Rafting is one of the important deformation mechanisms of sea ice. This process is widespread in the north Caspian Sea, where multiple rafting produces thick sea ice features, which are a hazard to offshore operations. Here we present a one-dimensional, thermal consolidation model for rafted sea ice. We consider the consolidation between the layers of both a two-layer and a three-layer section of rafted sea ice. The rafted ice is assumed to be composed of layers of sea ice of equal thickness, separated by thin layers of ocean water. Results show that the thickness of the liquid layer reduced asymptotically with time, such that there always remained a thin saline liquid layer. We propose that when the liquid layer is equal to the surface roughness the adjacent layers can be considered consolidated. Using parameters representative of the north Caspian, the Arctic, and the Antarctic, our results show that for a choice of standard parameters it took under 15 h for two layers of rafted sea ice to consolidate. Sensitivity studies showed that the consolidation model is highly sensitive to the initial thickness of the liquid layer, the fraction of salt release during freezing, and the height of the surface asperities. We believe that further investigation of these parameters is needed before any concrete conclusions can be drawn about rate of consolidation of rafted sea ice features

The Obliteration of Truth by Management: Badiou, St. Paul and the Question of Economic Managerialism in Education

This paper considers the questions that Badiou’s theory of the subject poses to cultures of economic managerialism within education. His argument that radical change is possible, for people and the situations they inhabit, provides a stark challenge to the stifling nature of much current educational climate. In 'Saint Paul: The Foundation of Universalism', Badiou describes the current universalism of capitalism, monetary homogeneity and the rule of the count. Badiou argues that the politics of identity are all too easily subsumed by the prerogatives of the marketplace and unable to present, therefore, a critique of the status quo. These processes are, he argues, without the potential for truth. What are the implications of Badiou’s claim that education is the arranging of ‘the forms of knowledge in such a way that truth may come to pierce a hole in them’ (Badiou, 2005, p. 9)? In this paper, I argue that Badiou’s theory opens up space for a kind of thinking about education that resists its colonisation by cultures of management and marketisation and leads educationalists to consider the emancipatory potential of education in a new light

A mathematical model of melt lake development on an ice shelf

The accumulation of surface meltwater on ice shelves can lead to the formation of melt lakes. Melt lakes have been implicated in ice shelf collapse; Antarctica's Larsen B Ice Shelf was observed to have a large amount of surface melt lakes present preceding its collapse in 2002. Such collapse can affect ocean circulation and temperature, cause habitat loss and contribute to sea level rise through the acceleration of tributary glaciers. We present a mathematical model of a surface melt lake on an idealised ice shelf. The model incorporates a calculation of the ice shelf surface energy balance, heat transfer through the firn, the production and percolation of meltwater into the firn, the formation of ice lenses and the development and refreezing of surface melt lakes. The model is applied to the Larsen C Ice Shelf, where melt lakes have been observed. This region has warmed several times the global average over the last century and the Larsen C firn layer could become saturated with meltwater by the end of the century. When forced with weather station data, our model produces surface melting, meltwater accumulation, and melt lake development consistent with observations. We examine the sensitivity of lake formation to uncertain parameters, and provide evidence of the importance of processes such as lateral meltwater transport. We conclude that melt lakes impact surface melt and firn density and warrant inclusion in dynamic-thermodynamic models of ice shelf evolution within climate models, of which our model could form the basis for the thermodynamic component