Modelling the fate of surface melt on the Larsen C Ice Shelf

Surface melt lakes lower the albedo of ice shelves, leading to additional surface melting. This can substantially alter the surface energy balance and internal temperature and density profiles of the ice shelf. Evidence suggests that melt lakes also played a pivotal role in the sudden collapse of the Larsen B Ice Shelf in 2002. Here a recently developed, high-physical-fidelity model accounting for the development cycle of melt lakes is applied to the Larsen C Ice Shelf, Antarctica’s most northern ice shelf and one where melt lakes have been observed. We simulate current conditions on the ice shelf using weather station and reanalysis data and investigate the impacts of potential future increases in precipitation and air temperature on melt lake formation, for which concurrent increases lead to an increase in lake depth. Finally, we assess the viability in future crevasse propagation through the ice shelf due to surface meltwater accumulation

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

Experimental evidence of the benefit of wild flower strips to crop pollination

Wild bees provide a free and potentially diverse ecosystem service to farmers growing pollinator dependent crops. Whilst many crops benefit from insect pollination, soft fruit crops, including strawberries are commonly dependent on this ecosystem service to produce viable fruit. However, as a result of intensive farming practices and declining pollinator populations, farmers are increasingly turning to commercially reared bees to ensure that crops are adequately pollinated throughout the season. Wildflower strips are a commonly used measure aimed at the conservation of wild pollinators. It has been suggested that commercial crops may also benefit from the presence of sown wild flowers however, the efficacy and economic benefits of sowing flower strips for crops has been little investigated. Here we test whether wildflower strips increase the number of visits to adjacent commercial strawberry crops by wild pollinators. This was quantified by experimentally sowing wildflower strips approximately 20 meters away from the crop and recording the number of pollinator visits to crops with, and without, flower strips. Between June and August 2013 we walked 292 crop transects at six farms in Scotland, recording a total of 3,102 pollinators. On average, the frequency of pollinator visits was 25% higher for crops with adjacent flower strips compared to those without, with bumblebees (Bombus spp.) accounting for 62% of all pollinators observed. This effect was independent of other (potentially important) confounding effects, such as the number of flowers on the crop, date and temperature. Whilst commercial bees may still be required early in the season, this study provides evidence that soft fruit farmers can increase the number of pollinators that visit their crops by sowing inexpensive flower seed mixes nearby. The cost of planting these strips was substantially lower than the annual cost of purchasing commercial bumblebees, with the added advantage that this management option has the potential to increase and sustain pollinator populations over time

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'

Anisotropic model for granulated sea ice dynamics

A continuum model describing sea ice as a layer of granulated thick ice, consisting of many rigid, brittle floes, intersected by long and narrow regions of thinner ice, known as leads, is developed. We consider the evolution of mesoscale leads, formed under extension, whose lengths span many floes, so that the surrounding ice is treated as a granular plastic. The leads are sufficiently small with respect to basin scales of sea ice deformation that they may be modelled using a continuum approach. The model includes evolution equations for the orientational distribution of leads, their thickness and width expressed through second-rank tensors and terms requiring closures. The closing assumptions are constructed for the case of negligibly small lead ice thickness and the canonical deformation types of pure and simple shear, pure divergence and pure convergence. We present a new continuum-scale sea ice rheology that depends upon the isotropic, material rheology of sea ice, the orientational distribution of lead properties and the thick ice thickness. A new model of lead and thick ice interaction is presented that successfully describes a number of effects: (i) because of its brittle nature, thick ice does not thin under extension and (ii) the consideration of the thick sea ice as a granular material determines finite lead opening under pure shear, when granular dilation is unimportant. © 2006 Elsevier Ltd. All rights reserved

Dependence of sea ice yield-curve shape on ice thickness

In this note, the authors discuss the contribution that frictional sliding of ice floes (or floe aggregates) past each other and pressure ridging make to the plastic yield curve of sea ice. Using results from a previous study that explicitly modeled the amount of sliding and ridging that occurs for a given global strain rate, it is noted that the relative contribution of sliding and ridging to ice stress depends upon ice thickness. The implication is that the shape and size of the plastic yield curve is dependent upon ice thickness. The yield-curve shape dependence is in addition to plastic hardening/weakening that relates the size of the yield curve to ice thickness. In most sea ice dynamics models the yield-curve shape is taken to be independent of ice thickness. The authors show that the change of the yield curve due to a change in the ice thickness can be taken into account by a weighted sum of two thickness-independent rheologies describing ridging and sliding effects separately. It would be straightforward to implement the thickness-dependent yield-curve shape described here into sea ice models used for global or regional ice prediction. © 2004 American Meteorological Society

A continuum anisotropic model of sea-ice dynamics

We develop the essential ingredients of a new, continuum and anisotropic model of sea-ice dynamics designed for eventual use in climate simulation. These ingredients are a constitutive law for sea-ice stress, relating stress to the material properties of sea ice and to internal variables describing the sea-ice state, and equations describing the evolution of these variables. The sea-ice cover is treated as a densely flawed two-dimensional continuum consisting of a uniform field of thick ice that is uniformly permeated with narrow linear regions of thinner ice called leads. Lead orientation, thickness and width distributions are described by second-rank tensor internal variables: the structure, thickness and width tensors, whose dynamics are governed by corresponding evolution equations accounting for processes such as new lead generation and rotation as the ice cover deforms. These evolution equations contain contractions of higher-order tensor expressions that require closures. We develop a sea-ice stress constitutive law that relates sea-ice stress to the structure tensor, thickness tensor and strain rate. For the special case of empty leads (containing no ice), linear closures are adopted and we present calculations for simple shear, convergence and divergence

Modelling the rheology of sea ice as a collection of diamond-shaped floes

In polar oceans, seawater freezes to form a layer of sea ice of several metres thickness that can cover up to 8% of the Earth's surface. The modelled sea ice cover state is described by thickness and orientational distribution of interlocking, anisotropic diamond-shaped ice floes delineated by slip lines, as supported by observation. The purpose of this study is to develop a set of equations describing the mean-field sea ice stresses that result from interactions between the ice floes and the evolution of the ice floe orientation, which are simple enough to be incorporated into a climate model. The sea ice stress caused by a deformation of the ice cover is determined by employing an existing kinematic model of ice floe motion, which enables us to calculate the forces acting on the ice floes due to crushing into and sliding past each other, and then by averaging over all possible floe orientations. We describe the orientational floe distribution with a structure tensor and propose an evolution equation for this tensor that accounts for rigid body rotation of the floes, their apparent re-orientation due to new slip line formation, and change of shape of the floes due to freezing and melting. The form of the evolution equation proposed is motivated by laboratory observations of sea ice failure under controlled conditions. Finally, we present simulations of the evolution of sea ice stress and floe orientation for several imposed flow types. Although evidence to test the simulations against is lacking, the simulations seem physically reasonable. © 2006 Elsevier B.V. All rights reserved