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

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

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'

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

Study of the impact of ice formation in leads upon the sea ice pack mass balance using a new frazil and grease ice parameterisation

Leads are cracks in sea ice that often form due to deformation. During winter months leads expose the ocean to the cold atmosphere resulting in supercooling and the formation of frazil ice crystals within the mixed layer. Here we investigate the role of frazil ice formation in leads on the mass balance of the sea ice pack through the incorporation of a new module into the Los Alamos sea ice model (CICE). The frazil ice module considers a initial cooling of leads followed by a steady state formation of uniformly distributed single size frazil ice crystals that precipitate to the ocean surface as grease ice. The grease ice is pushed against one of the lead edges by wind and water drag that we represent through a variable collection thickness for new sea ice. Simulations of the sea ice cover in the Arctic and Antarctic are performed and compared to a model that treats leads the same as the open ocean. The processes of ice formation in the new module slows down the refreezing of leads resulting in an longer period of frazil ice production. The fraction of frazil-derived sea ice increases from 10% to 50%, corresponding better to observations. The new module has higher ice formation rates in areas of high ice concentration and thus has a greater impact within multiyear ice than it does in the marginal seas. The thickness of sea ice in the central Arctic increases by over 0.5 m whereas within the Antarctic it remains unchanged

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

Skillful spring forecasts of September Arctic sea ice extent using passive microwave sea ice observations

In this study, we demonstrate skillful spring forecasts of detrended September Arctic sea ice extent using passive microwave observations of sea ice concentration (SIC) and melt onset (MO). We compare these to forecasts produced using data from a sophisticated melt pond model, and find similar to higher skill values, where the forecast skill is calculated relative to linear trend persistence. The MO forecasts shows the highest skill in March–May, while the SIC forecasts produce the highest skill in June–August, especially when the forecasts are evaluated over recent years (since 2008). The high MO forecast skill in early spring appears to be driven primarily by the presence and timing of open water anomalies, while the high SIC forecast skill appears to be driven by both open water and surface melt processes. Spatial maps of detrended anomalies highlight the drivers of the different forecasts, and enable us to understand regions of predictive importance. Correctly capturing sea ice state anomalies, along with changes in open water coverage appear to be key processes in skillfully forecasting summer Arctic sea ice

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