ALBERT

Description: A new rheological model is developed that builds on an elasto-brittle (EB) framework used for sea ice and rock mechanics, with the intent of representing both the small elastic deformations associated with fracturing processes and the larger deformations occurring along the faults/leads once the material is highly damaged and fragmented. A viscous-like relaxation term is added to the linear-elastic constitutive law together with an effective viscosity that evolves according to the local level of damage of the material, like its elastic modulus. The coupling between the level of damage and both mechanical parameters is such that within an undamaged ice cover the viscosity is infinitely large and deformations are strictly elastic, while along highly damaged zones the elastic modulus vanishes and most of the stress is dissipated through permanent deformations. A healing mechanism is also introduced, counterbalancing the effects of damaging over large timescales. In this new model, named Maxwell-EB after the Maxwell rheology, the irreversible and reversible deformations are solved for simultaneously; hence drift velocities are defined naturally. First idealized simulations without advection show that the model reproduces the main characteristics of sea ice mechanics and deformation: strain localization, anisotropy, intermittency and associated scaling laws.

Description: In this paper, we evaluate the neXtSIM sea ice model with respect to the observed scaling invariance properties of sea ice deformation in the spatial and temporal domains. Using an Arctic setup with realistic initial conditions, state-of-the-art atmospheric reanalysis forcing and geostrophic currents retrieved from satellite data, we show that the model is able to reproduce the observed properties of this scaling in both the spatial and temporal domains over a wide range of scales, as well as their multi-fractality. The variability of these properties during the winter season is also captured by the model. We also show that the simulated scaling exhibits a space–time coupling, a suggested property of brittle deformation at geophysical scales. The ability to reproduce the multi-fractality of this scaling is crucial in the context of downscaling model simulation outputs to infer sea ice variables at the sub-grid scale and also has implications for modeling the statistical properties of deformation-related quantities, such as lead fractions and heat and salt fluxes.

Description: This paper presents a first implementation of a new rheological model for sea ice on geophysical scales. This continuum model, called Maxwell elasto-brittle (Maxwell-EB), is based on a Maxwell constitutive law, a progressive damage mechanism that is coupled to both the elastic modulus and apparent viscosity of the ice cover and a Mohr–Coulomb damage criterion that allows for pure (uniaxial and biaxial) tensile strength. The model is tested on the basis of its capability to reproduce the complex mechanical and dynamical behaviour of sea ice drifting through a narrow passage. Idealized as well as realistic simulations of the flow of ice through Nares Strait are presented. These demonstrate that the model reproduces the formation of stable ice bridges as well as the stoppage of the flow, a phenomenon occurring within numerous channels of the Arctic. In agreement with observations, the model captures the propagation of damage along narrow arch-like kinematic features, the discontinuities in the velocity field across these features dividing the ice cover into floes, the strong spatial localization of the thickest, ridged ice, the presence of landfast ice in bays and fjords and the opening of polynyas downstream of the strait. The model represents various dynamical behaviours linked to an overall weakening of the ice cover and to the shorter lifespan of ice bridges, with implications in terms of increased ice export through narrow outflow pathways of the Arctic.

Description: In this paper, we evaluate the neXtSIM sea ice model with respect to the observed scaling invariance properties of sea ice deformation in the spatial and temporal domains. Using an Arctic set-up with realistic initial conditions, state-of-the-art atmospheric reanalysis forcing and geostrophic currents retrieved from satellite data, we show that the model is able to reproduce the observed properties of these scaling in both the spatial and temporal do- mains over a wide range of scales and, for the first time, their multi-fractality. The variability of these properties during the winter season are also captured by the model. We also show that the simulated scaling exhibit a space-time coupling, a suggested property of brittle deformation at geophysical scales. The ability to reproduce the multi-fractality of these scaling is crucial in the context of downscaling model simulation outputs to infer sea ice variables at the sub-grid scale, and also has implication in modeling the statistical properties of deformation-related quantities such as lead fractions, and heat and salt fluxes.

Description: Mechanics plays a key role in the evolution of the sea ice cover through its control on drift, on momentum and thermal energy exchanges between the polar oceans and the atmosphere along cracks and faults, and on ice thickness distribution through opening and ridging processes. At the local scale, a significant variability of the mechanical strength is associated with the microstructural heterogeneity of saline ice, however characterized by a small correlation length, below the ice thickness scale. Conversely, the sea ice mechanical fields (velocity, strain and stress) are characterized by long-ranged (more than 1000 km) and long-lasting (approx. few months) correlations. The associated space and time scaling laws are the signature of the brittle character of sea ice mechanics, with deformation resulting from a multi-scale accumulation of episodic fracturing and faulting events. To translate the short-range-correlated disorder on strength into long-range-correlated mechanical fields, several key ingredients are identified: long-ranged elastic interactions, slow driving conditions, a slow viscous-like relaxation of elastic stresses and a restoring/healing mechanism. These ingredients constrained the development of a new continuum mechanics modelling framework for the sea ice cover, called Maxwell–elasto-brittle. Idealized simulations without advection demonstrate that this rheological framework reproduces the main characteristics of sea ice mechanics, including anisotropy, spatial localization and intermittency, as well as the associated scaling laws. This article is part of the themed issue ‘Microdynamics of ice’.

Description: We explore several statistical properties of the observed and simulated Arctic sea-ice lead fraction, as well as the statistics of simulated Arctic ocean–atmosphere heat fluxes. First we show that the observed lead fraction in the Central Arctic has a monofractal spatial scaling, which we relate to the multifractal spatial scaling present in sea-ice deformation rates. We then show that the relevant statistics of the observed lead fraction in the Central Arctic are well represented by our model, neXtSIM. Given that the heat flux through leads may be up to 2 orders of magnitude larger than that through unbroken ice, we then explore the statistical properties (probability distribution function – PDF – and spatial scaling) of the heat fluxes simulated by neXtSIM. We demonstrate that the modelled heat fluxes present a multifractal scaling in the Central Arctic, where heat fluxes through leads dominate the high-flux tail of the PDF. This multifractal character relates to the multi- and monofractal character of deformation rates and the lead fraction. In the wider Arctic, the high-flux tail of the PDF is dominated by an exponential decay, which we attribute to the presence of coastal polynyas. Finally, we show that the scaling of the simulated lead fraction and heat fluxes depends weakly on the model resolution and discuss the role sub-grid-scale parameterisations of the ice heterogeneity may have in improving this result.

Description: Two parameterizations of turbulent boundary layer processes at the interface between an ice shelf and the ocean beneath are investigated in terms of their impact on simulated melt rates and feedbacks. The parameterizations differ in the transfer coefficients for heat and freshwater fluxes. In their simplest form, they are assumed constant and hence are independent of the velocity of ocean currents at the ice shelf base. An augmented melt rate parameterization accounts for frictional turbulence via transfer coefficients that do depend on boundary layer current velocities via a drag law. In simulations with both parameterizations for idealized as well as realistic cavity geometries under Pine Island Ice Shelf, West Antarctica, significant differences in melt rate patterns between the velocity-independent and velocity-dependent formulations are found. While patterns are strongly correlated to those of thermal forcing for velocity-independent transfer coefficients, melting in the case of velocity-dependent coefficients is collocated with regions of high boundary layer currents, in particular where rapid plume outflow occurs. Both positive and negative feedbacks between melt rates, boundary layer temperature, velocities, and buoyancy fluxes are identified. Melt rates are found to increase with increasing drag coefficient inline image, in agreement with plume model simulations, but optimal values of Cd inferred from plume models are not easily transferable. Uncertainties therefore remain, both regarding simulated melt rate spatial distributions and magnitudes.

Description: Submitted in partial fulfillment of the requirements for the degree of Master of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 2012

Description: Interactions between the ocean circulation in sub-ice shelf cavities and the overlying ice shelf have received considerable attention in the context of observed changes in flow speeds of marine ice sheets around Antarctica. Modeling these interactions requires parameterizing the turbulent boundary layer processes to infer melt rates from the oceanic state at the ice-ocean interface. Here we explore two such parameterizations in the context of the MIT ocean general circulation model coupled to the z-coordinates ice shelf cavity model of Losch (2008). We investigate both idealized ice shelf cavity geometries as well as a realistic cavity under Pine Island Ice Shelf (PIIS), West Antarctica. Our starting point is a three-equation melt rate parameterization implemented by Losch (2008), which is based on the work of Hellmer and Olbers (1989). In this form, the transfer coefficients for calculating heat and freshwater fluxes are independent of frictional turbulence induced by the proximity of the moving ocean to the fixed ice interface. More recently, Holland and Jenkins (1999) have proposed a parameterization in which the transfer coefficients do depend on the ocean-induced turbulence and are directly coupled to the speed of currents in the ocean mixed layer underneath the ice shelf through a quadratic drag formulation and a bulk drag coefficient. The melt rate parameterization in the MITgcm is augmented to account for this velocity dependence. First, the effect of the augmented formulation is investigated in terms of its impact on melt rates as well as on its feedback on the wider sub-ice shelf circulation. We find that, over a wide range of drag coefficients, velocity-dependent melt rates are more strongly constrained by the distribution of mixed layer currents than by the temperature gradient between the shelf base and underlying ocean, as opposed to velocity-independent melt rates. This leads to large differences in melt rate patterns under PIIS when including versus not including the velocity dependence. In a second time, the modulating effects of tidal currents on melting at the base of PIIS are examined. We find that the temporal variability of velocity-dependent melt rates under tidal forcing is greater than that of velocity-independent melt rates. Our experiments suggest that because tidal currents under PIIS are weak and buoyancy fluxes are strong, tidal mixing is negligible and tidal rectification is restricted to very steep bathymetric features, such as the ice shelf front. Nonetheless, strong tidally-rectified currents at the ice shelf front significantly increase ablation rates there when the formulation of the transfer coefficients includes the velocity dependence. The enhanced melting then feedbacks positively on the rectified currents, which are susceptible to insulate the cavity interior from changes in open ocean conditions.

Description: National Science and Engineering Research Council of Canada