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The internal wave climate in the deep Arctic Ocean, away from the shelves, is quiet because the ice cover shields the ocean from wind energy input, and tidal amplitudes are small. Hence, mixing due to internal wave breaking is small. The shrinking Arctic sea ice cover, however, exposes more open ocean areas to energy transfer by wind. Consequently, more energetic near‐inertial internal waves (NIWs) may carry energy to the bottom, potentially enhancing deep mixing. In the deep Canadian Basin, weakly stratified layers with local buoyancy frequencies smaller than the wave frequency may prevent NIW propagation to the seafloor. We estimate the distribution of these near‐inertial turning depths from temperature and salinity data of the years 2005–2014. Near‐inertial turning depths are ubiquitous in the deep Canadian Basin at ∼2,750 m depth, between 100 and 1,200 m above the bottom. A deep homogeneous layer below 3,300 m is characterized by small squared buoyancy frequencies N2 ∼ 0 with locally unstable layers (N2 < 0). The turning depths reflect NIWs and hence limit their contribution to deep mixing, but the waves create an evanescent perturbation with exponentially decreasing amplitude that can interact with the bathymetry, especially above slopes and ridges where the height of the turning depths above the seafloor is small. After reflection, the main part of the wave energy is trapped between turning depths and the surface, so that a potential increase of wave energy input mainly affects mixing of mid‐depth water masses like the Atlantic Water. Plain Language Summary: Over the last couple of years, Arctic Ocean summer sea ice has decreased. The larger ice‐free regions imply more open areas for wind to act on the ocean surface. As a result, energy from the atmosphere goes into the ocean, triggering more energetic waves in the ocean interior. These internal waves carry energy over longer distances and mix the waters where they break. To better understand this process, we studied temperature and salinity data from 2005 to 2014. Our findings show widespread areas in the deep Canadian Basin, at around 2,750 m depth, where the further propagation of the waves is constrained by weak stratification. These depths are called near‐inertial turning depths, and they shorten the path of near‐inertial waves and isolate the bottom from waves and mixing. In addition, we found weakly stratified and unstable layers below 3,300 m. Our results shed light on the link of surface‐generate waves to the interior mixing rates in the Arctic Ocean. Key Points: In the deep Canadian Basin, there are near‐inertial turning depths between 100 and 1,200 m above the seafloorBelow the turning depths, the deep layer is quasi‐homogeneous and locally unstableNear‐inertial turning depths inhibit internal gravity wave propagation and hence reduce near bottom mixing [ABSTRACT FROM AUTHOR]

Most viscous‐plastic sea ice models use the elliptical yield curve. This yield curve has a fundamental flaw: it excludes acute angles between deformation features at high resolution. Conceptually, the teardrop (TD) and parabolic lens (PL) yield curves offer an attractive alternative. These yield curves feature a non‐symmetrical shape, a Coulombic behavior for the low‐medium compressive stress, and a continuous transition to the ridging‐dominant mode, but their published formulation leads to negative or zero bulk and shear viscosities and, consequently, poor numerical convergence with stress states at times outside the yield curve. These issues are a consequence of the original assumption that the constitutive equations of the commonly used elliptical yield curve are also applicable to non‐symmetrical yield curves and yield curves with tensile strength. We derive a corrected formulation for the constitutive relations of the TD and PL yield curves. Results from simple uni‐axial loading experiments show that with the new formulation the numerical convergence of the solver improves and much smaller nonlinear residuals after a smaller number of total solver iterations can be reached, resulting in significant improvements in numerical efficiency and representation of the stress and deformation fields. The TD and PL yield curves lead to smaller angles of failure that better agree with observations. They are promising candidates to replace the elliptical yield curve in high‐resolution pan‐Arctic sea ice simulations. Plain Language Summary: Sea ice is a complicated dynamical system. It consists of many individual floes that interact in many ways. A sea‐ice model must contain many simplifying assumptions, sacrificing some observed properties. It is common to treat sea ice as an unusual fluid that behaves like an ideal plastic material and deforms permanently under high external loading (e.g., strong winds). The law that describes how the material yields to high loading contains a yield curve. This curve is usually an ellipse, a mathematically simple and acceptable approximation to the real yield curve. However, this yield curve cannot reproduce the orientation of conjugate failure lines when sea ice breaks. This paper discusses alternative yield curve shapes, the teardrop and parabolic lens yield curves, to reflect the sea ice's granular nature more accurately. We present improved constitutive equations that solve three issues in the original formulation that led to poor numerical and nonphysical behavior. Simple numerical experiments show that the improved formulation leads to a reduction of the computing time and large improvements in the representation of stresses and deformation within the sea‐ice model. The new formulation creates pairs of failure lines with smaller and more realistic angles than with the elliptical yield curve. Key Points: The constitutive equation of the elliptical yield curve is not applicable to yield curves such as the teardrop (TD) or parabolic lens (PL)We present new constitutive equations for the TD and PL that solve this problem and improve numerical convergenceThe TD and PL yield curves lead to failure angles that better agree with observations [ABSTRACT FROM AUTHOR]

As the sea‐ice modeling community is shifting to advanced numerical frameworks, developing new sea‐ice rheologies, and increasing model spatial resolution, ubiquitous deformation features in the Arctic sea ice are now being resolved by sea‐ice models. Initiated at the Forum for Arctic Modeling and Observational Synthesis, the Sea Ice Rheology Experiment (SIREx) aims at evaluating state‐of‐the‐art sea‐ice models using existing and new metrics to understand how the simulated deformation fields are affected by different representations of sea‐ice physics (rheology) and by model configuration. Part 1 of the SIREx analysis is concerned with evaluation of the statistical distribution and scaling properties of sea‐ice deformation fields from 35 different simulations against those from the RADARSAT Geophysical Processor System (RGPS). For the first time, the viscous‐plastic (and the elastic‐viscous‐plastic variant), elastic‐anisotropic‐plastic, and Maxwell‐elasto‐brittle rheologies are compared in a single study. We find that both plastic and brittle sea‐ice rheologies have the potential to reproduce the observed RGPS deformation statistics, including multi‐fractality. Model configuration (e.g., numerical convergence, atmospheric representation, spatial resolution) and physical parameterizations (e.g., ice strength parameters and ice thickness distribution) both have effects as important as the choice of sea‐ice rheology on the deformation statistics. It is therefore not straightforward to attribute model performance to a specific rheological framework using current deformation metrics. In light of these results, we further evaluate the statistical properties of simulated Linear Kinematic Features in a SIREx Part 2 companion paper. Plain Language Summary: The ice in the Arctic Ocean is not continuous: it is broken into individual pieces of ice (floes). As the winds and ocean currents continually move these ice floes, they get piled up together or pushed away from each other, forming regions of increased ice thickness (ridges) or regions of open water (leads). These leads and ridges (ice deformations) are important features of the Arctic pack ice because they control the amount of energy that can be exchanged between the atmosphere and the ocean. Current climate models cannot simulate individual ice floes and their deformations. Instead, various methods are used to represent the movement and deformation of the Arctic sea‐ice cover. The goal of the Sea Ice Rheology Experiment (SIREx) is to compare these different methods and evaluate the ability of a large number of sea‐ice models to reproduce observed sea‐ice deformations from satellite imagery. SIREx is divided in two parts. In Part 1 (this study), we evaluate how the intensity of ice deformations varies in space and time. In Part 2 (companion paper), we track and evaluate the occurrence of specific deformation features. With this work, we show how to improve sea‐ice models for realistic simulations of sea‐ice deformations. Key Points: Power law scaling and multi‐fractality of deformations in space and time can be achieved by both plastic and brittle sea‐ice rheologiesScaling statistics of simulated sea‐ice deformation fields depend on the model configuration and physical parameterizationsFinite‐difference plastic models need to be run at higher resolution than observations to agree with the observed deformation statistics [ABSTRACT FROM AUTHOR]

Simulating sea ice drift and deformation in the Arctic Ocean is still a challenge because of the multiscale interaction of sea ice floes that compose the Arctic Sea ice cover. The Sea Ice Rheology Experiment (SIREx) is a model intercomparison project of the Forum of Arctic Modeling and Observational Synthesis (FAMOS). In SIREx, skill metrics are designed to evaluate different recently suggested approaches for modeling linear kinematic features (LKFs) to provide guidance for modeling small‐scale deformation. These LKFs are narrow bands of localized deformation that can be observed in satellite images and also form in high resolution sea ice simulations. In this contribution, spatial and temporal properties of LKFs are assessed in 36 simulations of state‐of‐the‐art sea ice models and compared to deformation features derived from the RADARSAT Geophysical Processor System. All simulations produce LKFs, but only very few models realistically simulate at least some statistics of LKF properties such as densities, lengths, or growth rates. All SIREx models overestimate the angle of fracture between conjugate pairs of LKFs and LKF lifetimes pointing to inaccurate model physics. The temporal and spatial resolution of a simulation and the spatial resolution of atmospheric boundary condition affect simulated LKFs as much as the model's sea ice rheology and numerics. Only in very high resolution simulations (≤2 km) the concentration and thickness anomalies along LKFs are large enough to affect air‐ice‐ocean interaction processes. Plain Language Summary: Winds and ocean currents continuously move and deform the sea ice cover of the Arctic Ocean. The deformation eventually breaks an initially closed ice cover into many individual floes, piles up floes, and creates open water. The distribution of ice floes and open water between them is important for climate research, because ice reflects more light and energy back to the atmosphere than open water, so that less ice and more open water leads to warmer oceans. Current climate models cannot simulate sea ice as individual floes. Instead, a variety of methods is used to represent the movement and deformation of the sea ice cover. The Sea Ice Rheology Experiment (SIREx) compares these different methods and assesses the deformation of sea ice in 36 numerical simulations. We identify and track deformation features in the ice cover, which are distinct narrow areas where the ice is breaking or piling up. Comparing specific spatial and temporal properties of these features, for example, the different amounts of fractured ice in specific regions, or the duration of individual deformation events, to satellite observations provides information about the realism of the simulations. From this comparison, we can learn how to improve sea ice models for more realistic simulations of sea ice deformation. Key Points: All models simulate linear kinematic features (LKFs), but none accurately reproduces all LKF statisticsResolved LKFs are affected strongest by spatial and temporal resolution of model grid and atmospheric forcing and rheologyAccurate scaling of deformation rates is a proxy only for realistic LKF numbers but not for any other LKF static [ABSTRACT FROM AUTHOR]

Basal melting of marine‐terminating glaciers, through its impact on the forces that control the flow of the glaciers, is one of the major factors determining sea level rise in a world of global warming. Detailed quantitative understanding of dynamic and thermodynamic processes in melt‐water plumes underneath the ice‐ocean interface is essential for calculating the subglacial melt rate. The aim of this study is therefore to develop a numerical model of high spatial and process resolution to consistently reproduce the transports of heat and salt from the ambient water across the plume into the glacial ice. Based on boundary layer relations for momentum and tracers, stationary analytical solutions for the vertical structure of subglacial non‐rotational plumes are derived, including entrainment at the plume base. These solutions are used to develop and test convergent numerical formulations for the momentum and tracer fluxes across the ice‐ocean interface. After implementation of these formulations into a water‐column model coupled to a second‐moment turbulence closure model, simulations of a transient rotational subglacial plume are performed. The simulated entrainment rate of ambient water entering the plume at its base is compared to existing entrainment parameterizations based on bulk properties of the plume. A sensitivity study with variations of interfacial slope, interfacial roughness and ambient water temperature reveals substantial performance differences between these bulk formulations. An existing entrainment parameterization based on the Froude number and the Ekman number proves to have the highest predictive skill. Recalibration to subglacial plumes using a variable drag coefficient further improves its performance. Plain Language Summary: In a world of global warming, the melting of glaciers terminating as floating ice tongues into the oceans of Arctic and Antarctic regions allows those glaciers to flow faster and hence to make a considerable contribution to global mean sea‐level rise. Underneath the ice‐ocean interface, turbulent currents of the order of 10 m thickness (so‐called plumes) develop that transport the melt water from the grounding line where the glacier enters the ocean toward the calving front that marks the seaward end of the glacier. At its base, ambient relatively warm and salty ocean water is mixed into the plumes and is vertically transported toward the ice‐ocean interface, where the melting is increased due to the additional heat supply. Understanding these processes is essential for their incorporation into computer models for the prediction of such melt processes. In this study, an accurate simulation model for the water column is constructed that is able to consistently reproduce these processes. The algorithms developed here are proven to provide reliable results also for models with only a few grid points across the plume and can therefore be implemented into climate models with surface‐following coordinates to more accurately simulate future scenarios of sea level rise. Key Points: A vertically resolving model with second‐moment turbulence closure has been constructed for subglacial plumesConvergent numerical formulations for the ocean‐to‐ice fluxes of momentum, freshwater and heat have been derived from an analytical modelModel results are consistent with bulk parameterizations for the entrainment of ambient water [ABSTRACT FROM AUTHOR]

The extreme Arctic sea ice minima in the twenty-first century have been attributed to multiple factors, such as anomalous atmospheric circulation, excess solar radiation absorbed by open ocean, and thinning sea ice in a warming world. Most likely it is the combination of these factors that drives the extreme sea ice minima, but how the factors rank in setting the conditions for these events has not been quantified. To address this question, the sea ice budget of an Arctic regional sea ice–ocean model forced by atmospheric reanalysis data is analyzed to assess the development of the observed sea ice minima. Results show that the ice area difference in the years 2012, 2019, and 2007 is driven to over 60% by the difference in summertime sea ice area loss due to air–ocean heat flux over open water. Other contributions are small. For the years 2012 and 2020 the situation is different and more complex. The air–ice heat flux causes more sea ice area loss in summer 2020 than in 2012 due to warmer air temperatures, but this difference in sea ice area loss is compensated by reduced advective sea ice loss out of the Arctic Ocean mainly caused by the relaxation of the Arctic dipole. The difference in open water area in early August leads to different air–ocean heat fluxes, which distinguishes the sea ice minima in 2012 and 2020. Further, sensitivity experiments indicate that both the atmospheric circulation associated with the Arctic dipole and extreme storms are essential conditions for a new low record of sea ice extent. [ABSTRACT FROM AUTHOR]

The standard viscous–plastic (VP) sea ice model with an elliptical yield curve and a normal flow rule has at least two issues. First, it does not simulate fracture angles below 30 ∘ in uni-axial compression, in contrast with observations of linear kinematic features (LKFs) in the Arctic Ocean. Second, there is a tight, but unphysical, coupling between the fracture angle, post-fracture deformation, and the shape of the yield curve. This tight coupling was identified as the reason for the overestimation of fracture angles. In this paper, these issues are addressed by removing the normality constraint on the flow rule in the standard VP model. The new rheology is tested in numerical uni-axial loading tests. To this end, an elliptical plastic potential – which defines the post-fracture deformations, or flow rule – is introduced independently of the elliptical yield curve. As a consequence, the post-fracture deformation is decoupled from the mechanical strength properties of the ice. We adapt Roscoe's angle theory, which is based on observations of granular materials, to the context of sea ice modeling. In this framework, the fracture angles depend on both yield curve and plastic potential parameters. This new formulation predicts accurately the results of the numerical experiments with a root-mean-square error below 1.3 ∘. The new rheology allows for angles of fracture smaller than 30 ∘ in uni-axial compression. For instance, a plastic potential with an ellipse aspect ratio smaller than 2 (i.e., the default value in the standard viscous–plastic model) can lead to fracture angles as low as 22 ∘. Implementing an elliptical plastic potential in the standard VP sea ice model requires only small modifications to the standard VP rheology. The momentum equations with the modified rheology, however, are more difficult to solve numerically. The independent plastic potential solves the two issues with VP rheology addressed in this paper: in uni-axial loading experiments, it allows for smaller fracture angles, which fall within the range of satellite observations, and it decouples the angle of fracture and the post-fracture deformation from the shape of the yield curve. The orientation of the post-fracture deformation along the fracture lines (convergence and divergence), however, is still controlled by the shape of the plastic potential and the location of the stress state on the yield curve. A non-elliptical plastic potential would be required to change the orientation of deformation and to match deformation statistics derived from satellite measurements. [ABSTRACT FROM AUTHOR]

Optically active water constituents attenuate solar radiation and hence affect the vertical distribution of energy in the upper ocean. To understand their implications, we operate an ocean biogeochemical model coupled to a general circulation model with sea ice. Incorporating the effect of phytoplankton and colored dissolved organic matter (CDOM) on light attenuation in the model increases the sea surface temperature in summer and decreases sea ice concentration in the Arctic Ocean. Locally, the sea ice season is reduced by up to one month. CDOM drives a significant part of these changes, suggesting that an increase of this material will amplify the observed Arctic surface warming through its direct thermal effect. Indirectly, changing advective processes in the Nordic Seas may further intensify this effect. Our results emphasize the phytoplankton and CDOM feedbacks on the Arctic ocean and sea ice system and underline the need to consider these effects in future modeling studies to enhance their plausibility. Plain Language Summary: The amount of microalgae and colored dissolved organic material in the ocean determines how much light is absorbed in the surface waters and how much can reach greater depths. The vertical distribution of energy affects the upper ocean temperature and general circulation. Here, we use a numerical ocean model with biogeochemistry and sea ice, in which the individual effects of microalgae and colored dissolved organic matter can be turned on and off separately. When both effects are turned on, the summertime surface temperatures in the Arctic are larger and consequently more sea ice melts, so that the sea ice season is shorter by up to one month. We find that, to a large extent, the colored dissolved material is responsible for these changes. An increase of this material due to climate change will amplify the observed Arctic surface warming. For better projections of climate change, new models should account for the effect of these light‐absorbing water constituents. Key Points: Colored dissolved material is responsible for a significant part of the induced surface warming and sea ice loss in the Arctic OceanThe combined effect of optical constituents reduces the sea ice season by up to one monthConsidering the properties of optical constituents and their variability will enhance the plausibility of future modeling studies [ABSTRACT FROM AUTHOR]

Sea ice models have become essential components of weather, climate, and ocean models. A realistic representation of sea ice affects the reliability of process representation, environmental forecast, and climate projections. Realistic simulations of sea ice kinematics require the consideration of both large scale and fine scale geomorphological structures such as linear kinematic features (LKF). We propose a multi scale directional analysis (MDA) that diagnoses the spatial characteristics of LKFs. The MDA is different from previous analyses in that it (i) does not detect LKFs as objects, (ii) takes into account the width of LKFs, and (iii) estimates scale-dependent orientation and intersection angles. The MDA is applied to pairs of deformation fields derived from satellite remote sensing data and from a numerical model simulation with a horizontal grid spacing of; 4.5 km. The orientation and intersection angles of LKFs agree with the observations and confirm the visual impression that the intersection angles tend to be smaller in the satellite data compared to the model data. The MDA distributions can be used to compare satellite data and numerical model fields using conventional metrics such as a Euclidean distance, the Bhattacharyya coefficient, or the Earth mover’s distance. The latter is found to be the most meaningful metric to compare distributions of LKF orientations and intersection angles. The MDA proposed here provides a tool to diagnose if modified sea ice rheologies lead to more realistic simulations of LKFs. [ABSTRACT FROM AUTHOR]

This paper describes and evaluates the assimilation component of a seamless sea ice prediction system, which is developed based on the fully coupled Alfred Wegener Institute, Helmholtz Center for Polar and Marine Research Climate Model (AWI‐CM, v1.1). Its ocean/ice component with unstructured‐mesh discretization and smoothly varying spatial resolution enables seamless sea ice prediction across a wide range of space and time scales. The model is complemented with the Parallel Data Assimilation Framework to assimilate observations in the ocean/ice component with an Ensemble Kalman Filter. The focus here is on the data assimilation of the prediction system. First, the performance of the system is tested in a perfect‐model setting with synthetic observations. The system exhibits no drift for multivariate assimilation, which is a prerequisite for the robustness of the system. Second, real observational data for sea ice concentration, thickness, drift, and sea surface temperature are assimilated. The analysis results are evaluated against independent in situ observations and reanalysis data. Further experiments that assimilate different combinations of variables are conducted to understand their individual impacts on the model state. In particular, assimilating sea ice drift improves the sea ice thickness estimate, and assimilating sea surface temperature is able to avert a circulation bias of the free‐running model in the Arctic Ocean at middepth. Finally, we present preliminary results obtained with an extended system where the atmosphere is constrained by nudging toward reanalysis data, revealing challenges that still need to be overcome to adapt the ocean/ice assimilation. We consider this system a prototype on the way toward strongly coupled data assimilation across all model components. Plain Language Summary: Sea ice prediction over seasonal time scale has attracted the focus from both the scientific and socioeconomic communities recently. We develop a system aiming for seamless sea ice prediction using a coupled model that is equipped with an unstructured ocean/sea ice component. The high‐resolution mesh over the polar regions allows us to explore its possible benefits on the prediction across a wide range of time scales. To this end, the sea surface temperature, sea ice concentration, sea ice thickness, and sea ice drift observations are assimilated in the current system to diagnose the performance of the model initialization for future forecasts. Key Points: A data assimilation system is developed for seamless sea ice prediction on a climate model equipped with an unstructured ocean/ice componentThe system performance is examined based on experiments assimilating synthetic (perfect model) and real observationsMultivariate assimilation of sea ice drift and sea surface temperature remarkably improves the ocean/ice model state in the polar regions [ABSTRACT FROM AUTHOR]

The sea ice modeling community is progressing towards pan-Arctic simulations that explicitly resolve leads in the simulated sea ice cover. Evaluating these simulations against observations poses new challenges. A new feature-based evaluation of simulated deformation fields is introduced, and the results are compared to a scaling analysis of sea ice deformation. Leads and pressure ridges – here combined into linear kinematic features (LKFs) – are detected and tracked automatically from deformation and drift data. LKFs in two pan-Arctic sea ice simulations with a horizontal grid spacing of 2 km are compared with an LKF dataset derived from the RADARSAT Geophysical Processor System (RGPS). One simulation uses a five-class ice thickness distribution (ITD). The simulated sea ice deformation follows a multi-fractal spatial and temporal scaling, as observed from RGPS. The heavy-tailed distribution of LKF lengths and the scale invariance of LKF curvature, which points to the self-similar nature of sea ice deformation fields, are reproduced by the model. Interannual and seasonal variations in the number of LKFs, LKF densities, and LKF orientations in the ITD simulation are found to be consistent with RGPS observations. The lifetimes and growth rates follow a distribution with an exponential tail. The model overestimates the intersection angle of LKFs, which is attributed to the model's viscous-plastic rheology with an elliptical yield curve. In conclusion, the new feature-based analysis of LKF statistics is found to be useful for a comprehensive evaluation of simulated deformation features, which is required before the simulated features can be used with confidence in the context of climate studies. As such, it complements the commonly used scaling analysis and provides new useful information for comparing deformation statistics. The ITD simulation is shown to reproduce LKFs sufficiently well for it to be used for studying the effect of directly resolved leads in climate simulations. The feature-based analysis of LKFs also identifies specific model deficits that may be addressed by specific parameterizations, for example, a damage parameter, a grounding scheme, and a Mohr–Coulombic yield curve. [ABSTRACT FROM AUTHOR]

Sea ice data assimilation can greatly improve forecasts of Arctic sea ice evolution. Many previous sea ice data assimilation studies were conducted without assimilating ocean state variables, even though the sea ice evolution is closely linked to the oceanic conditions, both dynamically and thermodynamically. Based on the method of a localized ensemble error subspace transform Kalman filter, satellite‐retrieved sea ice concentration and sea ice thickness are assimilated into an Arctic sea ice‐ocean model. As a new addition, sea surface temperature (SST) data are also assimilated. The additional assimilation of SST improves not only the simulated ocean temperature in the mixed layer of the ocean substantially but also the accuracy of sea ice edge position, sea ice extent, and sea ice thickness in the marginal sea ice zone. The improvement in the simulated potential temperature in the upper 1,000 m can be attributed to the enhanced vertical convection processes in the regions where the assimilated observational SST is colder than the simulated SST without assimilation. The improvements in the sea ice edge position and sea ice thickness simulations are primarily caused by the SST data assimilation reducing biases in the simulated SST and the associated coupled ocean‐sea ice processes. Our investigation suggests that, due to the complex interaction between the sea ice and ocean, assimilating ocean data should be an indispensable component of numerical polar sea ice forecasting systems. Key Points: Sea surface temperature assimilation improves upper ocean temperature, sea ice edge, and marginal sea ice thickness simulationsSimulated upper ocean temperatures improve more where vertical convection processes are more importantSea ice edge and thickness simulations are improved due to the correction of the SST bias [ABSTRACT FROM AUTHOR]

Recent high-resolution pan-Arctic sea ice simulations show fracture patterns (linear kinematic features or LKFs) that are typical of granular materials but with wider fracture angles than those observed in high-resolution satellite images. Motivated by this, ice fracture is investigated in a simple uni-axial loading test using two different viscous–plastic (VP) rheologies: one with an elliptical yield curve and a normal flow rule and one with a Coulombic yield curve and a normal flow rule that applies only to the elliptical cap. With the standard VP rheology, it is not possible to simulate fracture angles smaller than 30∘. Further, the standard VP model is not consistent with the behavior of granular material such as sea ice because (1) the fracture angle increases with ice shear strength; (2) the divergence along the fracture lines (or LKFs) is uniquely defined by the shear strength of the material with divergence for high shear strength and convergent with low shear strength; (3) the angle of fracture depends on the confining pressure with more convergence as the confining pressure increases. This behavior of the VP model is connected to the convexity of the yield curve together with use of a normal flow rule. In the Coulombic model, the angle of fracture is smaller (θ=23∘) and grossly consistent with observations. The solution, however, is unstable when the compressive stress is too large because of non-differentiable corners between the straight limbs of the Coulombic yield curve and the elliptical cap. The results suggest that, although at first sight the large-scale patterns of LKFs simulated with a VP sea ice model appear to be realistic, the elliptical yield curve with a normal flow rule is not consistent with the notion of sea ice as a pressure-sensitive and dilatant granular material. [ABSTRACT FROM AUTHOR]

Leads and pressure ridges are dominant features of the Arctic sea ice cover. Not only do they affect heat loss and surface drag, but they also provide insight into the underlying physics of sea ice deformation. Due to their elongated shape they are referred to as linear kinematic features (LKFs). This paper introduces two methods that detect and track LKFs in sea ice deformation data and establish an LKF data set for the entire observing period of the RADARSAT Geophysical Processor System (RGPS). Both algorithms are available as open-source code and applicable to any gridded sea ice drift and deformation data. The LKF detection algorithm classifies pixels with higher deformation rates compared to the immediate environment as LKF pixels, divides the binary LKF map into small segments, and reconnects multiple segments into individual LKFs based on their distance and orientation relative to each other. The tracking algorithm uses sea ice drift information to estimate a first guess of LKF distribution and identifies tracked features by the degree of overlap between detected features and the first guess. An optimization of the parameters of both algorithms, as well as an extensive evaluation of both algorithms against handpicked features in a reference data set, is presented. A LKF data set is derived from RGPS deformation data for the years from 1996 to 2008 that enables a comprehensive description of LKFs. LKF densities and LKF intersection angles derived from this data set agree well with previous estimates. Further, a stretched exponential distribution of LKF length, an exponential tail in the distribution of LKF lifetimes, and a strong link to atmospheric drivers, here Arctic cyclones, are derived from the data set. Both algorithms are applied to output of a numerical sea ice model to compare the LKF intersection angles in a high-resolution Arctic sea ice simulation with the LKF data set. [ABSTRACT FROM AUTHOR]

Against the backdrop of Arctic sea ice decline, vertical mixing in the interior Arctic Ocean will most likely change, but it is still unclear how the Arctic Ocean and sea ice will respond. In this paper, a sea ice‐ocean model with a simple parameterization for interior background mixing is used to investigate the Arctic Ocean and sea ice response to a scenario of increased vertical mixing. It is found that more vertical mixing reduces sea ice thickness all year round and decreases summertime sea ice concentration. More vertical mixing leads to a cooling of the Arctic halocline layer and Atlantic Water layer below. The increased vertical mixing speeds up vertical heat and salinity exchange, brings the underlying warm and saline water into the surface layer, and contributes to the sea ice decline. Vertical salinity gradient of the Arctic halocline layer reduces together with a much fresher Atlantic Water layer, and more volume of saline water enters the deep ocean below the Atlantic Water layer. As a result, the reduced Arctic Ocean stratification leads to an adjustment of the circulation pattern. Cyclonic circulation anomalies occur in the surface layer shallower than 20‐m depth and in the interior ocean deeper than 700‐m depth, while anticyclonic circulation anomalies occur between these depths. Our study suggests that the extra heat and salinity exchange induced by more vertical mixing will have a noticeable impact on the upper ocean structure, ocean circulation, and sea ice in a changing Arctic Ocean. Plain Language Summary: In the Arctic, sea ice can isolate the ocean from wind forcing. So now, the Arctic Ocean is in a quasi‐motionless status. When global warming continues, sea ice in the Arctic Ocean will decrease, more wind energy will input into the ocean, then the Arctic Ocean will become active. More frequently, vertical heat and salt exchanges will happen. The heat in the deep ocean will be transported to the surface, then sea ice will further melt. Meanwhile, vertical distribution changes of temperature and salinity in the Arctic Ocean will induce changes of ocean currents. Key Points: Increased vertical mixing leads to a cooling of the Arctic halocline layer and Atlantic Water layerThe reduced Arctic Ocean stratification induces an adjustment of the circulation patternMore vertical mixing reduces sea ice thickness all year round and decreases summertime sea ice concentration [ABSTRACT FROM AUTHOR]

A key parameterization in sea ice models describes the subgrid scale ice thickness distribution. Based on only a few observations, the ice thickness distribution model was shown to be consistent with field data and to improve the simulation's large‐scale properties. The available submarine and airborne observations enable to evaluate in greater detail the ability of a pan‐Arctic sea ice‐ocean model with an ice thickness distribution parameterization to reproduce observed thickness distributions in different regions and seasons. Many observations are reproduced accurately. Some cases of poorly simulated modes and tails of the distributions are tentatively attributed to simplified thermodynamics and inaccurate deformation fields. Variability on decadal timescales, however, is generally underestimated. Thickness distributions in individual grid cells of the model show similar differences between regions and seasons as observed regional mean distributions, but the modeled grid‐scale variability is lower than observed. Simulated modal thicknesses of first‐year ice are only insufficiently different from those of multiyear ice. The modal thickness proves to be a useful metric for quantifying model biases in both dynamics and thermodynamics. In addition to improving basin‐wide mean variables, the ice thickness distribution parameterization provides reliable and valuable additional subgrid scale data. At the same time the low climate sensitivity of the parameterization may affect longer simulations with strong climate change aspects. Plain Language Summary: Sea ice is part of the climate system: computer models of sea ice are necessary for climate simulation. Many processes that shape sea ice in the Arctic Ocean cannot be represented in a computer model. For example, a sea ice model cannot distinguish between different ice thicknesses that are observed in a given area, but requires a submodel to calculate these ice thickness distributions, a model within the model. Any submodel must be tested against observations before it can be used with confidence. Here we repeat previous tests of the ice thickness distribution submodel, which had some data limitations, with a larger data set of new observations and a sea ice model of the entire Arctic Ocean. We find that the submodel works very well in many cases. Unfortunately, the model simulations do not agree with observed changes that happen slowly over 20 years and they do not contain as many small fluctuations as the observations. As a by‐product we find that we can learn a lot about computer models when we not only compare mean ice thickness to observations, but also the most frequent ice thickness. Key Points: Recent observations allow to evaluate ice thickness distributions in the Arctic on regional to local scalesA pan‐Arctic model simulates the observed regional and seasonal range of ice thickness distributions with some skillThe model underestimates the decadal variability of ice thickness distributions [ABSTRACT FROM AUTHOR]

Exploiting the complementary character of CryoSat‐2 and Soil Moisture and Ocean Salinity satellite sea ice thickness products, daily Arctic sea ice thickness estimates from October 2010 to December 2016 are generated by an Arctic regional ice‐ocean model with satellite thickness assimilated. The assimilation is performed by a Local Error Subspace Transform Kalman filter coded in the Parallel Data Assimilation Framework. The new estimates can be generally thought of as combined model and satellite thickness (CMST). It combines the skill of satellite thickness assimilation in the freezing season with the model skill in the melting season, when neither CryoSat‐2 nor Soil Moisture and Ocean Salinity sea ice thickness is available. Comparisons with in situ observations from the Beaufort Gyre Exploration Project, Ice Mass Balance Buoys, and the NASA Operation IceBridge demonstrate that CMST reproduces most of the observed temporal and spatial variations. Results also show that CMST compares favorably to the Pan‐Arctic Ice‐Ocean Modeling and Assimilation System product and even appears to correct known thickness biases in the Pan‐Arctic Ice‐Ocean Modeling and Assimilation System. Due to imperfect parameterizations in the sea ice model and satellite thickness retrievals, CMST does not reproduce the heavily deformed and ridged sea ice along the northern coast of the Canadian Arctic Archipelago and Greenland. With the new Arctic sea ice thickness estimates sea ice volume changes in recent years can be further assessed. Plain Language Summary: Sea ice plays a crucial role in climate changes; however, sea ice thickness is difficult to measure directly from space. The novel satellite thickness products from CryoSat‐2 and Soil Moisture and Ocean Salinity have complementary characters, which facilitate the assimilation into the model to generate a new Arctic thickness record in this study. Also, benefitting from the model dynamics and sea ice concentration assimilation, the new data can further cover the melting seasons when satellite thickness data are unavailable. Compared to the in situ observations, the new thickness data show some advantages over the statistically merged satellite product CS2SMOS and Pan‐Arctic Ice‐Ocean Modeling and Assimilation System thickness product. Key Points: A new Arctic sea ice thickness record is generated by assimilating CryoSat‐2 and SMOS thickness products simultaneouslyThe new sea ice thickness data are close to satellite data in freezing seasons and further cover the summer seasonsComparisons with in situ observations show that the new record has some advantages over PIOMAS and CS2SMOS thickness [ABSTRACT FROM AUTHOR]

The impact of tides on the simulated landfast ice cover is investigated. Pan‐Arctic simulations are conducted with an ice‐ocean (CICE‐NEMO) model with a modified rheology and a grounding scheme. The reference experiment (without tides) indicates there is an overestimation of the extent of landfast ice in regions of strong tides such as the Gulf of Boothia, Prince Regent Inlet, and Lancaster Sound. The addition of tides in the simulation clearly leads to a decrease of the extent of landfast ice in some tidally active regions. This numerical experiment with tides is more in line with observations of landfast ice in all the regions studied. Thermodynamics and changes in grounding cannot explain the lower landfast ice area when tidal forcing is included. We rather demonstrate that this decrease in the landfast ice extent is dynamically driven by the increase of the ocean‐ice stress due to the tides. Plain Language Summary: Landfast ice is sea ice that is immobile near a coast for a certain period of time. This coastal ice can stay at rest because it is attached to the coast and/or anchored to the seafloor in shallow water. To study landfast ice, we used a numerical model that represents the physical interactions between the atmosphere, the ocean, and the sea ice. We compared two simulations done with this model: one without ocean tides and one that includes the tides. The experiment with tides exhibits a lower extent of landfast ice which is more in line with the observations. This decrease in the landfast ice extent when adding the tides is a dynamical process; the strong tidal currents constantly set the sea ice in motion, preventing it to become landfast. Key Points: Tides decrease the extent of simulated landfast ice in tidally active regionsSimulated landfast ice is more in line with the observationsThe lower extent of landfast ice is dynamically driven by the ocean stress on the ice [ABSTRACT FROM AUTHOR]

We present a dynamically consistent gridded data set of the global, monthly mean oxygen isotope ratio of seawater (δ18Osw). The data set was created from an optimized simulation of an ocean general circulation model constrained by global monthly δ18Osw data collected from 1950 to 2011 and climatological salinity and temperature data collected from 1951 to 1980. The optimization was obtained using the adjoint method for variational data assimilation, which yields a simulation that is consistent with the observational data and the physical laws embedded in the model. Our data set performs equally well as a previous data set in terms of model‐data misfit but brings an improvement in terms of the seasonal cycle and physical consistency. As a result the data set does not show any sharp transitions between water masses or in areas where the data coverage is low. The data assimilation method shows high potential for interpolating sparse data sets in a physically meaningful way. Comparatively big errors, however, are found in our data set in the surface levels in the Arctic Ocean mainly because the influence of isotopically highly depleted precipitation is not preserved in the sea ice model, and the low model resolution of about 285 km horizontally. The data set is publicly available, and it is anticipated to be useful for a large range of applications in (paleo‐) oceanographic studies. Plain Language Summary: The ratio of the heavier to the lighter oxygen isotope in seawater varies over different areas and for different water masses in the ocean. In this study we present a global gridded data set of the monthly mean oxygen isotope ratio of seawater (δ18Osw). The data set is publicly available and will be useful for a large range of applications. It can, for example, help to reconstruct past ocean states or be used as lower boundary for an atmospheric model to investigate the isotopic composition of the atmosphere. The data set is taken from a simulation of a numerical ocean model that is in consistency with global δ18Osw observations collected from 1950 to 2011 and monthly salinity and temperature observations collected from 1951 to 1980. To obtain the model simulation, we used a data assimilation method that brings the model simulation into consistency with the observational data. The ocean model is based on physical laws, and therefore, our data set is also in consistency with the ocean physics. Our data set is similarly close to the observations than a previous data set but brings an improvement because it is based on the ocean physics and because it has a seasonal cycle. Key Points: We present a physically consistent data set of the global, three‐dimensional oxygen isotopic distribution of the oceanThe optimization was obtained using the adjoint method to fit an ocean general circulation model to observational dataThe data set is available for potential applications in (paleo‐)oceanography [ABSTRACT FROM AUTHOR]

Many state-of-the-art coupled sea ice-ocean models use atmospheric and oceanic drag coefficients that are at best a function of the atmospheric stability but otherwise constant in time and space. Constant drag coefficients might lead to an incorrect representation of the ice-air and ice-ocean momentum exchange, since observations of turbulent fluxes imply high variability of drag coefficients. We compare three model runs, two with constant drag coefficients and one with drag coefficients varying as function of sea-ice characteristics. The computed drag coefficients range between 0.88 × 10 − 3 and 4.68 × 10 − 3 for the atmosphere, and between 1.28 × 10 − 3 and 13.68 × 10 − 3 for the ocean. They fall in the range of observed drag coefficients and illustrate the interplay of ice deformation and ice concentration in different seasons and regions. The introduction of variable drag coefficients improves the realism of the model simulation. In addition, using the average values of the variable drag coefficients improves simulations with constant drag coefficients. When drag coefficients depend on sea-ice characteristics, the average sea-ice drift speed in the Arctic basin increases from 6.22 cm s − 1 to 6.64 cm s − 1 . This leads to a reduction of ice thickness in the entire Arctic and particularly in the Lincoln Sea with a mean value decreasing from 7.86 m to 6.62 m. Variable drag coefficients lead also to a deeper mixed layer in summer and to changes in surface salinity. Surface temperatures in the ocean are also affected by variable drag coefficients with differences of up to 0.06 °C in the East Siberian Sea. Small effects are visible in the ocean interior [ABSTRACT FROM AUTHOR]

The impact of assimilating weekly CryoSat‐2 sea ice thickness data together with daily SMOS sea ice thickness and daily SSMIS sea ice concentration data on the sea ice fields of a coupled sea ice–ocean model of the Arctic Ocean is investigated. The sea‐ice model is based on the Massachusetts Institute of Technology general circulation model (MITgcm) and the assimilation is performed by a localized Singular Evolutive Interpolated Kalman (LSEIK) filter coded in the Parallel Data Assimilation Framework (PDAF). A period of three months from 1 November 2011 to 30 January 2012 is selected to assess the skill of the assimilation system in the cold season. Compared to the unassimilated solution and a solution where only sea ice concentration is assimilated, the model–data misfits are substantially reduced in areas of both thick and thin ice. The sea ice thickness estimates agree significantly better with in situ observations in the central Arctic Ocean than the sea ice thickness obtained from assimilating SMOS data alone, while the sea ice concentration shows very small improvements. The sea ice fields obtained by the joint assimilation of SMOS and CryoSat‐2 data also have lower errors in thickness and concentration than those obtained from directly assimilating a statistically merged SMOS and CryoSat‐2 sea ice thickness product. These lower errors suggest that model dynamics play a significant role in data blending. [ABSTRACT FROM AUTHOR]

Algae growing in sea ice represent a source of carbon for sympagic and pelagic ecosystems and contribute to the biological carbon pump. The biophysical habitat of sea ice on large scales and the physical drivers of algae phenology are key to understanding Arctic ecosystem dynamics and for predicting its response to ongoing Arctic climate change. In addition, quantifying potential feedback mechanisms between algae and physical processes is particularly important during a time of great change. These mechanisms include a shading effect due to the presence of algae and increased basal ice melt. The present study shows pan-Arctic results obtained from a new Sea Ice Model for Bottom Algae (SIMBA) coupled with a 3-D sea-ice-ocean model. The model is evaluated with data collected during a ship-based campaign to the Eastern Central Arctic in summer 2012. The algal bloom is triggered by light and shows a latitudinal dependency. Snow and ice also play a key role in ice algal growth. Simulations show that after the spring bloom, algae are nutrient limited before the end of summer and finally they leave the ice habitat during ice melt. The spatial distribution of ice algae at the end of summer agrees with available observations, and it emphasizes the importance of thicker sea-ice regions for hosting biomass. Particular attention is given to the distinction between level ice and ridged ice. Ridge-associated algae are strongly light limited, but they can thrive toward the end of summer, and represent an additional carbon source during the transition into polar night. [ABSTRACT FROM AUTHOR]

Recent developments of the explicit elastic-viscous-plastic (EVP) solvers call for a new comparison with implicit solvers for the equations of viscous-plastic sea ice dynamics. In Arctic sea ice simulations, the modified and the adaptive EVP solvers, and the implicit Jacobian–free Newton–Krylov (JFNK) solver are compared against each other. The adaptive EVP method shows convergence rates that are generally similar or even better than those of the modified EVP method, but the convergence of the EVP methods is found to depend dramatically on the use of the replacement pressure (RP). Apparently, using the RP can affect the pseudo-elastic waves in the EVP methods by introducing extra non-physical oscillations so that, in the extreme case, convergence to the VP solution can be lost altogether. The JFNK solver also suffers from higher failure rates with RP implying that with RP the momentum equations are stiffer and more difficult to solve. For practical purposes, both EVP methods can be used efficiently with an unexpectedly low number of sub-cycling steps without compromising the solutions. The differences between the RP solutions and the NoRP solutions (when the RP is not being used) can be reduced with lower thresholds of viscous regularization at the cost of increasing stiffness of the equations, and hence the computational costs of solving them. [ABSTRACT FROM AUTHOR]

The sensitivity of assimilating sea ice thickness data to uncertainty in atmospheric forcing fields is examined using ensemble-based data assimilation experiments with the Massachusetts Institute of Technology General Circulation Model (MITgcm) in the Arctic Ocean during November 2011-January 2012 and the Met Office (UKMO) ensemble atmospheric forecasts. The assimilation system is based on a local singular evolutive interpolated Kalman (LSEIK) filter. It combines sea ice thickness data derived from the European Space Agency's (ESA) Soil Moisture Ocean Salinity (SMOS) satellite and Special Sensor Microwave Imager/Sounder (SSMIS) sea ice concentration data with the numerical model. The effect of representing atmospheric uncertainty implicit in the ensemble forcing is assessed by three different assimilation experiments. The first two experiments use a single deterministic forcing dataset and a different forgetting factor to inflate the ensemble spread. The third experiment uses 23 members of the UKMO atmospheric ensemble prediction system. It avoids additional ensemble inflation and is hence easier to implement. As expected, the model-data misfits are substantially reduced in all three experiments, but with the ensemble forcing the errors in the forecasts of sea ice concentration and thickness are smaller compared to the experiments with deterministic forcing. This is most likely because the ensemble forcing results in a more plausible spread of the model state ensemble, which represents model uncertainty and produces a better forecast. [ABSTRACT FROM AUTHOR]

The decrease in summer sea-ice extent in the Arctic Ocean opens shipping routes and creates potential for many marine operations. For these activities accurate predictions of sea-ice conditions are required to maintain marine safety. In an attempt at Arctic sea-ice prediction, the summer of 2010 is selected to implement an Arctic sea-ice data assimilation (DA) study. The DA system is based on a regional Arctic configuration of the Massachusetts Institute of Technology general circulation model (MITgcm) and a local singular evolutive interpolated Kalman (LSEIK) filter to assimilate Special Sensor Microwave Imager/Sounder (SSMIS) sea-ice concentration operational products from the US National Snow and Ice Data Center (NSIDC). Based on comparisons with both the assimilated NSIDC SSMIS concentration and concentration data from the Ocean and Sea Ice Satellite Application Facility, the forecasted sea-ice edge and concentration improve upon simulations without data assimilation. By the nature of the assimilation algorithm with multivariate covariance between ice concentration and thickness, sea-ice thickness fields are also updated, and the evaluation with in situ observation shows some improvement compared to the forecast without data assimilation. [ABSTRACT FROM AUTHOR]

The role of atmospheric uncertainty for the assimilation and prediction of Arctic sea ice is explored by running the Massachusetts Institute of Technology general circulation model (MITgcm) in data assimilation (DA) and prediction mode for summer 2010. The atmospheric ensemble forcing is taken from the UK Met Office (UKMO) system available through the TIGGE (THORPEX Interactive Grand Global Ensemble) database. The DA system is based on a Local Singular Evolutive Interpolated Kalman (LSEIK) filter, and Special Sensor Microwave Imager/Sounder (SSMIS) sea ice concentration operational products from the National Snow and Ice Data Center (NSIDC) are assimilated. Two kinds of experiments are carried out differing in the LSEIK configuration and forcing used: the first one uses a single deterministic control forcing and a forgetting factor necessary to inflate the ensemble spread in the DA phase; the second one uses 23 members from the UKMO atmospheric ensemble prediction system, thereby avoiding any additional ensemble inflation and making further tuning unnecessary. With both systems the model data misfit improves as expected, but the ensemble approach outperforms the deterministic filter. The ice concentration of 24 h forecasts is consistently closer to observations with the ensemble approach, because a larger and more realistic ensemble spread, representing model uncertainty, leads to a better adjustment. Fifteen-day forecasts are also better with ensemble forcing than with deterministic forcing, because of both the larger spread and the better initial state in the ensemble forced system. The ensemble forcing can also improve poor initial states obtained with the deterministic control forcing, because the ensemble forcing introduces a larger spread that spans a larger range of model simulations. Ice thickness forecasts cannot be significantly improved with the ensemble forcing. [ABSTRACT FROM AUTHOR]

Abstract: The most common representation of sea ice dynamics in climate models assumes that sea ice is a quasi-continuous non-normal fluid with a viscous-plastic rheology. This rheology leads to non-linear sea ice momentum equations that are notoriously difficult to solve. Recently a Jacobian-free Newton–Krylov (JFNK) solver was shown to solve the equations accurately at moderate costs. This solver is extended for massive parallel architectures and vector computers and implemented in a coupled sea ice–ocean general circulation model for climate studies. Numerical performance is discussed along with numerical difficulties in realistic applications with up to 1920 CPUs. The parallel JFNK-solverʼs scalability competes with traditional solvers although the collective communication overhead starts to show a little earlier. When accuracy of the solution is required (i.e. reduction of the residual norm of the momentum equations of more that one or two orders of magnitude) the JFNK-solver is unrivalled in efficiency. The new implementation opens up the opportunity to explore physical mechanisms in the context of large scale sea ice models and climate models and to clearly differentiate these physical effects from numerical artifacts. [Copyright &y& Elsevier]

Between ~750 and 635 million years ago, during the Neoproterozoic era, the earth experienced at least two significant, possibly global, glaciations, termed 'Snowball Earth.' While many studies have focused on the dynamics and the role of the atmosphere and ice flow over the ocean in these events, only a few have investigated the related associated ocean circulation, and no study has examined the ocean circulation under a thick (~1 km deep) sea ice cover, driven by geothermal heat flux. Here, a thick sea ice-flow model coupled to an ocean general circulation model is used to study the ocean circulation under Snowball Earth conditions. The ocean circulation is first investigated under a simplified zonal symmetry assumption, and (i) strong equatorial zonal jets and (ii) a strong meridional overturning cell are found, limited to an area very close to the equator. The authors derive an analytic approximation for the latitude-depth ocean dynamics and find that the extent of the meridional overturning circulation cell only depends on the horizontal eddy viscosity and β (the change of the Coriolis parameter with latitude). The analytic approximation closely reproduces the numerical results. Three-dimensional ocean simulations, with reconstructed Neoproterozoic continental configuration, confirm the zonally symmetric dynamics and show additional boundary currents and strong upwelling and downwelling near the continents. [ABSTRACT FROM AUTHOR]

Abstract: Experiments with idealized geometry are used to compare model solutions of implicit VP- and explicit EVP-solvers in two very different ice-ocean codes: the regular-grid, finite-volume Massachusetts Institute of Technology general circulation model (MITgcm) and the Alfred Wegener Institute Finite Element Ocean Model (FEOM). It is demonstrated that for both codes the obtained solutions of implicit VP-and EVP-solvers can differ significantly, because the EVP solutions tend to have smaller ice viscosities (“weaker” ice). EVP solutions tend to converge only slowly to implicit VP solutions for very small sub-cycling time steps. Variable resolution in the unstructured-grid model FEOM also affects the solution as smaller grid cell size leads to smaller viscosity in EVP solutions. Models with implicit VP-solvers can block narrow straits under certain conditions, while EVP-models are found to always allow flow as a consequence of lower viscosities. [Copyright &y& Elsevier]

Abstract: This paper describes the sea ice component of the Massachusetts Institute of Technology general circulation model (MITgcm); it presents example Arctic and Antarctic results from a realistic, eddy-admitting, global ocean and sea ice configuration; and it compares B-grid and C-grid dynamic solvers and other numerical details of the parameterized dynamics and thermodynamics in a regional Arctic configuration. Ice mechanics follow a viscous-plastic rheology and the ice momentum equations are solved numerically using either line-successive-over-relaxation (LSOR) or elastic–viscous-plastic (EVP) dynamic models. Ice thermodynamics are represented using either a zero-heat-capacity formulation or a two-layer formulation that conserves enthalpy. The model includes prognostic variables for snow thickness and for sea ice salinity. The above sea ice model components were borrowed from current generation climate models but they were reformulated on an Arakawa C grid in order to match the MITgcm oceanic grid and they were modified in many ways to permit efficient and accurate automatic differentiation. Both stress tensor divergence and advective terms are discretized with the finite-volume method. The choice of the dynamic solver has a considerable effect on the solution; this effect can be larger than, for example, the choice of lateral boundary conditions, of ice rheology, and of ice-ocean stress coupling. The solutions obtained with different dynamic solvers typically differ by a few cms−1 in ice drift speeds, 50cm in ice thickness, and order 200km3 yr−1 in freshwater (ice and snow) export out of the Arctic. [Copyright &y& Elsevier]

Abstract: Vertical mixing and deep convection are routinely parameterized in basin-scale and global ocean general circulation models. These parameterizations are designed to work with homogeneous surface boundary conditions for an individual grid cell. A partial ice cover, however, yields heterogeneous fluxes of buoyancy that are not resolved by the computational grid. The effects of such heterogeneous surface boundary conditions are explored by comparing coarse resolution models with three common parameterizations for mixing and deep convection with large eddy simulations (LES) of free convection in idealized scenarios. Generally, models with parameterized convection reproduce the temperature profiles of the LES reference accurately when the surface boundary conditions are resolved by the grid. Significant biases are introduced when the surface boundary conditions are not resolved and buoyancy fluxes are averaged horizontally. These biases imply that mixing depths may locally be too shallow in large-scale simulations without proper handling of heterogeneous boundary conditions during convective events; also the grid cell averaged density may be vertically homogenized within the shallow boundary layer. Adaptation of present mixing schemes may overcome these spurious effects of horizontally averaging the surface buoyancy fluxes. [Copyright &y& Elsevier]

Abstract: A coding error in the s-Coordinate Primitive Equation Model (SPEM) has led to misleading statements about the behaviour of the Mellor–Yamada level 2 parameterization of vertical mixing. It has been claimed that the scheme removes static instability only very slowly and preserves statically unstable stratifications for an unrealistic long time. This note corrects this statement by demonstrating that the Mellor–Yamada mixing scheme, if implemented correctly, tends to overestimate rather than underestimate vertical mixing in seasonally ice-covered seas. Similar to other mixing schemes with the same behaviour, this leads to spurious open ocean deep convection, an unrealistic homogenization of the water column, and a significant reduction of sea ice volume. [Copyright &y& Elsevier]

We present a Newton-Krylov solver for a viscous-plastic sea-ice model. This constitutive relation is commonly used in climate models to describe the material properties of sea ice. Due to the strong nonlinearity introduced by the material law in the momentum equation, the development of fast, robust and scalable solvers is still a substantial challenge. In this paper, we propose a novel primal-dual Newton linearization for the implicitly-in-time discretized momentum equation. Compared to existing methods, it converges faster and more robustly with respect to mesh refinement, and thus enables numerically converged sea-ice simulations at high resolutions. Combined with an algebraic multigrid-preconditioned Krylov method for the linearized systems, which contain strongly varying coefficients, the resulting solver scales well and can be used in parallel. We present experiments for two challenging test problems and study solver performance for problems with up to 8.4 million spatial unknowns. • We propose a new Newton linearization for the sea-ice momentum equation. • The method results in fast and robust nonlinear convergence. • Combined with an algebraic multigrid method good parallel scalability is achieved. • The performance is compared to existing methods for two benchmarks. • We provide an implementation in the open-source Firedrake library. [ABSTRACT FROM AUTHOR]

Stability and convergence of the modified EVP implementation of the visco-plastic sea ice rheology by Bouillon et al., Ocean Modell., 2013, is analyzed on B- and C-grids. It is shown that the implementation on a B-grid is less restrictive with respect to stability requirements than on a C-grid. On C-grids convergence is sensitive to the discretization of the viscosities. We suggest to adaptively vary the parameters of pseudotime subcycling of the modified EVP scheme in time and space to satisfy local stability constraints. This new approach generally improves the convergence of the modified EVP scheme and hence its numerical efficiency. The performance of the new “adaptive EVP” approach is illustrated in a series of experiments with the sea ice component of the MIT general circulation model (MITgcm) that is formulated on a C-grid. [ABSTRACT FROM AUTHOR]

Most dynamic sea ice models for climate type simulations are based on the viscous–plastic (VP) rheology. The resulting stiff system of partial differential equations for ice velocity is either solved implicitly at great computational cost, or explicitly with added pseudo-elasticity (elastic–viscous–plastic, EVP). A recent modification of the EVP approach seeks to improve the convergence of the EVP method by re-interpreting it as a pseudotime VP solver. The question of convergence of this modified EVP method is revisited here and it is shown that convergence is reached provided the stability requirements are satisfied and the number of pseudotime iterations is sufficiently high. Only in this limit, the VP and the modified EVP solvers converge to the same solution. Related questions of the impact of mesh resolution and incomplete convergence are also addressed. [ABSTRACT FROM AUTHOR]

Abstract: Current sea ice models use numerical schemes based on a splitting in time between the momentum and continuity equations. Because the ice strength is explicit when solving the momentum equation, this can create unrealistic ice stress gradients when using a large time step. As a consequence, noise develops in the numerical solution and these models can even become numerically unstable at high resolution. To resolve this issue, we have implemented an iterated IMplicit–EXplicit (IMEX) time integration method. This IMEX method was developed in the framework of an already implemented Jacobian-free Newton–Krylov solver. The basic idea of this IMEX approach is to move the explicit calculation of the sea ice thickness and concentration inside the Newton loop such that these tracers evolve during the implicit integration. To obtain second-order accuracy in time, we have also modified the explicit time integration to a second-order Runge–Kutta approach and by introducing a second-order backward difference method for the implicit integration of the momentum equation. These modifications to the code are minor and straightforward. By comparing results with a reference solution obtained with a very small time step, it is shown that the approximate solution is second-order accurate in time. The new method permits to obtain the same accuracy as the splitting in time but by using a time step that is 10 times larger. Results show that the second-order scheme is more than five times more computationally efficient than the splitting in time approach for an equivalent level of error. [Copyright &y& Elsevier]

Abstract: The adjoint of an ocean general circulation model is at the heart of the ocean state estimation system of the Estimating the Circulation and Climate of the Ocean (ECCO) project. As part of an ongoing effort to extend ECCO to a coupled ocean/sea-ice estimation system, a dynamic and thermodynamic sea-ice model has been developed for the Massachusetts Institute of Technology general circulation model (MITgcm). One key requirement is the ability to generate, by means of automatic differentiation (AD), tangent linear (TLM) and adjoint (ADM) model code for the coupled MITgcm ocean/sea-ice system. This second part of a two-part paper describes aspects of the adjoint model. The adjoint ocean and sea-ice model is used to calculate transient sensitivities of solid (ice and snow) freshwater export through Lancaster Sound in the Canadian Arctic Archipelago (CAA). The adjoint state provides a complementary view of the dynamics. In particular, the transient, multi-year sensitivity patterns reflect dominant pathways and propagation timescales through the CAA as resolved by the model, thus shedding light on causal relationships, in the model, across the Archipelago. The computational cost of inferring such causal relationships from forward model diagnostics alone would be prohibitive. The role of the exact model trajectory around which the adjoint is calculated (and therefore of the exactness of the adjoint) is exposed through calculations using free-slip vs no-slip lateral boundary conditions. Effective ice thickness, sea surface temperature, and precipitation sensitivities, are discussed in detail as examples of the coupled sea-ice/ocean and atmospheric forcing control space. To test the reliability of the adjoint, finite-difference perturbation experiments were performed for each of these elements and the cost perturbations were compared to those “predicted” by the adjoint. Overall, remarkable qualitative and quantitative agreement is found. In particular, the adjoint correctly “predicts” a seasonal sign change in precipitation sensitivities. A physical mechanism for this sign change is presented. The availability of the coupled adjoint opens up the prospect for adjoint-based coupled ocean/sea-ice state estimation. [Copyright &y& Elsevier]

Abstract: Numerical convergence properties of a recently developed Jacobian-free Newton–Krylov (JFNK) solver are compared to the ones of the widely used EVP model when solving the sea ice momentum equation with a Viscous-Plastic (VP) formulation. To do so, very accurate reference solutions are produced with an independent Picard solver with an advective time step of 10s and a tight nonlinear convergence criterion on 10, 20, 40, and 80-km grids. Approximate solutions with the JFNK and EVP solvers are obtained for advective time steps of 10, 20 and 30min. Because of an artificial elastic term, the EVP model permits an explicit time-stepping scheme with a relatively large subcycling time step. The elastic waves excited during the subcycling are intended to damp out and almost entirely disappear such that the approximate solution should be close to the VP solution. Results show that residual elastic waves cause the EVP approximate solution to have notable differences with the reference solution and that these differences get more important as the grid is refined. Compared to the reference solution, additional shear lines and zones of strong convergence/divergence are seen in the EVP approximate solution. The approximate solution obtained with the JFNK solver is very close to the reference solution for all spatial resolutions tested. [Copyright &y& Elsevier]

Optically active water constituents can strongly attenuate in-water penetrative radiation and affect the upper ocean heat content. Arctic rivers supply the Arctic Ocean with a considerable amount of highly-absorbing organic material which is expected to increase, as a result of thawing permafrost in Siberia. Here, we investigate the effect of the variability of optically active water constituents on the heat budget of the Arctic Ocean. As a first step, we simulate locally the radiative heating by means of coupled atmosphere-ocean radiative transfer modelling (RTM SCIATRAN). By using satellite remote sensing retrievals of Coloured Dissolved Organic Matter (CDOM), Total Suspended Matter (TSM), Chlorophyll-a (Chl-a) and sea surface temperature data as input to the RTM simulations, we present the spatial distribution of potential radiative heating in the Laptev Sea. For upscaling, we use an ocean biogeochemical model coupled to a general circulation model (Darwin-MITgcm) to simulate the dynamics of the different constituents in response to Arctic amplification. We further set up the general circulation model to take into account the biogeochemical processes so that their feedback on Arctic Ocean's surface heating, stratification and sea ice melting can be assessed. Results show that high concentration of CDOM, TSM and Chl-a in Arctic waters increase the heating rate at the surface of the ocean and affect the heat fluxes to the atmosphere. The induced surface heating result in higher ice melting rates with potential implications to upper ocean stratification and primary production. [ABSTRACT FROM AUTHOR]

The use of elastic-viscous-plastic (EVP) solver to simulate sea ice dynamics is computationally demanding, especially at high resolution when linear kinematic features (leads, cracks) are present in solutions. At such resolutions, numerical stability requires that sub-cycling time steps be sufficiently short, therefore their number increases compared to low-resolution simulations. A modified formulation of the EVP solver changes the EVP algorithm such that its stability is no longer connected to the number of sub-cycles, which only determine convergence to the viscous-plastic rheology. It has been shown in a low-resolution setting (27 km in the Arctic Ocean) that practically appropriate solutions can be obtained with much smaller numbers of sub-cycles. We demonstrate that this conclusion carries over to high resolution when linear kinematic features such as leads emerge. We show that the computational burden can be dramatically reduced in 4.5 km Arctic Ocean simulations with FESOM2 sea ice-ocean model by using modified and adaptive versions of EVP with the reduced number of sub-cycles. The simulated sea ice fields retain characteristics obtained with more traditional EVP at a large number of sub-cycles. This result is expected to carry over to even higher resolutions; however in each case additional tuning of parameters ensuring stability may be needed. [ABSTRACT FROM AUTHOR]