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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]

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]

Geological evidence suggests that marine ice extended to the Equator at least twice during the Neoproterozoic era (about 750 to 635 million years ago), inspiring the Snowball Earth hypothesis that the Earth was globally ice-covered. In a possible Snowball Earth climate, ocean circulation and mixing processes would have set the melting and freezing rates that determine ice thickness, would have influenced the survival of photosynthetic life, and may provide important constraints for the interpretation of geochemical and sedimentological observations. Here we show that in a Snowball Earth, the ocean would have been well mixed and characterized by a dynamic circulation, with vigorous equatorial meridional overturning circulation, zonal equatorial jets, a well developed eddy field, strong coastal upwelling and convective mixing. This is in contrast to the sluggish ocean often expected in a Snowball Earth scenario owing to the insulation of the ocean from atmospheric forcing by the thick ice cover. As a result of vigorous convective mixing, the ocean temperature, salinity and density were either uniform in the vertical direction or weakly stratified in a few locations. Our results are based on a model that couples ice flow and ocean circulation, and is driven by a weak geothermal heat flux under a global ice cover about a kilometre thick. Compared with the modern ocean, the Snowball Earth ocean had far larger vertical mixing rates, and comparable horizontal mixing by ocean eddies. The strong circulation and coastal upwelling resulted in melting rates near continents as much as ten times larger than previously estimated. Although we cannot resolve the debate over the existence of global ice cover, we discuss the implications for the nutrient supply of photosynthetic activity and for banded iron formations. Our insights and constraints on ocean dynamics may help resolve the Snowball Earth controversy when combined with future geochemical and geological observations. [ABSTRACT FROM AUTHOR]

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]

Finite-element models on unstructured meshes are frequently formulated in terms of continuous linear elements, which suffer from pressure modes and require stabilization. Alternatively, horizontal velocities may be represented with linear nonconforming elements. While the latter formulation uses three times more degrees of freedom for the velocity, it does not support pressure modes. The effects of stabilization are estimated by comparing the performance of continuous linear and nonconforming versions of the finite-element ocean circulation model (FEOM) in two simple configurations: a Munk gyre and baroclinic turbulence in a zonally reentrant channel. It is shown that, outside the free slip boundary layers, the presence of stabilization does not lead to noticeable effects if its strength is kept within certain limits. In order to evaluate the performance of FEOM, the baroclinic turbulence test is repeated with the MIT general circulation model (MITgcm), which serves as a benchmark, and reasonable agreement between different model codes is found. The two versions of FEOM have a similar computational cost, but both are significantly slower (per node) than the regular-mesh MITgcm. The paper also provides a brief description of the implementation of the nonconforming version of FEOM. [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]

Sea ice dynamics determine the drift and deformation of sea ice. Nonlinear physics, usually expressed in a viscous-plastic rheology, makes the sea ice momentum equations notoriously difficult to solve. At increasing sea ice model resolution the nonlinearities become stronger as linear kinematic features (leads) appear in the solutions. Even the standard elastic-viscous-plastic (EVP) solver for sea ice dynamics, which was introduced for computational efficiency, becomes computationally very expensive, when accurate solutions are required, because the numerical stability requires very short, and hence more, subcycling time steps at high resolution. Simple modifications to the EVP solver have been shown to remove the influence of the number of subcycles on the numerical stability. At low resolution appropriate solutions can be obtained with only partial convergence based on a significantly reduced number of subcycles as long as the numerical procedure is kept stable. This previous result is extended to high resolution where linear kinematic features start to appear. The computational cost can be strongly reduced in Arctic Ocean simulations with a grid spacing of 4.5 km by using modified and adaptive EVP versions because fewer subcycles are required to simulate sea ice fields with the same characteristics as with the standard EVP. [ABSTRACT FROM AUTHOR]

The article focuses on role of the polar prediction systems towards advancements for prediction capacity in polar regions. It mentions issues concerning climatic changes across the Arctic and Antarctica regions. It also highlights contribution for making the polar regions a target for application of improved environmental prediction science.

Unlike the rapid sea ice losses reported in the Arctic, satellite observations show an overall increase in Antarctic sea ice concentration over recent decades. However, observations of decadal trends in Antarctic ice thickness, and hence ice volume, do not currently exist. In this study a model of the Southern Ocean and its sea ice, forced by atmospheric reanalyses, is used to assess 1992-2010 trends in ice thickness and volume. The model successfully reproduces observations of mean ice concentration, thickness, and drift, and decadal trends in ice concentration and drift, imparting some confidence in the hindcasted trends in ice thickness. The model suggests that overall Antarctic sea ice volume has increased by approximately 30 km3 yr−1 (0.4% yr−1) as an equal result of areal expansion (20 × 103 km2 yr−1 or 0.2% yr−1) and thickening (1.5 mm yr−1 or 0.2% yr−1). This ice volume increase is an order of magnitude smaller than the Arctic decrease, and about half the size of the increased freshwater supply from the Antarctic Ice Sheet. Similarly to the observed ice concentration trends, the small overall increase in modeled ice volume is actually the residual of much larger opposing regional trends. Thickness changes near the ice edge follow observed concentration changes, with increasing concentration corresponding to increased thickness. Ice thickness increases are also found in the inner pack in the Amundsen and Weddell Seas, where the model suggests that observed ice-drift trends directed toward the coast have caused dynamical thickening in autumn and winter. Modeled changes are predominantly dynamic in origin in the Pacific sector and thermodynamic elsewhere. [ABSTRACT FROM AUTHOR]

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]

Fertilization of the ocean by adding iron compounds has induced diatom-dominated phytoplankton blooms accompanied by considerable carbon dioxide drawdown in the ocean surface layer. However, because the fate of bloom biomass could not be adequately resolved in these experiments, the timescales of carbon sequestration from the atmosphere are uncertain. Here we report the results of a five-week experiment carried out in the closed core of a vertically coherent, mesoscale eddy of the Antarctic Circumpolar Current, during which we tracked sinking particles from the surface to the deep-sea floor. A large diatom bloom peaked in the fourth week after fertilization. This was followed by mass mortality of several diatom species that formed rapidly sinking, mucilaginous aggregates of entangled cells and chains. Taken together, multiple lines of evidence-although each with important uncertainties-lead us to conclude that at least half the bloom biomass sank far below a depth of 1,000 metres and that a substantial portion is likely to have reached the sea floor. Thus, iron-fertilized diatom blooms may sequester carbon for timescales of centuries in ocean bottom water and for longer in the sediments. [ABSTRACT FROM AUTHOR]