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Understanding sea-ice dynamics at the floe scale is crucial to comprehend polar climate systems. While continuum models are commonly used to simulate large-scale sea-ice dynamics, they have limitations in accurately representing sea-ice behaviour at small scales. DEMs, on the other hand, are well-suited for modelling the behaviour of individual ice floes but face limitations due to computational constraints. To address the limitations of both approaches while combining their strengths, we explored the feasibility of using a DEM within a continuum model, where the latter provides boundary conditions for a rectangular high-resolution DEM domain. This paper presents a feasibility study where a discrete model of a 100 × 100 km2 icefield was created using high-resolution optical satellite imagery. Sea-ice dynamics were simulated in the DEM considering environmental forces and integrating large-scale ice-drift velocities as boundary conditions. Model predictions were compared with satellite observations for ice drift and deformation parameters. This numerical approach showed potential for offering accurate, high-resolution predictions of sea ice, particularly in coastal areas and near islands, and may find applications in ice navigation and climate studies. However, further development of the DEM, along with upgrades to the coupled ocean models providing data for the ice component, may be necessary. Additionally, challenges remain to develop a two-way coupling between the DEM and a continuum model, which may be needed to improve the accuracy of large-scale simulations.

At least in conventional hydrostatic ice-sheet models, the numerical error associated with grounding line dynamics can be reduced by modifications to the discretization scheme. These involve altering the integration formulae for the basal traction and/or driving stress close to the grounding line and exhibit lower – if still first-order – error in the MISMIP3d experiments. MISMIP3d may not represent the variety of real ice streams, in that it lacks strong lateral stresses, and imposes a large basal traction at the grounding line. We study resolution sensitivity in the context of extreme forcing simulations of the entire Antarctic ice sheet, using the BISICLES adaptive mesh ice-sheet model with two schemes: the original treatment, and a scheme, which modifies the discretization of the basal traction. The second scheme does indeed improve accuracy – by around a factor of two – for a given mesh spacing, but$\\lesssim 1$km resolution is still necessary. For example, in coarser resolution simulations Thwaites Glacier retreats so slowly that other ice streams divert its trunk. In contrast, with$\\lesssim 1$km meshes, the same glacier retreats far more quickly and triggers the final phase of West Antarctic collapse a century before any such diversion can take place.

Iceberg calving is a major source of ice loss from the Antarctic and Greenland ice sheets. However, it is still one of the most poorly understood aspects of ice sheet dynamics, in part due to its variability at a wide range of spatial and temporal scales. Despite this variability, most current large-scale ice sheet models assume that calving can be represented as a deterministic flux. In this study, we describe an approach to modeling calving as a stochastic process, using a one-dimensional depth-integrated marine-terminating glacier model as a demonstration. We show that for glaciers where calving occurs more frequently than the typical model time steps (days-months), stochastic calving schemes sampling a binomial distribution accurately simulate the probabilistic distribution of glacier state. We also find that incorporating stochastic calving into simulations of a glacier with a buttressing ice shelf changes the simulated mean glacier state, due to nonlinearities in ice shelf dynamics. Relatedly, we find that changes in calving frequency, without changes in the mean calving flux, can cause ice shelf retreat. This new stochastic approach can be implemented in large-scale ice sheet models, which should improve our capability to quantify uncertainty in predictions of future ice sheet change.

Linear kinematic features (LKFs) are found everywhere in the Arctic sea‐ice cover. They are strongly localized deformations often associated with the formation of leads and pressure ridges. In viscous‐plastic (VP) sea‐ice models, the simulation of LKFs depends on several factors such as the grid resolution, the numerical solver convergence, and the placement of the variables on the mesh. In this study, we compare two recently proposed discretization with a CD‐grid placement with respect to their ability to reproduce LKFs. The first (CD1) is based on a nonconforming finite element discretization, whereas the second (CD2) uses a conforming subgrid discretization. To analyze their resolution properties, we evaluate runs from different models (e.g., FESOM, MPAS) on a benchmark problem using quadrilateral, hexagonal and triangular meshes. Our findings show that the CD1 setup simulates more deformation structure than the CD2 setup. This highlights the importance of the type of spatial discretization for the simulation of LKFs. Due to the higher number of degrees of freedom, both CD‐grids resolve more LKFs than traditional A, B, and C‐grids at fixed mesh level. This is an advantage of the CD‐grid approach, as high spatial mesh resolution is needed in VP sea‐ice models to simulate LKFs. Plain Language Summary Sea ice in the polar regions is an important component of the climate system. Satellite images demonstrate that the sea‐ice cover can contain long features, such as cracks or leads and areas of increased sea‐ice density known as pressure ridges. In order to simulate these features, mathematical equations that describe the drift of ice are solved on a computational grid. A recent study showed that the simulation of these features on a grid with a given spacing is influenced by the way the variables are placed on grid cells. Locating them at the edge midpoints of the cells leads to simulations with more features than placing the variables on vertices or centers of cells. In this contribution, we show that, along with the placement, also the mathematical method used to approximate the equations on the computational grid plays a pivotal role on the number of simulated features. Key Points The type of spatial discretization used in CD‐grid approximations is important for the amount of simulated local kinematic features (LKFs) The CD‐grid discretization based on nonconforming finite elements simulates the highest amount of LKFs The CD‐grids resolve more LKFs than A‐grids, B‐grids, or C‐grids

Purpose of Review This paper reviews the recent literature on numerical modelling of the dynamics of the Greenland ice sheet with the goal of providing an overview of advancements and to highlight important directions of future research. In particular, the review is focused on large-scale modelling of the ice sheet, including future projections, model parameterisations, paleo applications and coupling with models of other components of the Earth system. Recent Findings Data assimilation techniques have been used to improve the reliability of model simulations of the Greenland ice sheet dynamics, including more accurate initial states, more comprehensive use of remote sensing as well as paleo observations and inclusion of additional physical processes. Summary Modellers now leverage the increasing number of high-resolution satellite and air-borne data products to initialise ice sheet models for centennial time-scale simulations, needed for policy relevant sea-level projections. Modelling long-term past and future ice sheet evolution, which requires simplified but adequate representations of the interactions with the other components of the Earth system, has seen a steady improvement. Important developments are underway to include ice sheets in climate models that may lead to routine simulation of the fully coupled Greenland ice sheet–climate system in the coming years.

The Ice-sheet and Sea-level System Model (ISSM) provides numerical solutions for ice sheet dynamics using finite element and fine mesh adaption. However, considering ISSM is compatible only with central processing units (CPUs), it has limitations in economizing computational time to explore the linkage between climate forcings and ice dynamics. Although several deep learning emulators using graphic processing units (GPUs) have been proposed to accelerate ice sheet modeling, most of them rely on convolutional neural networks (CNNs) designed for regular grids. Since they are not appropriate for the irregular meshes of ISSM, we use a graph convolutional network (GCN) to replicate the adapted mesh structures of the ISSM. When applied to transient simulations of the Pine Island Glacier (PIG), Antarctica, the GCN successfully reproduces ice thickness and velocity with a correlation coefficient of approximately 0.997, outperforming non-graph models, including fully convolutional network (FCN) and multi-layer perceptron (MLP). Compared to the fixed-resolution approach of the FCN, the flexible-resolution structure of the GCN accurately captures detailed ice dynamics in fast-ice regions. By leveraging 60–100 times faster computational time of the GPU-based GCN emulator, we efficiently examine the impacts of basal melting rates on the ice sheet dynamics in the PIG.

The Arctic region is experiencing significant changes due to climate change, and the resulting decline in sea ice concentration and extent is already impacting ocean dynamics and exacerbating coastal hazards in the region. In this context, numerical models play a crucial role in simulating the interactions between the ocean, land, sea ice, and atmosphere, thus supporting scientific studies in the region. This research aims to evaluate how different sea ice products with spatial resolutions varying from 2 to 25 km influence a phase averaged spectral wave model results in the Alaskan Arctic under storm conditions. Four events throughout the Fall to Winter seasons in 2019 were utilized to assess the accuracy of wave simulations generated under the dynamic sea ice conditions found in the Arctic. The selected sea ice products used to parameterize the numerical wave model include the National Snow and Ice Data Center (NSIDC) sea ice concentration, the European Centre for Medium‐Range Weather Forecasts (ECMWF) Re‐Analysis (ERA5), the HYbrid Coordinate Ocean Model‐Community Ice CodE (HYCOM‐CICE) system assimilated with Navy Coupled Ocean Data Assimilation (NCODA), and the High‐resolution Ice‐Ocean Modeling and Assimilation System (HIOMAS). The Simulating WAves Nearshore (SWAN) model's accuracy in simulating waves using these sea ice products was evaluated against Sea State Daily Multisensor L3 satellite observations. Results show wave simulations using ERA5 consistently exhibited high correlation with observations, maintaining an accuracy above 0.83 to the observations across all events. Conversely, HIOMAS demonstrated the weakest performance, particularly during the Winter, with the lowest correlation of 0.40 to the observations. Remarkably, ERA5 surpassed all other products by up to 30% in accuracy during the selected storm events, and even when an ensemble was assessed by combining the selected sea ice products, ERA5's individual performance remained unmatched. Our study provides insights for selecting sea ice products under different sea ice conditions for accurately simulating waves and coastal hazards in high latitudes. Plain Language Summary The Arctic is changing rapidly due to climate change, resulting in a significant decrease in sea ice. This reduction affects ocean conditions and increases coastal hazards. Our study examines how varying sea ice data resolutions, ranging from 2 to 25 km, influence the results of a wave model during four storm events in the Alaskan Arctic from Fall to Winter 2019. We incorporated sea ice data into our wave model from various sources: the National Snow and Ice Data Center (NSIDC), the European Centre for Medium‐Range Weather Forecasts (ECMWF, known as ERA5), the HYbrid Coordinate Ocean Model‐Community Ice CodE (HYCOM‐CICE) system, and the High‐resolution Ice‐Ocean Modeling and Assimilation System (HIOMAS). We then evaluated the accuracy of wave forecasts produced by the Simulating Waves Nearshore (SWAN) model by comparing them with satellite observations. Our findings indicate that the ERA5 data provided the most accurate wave predictions, demonstrating a high correlation (above 0.83) with satellite observations during all storm events. Conversely, the HIOMAS data showed the weakest results relative to the other products, particularly in Winter, with the lowest correlation (0.40) and higher errors. Notably, ERA5 outperformed the other products by up to 30% in accuracy during the storms, and even when combining different sea ice data, ERA5's performance remained superior. This study offers valuable insights into selecting sea ice data for accurately predicting waves and coastal hazards in the Arctic. These findings are crucial for understanding and preparing for the impacts of climate change in this vulnerable region. Key Points The wave model was able to accurately represent four different extreme events in the Alaskan Arctic under different sea ice conditions ERA5 showed the highest correlation values during all events in this study when compared to the satellite observations An ensemble combining all sea ice products was also evaluated and produced consistently high correlation to the observations

Sea-ice ridges constitute a large fraction of the ice volume in the Arctic Ocean, yet we know little about the evolution of these ice masses. Here we examine the thermal and morphological evolution of an Arctic first-year sea-ice ridge, from its formation to advanced melt. Initially the mean keel depth was 5.6 m and mean sail height was 0.7 m. The initial rubble macroporosity (fraction of seawater filled voids) was estimated at 29% from ice drilling and 43%–46% from buoy temperature. From January until mid-April, the ridge consolidated slowly by heat loss to the atmosphere and the total consolidated layer growth during this phase was 0.7 m. From mid-April to mid-June, there was a sudden increase of ridge consolidation rate despite no increase in conductive heat flux. We surmise this change was related to decreased macroporosity due to transport of snow-slush to the ridge keel rubble via adjacent open leads. In this period, the mean thickness of the consolidated layer increased by 2.1 m. At the peak of melt in June–July we suggest that the consolidation was related to the refreezing of surface snow and ice meltwater and of ridge keel meltwater (the latter only about 15% of total consolidation). We used the morphology parameters of the ridge to calculate its hydrostatic equilibrium and obtained a more accurate estimate of the actual consolidation of the keel, correcting from 2.2 m to 2.8 m for average keel consolidation. This approach also allowed us to estimate that the average keel melt of 0.3 m, in June–July, was accompanied by a decrease in ridge draft of 0.9 m. An ice mass balance buoy in the ridge indicated total consolidation of 2.8 m, of which 2.1 m was related to the rapid mode of consolidation from April to June. By mid-June, consolidation resulted in a drastic decrease of the macroporosity of the interior of keel while the flanks had little or no change in macroporosity. These results are important to understanding the role of ridge keels as meltwater sources and sinks and as sanctuary for ice-associated organisms in Arctic pack ice.

Subglacial lakes have been mapped across Antarctica with two methods, radio‐echo sounding (RES) and ice‐surface deformation. At sites where both are coincident, these methods typically provide conflicting interpretations about the ice‐bed interface. With a single exception, active subglacial lakes identified by surface deformation do not display the expected flat, bright, and specular bed reflection in RES data, characteristic of non‐active lakes. This observational conundrum suggests that our understanding of Antarctic subglacial hydrology, especially beneath important fast‐moving ice streams, remains incomplete. Here, we use an airborne RES campaign that surveyed a well‐characterized group of active subglacial lakes on lower Mercer and Whillans ice streams, West Antarctica, to explore inconsistency between the two observational techniques. We test hypotheses of increased scattering and attenuation due to the presence of an active subglacial lake system that could suppress reflected bed‐echo power for RES observations in these locations, finding that entrained water is most plausible. Plain Language Summary The bottom of an ice sheet is insulated from cold air temperatures, often warm enough to melt and pond liquid water into lakes. These lakes beneath the ice sheet have been identified by two independent measurements, first with radar methods and second with changes in height of the ice surface (altimetry). Interestingly, the two methods rarely identify the same lakes: radar generally detects lakes in the ice‐sheet interior, whereas altimetry detects active lakes near the ice‐sheet margins that fill and drain within the time series of repeated measurements (∼years). In this study, we investigate a group of active subglacial lakes at which both radar and altimetry data sets are available. We demonstrate that the radar returns from active lake reflections are much dimmer than expected based on non‐active lake signatures and investigate the physical processes controlling those dim reflections. We argue that water moves into the ice when the lake fills or drains and that is the most plausible explanation for the observational discrepancy. Key Points Active subglacial lakes, identified by surface deformation, do not create the expected bright and specular radar reflection Entrained water in basal ice suppresses radar power by scattering and attenuation, and it also likely alters the basal ice mechanics Understanding the radar expression of subglacial water on Earth provides context for investigations of subsurface water on planetary bodies

Sea ice monitoring by polar orbiting satellites has been developed over more than four decades and is today one of the most well-established applications of space observations. This article gives an overview of data product development from the first sensors to the state-of-the-art regarding retrieval methods, new products and operational data sets serving climate monitoring as well as daily operational services including ice charting and forecasting. Passive microwave data has the longest history and represents the backbone of global ice monitoring with already more than four decades of consistent observations of ice concentration and extent. Time series of passive microwave data is the primary climate data set to document the sea ice decline in the Arctic. Scatterometer data is a valuable supplement to the passive microwave data, in particular to retrieve ice displacement and distinguish between firstyear and multiyear ice. Radar and laser altimeter data has become the main method to estimate sea ice thickness and thereby fill a gap in the observation of sea ice as an essential climate variable. Data on ice thickness allows estimation of ice volume and masses as well as improvement of the ice forecasts. The use of different altimetric frequencies also makes it possible to measure the depth of the snow covering the ice. Synthetic Aperture Radar (SAR) has become the work horse in operational ice observation on regional scale because high-resolution radar images are delivered year-round in nearly all regions where national ice services produce ice charts. Synthetic Aperture Radar data are also important for sea ice research because the data can be used to observe a number of sea ice processes and phenomena, like ice type development and sea ice dynamics, and thereby contribute to new knowledge about sea ice. The use of sea ice data products in modelling and forecasting services as well as in ice navigation is discussed. Finally, the article describes future plans for new satellites and sensors to be used in sea ice observation.