The marginal ice zone represents the periphery of the sea ice cover. In this region, the macroscale behaviour of the sea ice results from collisions and enduring contact between ice floes. This configuration closely resembles that of dense granular flows, which have been modelled successfully with the $\mu (I)$ rheology. Here, we present a continuum model based on the $\mu (I)$ rheology that treats sea ice as a compressible fluid, with the local sea ice concentration given by a dilatancy function $\varPhi (I)$. We infer expressions for $\mu (I)$ and $\varPhi (I)$ by nonlinear regression using data produced with a discrete element method (DEM) that considers polygon-shaped ice floes. We do this by driving the sea ice with a one-dimensional shearing ocean current. The resulting continuum model is a nonlinear system of equations with the sea ice velocity, local concentration and pressure as unknowns. The rheology is given by the sum of a plastic term and a viscous term. In the context of a periodic patch of ocean, which is effectively a one-dimensional problem, and under steady conditions, we prove this system to be well-posed, present a numerical algorithm for solving it, and compare its solutions to those of the DEM. These comparisons demonstrate the continuum model's ability to capture most of the DEM results accurately. The continuum model is particularly accurate for ocean currents faster than 0.25 m s$^{-1}$; however, for low concentrations and slow ocean currents, the continuum model is less effective in capturing the DEM results. In the latter case, the lack of accuracy of the continuum model is found to be accompanied by the breakdown of a balance between the average shear stress and the integrated ocean drag extracted from the DEM. Since this balance is expected to hold independently of our choice of rheology, this finding indicates that continuum models might not be able to describe sea ice dynamics for low concentrations and slow ocean currents.

In this study, the U-net with ResNet-34, i.e. a residual neural network with 34 layers, backbone semantic segmentation network is applied to C-band sea-ice SAR imagery over the Baltic Sea. Sentinel-1 Extra Wide Swath mode HH/HV-polarized SAR data acquired during the winter season 2018–2019, and corresponding segments derived from the daily Baltic Sea ice charts were used for training the segmentation algorithm. C-band SAR image mosaics of the winter season 2020–2021 were then used to evaluate the segmentation. The major objective was to study the suitability of semantic segmentation of SAR imagery for automated SAR segmentation and also to find a potential replacement for the outdated iterated conditional modes (ICM) algorithm currently in operational use. The results compared to the daily Baltic Sea ice charts and the operational ICM segmentation and visual interpretation were encouraging from the operational point of view. Open water areas were located very well and the oversegmentation produced by ICM was significantly reduced. The correspondence between the ice chart polygons and the segmentation results was also reasonably good. Based on the results, the studied method is a potential candidate to replace the operational ICM SAR segmentation used in the Copernicus Marine Service automated sea-ice products at Finnish Meteorological Institute.

Melting and solidification in periodically time-modulated thermal convection are relevant for numerous natural and engineering systems, for example, glacial melting under periodic sun radiation and latent thermal energy storage under periodically pulsating heating. It is highly relevant for the estimation of melt rate and melt efficiency management. However, even the dynamics of a solid–liquid interface shape subjected to a simple sinusoidal heating has not yet been investigated in detail. In this paper, we offer a better understanding of the modulation frequency dependence of the melting and solidification front. We numerically investigate periodic melting and solidification in turbulent convective flow with the solid above and the melted liquid below, and sinusoidal heating at the bottom plate with the mean temperature equal to the melting temperature. We investigate how the periodic heating can prevent the full solidification, and the resulting flow structures and the quasi-equilibrium interface height. We further study the dependence on the heating modulation frequency. As the frequency decreases, we found two distinct regimes, which are ‘partially solid’ and ‘fully solid’. In the fully solid regime, the liquid freezes completely, and the effect of the modulation is limited. In the partially solid regime, the solid partially melts, and a steady or unsteady solid–liquid interface forms depending on the frequency. The interface height can be derived based on the energy balance through the interface. In the partially solid regime, the interface height oscillates periodically, following the frequency of modulation. Here, we propose a perturbation approach that can predict the dependency of the oscillation amplitude on the modulation frequency.

Photosynthetically active radiation (PAR) at the ice-ocean interface is critical for primary production. The value of PAR is affected by the thickness of snow and sea ice, with additional absorbers (e.g. algae) further attenuating PAR. Sea-ice algae exhibit a substantial geo-temporal variance in column-integrated concentration (0–500 mg chl-a m−2) and are typically present within the bottom 0.01–0.2 m of sea ice. PAR transmittance is affected by algae concentrations and vertical thicknesses of ice algal layers. Small column-integrated concentrations of chl-a (~<10 mg chl-a m−2) have a negligible effect on the value of PAR transmittance, and large column-integrated concentrations of chl-a (~>10 mg chl-a m−2) can significantly reduce the value of PAR transmittance. Large column-integrated concentrations of chl-a need consideration when calculating PAR transmittance in areas of high sea-ice algae biomass (e.g. the ‘interior’ shelves of the Arctic Ocean, the Canadian Arctic and Antarctica).

The retrieval of sea ice thickness using L-band passive remote sensing requires robust models for emission from sea ice. In this work, measurements obtained from surface-based radiometers during the MOSAiC expedition are assessed with the Burke, Wilheit and SMRT radiative transfer models. These models encompass distinct methodologies: radiative transfer with/without wave coherence effects, and with/without scattering. Before running these emission models, the sea ice growth is simulated using the Cumulative Freezing Degree Days (CFDD) model to further compute the evolution of the ice structure during each period. Ice coring profiles done near the instruments are used to obtain the initial state of the computation, along with Digital Thermistor Chain (DTC) data to derive the sea ice temperature during the analyzed periods. The results suggest that the coherent approach used in the Wilheit model results in a better agreement with the horizontal polarization of the in situ measured brightness temperature. The Burke and SMRT incoherent models offer a more robust fit for the vertical component. These models are almost equivalent since the scattering considered in SMRT can be safely neglected at this low frequency, but the Burke model misses an important contribution from the snow layer above sea ice. The results also suggest that a more realistic permittivity falls between the spheres and random needles formulations, with potential for refinement, particularly for L-band applications, through future field measurements.

In this study an operational sea ice thickness (SIT) estimation algorithm, based on HH-polarized X-band synthetic aperture radar (SAR) data, background information from the most recent, typically from the previous day, available daily Baltic Sea ice chart and the operational Finnish Meteorological Institute (FMI) thermodynamic ice model, was developed and evaluated. The algorithm was designed to complement the C-band SAR SIT algorithm developed earlier at FMI and applied daily as part of the operational Copernicus Marine Service (CMS). The X-band SIT algorithm was developed by utilizing the sea ice thickness measurements made onboard the Finnish and Swedish ice breakers during two winters seasons: 2021–2022 and 2022–2023. The former season measurements were used for defining the algorithm parameters and the later season for evaluation of the algorithm performance. According to the evaluation metrics the X-band algorithm performance is slightly better than that of the operational CMS C-band SAR SIT algorithm, indicating its suitability for operational use in CMS.

The changing conditions in which sea ice forms and exists are likely to affect the properties of sea ice itself, and potential climate feedbacks need to be identified and understood to improve future projections. Here we perform a set of idealised laboratory experiments that model sea-ice growth under a range of freezing conditions. The results confirm existing theories; sea-ice growth rate is largest for cooler freezing temperatures, fresher ambient salinities and cases with bottom cooling. Our primary metric of interest is the brine fraction (the volume ratio of brine inclusions to the total sea ice), which we quantify and determine its sensitivity with respect to the ambient salinity, freezing temperature and, for the first time, the freezing direction. We find that the brine fraction of our model sea ice is most sensitive to freezing temperature, and increases 2.5% per 1$^\circ$C increase of freezing temperature.

Existing theoretical results for attenuation of surface waves propagating on water of random fluctuating depth are shown to over-predict the rate of decay due to the way in which ensemble averaging is performed. A revised approach is presented which corrects this and is shown to conserve energy. New theoretical predictions are supported by numerical results which use averaging of simulations of wave scattering over finite sections of random bathymetry for which transfer matrix eigenvalues are used to accurately measure decay. The model of wave propagation used in this paper is derived from a linearised long-wavelength assumption whereby depth averaging leads to time harmonic waves being represented as solutions to a simple ordinary differential equation. In this paper it is shown how this can be adapted to incorporate a model of a continuous covering of the surface by fragmented floating ice. Attenuation of waves through broken ice of random thickness is then analysed in a similar manner as bed variations have been previously. General features of the predicted attenuation are discussed in relation to existing theoretical models for attenuation due to multiple scattering through random ice environments and to field data, particularly in the model's ability to capture a ‘rollover effect’ at higher frequencies.

We estimate sea-ice type specific incidence angle (IA) dependencies for dual polarized (HH/HV) L and C-band synthetic aperture radar (SAR) for the winter, melt onset and advanced melt seasons for level and deformed ice, using time-series of Advanced Land Observing Satellite-2 (ALOS-2) and Sentinel-1 imagery off the north-east coast of Greenland. The IA dependencies are used to radiometrically correct the L and C-band backscatter time-series, which enables analysis of their seasonal evolution. From this, we observe that the L-band backscatter intensity increases for both ice types at the transition from winter to melt onset. We use these results to estimate ice type separability and to train an IA aware Bayesian classifier at both frequencies. These results show that while both frequencies are capable of distinguishing level and deformed ice during the winter, only L-band SAR can reliably make this separation during the melt onset season. During the advanced melt season, the overall classification accuracies are similarly low for L and C-band. This study demonstrates the potential of L-band SAR for sea-ice mapping, which is highly relevant in the light of several upcoming L-band SAR missions.

Evaluating CMIP6 model performance helps to improve the prediction of future changes in Arctic sea ice. We analyze the seasonal cycles, distribution, and evolution of sea ice in different regions from 1979 to 2014. We compare the output from selected CMIP6 models with reference data for sea ice motion. We also discuss the correlations between sea ice motion(SIM) and sea ice thickness (SIT) in reference data, and how CMIP6 models explain them. We select EC-Earth3, ACCESS-CM2, BCC-CSM2-MR, MPI-ESM1-2-HR, and NorESM2-LM for CMIP6 study. We compare outputs with reference data: Sea ice extent (SIE) from NSIDC; SIT from PIOMAS; and SIM from the IABP buoy data. Analytical techniques include Theil-Sen and Ordinary least squares (OLS) regression. Most selected CMIP6 models have seasonal cycles of SIM lagging behind IABP observations by 1-2 month and overestimate central Arctic SIM magnitude, with MPI-ESM1-2-HR having the highest discrepancy and NorESM2-LM lowest. The models show better simulation of SIM in the ice melting season than in the growing season. Models perform worse at capturing regional differences in SIM evolution and are overly conservative when simulating the increasing trend in ice motion, especially in coastal Arctic seas during summer. There is significant negative correlation between SIT and SIM in October.

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.

In light of the recent increase in polar shipping and potential future increase with continued climate change reliable routing in ice-covered waters becomes increasingly important for environmental, economic and safety concerns. Dependable route suggestions have the potential to reduce travel times through polar waters significantly. We apply the Anytime Repairing A* pathfinding algorithm to classified Copernicus Sentinel 1 radar images to estimate how much travel times can be reduced. For multiple example scenarios, it is quantified how much the travel time is reduced if a ship follows these suggestions compared to navigating without any ice information available exterior to the visual range (VR). It was found that having ice information available is most beneficial in complex ice situations, where it can reduce travel time by up to 34% for a VR of 2 km.

Salt is often present in the snow overlying seasonal sea ice, and has profound thermodynamic and electromagnetic effects. However, its provenance and behaviour within the snow remain uncertain. We describe two investigations tracing upward brine movement in snow: one conducted in the laboratory and one in the field. The laboratory experiments involved the addition of dyed brine to the base of terrestrial snow samples, with subsequent wicking being measured. Our field experiment involved dye being added directly (without brine) to bare sea-ice and lake ice surfaces, with snow then accumulating on top over several days. On the sea ice, the dye migrated upwards into the snow by up to 5 cm as the snow's basal layer became more salty, whereas no migration occurred in our control experiment over non-saline lake ice. This occurred in relatively dry snowpacks where brine took up $< 6\%$ of the snow's calculated pore volume, suggesting pore saturation is not required for upward salt transport. Our results highlight the potential role of microstructural parameters beyond those currently retrievable with penetrometry, and the potential value of longitudinal, process-based field studies of young snowpacks.

We present a fully-automated workflow to map sea ice types from Sentinel-1 data and transfer the results in near real-time to the research vessel Kronprins Haakon (KPH) in order to support tactical navigation and decision-making during a research cruise conducted towards Belgica Bank in April and May 2022. We used overlapping SAR and optical imagery to train a pixel-wise classifier for the required season and region, and implemented a processing chain with the Norwegian Ice Service at MET Norway that automatically classifies all Sentinel-1 images covering the area of interest. During the cruise, classification results were available on KPH within hours after image acquisition, which is significantly faster than manually produced ice charts. We evaluate the results both quantitatively, based on manually selected validation regions, and qualitatively in comparison to in-situ observations and photographs. Our findings show that open water, level ice, and deformed ice are classified with high accuracy, while young ice remains challenging due to its variable small-scale surface roughness. This work presents one of the first attempts to transfer automated ice type classification results into the field in near real-time and contributes to bridging the gap between research and operations in automated sea ice mapping.

The interaction between a uniform current with a circular cylinder submerged in a fluid covered by a semi-infinite ice sheet is considered analytically. The ice sheet is modelled as an elastic thin plate, and the fluid flow is described by the linearised velocity potential theory. The Green function or the velocity potential due to a source is first obtained. As the water surface is divided into two semi-infinite parts with different boundary conditions, the Wiener–Hopf method (WHM) offers significant advantages over alternative approaches and is consequently adopted. To do that, the distribution of the roots of the dispersion equation for fluid fully covered by an ice sheet in the complex plane is first analysed systematically, which does not seem to have been done before. The variations of these roots with the Froude number are investigated, especially their effects or factorisation and decomposition required in the WHM. The result is verified by comparing with that obtained from the matched eigenfunction expansion method. Through differentiating the Green function with respect to the source position, the potentials due to multipoles are obtained, which are employed to construct the velocity potential for the circular cylinder. Extensive results are provided for hydrodynamic forces on the cylinder and wave profiles, and some unique features are discussed. In particular, it is found that the forces can be highly oscillatory with the Froude number when the body is below the ice sheet, whereas such an oscillation does not exist when the body is below the free surface.

Recent studies have reported a shift in the Arctic sea ice to a younger state after around 2007. This study reveals that this shift can be primarily attributed to a stepwise-type reduction in the extent of 4 years or older (4+ year) ice and its linked survivability. After this shift, the fraction of 4+ year ice extent relative to the total ice changed from 30.5 to 10.0%. Sea-ice survivability can serve as a key indicator of sea-ice persistence in response to other factors. We demonstrate that the decrease of 4+ year ice is controlled by the decrease of its linked survivability in a non-linear manner, signifying small alterations in the survivability can result in relatively large changes in the extent of 4+ year ice. The decrease in survivability is affected by both winter and summer processes. Summer melting contributed the most, while the contribution of the export through Fram Strait was minor. However, the significant rise in residual loss during the growth season suggests that other winter processes may also have played an important role.

We study nonlinear resonant wave–wave interactions which occur when ocean waves propagate into a thin floating ice sheet. Using multiple-scale perturbation analysis, we obtain theoretical predictions of the wave amplitude evolution as a function of distance travelled past the ice edge for a semi-infinite ice sheet. The theoretical predictions are supported by a high-order spectral (HOS) method capable of simulating nonlinear interactions in both open water and the ice sheet. Using the HOS method, the amplitude evolution predictions are extended to multiple (coupled) triad interactions and a single ice sheet of finite length. We relate the amplitude evolution to mechanisms with strong frequency dependence – ice bending strain, related to ice breakup, as well as wave reflection and transmission. We show that, due to sum-frequency interactions, the maximum strain in the ice sheet can be more than twice that predicted by linearised theory. For an ice sheet of finite length, we show that nonlinear wave reflection and transmission coefficients depend on a parameter in terms of wave steepness and ice length, and can have values significantly different than those from linear theory. In particular, we show that nonlinear sum-frequency interactions can appreciably decrease the total wave energy transmitted past the ice sheet. This work has implications for understanding the occurrence of ice breakup, wave attenuation due to scattering in the marginal ice zone and the resulting ice floe size distribution.

Passive-microwave sea ice concentration (SIC) algorithms employ different frequencies and polarisations in their operational implementations. Commonly, these algorithms utilise combinations such as 19/37 GHz, yielding reduced measurement uncertainties but at a coarse spatial resolution. Alternatively, these algorithms can solely use 89 GHz, producing a higher spatial resolution but with increased measurement uncertainties. This study evaluates the application of a resolution-enhancing SIC algorithm (reSICCI3LF), initially developed for the coarser Special Sensor Microwave Imager / Sounder, on the Advanced Microwave Scanning Radiometer. By applying reSICCI3LF, we aim to produce a 5 km SIC for 2013–2020 in the Fram Strait and the Barents and Kara Sea region that gains the benefits of both types of algorithms, high spatial resolution and low measurement uncertainty.

We present the algorithm tuning, spectral analysis of spatial resolutions, and validation against the Round Robin Data Package of 0% and 100% SIC points and SIC derived from Landsat-8. The findings demonstrate that the reSICCI3LF algorithm produces a SIC field with fine details, achieving a balance between high spatial resolution and lower measurement uncertainties compared to a 89 GHz based SIC. Consequently, this resolution-enhanced SIC technique can potentially initialise higher-resolution coupled ocean and sea ice forecasting systems through data assimilation.

Iceberg melting is a critical factor for climate change. However, the shape of an iceberg is an often neglected aspect of its melting process. Our study investigates the influence of different ice shapes and ambient flow velocities on melt rates by conducting direct numerical simulations of a simplified system of bluff body flow. Our study focuses on the ellipsoidal shape, with the aspect ratio as the control parameter. We found the shape plays a crucial role in the melting process, resulting in significant variations in the melt rate between different shapes. Without flow, the optimal shape for a minimal melt rate is the disk (two-dimensional) or sphere (three-dimensional), due to the minimal surface area. However, as the ambient flow velocity increases, the optimal shape changes with the aspect ratio. We find that ice with an elliptical shape (when the long axis is aligned with the flow direction) can melt up to 10 % slower than a circular shape when exposed to flowing water. Following the approach considered by Huang et al. (J. Fluid Mech., vol. 765, 2015, R3) for dissolving bodies, we provide a quantitative theoretical explanation for this optimal shape, based on the combined contributions from both surface-area effects and convective-heat-transfer effects. Our findings provide insight into the interplay between phase transitions and ambient flows, contributing to our understanding of the iceberg melting process and highlighting the need to consider the aspect-ratio effect in estimates of iceberg melt rates.

An outdoor sea-ice tank system for measuring the microwave properties of sea ice has been developed. With the natural cooling and the help of a cooling unit in the movable roof attached to the tank, the system can grow sea ice to about 50 cm thickness continuously without the effects of snowfall and/or melting. Portable microwave radiometers are attached beside the tank to measure the brightness temperature of the ice. As sea ice grows, the system can measure microwave brightness temperature, and seawater/ice temperature at each depth and thickness of sea ice. The bulk salinity of sea ice is measured by sampling. The following results were obtained from experiments conducted during two winters. (1) Rapid desalination was observed during the early stages of growth with ice thicknesses of 0–5 cm. (2) A new relational expression between ice thickness and bulk salinity at this thickness was obtained. (3) The rapid rise in microwave brightness temperature associated with the increase in sea-ice thickness during the early stages of sea-ice growth was captured in each frequency band. The microwave measurements from the sea-ice tank system are expected to provide new insights into the microwave properties of sea ice.