These authors contributed equally to this work.

Despite its relevance for the Arctic climate and ecosystem, modeling sea-ice deformation, i.e., the opening, shearing, and ridging of sea ice, along linear kinematic features (LKFs) remains challenging, as the mechanical properties of sea ice are not yet fully understood. The intersection angles between LKFs provide valuable information on the internal mechanical properties, as they are linked to them. Currently, the LKFs emerging from sea-ice rheological models do not reproduce the observed LKF intersection angles, pointing to a gap in the model physics. We aim to obtain an intersection angle distribution (IAD) from observational data to serve as a reference for high-resolution sea-ice models and to infer the mechanical properties of the sea-ice cover.
We use the sea-ice vorticity to discriminate between acute and obtuse LKF intersection angles within two sea-ice deformation datasets: the RADARSAT Geophysical Processor System (RGPS) and a new dataset from the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) drift experiment. Acute angles dominate the IAD, with single peaks at

Sea-ice deformation is a crucial process for the polar climate. It creates areas of open water that allow enhanced heat and gas exchange, and it also forms ridges that serve as a habitat for biota and provide barriers against winds and ocean currents.
The deformation patterns of sea ice in the Arctic Ocean are dominated by narrow lines where deformation concentrates

LKFs emerge from the mechanical properties of sea ice. Sea ice is often described as a granular material

Previous studies on LKF intersection angles report single intersection angles based on small sample sizes across large spatial scales (100 m–100 km), for example,

None of the current sea-ice models can reproduce the observed distribution of LKF intersection angles

Studying the intersection angles can provide important insights into two key questions. First, is there a relationship between intersection angles and the divergence (opening or ridging) along the LKF? In other words, does the hypothesis of the normal flow rule

In this paper, we use satellite-derived sea-ice drift and deformation to address the gaps outlined above. Deformation concentrates along the LKFs, and vorticity identifies the LKFs formed under compressive force. Tracking of the LKFs allows for the identification of those that formed simultaneously. Therefore, we can distinguish between conjugate and non-conjugate intersection angles and discriminate between conjugate obtuse and acute intersection angles. We apply this method to the RGPS dataset and new high-resolution deformation data surrounding the 2019–2020 Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) expedition. Both datasets have different temporal and spatial coverage and resolution; thus, they indicate if intersection angles vary in the ice cover depending on the spatial scale and geographical location in the Arctic. We aim to obtain an IAD as a reference for high-resolution sea-ice models and to infer the mechanical properties of the sea-ice cover, e.g., the yield condition and/or the plastic potential.

The remainder of this paper is structured as follows: Sect.

In this study, we will use two satellite-based sea-ice drift datasets from which sea-ice deformation is derived. Thanks to the synthetic aperture radar (SAR) data from which the drift is calculated, the datasets are available independent of weather conditions and during the polar night. The high spatial resolution (1.4 km for MOSAiC and 12.5 km for RGPS) of the deformation datasets enables us to identify individual LKFs.

RGPS is a widely used drift and deformation dataset based on RADARSAT SAR images

In addition, we compute ice drift and deformation based on Sentinel-1 SAR scenes

Coverage of the RGPS and MOSAiC LKF datasets. For the RGPS dataset, the transparency indicates the relative frequency of the coverage in the respective geographical regions.

We use the algorithms presented in

For RGPS, we use the publicly available deformation data

In both LKF datasets, pairs of LKF that intersect and are formed within the same time step are extracted, and the angle of intersection is measured following the approach of

To differentiate between intersection angles that are acute (

Schematics showing the difference between conjugate failure lines with acute and obtuse angles and those with non-conjugate failure lines. The vorticity of the ice motion (black circles with

While the generation of conjugate faults is explained by the failure of ice under compressive loading, the reasons for the existence of non-conjugate failure are less obvious. We show the distribution of the non-conjugate angles and explore reasons for these non-conjugate faults in Appendix

In the following sections, we present the results of our investigation of intersection angles in both the MOSAiC and RGPS datasets. We compare the intersection angle distribution (IAD), the relationship between angles and dilatancy, and how these distributions inform us about sea-ice dynamics, especially the internal angle of friction, and the possible shape of the yield curve or the plastic potential for sea-ice VP models.

Figure

Examples of LKF intersections with the vorticity anomaly and sea-ice drift within the MOSAiC dataset. Panel

In the following, we focus on intersection angles between conjugate LKFs, which we can classify as acute or obtuse. We include only LKFs that formed during the same time step of observation.

Figure

To characterize the PDF, we fit both PDFs to an exponentially modified Gaussian (exGaussian) distribution with a maximum likelihood estimator (MLE). The parameters of the fit are given in the caption of Fig.

Probability density function of the conjugate intersection angles for the MOSAiC (blue) and RGPS (orange) datasets. The dashed lines show the MLE fit to an exponentially modified Gaussian (exGaussian) distribution (Eq.

The PDF of the intersection angles does not vary seasonally for the RGPS dataset. For the MOSAiC dataset, there are too few intersection angles to study seasonal variations (not shown). Appendix

We extract the deformation rates from all pixels defined as part of an LKF to compare the characteristics of the deformation in the MOSAiC and RGPS datasets. As for the IAD, both the MOSAiC and RGPS datasets agree with respect to the shape of the distribution of the divergence, shear, and total deformation rates along LKFs (Fig.

Probability distribution function of normalized convergence

We can calculate the dilatancy angle along the LKF,

Further, we analyze the relationship between intersection angles and dilatancy angles (Fig.

Scatterplot of the dilatancy angle

These findings contradict the concept of the Roscoe angle

The peak of the IAD shows a preferred angle of failure of sea ice that can be used to estimate the internal angle of friction of sea ice within the framework of the Mohr–Coulomb failure criterion

The internal angle of friction is given by

Using these formulas with the observed IAD from our study, we find the following:

The peak intersection angle for the RGPS dataset of

For the MOSAiC dataset, for the intersecting angle of

Note that we only take the peak of the IAD into account for this calculation, thereby neglecting the presence of other intersection angles in the PDF.

Instead of using only a single angle to derive the mechanical properties of sea ice, we can also use the complete PDF of the intersection angles (Fig.

For each bin of angles in the PDF of the intersection angles (Fig.

Example of the approximation method for the yield curve or plastic potential from the intersection angle distribution (IAD). Each bin of the distribution is used to create a segment of the curve with the length of the PDF value and the angle corresponding to the center of the bin, starting from the smaller bin.

Yield curve or plastic potential constructed from the PDF of the intersection angles. The red dot-dash line, the green dashed line, and the violet dotted line show a Mohr–Coulomb yield curve

The estimations of the obtained curves for the RGPS and MOSAiC datasets resemble a teardrop yield curve

Note that the starting point of our curve is arbitrarily placed at the origin, as we did not consider tensile strength. However, adding tensile strength would not change the shape of the curve, which is central, but only the actual values of

In Appendix

We show the intersection angle distribution (IAD) of conjugate faults in Arctic sea ice during faulting events. The IAD shows the predominance of small intersection angles of

Using the peak of the IAD, we made an estimation of the internal angle of friction from the Mohr–Coulomb framework.
Our estimates of

In VP models, the orientation of the LKFs is tightly linked to the flow rule, i.e., the dilatancy or post-failure deformation, at least for the elliptical yield curve and plastic potentials

The presented results of the IAD are robust in scale, resolution, and geographic area. The RGPS dataset has low spatial and temporal resolution but a large spatial and time coverage, whereas the MOSAiC dataset has higher resolution but only covers the track of the MOSAiC drift experiment. The scale independence of the intersection angles agrees with the self-similarity and scaling properties of sea-ice deformation

Using the vorticity in sea-ice deformation, we show that we can separate obtuse and acute intersection angles between sea-ice linear kinematic features (LKFs). Using this technique, we can now extract the probability density function (PDF) of the intersection angles between 0 and 180

The PDFs of intersection angles show that acute angles dominate in both datasets, with PDFs peaking at 48

We infer the mechanical properties of sea ice from the observed IAD. Following methods from previous papers, we estimate the internal angle of friction to be

Reproducing the observed patterns of LKFs in Arctic sea ice is one of the remaining challenges of the sea-ice modeling community

In Sect.

Probability density function (PDF) of the intersection angles in Arctic sea ice. The panels show the conjugate and non-conjugate angles for all

The intersecting LKFs with the same vorticity can have several origins:

The time step of the observations is too large to resolve the actual vorticity during the deformation. The vorticity recorded over a (multi-)day-long period is not necessarily representative of the deformation rates during the formation. Even if two intersection LKFs are formed under compressive forcing, rapidly changing winds can induce a different ice motion. In this case, the initial failure allows the more mobile ice to deform in shear motion, which leads to the same vorticity sign. This behavior may be especially present for deformation data with a low temporal resolution, e.g., the RGPS dataset.

The presence of the same vorticity sign on both intersecting LKFs could emerge from rotation. LKF dynamics can involve rotation under shear

If an LKF is not detected properly and is cut into two parts, both parts will have the same sign vorticity and (due to their proximity) will be identified as intersecting LKFs in our analysis. We tuned the parameters of the detection algorithms to minimize this effect; however, especially for the MOSAiC data, we find instances of this effect.

In the following, we show, as a proof of concept, that the method used in Sect.

First, we compute the expected PDF of the intersection angles in a high-resolution sea-ice viscous–plastic model that uses an elliptical yield curve (Fig.

The histogram lines in Fig.

Elliptic yield curves in invariant space

In Fig.

The deformation data based on Sentinel-1 SAR imagery
(

DR coordinated this study, derived the sea-ice properties (internal angle of friction and curve shape), made figures, and contributed to writing the paper. NH performed the LKF extraction, carried out the intersection angle measurement and classification for both datasets, made figures, and contributed to writing the paper. LvA provided the MOSAiC deformation dataset, made figures, and contributed to writing the paper. All authors edited the manuscript.

The contact author has declared that none of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The authors thank Harry Heorton and Stephanie Rynder for their comments and suggestion that greatly improved this paper. The authors are also grateful to Jennifer Hutchings, Daniel Watkins, and Bruno Tremblay for their comments on an earlier version of this work.

This research has been supported by the Deutsche Forschungsgemeinschaft (grant no. IRTG 1904 ArcTrain). This publication is partially funded by the Cooperative Institute for Climate, Ocean, & Ecosystem Studies (CICOES) under NOAA Cooperative Agreement NA20OAR4320271, Contribution No. 2023-1306.The article processing charges for this open-access publication were covered by the University of Bremen.

This paper was edited by Yevgeny Aksenov and reviewed by Harry Heorton and Stefanie Rynders.