Using Copernicus Sentinel-2 images we derive a statistical lead-width distribution for the Weddell Sea. While previous work focused on the Arctic, this is the first lead-width distribution for Antarctic sea ice. Previous studies suggest that the lead-width distribution follows a power law with a positive exponent; however their results for the power-law exponents are not all in agreement with each other.
To detect leads we create a sea-ice surface-type classification based on 20 carefully selected cloud-free Sentinel-2 Level-1C products, which have a resolution of 10 m. The observed time period is from November 2016 until February 2018, covering only the months from November to April. We apply two different fitting methods to the measured lead widths. The first fitting method is a linear fit, while the second method is based on a maximum likelihood approach. Here, we use both methods for the same lead-width data set to observe differences in the calculated power-law exponent.
To further investigate influences on the power-law exponent, we define two different thresholds: one for open-water-covered leads and one for open-water-covered and nilas-covered leads. The influence of the lead threshold on the exponent is larger for the linear fit than for the method based on the maximum likelihood approach. We show that the exponent of the lead-width distribution ranges between 1.110 and 1.413 depending on the applied fitting method and lead threshold. This exponent for the Weddell Sea sea ice is smaller than the previously observed exponents for the Arctic sea ice.
Leads are created by dynamic motions of the sea ice
Furthermore, the heat exchange between atmosphere and ocean is strongly enhanced over leads. Using a simple heat flux model,
Different studies suggested that the overall heat exchange over leads depends not only on lead area fraction or ice thickness but also on lead width.
Using a fetch-dependent formulation of the heat exchange,
To account for these lead-width-dependent processes in models, the lead width needs to be parametrized. One possibility is to apply a lead-width distribution. Several studies estimating shear and divergence rates for Arctic sea ice using satellite observations suggest that these quantities follow a power law
For the Antarctic, different studies have derived lead fractions
The main advantage of the recently launched Sentinel-2 satellites is their high resolution up to 10 m. This enables us to also detect very narrow leads, which most of the former studies were not capable of.
We use cloud-free Sentinel-2 Level-1C products, which give the top-of-the-atmosphere (TOA) reflectance
The two sun-synchronous Sentinel-2 satellites carry the passively working MultiSpectral Instrument (MSI) with 13 different spectral bands from 443
Display of the selection steps for the 20 Sentinel-2 Level-1C products. The location of the 20 different Sentinel-2 Level-1C products for this study is the Weddell Sea. Of the 20 products, 9 were used for the sea-ice surface-type classification (red border), while for the lead-width detection all 20 were used (red and blue border). For the border of the product the “real image outlines” are displayed, which are not always rectangular since the satellite swath does not always overlap completely with the processing grid applied by ESA. Displayed in gray is the Antarctic continent border including the shelf ice border measured with different satellite radar from 2007–2009
We selected the Weddell Sea as a case study, since Sentinel-2 is a land mission and acquires data over oceans only in the vicinity of land
Sentinel-2 Level-1C products used for measuring the lead width. Products which are also used for the classification are labeled with “yes”.
The lead-width detection method (Sect.
The threshold identification contains the following main steps (Fig.
Data analysis steps for obtaining the Gaussian curves for each surface type.
For the surface-type classification 9 out of 20 later-used Sentinel-2 Level-1C products are utilized (Sect.
The number of pixels within every surface type for a specific TOA reflectance. The TOA reflectance threshold for each surface type is the point of intersection of two curves adjacent to each other. The error is shown as the overlap error of these two curves below each threshold. The red arrows show the two thresholds later used for the lead identification for the lead-width measurement: the open-water (OW) threshold and the open-water-and-nilas (OWN) threshold.
To analyze the range of the TOA reflectance for each surface type, histograms are created, which show the occurrence of pixels with a specific TOA reflectance. These histograms are used to fit a summation over Gaussian functions with the mean
The threshold for each surface category is then determined as the values of the TOA reflectance at the point of intersection of two curves adjacent to each other. An exception is the threshold for open water, where two points of intersection occur. In this case the second point of intersection is chosen to be the threshold because the first point of intersection is before the maximum. The area of intersection of two curves is then the overlap error of those thresholds and describes where we manually classified pixels with the same TOA reflectance in different sea-ice surface categories.
For the lead identification two different thresholds are used to create binary images: one for leads covered with open water (OW threshold) and one for leads covered with open water and nilas (OWN threshold). We decided to use two thresholds to observe the effect of the coverage of the lead on the power law similarly to
Since the leads within each image can have arbitrary orientations, it is not guaranteed that the “true lead width” orthogonally to the leads' orientation is measured but the width of a line across the lead at an angle other then 90
The obtained data set of apparent lead widths can then be displayed as a histogram showing the occurrence
We apply two different methods to estimate the power-law exponent
The second method for estimating the exponent
To reduce the influence of possible single outlying measurements on the result of the power-law exponent, we estimated the lead-width distribution 100 times with a random selection of 70 % of the measured apparent lead widths. We choose 70 % to still have enough measured widths while having variation between the data sets. The final power-law exponent is then estimated as the mean over the 100 calculations. Additionally, as a measure for uncertainty, the standard deviation is also estimated from the 100 calculations.
The thresholds between surface categories and corresponding overlap errors are determined using the method described in Sect.
The table displays the threshold for each surface type from the surface classification. The thresholds are the point of intersection between the Gaussian curves describing the TOA reflectance values that occurred for each surface type (Fig.
The common value used to compare optical properties of sea ice is the albedo. In this study, we measure TOA reflectance instead of albedo. Both properties increase with the sea ice and snow cover thickness, especially for young, thin sea ice in the absence of melting processes. In addition to this, we only use cloud-free Sentinel-2 band-4 images. Thus, the atmosphere has a negligible influence on the reflectance measurement. We estimated the thresholds with Sentinel-2 band-4 images from January to April 2017 to include different sun and look angles. Before estimating the thresholds we also compared the TOA reflectance values for each surface type within the products with each other and found no significant difference. To evaluate the two thresholds, which are later used for the lead detection, they are compared to measured albedo values from the East Antarctic sea-ice zone in austral spring and summer by
Additionally, since leads normally have sharp edges the selection of areas as example values for open water and nilas was comparatively easy compared to the other sea-ice surface types. The thicker the ice and snow cover, the more unreliable these observations become. To obtain a more precise classification of the surface types' validation with other data sources like field measurements could be beneficial. Nevertheless, the TOA reflectance thresholds (0.10 for OW and 0.16 for OWN) were used for the lead detection and agree with values from previous measurements
The lead-width distribution derived from 20 Sentinel-2 products using both the open-water (OW) and the open-water-and-nilas (OWN) threshold is presented in Fig.
Relative lead occurrence as a function of measured lead width (dots). Lead widths were measured using
Same as Fig.
Different results from the literature and this study for the Weddell Sea sorted by publishing date. The threshold definition for lead identification differs between the studies.
As described in Sect.
Secondly, we compare the results for the same method with both thresholds to show the importance of the choice of thresholds (Fig.
Previous studies about lead-width distributions (Table
In addition to the different measurement systems (different satellites and submarines) and different methods regarding lead definition and measurement, the studies for the Arctic observe leads in different regions (Table
Furthermore, the results for the power-law exponent displayed in Table
Another possible reason for the differences is the different conditions in both regions. While the Arctic Ocean is surrounded by land mass, the Southern Ocean surrounds the Antarctic continent. The Antarctic sea ice is exposed to the Antarctic Circumpolar Current and strong circumpolar winds. The Antarctic sea-ice cover is generally more divergent than much of the Arctic ice cover
We introduce a lead-width distribution for Antarctic sea ice using the Weddell Sea as a case study. To observe leads and their width with Sentinel-2 Level-1C products, it is necessary to have a surface-type classification. Therefore we analyzed Sentinel-2 Level-1C products (band 4, 665 nm) with a resolution of 10 m and created a surface-type classification based on the top-of-the-atmosphere (TOA) reflectance. With this classification the Sentinel-2 Level-1C data can be used to detect and observe sea-ice leads under cloud-free conditions with a resolution of 10 m. The local overpass time of the two Sentinel-2 satellites matches the SPOT satellite and is close to Landsat 8, which provides the possibility for a future combination of the data sets to form longer time series. The mission lifetime for Sentinel-2 satellites, which were launched in 2015 and 2017, is planned to be 15 years
We apply two different fitting methods, which have been used in previous studies for Arctic sea ice
Thus, it is necessary to carry out further research on leads in the Southern Ocean to fully understand differences and similarities between the Arctic and Antarctic sea ice and account for possible regional differences in lead widths throughout the Antarctic sea ice. For future comparison the same fitting method should be applied, since our study shows that with the same data different results occur.
All Sentinel-2 Level-1C products used are given in Table
MM acquired and checked the data, created the surface-type classification, and derived the lead-width distribution under the supervision of LK. AUS helped with the derivation of the lead-width distribution and editing the paper. MM prepared the paper with contributions of all co-authors.
The authors declare that they have no conflict of interest.
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This work was financially supported by the German Science Foundation (DFG) with the project number 314651818, and the publication was supported by Johanna Baehr from the Institute of Oceanography, Universität Hamburg. The authors acknowledge the Copernicus program and the European Space Agency (ESA) for providing the imagery data for the Sentinel-2 satellites with the Copernicus Open Access Hub.
We thank the editors Yevgeny Aksenov and Jennifer Hutchings and the two anonymous referees for their helpful criticism.
This work was financially supported by the German Science Foundation (DFG) with the project number 314651818, and the publication was supported by Johanna Baehr from the Institute of Oceanography, Universität Hamburg.
This paper was edited by Yevgeny Aksenov and Jennifer Hutchings and reviewed by two anonymous referees.