Arctic marginal ice zone interannual variability and change point detection using two definitions (1983–2022)

The ongoing decline in Arctic sea ice extent and thickness underscores the scientific significance of monitoring the marginal ice zone (MIZ), a transitional region between the open ocean and pack ice. In this study, we used Bootstrap sea ice concentration (SIC) to detect the trend and change point of the Arctic MIZ over 40 years (1983–2022) using two different MIZ definitions: SIC threshold-based (MIZ t ) and SIC anomaly-based (MIZ σ ). This study marks the exploration of a SIC anomaly-based definition of the MIZ over the Arctic. While the two MIZ definitions yield comparable seasonal trends in marginal ice zone fraction (MIZF), the MIZ σ fraction values peak during the transition periods (e.g. freeze-up and break-up), while the MIZ t fraction values peak in August. The analysis also uncovers consistently higher MIZF values for the MIZ σ than for MIZ t across all seasons. Moreover, October and August show the fastest rate of increase in MIZ t fraction and MIZ σ fraction, reflecting the coinciding rapid decrease in sea ice extent during those particular months. Employing the pruned exact linear time, a multiple change point detection method, highlights a significant increase in the MIZ t fraction in October (after 2005) and MIZ σ fraction in August (after 2007). This can be indicative of the recent climate change impacts in the Arctic region that may be linked with shifts in SIC and sea ice mobility for MIZ t and MIZ σ , respectively.


Introduction
The marginal ice zone (MIZ) can be defined as the region between the consolidated ice cover and the open ocean.It is often considered the area where ocean waves interact with sea ice, penetrate ice cover (Dumont et al 2011), and impact the ice thickness (Sutherland and Dumont 2018).A more practical definition of the MIZ is defined as the region where the sea ice concentration (SIC, the fractional coverage of sea ice within a grid cell) is between 0.15 and 0.80 (Strong and Rigor 2013), where SIC is often obtained using data from passive microwave sensors.Irrespective of the definition applied, investigating the MIZ is vital as it supports a diverse range of life, from sea ice algae and other primary producers to marine mammals and seabirds (LeBlanc et al 2019) and has implications for human access to the Arctic (Rogers et al 2013).The MIZ is highly dynamic and responsive to fluctuations in cyclones (Finocchio et al 2020), wind and ocean currents, making it a rapidly changing environment (Notz 2012).Due to its dynamic nature, the MIZ plays a significant role in modulating the exchange of heat and gases between the atmosphere and ocean (Rolph et al 2020).Furthermore, MIZ can impact Arctic amplification, as it serves as a zone for Arctic cyclogenesis, which plays a crucial role in northward meridional heat transport (Inoue and Hori 2011).Therefore, improving our understanding of Arctic climate change requires an enhanced understanding of MIZ spatial and temporal variability.Strong and Rigor (2013) used several passive microwave SIC products in the Arctic (1979Arctic ( -2011) ) and indicated that the Arctic summer MIZ (July-September) expanded in width by 39%, while the Arctic winter MIZ (December-February) decreased in width by 15%.The observed widening of the MIZ is reported to be closely associated with the decline of thick and multi-year sea ice.MIZ widening facilitates ship access to the Arctic (Aksenov et al 2017).Utilizing various passive microwave SIC products, another study in the Arctic (1978Arctic ( -2018) ) reported a constant MIZ extent trend that was attributed to a decrease in the perimeter as the MIZ moved north (Rolph et al 2020).Several other studies tend to assume that the MIZ extent is increasing (Horvat and Tziperman 2015, Tsamados et al 2015, Strong et al 2017, Boutin et al 2020).Horvat (2021) suggested using the marginal ice zone fraction (MIZF, the fraction of sea ice cover that is MIZ) as an alternative to solely relying on sea ice area for evaluating how changes in sea ice models affect past, present, and projected sea ice state.The strong correlation between sea ice area and global mean temperature (unlike the MIZF) makes it difficult to determine whether improvements in modeled sea ice are due to advancements in sea ice models or other components of climate models.This makes MIZF a more plausible method of assessing improvements in sea ice models.Considering the significance of passive microwave SIC products in activities such as long-term shipping route planning, reanalysis data production, climate monitoring, and forecasting, MIZF can potentially provide a realistic understanding of future climate conditions.
As an alternative approach to delineating the MIZ without relying on a fixed threshold (0.15 ⩽ SIC < 0.80), the study by Vichi (2022) introduced an innovative method involving an indicator derived from the SIC anomaly.This indicator (denoted as σ m SIA and referred to as σ a in our study) signifies the deviation of SIC at a specific grid cell from its longterm average over a given time period.Vichi concluded the indicator provides insight into the variability of the Antarctic MIZ, while the SIC thresholdbased approach suffices for defining the Arctic MIZ; although this study did not explicitly examine the details of the anomaly-based approach in the Arctic.The decline of Arctic sea ice extent (Stroeve et al 2007, Cavalieri andParkinson 2012), the replacement of thick and multi-year ice by thin and first-year ice (Maslanik et al 2007(Maslanik et al , 2011) ) and the more fragmented thinner sea ice, coupled with stronger winds and waves than in the past (Aksenov et al 2017) highlight potential alteration in SIC anomaly.These observations, motivated us to explore the efficacy of the SIC anomaly-based MIZ definition in capturing meaningful insights, comparable to the established SIC threshold-based definitions, in the Arctic.
Given the vulnerability of the Arctic MIZ to the effects of climate change (Palma et al 2019), there is a compelling need to investigate when (or if) significant shifts occur within the 40 year time series of the Arctic MIZF, which has not been examined previously.By understanding historical shifts, more accurate models for forecasting future sea ice conditions can be developed.This analysis affects not only human activities and ship navigation planning but also other sectors such as marine habitat life (Sumata et al 2023).Knowledge of these shift points in the time series can provide data-driven insights into the timing and magnitude of environmental changes, which can guide conservation efforts and policies aimed at mitigating climate change impacts.In this study, we used Bootstrap SIC, a long-term passive microwave SIC product, to investigate Arctic MIZ interannual and seasonal variability and possible change points over the last 40 years using two different MIZ definitions: SIC threshold-based, and SIC anomaly-based.

SIC product
The Bootstrap SIC (Comiso 2007) was chosen because it provides a long-term, consistent, and comprehensive SIC product.The Bootstrap ice edge also shows good agreement with the daily Canadian Ice Service ice charts over the eastern Canadian Arctic, compared to other passive microwave products (Soleymani et al 2023).We obtained Bootstrap SIC with a 25 km gridded resolution for the entire available dataset, spanning from 1983 to 2022, from the United States National Snow and Ice Data Center.

MIZ fraction (MIZF)
The concept of MIZF is defined as (Horvat 2021) where MIZA represents the MIZ area, which is the summation of each grid cell area multiplied by its SIC, provided it is MIZ.SIA denotes the sea ice area, which is the summation of each grid cell area multiplied by its SIC, provided it has at least 0.15 concentration.

SIC threshold-based MIZ fraction (MIZ t F)
To define the monthly MIZ t F in each year, we first calculated the monthly mean SIC values for a particular grid cell for a given year.Next, we determined the MIZ using the SIC criterion (MIZ t ) as 0.15 ⩽ SIC < 0.80.Finally, we used equation (1) to find the MIZ t F.

SIC anomaly
The SIC anomaly refers to the deviation of SIC at a particular grid cell from its long-term average, which is taken over a given month for the years 1983-2022.
To calculate the monthly SIC anomaly for a grid cell located at i, j, the following equation was used where SIC m i,j,d is the SIC value at the grid cell with the location of i, j on each day d in a given month m, and SIC i,j,m is the long-term average SIC value for the same grid cell over the same month.Choosing a monthly time window for climatology reduces shortterm fluctuations compared to daily process, providing a smoother dataset that can reflect long-term SIC patterns and trends.

SIC anomaly variability
The standard deviation (SD) of the monthly SIC anomaly (σ) captures the SIC variability of a given grid cell over a month.The monthly SIC anomaly for a given grid cell located at i, j or σ a i,j over month m with n total days (d = 1 to n) can be calculated by taking the square root of the variance, which is the mean of the squared daily SIC anomalies or a m i,j,d (Vichi 2022).Mathematically, σ a i,j can be expressed as (3)

SIC anomaly distribution
Following defining the σ a i,j , we calculated the median value of each grid cell over the Arctic (1983Arctic ( -2022)). Figure 1, panel (a), shows the probability density function (PDF), empirical cumulative distribution functions (ECDFs), and fitted Pareto distribution cumulative distribution function (fitted CDF) for the median of SIC anomaly SD (σ a ).To check the goodness-of-fit of the Pareto distribution, we used the Kolmogorov-Smirnov (K-S) test, and the resulting p-value was smaller than the chosen significance level of 0.05.Panels (b) and (c) in figure 1 display the mean SIC and median σ a spatial maps, respectively.The PDF plot displays two distinct peaks: peak 1 is centered approximately at 0.02, and peak 2 is situated around 0.15, with the trough between the peaks apparent around 0.11.Based on figure 1, regions with mean SIC values close to 1 correspond to the median σ a values below 0.11, hence these values correspond to regions of high ice concentration.Areas where the mean SIC values are less than 1 are associated with median σ a values exceeding 0.11.Consequently, we established a threshold of 0.11 to identify significant anomalies in SIC for MIZ determination.To define the monthly MIZ σ F in each year, we first calculated the σ a i,j (equation ( 3)).Then, we determined the MIZ using the SIC anomaly criterion (MIZ σ ) as σ a > 0.11.

Change point detection
To investigate if there are change points within the 40 year time series of the Arctic MIZF, we employed the pruned exact linear time (PELT), a multiple change point detection method, introduced by Killick et al (2012) and used in sea-ice related studies (Gimeno-Sotelo et al 2018, Purich and Doddridge 2023).The PELT algorithm initiates with a single segment encompassing the entire time series.If the reduction in cost is less than a defined penalty value (>0), the penalized cost increases, and the year under consideration is not identified as a change point.Conversely, if the cost reduction surpasses the added penalty, the algorithm marks the year as a change point.Subsequently, the dataset is divided at this change point.Among the remaining candidate split points, PELT selects the one with the lowest cost, thus dividing the time series into two new segments.This process iterates for the two newly created datasets, both before and after the identified change point.If change points are detected in either of these new segments, they are further divided.This recursive procedure continues until no more change points are found within any part of the dataset.To implement the PELT algorithm, we utilized the 'ruptures' Python library with a built-in cost function based on the radial basis function (RBF), which is a Gaussian kernel and is a good option when we have no information about the underlying data (Feasel 2022).The RBF cost function quantifies the similarity between consecutive segments of the time series.If there is a shift or alteration in the data distribution, it is reflected in a noticeable change in the similarity scores between these segments.In contrast, when the data distribution remains stable, the similarity scores between consecutive segments remain relatively constant.A significant drop in similarity scores signals the presence of a potential change point.The statistical significance of the change points is assessed using Welch's t-test with a significance level of 0.05.

MIZ interannual variability
The trend, mean, and SD for the Arctic sea ice extent, MIZ t F, and MIZ σ F are presented in table 1.A declining trend has been observed in sea ice extent over the last 40 years.For sea ice extent, September shows the fastest rate of decline (consistent with other studies, e.g.In panel (a), the trough between peak 1 and 2 is indicated by a red asterisk located at 0.11.The Bootstrap SIC data are over the Arctic .The Freedman-Diaconis rule is used to find the number of histogram bins for the PDF distribution.The outliers (defined by the interquartile range method) and grid cells with σ a = 0 are excluded from the median σ a spatial map.These regions are shown in white, while the land is grey.
Table 1.Trend, mean, and standard deviation (SD) values for the Arctic sea ice extent, MIZtF, and MIZσF over 1983-2022.Sea ice extent is the area of grid cells with SIC ⩾ 0.15.The MIZt grid cells are defined using the criterion of 0.15 ⩽ SIC < 0.80.The MIZσ grid cells are defined using the criterion of σ a > 0.11.The results are statistically significant at a 0.05 level using Student's t-test.Focusing on the interannual variations of MIZF using the SIC threshold-based definition (figure 2) and the SIC anomaly-based definition (figure 3) we noticed some months with significantly different behavior for these two MIZ definitions.We focused on two noticeable ones: July (from 2011 to 2013) and November (from 2020 to 2022).For the month of July, from 2011 to 2012, the MIZ t F value shows a sharp increase, followed by a sharp decrease from 2012 to 2013.This behavior is the opposite for the MIZ σ F. The year 2012 was an anomalously low year for sea ice extent in the Arctic (see July panel in appendix figure A1), which could lead to low SIC fluctuations for months and regions with ice-free conditions.To gain deeper insights into this, MIZ spatial maps are presented in figure 4 (see appendix figure A2 for sub-regions of the Arctic).For the MIZ t , in July 2012 the East Siberian, Chukchi, and the Beaufort Seas, were flagged as MIZ, but were not flagged in July 2011 and 2013.In contrast, MIZ σ shows a more fragmented MIZ region in the Beaufort, Chukchi, and East Siberian Seas compared to MIZ t in July 2012.For MIZ σ , the primary sub-regions contributing to the negative shift in July 2012 are Hudson Bay, Baffin Bay, Greenland and Barents Seas, which are flagged as MIZ and in July 2011 and 2013 (not in July   2012).These observed differences between MIZ t F and MIZ σ F align with the fact that the sea ice in the East Siberian, Beaufort, and Chukchi Seas is thicker than that in Hudson Bay, Baffin Bay, Greenland, and Barents Seas, which is thinner and more seasonal (Onarheim et al 2018).Differences between MIZ t and MIZ σ can also be seen in the Canadian Archipelago, which has experienced a transition to thinner ice and more mobile ice, due to ongoing warming (Howell and Brady 2019).These results should be further investigated in relation to ice charts.Melt conditions lead to fluctuations in brightness temperatures, in particular during melt onset, which occurs in June and July in this region (Bliss et al 2019, Marshall et al 2019).These fluctuations are reflected in SIC estimates from passive microwave sensors.

Month
For the month of November, the MIZ t F value, shows a slight decrease from 2020 to 2021 and a decline from 2021 to 2022.While the MIZ σ F value shows a significant increase from November 2020 to 2021, followed by a steep decline from 2021 to 2022.To better understand this, we examined the MIZ spatial maps, presented in figure 5.For MIZ t , there is a slight difference between the region identified as MIZ from 2020-2022 mainly associated with the Chukchi Sea, Baffin Bay and part of Hudson Bay.For MIZ σ , the primary sub-regions varying across these three years include the Beaufort, Chukchi, East Siberian and Laptev Seas, Baffin, and Hudson Bay.Significant differences between the two MIZ definitions are found in 2021 across the East Siberian, Laptev, Kara and Barents Seas.The observed disparities between MIZ t and MIZ σ align with the findings reported in the Sea Ice Outlook, stating that in 2021, the Chukchi and Barents Seas underwent an early freeze-up in November, with the Chukchi Sea reaching its largest sea ice extent in 20 years and in November 2021.While in 2021, Hudson Bay exhibited significantly delayed freeze-up events compared to the average (Bhatt et al 2022).

MIZ change point analysis
The change points in the monthly MIZ t and MIZ σ time series are detected using the PELT test (shown with a red dashed line in figures 2 and 3).For MIZ t F (figure 2), a change point was detected in October corresponding to the year 2005.Other months did not show a significant change point year.To investigate this observation, figure 6 illustrates the MIZ t map in October before and after the change point (panels (a) and (b), respectively).The most noticeable   2005) is detected using the PELT method which was statistically significant at a 0.05 level using Welch's t-test.The MIZt grid cells are defined using the criterion of 0.15 ⩽ SIC < 0.80.The projection coordinate system is Polar Stereographic.The land is shown in grey.2007) is detected using the PELT method which was statistically significant at a 0.05 level using Welch's t-test.The MIZσ grid cells are defined using the criterion of σ a > 0.11.The projection coordinate system is Polar Stereographic.The land is shown in grey.change after 2005 is an increase in the regions flagged as MIZ for the Amundsen Gulf, Beaufort, Chukchi, East Siberian and Laptev Seas.According to a recent study (over the period of 1990-2019), there was a shift in SIC in 2005 over the East Siberian and Laptev Seas (Sumata et al 2023).This can result in a large sea ice-covered area with intermediate SIC leading to an increase in the MIZ t in this year.
For the MIZ σ F (figure 3), the change point year for August was detected in the year 2007.Other months did not show a change point year.To investigate this observation, figure 7 illustrates the MIZ σ map in June before and after the change point (panels (a) and (b), respectively).The most noticeable change after 2007 is an increase in the regions flagged as MIZ for the Beaufort, Chukchi, and East Siberian seas.A shift in SIC in the Beaufort and Chukchi Seas and a strong increase in ice velocity with the strengthening of the rotation of the Beaufort Gyre have been noted for 2007, along with a decrease in sea ice residence time for the East Siberian Sea (study over the period of 1990-2019, Sumata et al 2023).These events, in particular a more mobile ice pack, can result in a large sea ice anomaly leading to an increase in the MIZ σ in this year.

MIZ seasonal cycle
To visualize the MIZ seasonal cycle, a box-whisker plot of MIZF over the Arctic (1983Arctic ( -2022) ) is shown in figure 8. August shows the highest mean value for MIZ t F (0.23).While for MIZ σ F, July and October show the highest mean value.A consistent MIZF trend is observed for both definitions from January to May.Possibly because, as the ice grows, both the SIA and the MIZA increase, and this results in a constant MIZF (equation ( 1)).Subsequent to May, MIZ t F experiences growth, peaking in August (consistent with a study by Rolph et al 2020).The MIZ t F retreats in September and stays almost the same in October.Thereafter, MIZ t F decreases until December.However, the MIZ σ F displays a substantial increase from May to July, reaching its first peak, and then gradually recedes until December, with the exception of an increase in October where it reaches its second peak.The most notable difference in mean MIZF values between MIZ t F and MIZ σ F is evident in October.Given that October is within the freezeup period, the associated SIC fluctuations linked to ice growth and consolidation can be captured by the MIZ σ .Indeed, the average value of MIZ t F remained constant in October when compared to September.This indicates that both MIZA and SIA (equation (1)) were changing at a consistent rate in October.On the other hand, for MIZ σ F, the variations in SIC could result in a change in MIZA that exceeds the change in SIA (equation ( 1)).Consequently, this can result in an increase in the mean value of MIZ σ F in October.Additionally, for several months (July, August and November), the interquartile range (box length) is larger for the MIZ σ F than the MIZ t F, which  .The MIZt grid cells are defined using the criterion of 0.15 ⩽ SIC < 0.80.The MIZσ grid cells are defined using the criterion of σ a > 0.11.The MIZF average values are indicated by a triangle.The box length indicates the MIZF interquartile range.
demonstrates the capability of MIZ σ in capturing transition periods characterized by substantial fluctuations in SIC.

Discussion
In contrast to the consistent downward trend observed in Arctic sea ice extent across all months from 1983 to 2022, the trends in MIZ t F and MIZ σ F are more variable.Over the study period, the Arctic MIZ t reached its maximum fraction in July 2012, while its minimum fraction was recorded in March 2010.On the other hand, the Arctic MIZ σ attained its highest fraction in August 2016, contrasting with its lowest fraction observed in December 1987.August also showed the fastest rate of increase of MIZ σ F. Concerning monitoring Arctic sea ice extent, September stands out as a pivotal month, given that it consistently displays the lowest annual sea ice extent.For a comprehensive analysis of MIZ, however, July, August and October can offer information about the changes in ice-covered areas that cannot be obtained solely by focusing on the month with the minimum sea ice extent.We found various passive microwave SIC products yield distinct MIZF values, primarily due to differences in SIC and SIC anomaly values and in turn different PDF distributions with different σ a thresholds.The choice of passive microwave SIC product can influence the results for both MIZ t F and MIZ σ F (appendix figures A4-A7).Results may differ if the PDF distributions were constructed based on regional statistics.
The SIC threshold-based definition of MIZ provides a practical means of identifying the transition between consolidated ice and open water.This definition proves useful in many applications, for example, SIC serves as an input in higher-level geophysical products, such as Level 4 sea surface temperature, and ice velocity drift products.However, there might be merit in the MIZ σ use of the SIC anomaly in these products as well.MIZF can also be used to study habitat changes for marine mammals and seabirds, which could be more sensitive to fluctuations in SIC than the SIC value.Moreover, the SIC anomaly-based definition captures unusual or extreme fluctuations (e.g.rapid ice retreat/advance, cyclones) more effectively than absolute SIC values.For example, there was a strong Arctic cyclone recorded in August 2016 (Yamagami et al 2017), the impact of which was captured in MIZ σ (appendix figure A3).The impact of a particular cyclone on sea ice cover depends on the location of the event (e.g.proximity to the coast, ice edge) in addition to the characteristics of the sea ice (Finocchio and Doyle 2021).Monitoring the location of these and similar events that lead to fluctuations in SIC is crucial, especially for planning safe navigation routes in the Arctic region.Although the two MIZ definitions yield comparable seasonal trends in MIZF, MIZ σ captures transition periods, such as freeze-up and break-up seasons.These periods are characterized by heightened SIC fluctuations, for example, owing to the presence of thin or fragmented ice, and fluctuations in other variables such as air temperature and solar radiation.As observed, the regions exhibiting significant contrast between the two MIZ definitions are those dominated by thin seasonal ice, in comparison to regions dominated by thick multi-year ice.With the Arctic sea ice thinning (Kwok 2018), the associated increased SIC variability, the strengthening effect of air temperature on sea ice (Yu et al 2021), greater sensitivity of the pack ice to wind forcing (Serreze et al 2003), and the extension of melt season (Stroeve et al 2014), tracking SIC anomaly becomes increasingly pertinent.Thin ice and its variable concentration values could lead to a different PDF distribution for the median σ a , necessitating updates to the σ a threshold.In light of the Arctic's increasingly dynamic ice conditions, the SIC anomaly-based MIZ definition offers an additional approach to characterizing the climatically crucial region beyond the sea ice extent or the SIC thresholdbased MIZ definition.

Conclusion
In this study, we used Bootstrap SIC product to detect the trend and change point of the Arctic MIZ (1983MIZ ( -2022) ) using two MIZ definitions: MIZ t and MIZ σ .Our observations indicate that over the last 40 years, the Arctic MIZ t reached its maximum fraction in August 2012, while its minimum fraction was recorded in December 1987.The Arctic MIZ σ attained its highest fraction in November 2021, contrasting with its lowest fraction observed in December 1987.While the two MIZ definitions yield comparable seasonal trends in MIZF, MIZ σ F values are highest in transition periods (e.g.freeze-up and break-up) in comparison with MIZ t , which peaks in August.We also observed consistently higher MIZF values for the MIZ σ than for MIZ t across all seasons.Remarkably, October and August show the fastest rate of increase in MIZ t F and MIZ σ F, mirroring the accelerated decline in sea ice extent during the same months.
Using the PELT change point method, we observed that for MIZ t F in October, the change point year happened in 2005.For MIZ σ F in August, the change point year occurred in 2007.For both MIZ definitions, the MIZ region is increased for the period after the change point year and other months did not show a significant change point year.These change point years might be linked with shifts in sea ice concentration and sea ice velocity (Sumata et al 2023) for MIZ t and MIZ σ , respectively.This knowledge aids in the improvement of seasonal ice forecasts, safer navigation, resilient coastal communities, and marine habitat protection.In a forthcoming study, we will compare these two MIZ definitions using synthetic aperture radar imagery and provide information on the advantages and disadvantages of each definition.(2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019)(2020).The Freedman-Diaconis rule is used to find the number of histogram bins for the PDF distribution.The outliers (defined by the interquartile range method) and grid cells with σ a = 0 are excluded from the median σ a spatial map.The corresponding grid cells are also excluded from the mean SIC spatial map.These regions are shown in white, while the land is grey.(2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019)(2020).The Freedman-Diaconis rule is used to find the number of histogram bins for the PDF distribution.The outliers (defined by the interquartile range method) and grid cells with σ a = 0 are excluded from the median σ a spatial map.The corresponding grid cells are also excluded from the mean SIC spatial map.These regions are shown in white, while the land is grey.

Figure 1 .
Figure 1.The PDF, ECDF, and fitted Pareto distribution CDF of the median of SIC anomaly standard deviation or σ a (panel (a)), the mean SIC spatial map (panel (b)), and the median σ a spatial map (panel (c)).In panel (a), the trough between peak 1 and 2 is indicated by a red asterisk located at 0.11.The Bootstrap SIC data are over the Arctic.The Freedman-Diaconis rule is used to find the number of histogram bins for the PDF distribution.The outliers (defined by the interquartile range method) and grid cells with σ a = 0 are excluded from the median σ a spatial map.These regions are shown in white, while the land is grey.

Figure 2 .
Figure 2. Temporal variability of the Arctic marginal ice zone fraction using the SIC threshold-based definition (MIZtF) over 1983-2022.The MIZt grid cells are defined using the criterion of 0.15 ⩽ SIC < 0.80.A PELT test is

Figure 3 .
Figure 3. Temporal variability of the Arctic marginal ice zone fraction using the SIC anomaly-based definition (MIZσF) over 1983-2022.The MIZσ grid cells are defined using the criterion of σ a > 0.11.A PELT test is used to

Figure 5 .
Figure 5. MIZt mean SIC spatial map (first row) and MIZσ mean SIC spatial map (second row) in November 2020 (left panel), 2021 (middle panel), and 2022 (right panel).The MIZt grid cells are defined using the criterion of 0.15 ⩽ SIC < 0.80.The MIZσ grid cells are defined using the criterion of σ a > 0.11.The projection coordinate system is Polar Stereographic.The land is shown in grey.

Figure 6 .
Figure 6.MIZt map in October before the change point year (panel (a)) and after the change point (panel (b)).The change point year (2005) is detected using the PELT method which was statistically significant at a 0.05 level using Welch's t-test.The MIZt grid cells are defined using the criterion of 0.15 ⩽ SIC < 0.80.The projection coordinate system is Polar Stereographic.The land is shown in grey.

Figure 7 .
Figure 7. MIZσ map in August before the change point year (panel (a)) and after the change point (panel (b)).The change point year (2007) is detected using the PELT method which was statistically significant at a 0.05 level using Welch's t-test.The MIZσ grid cells are defined using the criterion of σ a > 0.11.The projection coordinate system is Polar Stereographic.The land is shown in grey.

Figure 8 .
Figure 8.A box-whisker plot visualization of the seasonal cycle of MIZtF (red box) and MIZσF (blue box) over the Arctic.The MIZt grid cells are defined using the criterion of 0.15 ⩽ SIC < 0.80.The MIZσ grid cells are defined using the criterion of σ a > 0.11.The MIZF average values are indicated by a triangle.The box length indicates the MIZF interquartile range.

Figure A2 .
Figure A2.Sub-regions of the Arctic (based on the National Snow and Ice Data Center).The projection coordinate system is Polar Stereographic.The land is shown in grey.

Figure A3 .
Figure A3.MIZt spatial map (panel (a)) and MIZσ map (panel (b)) in August 2016.The MIZt grid cells are defined using the criterion of 0.15 ⩽ SIC < 0.80.The MIZσ grid cells are defined using the criterion of σ a > 0.11.The strong Arctic cyclone affected sea ice in the Laptev Sea and Central Arctic Ocean (Yamagami et al 2017).The projection coordinate system is Polar Stereographic.The land is shown in grey.

Figure A4 .
Figure A4.The PDF, ECDF, and fitted Pareto distribution CDF of the median of SIC anomaly standard deviation or σ a (panel (a)), the mean SIC spatial map (panel (b)), and the median σ a spatial map (panel (c)).The Arctic Radiation and Turbulence Interaction Study (ASI) sea ice SIC data are over the Arctic(2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019)(2020).The Freedman-Diaconis rule is used to find the number of histogram bins for the PDF distribution.The outliers (defined by the interquartile range method) and grid cells with σ a = 0 are excluded from the median σ a spatial map.The corresponding grid cells are also excluded from the mean SIC spatial map.These regions are shown in white, while the land is grey.

Figure A5 .
Figure A5.The PDF, ECDF, and fitted Pareto distribution CDF of the median of SIC anomaly standard deviation or σ a (panel (a)), the mean SIC spatial map (panel (b)), and the median σ a spatial map (panel (c)).The enhanced NASA Team 2 (NT2) SIC data are over the Arctic(2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019)(2020).The Freedman-Diaconis rule is used to find the number of histogram bins for the PDF distribution.The outliers (defined by the interquartile range method) and grid cells with σ a = 0 are excluded from the median σ a spatial map.The corresponding grid cells are also excluded from the mean SIC spatial map.These regions are shown in white, while the land is grey.

Figure A6 .
Figure A6.The PDF, ECDF, and fitted Pareto distribution CDF of the median of SIC anomaly standard deviation or σ a (panel (a)), the mean SIC spatial map (panel (b)), and the median σ a spatial map (panel (c)).The Ocean and Sea Ice Satellite Application Facility-458 (OSI-458) SIC data are over the Arctic(2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019)(2020).The Freedman-Diaconis rule is used to find the number of histogram bins for the PDF distribution.The outliers (defined by the interquartile range method) and grid cells with σ a = 0 are excluded from the median σ a spatial map.The corresponding grid cells are also excluded from the mean SIC spatial map.These regions are shown in white, while the land is grey.

Figure A7 .
Figure A7.The PDF, ECDF, and fitted Pareto distribution CDF of the median of SIC anomaly standard deviation or σ a (panel (a)), the mean SIC spatial map (panel (b)), and the median σ a spatial map (panel (c)).The Bootstrap (BT) SIC data are over the Arctic(2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019)(2020).The Freedman-Diaconis rule is used to find the number of histogram bins for the PDF distribution.The outliers (defined by the interquartile range method) and grid cells with σ a = 0 are excluded from the median σ a spatial map.The corresponding grid cells are also excluded from the mean SIC spatial map.These regions are shown in white, while the land is grey.
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