18 year record of circum-Antarctic landfast sea ice distribution allows detailed baseline characterisation, reveals trends and variability

Landfast sea ice (fast ice) is an important though poorly-understood component of the cryosphere on the Antarctic continental shelf, where it plays a key role in atmosphere-ocean-ice sheet interaction and coupled ecological and biogeochemical processes. Here, we present a first in-depth baseline analysis of variability and change in circum-Antarctic fast-ice distribution (including its relationship to bathymetry), based on a new high-resolution satellite-derived time series for the period 2000 to 2018. This reveals a) an overall trend of -882 ± 824 km/y (-0.19 ±0.18 %/y); and b) eight distinct regions in 5 terms of fast-ice coverage and modes of formation. Of these, four exhibit positive trends over the 18 y period and four negative. Positive trends are seen in East Antarctica and in the Bellingshausen sea, with this region claiming the largest positive trend of +1,198 ± 359 km/y (+1.10 ± 0.35 %/y). The four negative trends predominantly occur in West Antarctica, with the largest negative trend of -1,206 ± 277 km/y (-1.78 ± 0.41 %/y) occurring in the Victoria and Oates Lands region in the eastern Ross Sea. All trends are significant. This new baseline analysis represents a significant advance in our knowledge of the current state 10 of both the global cryosphere and the complex Antarctic coastal system that is vulnerable to climate variability and change. It will also inform a wide range of other studies.

. This dataset contains 432 contiguous maps of fast ice extent at a 1 km and 15 d resolution, generated by compositing cloud-free visible and thermal infrared imagery from NASA Moderate Resolution Imaging Spectroradiometer (MODIS) sensors onboard the Terra and Aqua satellites (Fraser et al., 2009(Fraser et al., , 2010. Here, we use this newly-released dataset to perform a first detailed characterisation of circum-Antarctic fast ice distribution, 55 change and variability. We first identify eight distinct regions in terms of fast ice co-variability, which form the basis of the new analysis of fast ice trends around Antarctica. These regions differ from those more traditionally used in Antarctic sea ice analyses (Zwally et al., 1983). We then present the overall extent time series and annual climatology, spatial characterisation of mean fast ice persistence, age and timing of minimum/maximum extent across the 18 y dataset. We also analyse fast ice persistence in concert with bathymetric depth, and interpret this regionally, to more widely assess and determine the linkages 60 between fast ice and grounded icebergs, which act both as stable anchor points for fast ice formation (e.g., Massom et al., 2009;Li et al., 2020) and to intercept and retain encroaching pack ice, thus encouraging fast ice formation upstream (Massom et al., 2001;Massom, 2003).

Datasets and methods
15 day temporal resolution fast ice maps were obtained from a recently-published NASA Moderate Resolution Imaging Spec-65 troradiometer (MODIS)-derived 18 y record of Antarctic fast ice extent . This dataset consists of 432 contiguous maps of fast ice extent at a 1 km spatial resolution. This dataset is freely available at http://dx.doi.org/doi:10.26179/5d267d1ceb60c.
In this dataset, fast ice maps were constructed following a semi-automated method whereby persistent edges over a 15 d period were taken to be the fast ice edge. Manual intervention was required for times and regions where cloud cover persisted throughout the 15 d window. However, semi-automation was achieved, with 58% of fast ice edge pixels able to be automatically 70 retrieved, marking an advance over earlier, more subjective large-scale fast ice maps (e.g., Fraser et al., 2012).
To underpin definition of new regions of fast ice co-variability, fast ice anomaly time series are produced for each 1/4 • of longitude by subtracting the observed 1/4 • total fast ice from its repeating climatological cycle. New fast ice regions are defined by performing a spatial cross-correlation of these 1/4 • longitude fast ice anomaly time series. Nearby regions exhibiting similar anomaly co-variability are indicated by positive correlation "pockets", and these are grouped manually to define regions. 75 Automated region selection using a decorrelation length scale minimum-based approach to region delineation, as in Raphael and Hobbs Raphael and Hobbs (2014), was unable to be implemented due to extensive coastal regions with no fast ice. The final step of manual regional selection a) allows grouping of fast ice regions across gaps; and b) avoids excessive partitioning of broader regions. This selection of new regions of fast ice co-variability is detailed in Appendices A and B.
Fast ice persistence distribution is characterised by calculating the the fraction of the time series which each pixel is covered 80 by fast ice, after Fraser et al. (2012). This "per-pixel" mapping is also exploited to visualise per-pixel a) timing of minimum and maximum fast ice extent, b) fast ice age and c) trends in extent. The per-pixel trend map is constructed by fitting a linear trend to each pixel's 18 y time series of extent, and plotting the slope (trend) for each pixel. The map of timing of minimum/maximum fast ice extent is constructed by fitting a Fourier series with fundamental (yearly) component as well as 2nd to 4th harmonics minimisation (Markwardt, 2009). The resulting timing of minimum/maximum extent is then extracted from the Fourier fit.
Here, we prefer to display timing information in this "day of minimum/maximum" format rather than the traditional maps of "day of advance/retreat" used in other sea ice seasonality studies (e.g., Massom et al., 2013) due to the event-based formation and breakout of fast ice, in contrast to the more fine-grained advance/retreat of sea ice. The mean fast ice age map is constructed by calculating the mean time between fast ice formation and subsequent breakout. 90 We characterise the distribution of fast ice over bathymetry of varying depth by constructing 2D probability distribution functions of International Bathymetric Chart of the Southern Ocean (IBCSO, Arndt et al. (2013))-derived bathymetric depth (50 m bins) vs fast ice persistence (5 % bins). We use this circum-Antarctic bathymetry compilation despite the caveat that all such compilations suffer from a scarcity of data in fast ice-infested waters, owing to a lack of shipboard sonar measurements (Smith et al., in press). We retrieve the modal value for each persistence bin, then compute the persistence-weighted mean of 95 these modal values to characterise modal formation depth on a circumpolar basis, as well as within the new regions defined here.
We also use sea ice concentration from the National Oceanic and Atmospheric Administration/National Snow and Ice Data Center Climate Data Record of Passive Microwave Sea Ice Concentration, Version 3, to compare timing of sectoral fast ice extent to that of overall sea ice. For this timing comparison, we exploit a new technique to model the seasonal cycle of both 100 sea ice and fast ice presented by Handcock and Raphael (2020). This technique, which models each year's annual cycle as an invariant smoothed spline plus a smoothed trend over time, allows daily-resolution calculation of timing statistics even when the input dataset (i.e., the fast ice dataset) has a ∼bi-weekly resolution, thus facilitating a robust timing comparison between fast ice and overall sea ice extent. Circumpolar and regional fast ice trends are computed by calculating the sectoral total fast ice extent, computing the cli-105 matological cycle, removing the climatological cycle from the observed totals to form the sectoral anomalies, and fitting a linear trend to the anomalies in each sector. Trend confidence is determined by calculating 95% confidence intervals using the t-distribution. In the calculation of trends, pixels experiencing ice shelf retreat or advance during the 18 y period are removed from this calculation to remove the strong trend contributions caused by these processes.

Climatological patterns
For the analyses in the following sections, we consider only the eight newly-defined regions (as detailed in the Appendices A and B), plus circumpolar total statistics. Fig. 1 shows the total circumpolar extent time series (a) and its climatological annual cycle (b). A strong annual cycle is evident, with a relatively broad maximum (∼ 601,000 km 2 ) occurring throughout late winter/early spring (day-of-year 273; late September on average), and a well-defined minimum in March (∼221,000 km 2 , 115 day-of-year 71; mid-March). This indicates that fast ice experiences a seasonal approx. threefold increase in extent. As with overall sea ice (Eayrs et al., 2019;Parkinson, 2019), fast ice displays an asymmetrical annual cycle, experiencing on average ∼ 7 months of advance and 5 months of retreat. As such, fast ice as a percentage of overall sea ice area (extent) varies between a maximum of 12.8 % (8.5 %) in early-mid February (coinciding with the overall sea ice minimum in early-mid February) and around 4.0 % (3.2 %) throughout the winter (mid-July to late November). The largest fast ice contribution is from East 120 Antarctica, with the Western Indian Ocean, Eastern Indian Ocean and Australia regions together contributing over half of all fast ice in terms of areal coverage despite only covering 119 • of longitude (Table 1).       Table 1 indicates that both minimum and maximum fast ice extent (day-of-year 71 and 273, respectively) occur later than the corresponding timings for overall sea ice (comprising both pack and fast ice), which are day-of-year 50 (mid-February) and 264 (mid-September), respectively. Regionally, the result of later fast ice minimum is consistent across all regions, how-130 ever, a later fast ice maximum only occurs in five of eight newly-defined regions (although this may be a consequence of this considerable regional variability in the timing of overall sea ice extent maximum). Maps of timing of minimum and maximum fast ice extent are presented to provide a more localised context for regional studies involving fast ice (Fig. 3). These reveal remarkable differences within neighbouring areas. For example a) Enderby Land fast ice (39 • to 52 • E) achieves a minimum in April whereas along the Mawson Coast (55 • to 71 • E) this occurs in February-March; and b) fast ice on the western side of the 135 Antarctic Peninsula reaches minimum later (April) than that on the eastern side (February-March). Regional changes in maximum extent timing are more variable than minimum extent timing, likely due to the broad fast ice peak in the climatological cycle (Fig. 1b). No latitudinal gradient is apparent in either timing metric.
The map of fast ice mean age is presented in Figure 4a. Regions of multi-year fast ice (i.e., mean age >12 months) are typically located either east (upstream) of physical barriers to the westward drift of pack ice in the Antarctic Coastal Current, 140 within deep, sheltered embayments (e.g., Lützow-Holm Bay, ∼40 • E), or adjacent to coastal flaw leads indicating the presence of a shear zone (especially in the southern Weddell Sea). As such, the majority is in East Antarctica (e.g., along the Banzare Coast, ∼130 • E), although major areas are found throughout the Weddell Sea region and along the Marie Byrd Land coast (∼134 -159 • W). Multi-year ice is generally synonymous with highly-persistent fast ice (i.e., red pixels corresponding to near-100% persistence in Fig. 2), however we find limited regions where relatively low-persistence fast ice (e.g., persisting 145 through 80% of the year on average) can be multi-year (e.g., north of the Wilkins Ice Shelf, ∼74 • W), indicating a change to the annual cycle throughout the 18 y study period.

Fast ice extent anomalies and linear trends
The circumpolar total anomaly time series (Fig. 5a)  partitioning supports preservation of these opposing regional signals.
Per-pixel trends in fast ice extent (Fig. 4b) in excess of ±8 %/y are observed, corresponding to pixels exhibiting an extreme change in fast ice cover across the study period. These occur in areas exhibiting major icescape change, e.g., both upstream and downstream of the Mertz Glacier Tongue (∼144 • E), which calved in Fogwill et al. (2016, and in the Weddell Sea 160 between the Ronne-Filchner Ice Shelf and grounded iceberg A23A, which has gradually drifted northward (Li et al., 2020). Broader regions of similar signed (but weaker) trend are also apparent, e.g., the positive trend across much of the western half of East Antarctica (i.e., the Dronning Maud Land and Western Indian Ocean sectors), indicating a consistent fast ice response to environmental forcing over a large spatial scale.

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Analysis of the bathymetric distribution of fast ice provides fundamental knowledge on the formation mode of fast ice (i.e., iceberg-associated vs formation within embayments). Circumpolar fast ice persistence as a two-dimensional histogram, binned by bathymetric depth is given in Fig. 6. This analysis indicates that the weighted (by persistence) mean depth of fast ice persistence occurs at ∼403 m, in line with earlier estimates linking fast ice extent with grounded icebergs in East Antarctica (Massom et al., 2001). The 403 m bathymetric contour is shown on Figure 2 as a solid grey line. This isobath only bears visual 170 resemblance to areas containing persistent fast ice for much of East Antarctica (20 • W to 172 • E) and the Ross Sea (172 • E to 130 • W), indicating regional variability in either the actual iceberg grounding depth or the reliance of fast ice on the stability provided by grounded icebergs. Fig. S3 shows persistence-weighted histograms of fast ice formation depth for the eight newly- Here, we find that this trend, largely represented by the Western Indian Ocean region, did not persist after 2008 (see Fig. 5b). Furthermore, persistent (e.g., 12 months or greater duration) "events" are evident in 185 many anomaly plots (e.g., Fig. 5d, exhibiting a positive anomaly persisting from 2013 to 2014 in the Australia region, and contributing to the positive circumpolar total anomaly at the same time, Fig. 5a). Investigation of drivers of both regional trends and significant events within these regions is planned for the future. We note that the time series of circumpolar fast ice anomaly (Fig. 5a) bears close resemblance to that of overall sea ice extent (time series given in Fig. 2B of Parkinson (2019)), with positive anomalies in 2007/08 and 2013/14, with a decline from 2014-2017. This association will also be explored more comprehensively in future work.
We find here an approximately threefold difference between maximum and minimum fast ice extent, with a minimum occurring in mid-March and a maximum in late September. The circumpolar seasonal cycle is much lower in amplitude that that of overall sea ice extent (with a wintertime maximum extent nearly six times higher than its summertime minimum, (Eayrs et al., 2019;Parkinson, 2019)), a likely manifestation of the relatively large portion of fast ice which is multi-year combined 195 with the limit of maximum fast ice extent imposed by the distribution of grounded icebergs.

Timing of maximum and minimum extent
The circumpolar fast ice cycle is delayed relative to that of overall sea ice, with the fast ice minimum (maximum) occurring 21 (nine) days later than the that of sea ice (shown in Table 1), in agreement with the findings of Fraser et al. (2012). In the absence of particular case studies, which are out of scope here, we speculate that this lag may be due to one or more of the 200 following reasons: a) adjacent pack ice may act as a protective buffer against dynamically-induced breakout (e.g., swell may be attenuated by adjacent pack, protecting the fast ice (Ushio, 2006)); b) the presence of pack ice at the fast ice edge may reduce "mode-3" summertime solar heating of the surface water (Jacobs et al., 1992), leading to lower basal melt rates under the fast ice (Arndt et al., 2020) and higher mechanical strength (Fedotov et al. (1998) estimate only 20-30% of wintertime flexural fast ice strength remains by the time basal melt becomes widespread); or c) fast ice is simply able to persist longer into the summer 205 due to the inherent shelter afforded by its formation within certain embayments (e.g., Lützow-Holm Bay, ∼40 • E, (Ushio, 2006)).
Regarding timing of maximum extent, Fraser et al. (2012) found that fast ice maximum occurs earlier than overall sea ice in the Indian Ocean and the Western Pacific Ocean sectors (covering much of East Antarctica). We find here that this result holds for only three of eight newly-defined regions (Table 1), and that the timing in maximum extent is far more regionally 210 variable (range: 48 d) than that of minimum extent (range: 13 d), a result also indicated spatially in Fig. 3. This is likely related to the bathymetric limit imposed on maximum fast ice extent, i.e., fast ice coverage around the outermost grounded icebergs is generally achieved by midwinter, and limited further growth occurs only upstream of obstacles to the coastal current, until September. Such growth is likely stochastic and event-based, imparting variability to the timing of maximum extent.
Based on a dataset covering the years -2011-2017, Li et al. (2020 found a mean November extent of 215 ∼495,000 km 2 , which is much lower than the mean maximum extent found here (∼601,000 km 2 ). However, we have shown that November is after maximum fast ice extent in every region, so we suggest that circumpolar studies of maximum fast ice extent are best conducted around late September. Full consideration of the seasonality (i.e., timing of formation, breakout, and presence duration; and change in these quantities) of fast ice is outside of the scope of this paper, however complex regional patterns have been identified in an analysis of overall East Antarctic sea ice seasonality (Massom et al., 2013), so future work 220 on this is planned using the fast ice dataset .

Bathymetric controls on fast ice distribution
We have shown large regional variability in the formation depth of fast ice, ranging from ∼200 m to ∼450 m (Fig. S3).
Such regional variability has not been identified in earlier work (e.g., Massom et al., 2001;Fraser et al., 2012). This regional dependence on bathymetry may also suggest fundamental regional differences in fast ice formation mode. As an example of 225 this, consider the distribution of fast ice persistence by depth in the Bellingshausen Sea (Fig. S3, cyan line). In this region, relatively few grounded icebergs exist (Figure 4 in Li et al. (2020)), so fast ice predominantly forms between coastal margins (including islands), and is known as "regime 1" fast ice (Fraser et al., 2012). By contrast, in the Eastern Indian Ocean and Australia regions, "regime 2" fast ice predominates (Fraser et al., 2012), and a close relationship is found between grounded icebergs and persistent fast ice (Li et al., 2020). In East Antarctica, icebergs have been observed to ground at depths up to 230 around 400 m Massom (2003); Massom et al. (2009), although there is evidence for deeper grounding (in excess of 500 m) in some regions of the East Antarctic continental shelf (Beaman and Harris, 2005), and indeed newly-calved icebergs with keels of up to 600 m are known to calve from fast flowing outlet glaciers (Dowdeswell and Bamber, 2007). More detailed understanding of the mechanism of fast ice formation, as provided here, is crucial for development of the next generation of prognostic regional fast ice models which require tuning of tensile strength (Lemieux et al., 2016).  Figure 2). Most other regions may already have sufficient density of grounded icebergs to act as fast ice anchors, as detailed in (Li et al., 2020). We also consider a future scenario in which the recentlydetailed marine ice cliff instability mechanism is initiated (Pollard et al., 2015), whereby glacier/grounding line retreat results in high (>∼90 m) ice cliffs at the glacier terminus, resulting in calving of icebergs with extremely deep (in excess of 800 m) keels. Evidence for this process exists in the form of very deep sediment scours around Pine Island Glacier (∼101 • W, (Wise 245 et al., 2017)), estimated to have occurred in the early Holocene. Presence of such deeply-keeled icebergs around the Antarctic continental shelf would allow the grounding of icebergs in new regions, completely altering the distribution of fast ice. For this reason, the next generation of coupled Antarctic ice/ocean models with fast ice should consider prognostic iceberg calving and grounding. Near-coastal bathymetric data paucity, leading to high uncertainty in current Antarctic bathymetric compilations, is also a limiting factor for this kind of study, so should be addressed as a priority (Smith et al., in press). In addition to fields of 250 smaller grounded bergs, it is also worth re-iterating the profound and unpredictable effects that large tabular icebergs can have on regional fast ice extent (e.g., Fogwill et al. (2016)), particularly when grounded for several decades.
Compared to the earlier dataset covering only East Antarctica from 2000 to 2008 (Fraser et al., 2012), this new 18 y time series ) is a much more comprehensive dataset from which to gauge long-term change in fast ice extent.
rological Organisation (Arguez and Vose, 2011). Indeed, the residence times of large grounded icebergs which have profound effects on fast ice distribution can be as long as several decades (e.g., B09B which was grounded at ∼148 • E from 1992 to 2010 (Leane and Maddison, 2018); A23A which has been grounded in the central Weddell Sea since 1991, i.e., currently 29 y (Paul et al., 2015)). As such, the 30 y threshold may also be appropriate to apply to Antarctic fast ice, in order to preclude undue influence of stochastic large iceberg grounding, giving a strong impetus to extend this dataset.

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Although our fast ice analysis is circum-Antarctic in extent, performed at a high spatio-temporal resolution and covers 18 y, it is still only limited to extent/distribution. The underlying dataset  does not consider other physical fast ice properties, including freeboard/thickness, thickness of overlying snow, roughness or albedo. Complete physical characterisation of fast ice requires such data. Giles et al. (2008), working with synthetic aperture radar (SAR) imagery of East Antarctic fast ice, indicated that thickness and roughness are likely closely related, ascribing values of 1.7 and 5.0 m thickness 265 to "smooth" and "rough" fast ice, respectively, however this is an overly-simplistic methodology for estimating thickness. Work is underway on addressing this knowledge gap by remotely sensing circum-Antarctic fast ice roughness and thickness from altimetric satellite data.

Conclusions
Here, using a newly-released, long-term (18 y), high-quality and high-resolution dataset of circum-Antarctic fast ice, we have 270 for the first time: -Presented the baseline characterisation of fast ice mean persistence, annual cycle, mean age, and timing of minimum and maximum extent; -Defined eight new fast ice regions based on fast ice anomaly co-variability; -Determined and discussed fast ice extent trends in these eight regions, revealing marked regional variability in trend (as 275 well as inter-annual variability in fast ice extent within each region); and -Discussed fast ice characteristics in terms of its links with bathymetric depth, indicating formation modes within each region.
Although this work greatly advances the state of knowledge on Antarctic fast ice distribution and variability, deeper understanding of Antarctic fast ice is still limited by a paucity of studies on the environmental factors driving changes in fast ice 280 extent. One-dimensional thermodynamic studies have indicated the sensitivity of fast ice to environmental drivers, including both the atmosphere and the ocean (e.g., Heil, 2006;Lei et al., 2010;Hoppmann et al., 2015;Brett et al., 2020), however drivers of change in horizontal fast ice distribution are relatively poorly understood. Of the limited studies of fast ice extent formation/breakout, a wide range of potential drivers have been identified (including remote atmospheric teleconnections (Aoki, 2017), a range of local atmospheric parameters (Fraser, 2011;Zhai et al., 2019;Leonard et al., 2021), swell-induced breakup 285 and anomalous snow cover (Ushio, 2006) and basal melt (Arndt et al., 2020)), however no unifying picture has emerged. Work is planned to use the new circumpolar fast ice dataset  in conjunction with datasets of atmospheric and oceanic parameters to address this shortcoming, in order to elucidate such drivers. Due to regionally-specific drivers, we suggest that coupled ocean/sea ice models capable of realistically forming Antarctic fast ice are an important tool for studing fast ice variability, and urgently need to be developed. In the main text, we focus on fast ice characteristics in newly-defined regions, as defined in the following section. Here, however we report the fast ice extent anomaly (observation minus repeated climatological cycle) and linear trend for the five commonlyused oceanic sectors (Zwally et al., 1983), in order to assess their suitability for partitioning fast ice. These are shown in Fig.   295 A1. Two sectors show significant trends: the Ross Sea (-1.43 ± 0.26 %/y) and the Bellingshausen and Amundsen seas sectors (0.67 ± 0.55 %/y). The remainder are insignificant, which may either be genuine features, or may indicate inappropriate (for fast ice) region selection (i.e., regions defined in this way may split areas of fast ice which co-vary).

Appendix B: Selection of new regions
To investigate a more appropriate regional split, we perform cross-correlation on 1/4 • longitude fast ice extent anomaly time-300 series (Fig. B1). Regions which co-vary exhibit high cross-correlation. Investigation of the fast ice anomaly cross-correlation matrix as a function of longitude indicates that eight regions are needed to appropriately partition fast ice, indicated as blue boxes.
Although this fundamental new region definition is based on a simple and robust methodology, its implementation and the resulting regional definition in Antarctica require discussion. Firstly, since it is based on the cross-correlation of longitudinal 305 slices, it is unable to separate distinct fast ice areas which share a longitude but differ in latitude. Such cases are encountered around a) 163 -171 • E (Victoria and Oates Land coasts); and b) 60 -61 • W (the eastern side of the Antarctic Peninsula).
Although our technique is too simple to account for this longitudinal degeneracy, we note that in both cases, similar trends ( Fig. 3b in the main text) are encountered at both areas of fast ice within the longitude zone (i.e., weak negative in the former, and positive in the latter), giving confidence that the region definition is unaffected by this caveat.

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Our region selection methodology indicates that the fast ice on the eastern side of the Antarctic Peninsula should be considered a part of the Bellingshausen Sea sector, rather than the Weddell Sea sector. This is somewhat surprising given the oceanic connection from this region to the rest of the Weddell Sea. However, this ice is much more proximal to the western side of the Antarctic Peninsula than it is to the fast ice in the eastern flank of the Weddell Sea region, indicating that localised atmospheric conditions may be a dominant driver here. This hypothesis is supported by the positive fast ice trend encountered 315 in the Bellingshausen Sea region -a region which has experienced a trend toward cooler surface air temperatures since the late 1990s (Turner et al., 2016).
We also consider that the boundary between the Australia and Victoria and Oates Lands regions (at 146 • E) may be an artefact of the "ice-scape" regime shift which occurred in the region after the ungrounding of iceberg B09B and subsequent calving of the Mertz Glacier Tongue in 2010 (Leane and Maddison, 2018). To determine the influence of this event, the 320 regional selection algorithm was re-run using only pre-calving post-calving fast ice anomaly data, with the result that the boundary location is correctly located in the pre-calving regime, but the fast ice variability off the Adélie/George V Land coast becomes somewhat more homogeneous in the post-calving regime, as expected following the removal of a major dynamical barrier, with the apparent regime boundary shifting to ∼160 • E (not shown).  In addition to the two dimensional histogram of fast ice persistence by bathymetric depth presented in the main text, we present in Fig C1 the projection of this two dimensional histogram onto the x-axis, linearly weighted by persistence (so that high-persistence fast ice contributes more). We also present this histogram for each newly-defined fast ice region (colored lines).