The Stepwise Reduction of Multiyear Sea Ice Area in the Arctic Ocean Since 1980

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BABB ET AL.
10.1029/2023JC020157 3 of 19 readily drawn out of the Beaufort Gyre (Hansen et al., 2013;Kwok, 2009;Pfirman et al., 2004).The orientation of the Transpolar Drift Stream is dictated by the surface pressure patterns over the Arctic Ocean that is characterized by the Arctic Oscillation (AO) index.The negative phase of the AO shifts the Transpolar Drift Stream to the east, while the positive phase shifts the Transpolar Drift Stream to the west (Rigor et al., 2002).The shift from a prolonged negative AO to a positive AO in the late 1980s led to a "flushing" of MYI out of the Beaufort Gyre into the Transpolar Drift Stream and through Fram Strait (Pfirman et al., 2004).This flushing event is thought to have caused a permanent shift in the thickness and concentration of the Arctic ice pack (Lindsay & Zhang, 2005), a shift which ultimately conditioned it for the record minimum of 2007 (Lindsay et al., 2009).
In terms of the proportion of MYI passing through Fram Strait, Gow and Tucker (1987) reported that 84% of the ice in Fram Strait during the summer 1984 was MYI, while Kwok and Cunningham (2015) assumed 70% during winters (October-April) 2011-2014.More recently, Ricker et al. (2018) used the sea ice type product (OSI-403) from the EUMETSAT Ocean and Sea Ice Satellite Application Facility to estimate an MYI proportion between 64% and 94% during winters 2010-2017.Using the estimate of 706,000 km 2 of total ice export and the range in MYI proportion presented by Ricker et al. (2018), Babb et al. (2022) estimated that 453,000-660,000 km 2 of MYI was exported annually through Fram Strait.More recently, Wang et al. (2022) used another remotely sensed ice-type product (ECICE; Shokr et al., 2008) to determine that on average 343,000 km 2 of MYI was exported through Fram Strait during winter between 2002 and 2020.Given that approximately 87% of the annual total ice export through Fram Strait occurs during winter (Kwok, 2009), we assume that MYI export follows the annual cycle of total ice export and scale the results of Wang et al. (2022) to an annual average MYI export of 388,000 km 2 .However, Wang et al. (2022) note that MYI export through Fram Strait declined by 22% between the first and second half of their study period, due to a reduction in MYI transport from the Beaufort Sea and Siberian coast toward Fram Strait and therefore younger ice in the Transpolar Drift Stream (i.e., Comiso, 2012;Haas et al., 2008;Hansen et al., 2013;Krumpen et al., 2019;Sumata et al., 2023).Reduced MYI export aligns with the observed decrease in sea ice volume export through Fram Strait since the 1990s (Sumata et al., 2022).MYI export into Nares Strait and the QEI is an order of magnitude lower than MYI export through Fram Strait, yet export is increasing through both channels.This is particularly important because the oldest and thickest MYI in the Arctic is exported through these channels (Howell et al., 2023;Kwok et al., 2010;Moore et al., 2019).Furthermore, increasing MYI export through these channels has implications for ships operating downstream along the Northwest Passage (Howell et al., 2022;Pizzolato et al., 2014) and as far south as Newfoundland (Barber et al., 2018).Ice export through these channels is limited by the seasonal formation of ice arches (also known as ice bridges or barriers; Hibler et al., 2006;Kirillov et al., 2021;Melling, 2002) that impede ice motion, yet as the Arctic warms these arches are forming for shorter periods and occasionally not forming at all, allowing increased ice export (Howell et al., 2023;Howell & Brady, 2019;Moore, Howell, Brady, et al., 2021).Annual ice export into Nares Strait increased from 33,000 km 2 between 1996 and 2002 (Kwok, 2005) to 87,000 km 2 between 2019 and 2021 (Moore, Howell, Brady, et al., 2021) and more recently 95,000 km 2 between 2017 and 2021 (Howell et al., 2023).Meanwhile, annual ice export into the QEI increased from 8,000 km 2 between 1997 and 2002 (Kwok, 2006) to 25,000 km 2 between 1997 and 2018 (Howell & Brady, 2019), with a recent peak of 120,000 km 2 in 2020 (Howell et al., 2023).Assuming an MYI proportion of 50% in Nares Strait and 100% in the QEI, Babb et al. (2022) used the average total ice export of Howell and Brady (2019) and Moore, Howell, Brady, et al. (2021) to estimate an annual average MYI export of 68,500 km 2 through these channels.However, Howell et al. (2023) showed that between 2017 and 2021 an average of 113,200 km 2 of MYI was exported annually through these channels, which far exceeds the estimates of Babb et al. (2022) and is 29% of the estimated annual average MYI export through Fram Strait between 2002 and 2020 (Wang et al., 2022).Overall, MYI export into Nares Strait and the QEI is increasing in magnitude and playing a greater role in the overall MYI budget of the Arctic Ocean.

MYI Melt
Traditionally, very little MYI was thought to completely melt within the Arctic Ocean (Kwok & Cunningham, 2010) as lateral melt of MYI floes was assumed to be negligible when examining annual records of MYI area (Kwok, 2004a).However, Kwok and Cunningham (2010) found that export alone could not satisfy the dramatic reduction of MYI area in the early 2000s, highlighting the increasing contribution of melt.Although MYI can melt in any area of the Arctic Ocean, there has been a focus on MYI melt within the Beaufort Sea because of its broader role of retaining MYI within the Beaufort Gyre (Babb et al., 2022;Kwok & Cunningham, 2010).Between 1981 and 2005, 93% of MYI passing through the Beaufort Sea survived through the melt season, facilitating the redistribution of MYI via the Gyre and maintaining a relatively high MYI area in the Arctic Ocean (Maslanik et al., 2011).However, an accelerated ice-albedo feedback increased ice melt in the Beaufort Sea through the 2000s (i.e., Perovich et al., 2008), which led to reductions in MYI thickness (Krishfield et al., 2014;Mahoney et al., 2019) and increased MYI loss (Babb et al., 2022;Kwok & Cunningham, 2010).As a result, between 2006 and 2010 the survival rate of MYI passing through the Beaufort Sea declined to 73% (Maslanik et al., 2011), with approximately one-third of the pan-Arctic MYI loss between 2005 and 2008 being lost to melt in the Beaufort Sea (Kwok & Cunningham, 2010).Using a regional MYI budget, Babb et al. (2022) found that MYI melt in the Beaufort Sea quadrupled between 1997 and 2021, interrupting MYI transport through the Beaufort Gyre and precluding MYI from being advected onwards to other marginal seas.In particular, MYI melt in the Beaufort Sea peaked at 385,000 km 2 in 2018, which is similar to the estimated magnitude of MYI export through Fram Strait (Babb et al., 2022;Wang et al., 2022).

MYI Replenishment
As the sole source of MYI, annual replenishment of MYI from FYI that survives the melt season is a critical yet understudied term in the MYI budget.The first estimates of MYI replenishment were presented by Kwok (2004a), who constructed annual cycles of MYI area in the Arctic Ocean by taking the MYI area determined by QuickSCAT on January 1 and then adjusting the area by the record of MYI export through Fram Strait.MYI replenishment was then calculated as the difference between the estimated MYI area during the September minimum (projected forwards from 1 January) and the estimated MYI area in October (projected backward from 1 January).Using this method, replenishment averaged 1.1 × 10 6 km 2 from 2000 to 2002 (Kwok, 2004a), though there was subsequently near-zero replenishment in 2005 (Kwok, 2007) and 2007 (Kwok et al., 2009).Kwok (2007) found that ∼63% of the variance in MYI replenishment from 2000 to 2006 was explained by a combination of melting-degree-day (MDD) anomalies during summer and freezing-degree-day (FDD) anomalies during the preceding winter.Generally, warmer temperatures during summer increase ice melt and reduce the likelihood of FYI surviving through summer and replenishing MYI, while colder temperatures during the preceding winter create thicker FYI that is more likely to persist through the melt season and replenish MYI.The importance of ice growth during the preceding winter reflects the negative conductive feedback; thin ice grows faster thermodynamically than existing thick ice, and thereby stabilizes the ice pack (Bitz & Roe, 2004;Notz, 2009).However, this feedback has weakened since 2012 due to the occurrence of warmer winters limiting thermodynamic ice growth (Stroeve et al., 2018), particularly in 2015 when an anomalously warm winter reduced FYI volume by 13% at the end of winter and was proposed to have limited MYI replenishment (Ricker et al., 2017).Ultimately, reduced FYI growth during winter not only encourages lower summer sea ice extents, but also limits MYI replenishment and therefore amplifies annual sea ice loss.

Ice Age Data Set
The basis for this analysis is the EASE-Grid Sea Ice Age data set from the National Snow and Ice Data Center (NSIDC; Version 4- Tschudi et al., 2019a;updated 2021).The data set provides weekly fields of ice age at 12.5 km resolution across the Arctic Ocean since 1984 and has previously been employed to highlight MYI loss (e.g., Meier et al., 2021;Stroeve & Notz, 2018), and validate other remotely sensed ice-type products (Ye et al., 2023) and modeled MYI coverage (Jahn et al., 2012;Regan et al., 2023).The data set estimates ice age by Lagrangian parcel-tracking through the NSIDCs Polar Pathfinder Sea Ice Motion Data Set (Version 4- Tschudi et al., 2019b;updated 2021) and determining how long a parcel persists.Parcels age by 1-year after the week of the September sea ice minimum so long as the concentration of the grid cell they are in remains above 15%.A similar method was used by Rigor and Wallace (2004) to estimate ice age from gridded ice motion fields derived from buoy tracks, though Nghiem et al. (2006) found that insufficient coverage of buoys at certain times introduced uncertainties in the ice age model.The Ice Age product overcomes this by using an ice drift product that integrates buoy tracks with daily fields of ice motion derived from spaceborne passive microwave radiometers, providing a continuous record of ice motion necessary to track parcels for years.
The passive microwave record and therefore the ice motion record began in October 1978, yet the Ice Age product requires time to spin up and develop an ice age distribution (up to 5 years); hence it has typically only been available since 1984.However, following the September sea ice minimum of 1979, MYI can be distinguished from FYI, hence our analysis of MYI begins in September 1979 using data available from Meier and Stewart (2023), but ice age distributions are only available since 1984.
One limitation of the Ice Age product is that each grid cell is assigned the age of the oldest parcel within it at that time, meaning that there is no partial MYI concentration like in ice charts (i.e., Babb et al., 2022) or other remotely sensed ice type products (i.e., Comiso, 2012;Kwok, 2004a).As a result, there is an inherent overestimation of MYI area within the data set (Korosov et al., 2018;Tschudi et al., 2016), an error that grows during fall freeze-up when grid cells with low MYI concentrations (≥15%) freeze-up completely with new ice but continue to be identified as MYI.Korosov et al. (2018) suggest that this overestimation is greater in the marginal ice zone than the central Arctic because there is a greater mixture of MYI and FYI around the periphery of the ice pack.Additionally, the ice age product is subject to the uncertainty in the ice drift product, which is known to be greater during summer than winter (Sumata et al., 2014), and errors may accrue along the coast due to the way that the tracking system accounts for divergence and convergence from the shore.In particular, offshore winds result in the formation of young ice along the coast, but because the tracker does not compress the ice during onshore winds these areas of young ice may persist and accumulate.This is a particular issue north of Ellesmere Island where areas of young ice are occasionally present in an area that is known to contain the oldest sea ice (Figure 2).Despite these limitations, the Ice Age product has the critical advantage of being available year-round, whereas other remotely sensed ice-type products are confined to the ice growth season because once the ice/snow surface begins to melt, distinguishing ice types becomes more uncertain.

MYI Budget
To examine the MYI budget of the Arctic Ocean we must define the boundaries, calculate the weekly time series of MYI area within the region (Figure 1), and calculate MYI export across the boundaries.Following Kwok (2004a), the Arctic Ocean was defined by boundaries across Fram Strait, the channels between Svalbard, Franz Josef Land and Severnaya Zemlya, the Bering Strait, the western edge of the CAA and the northern entrance to Nares Strait (Figure 2).MYI area in the Arctic Ocean was calculated by summing the weekly mean sea ice area in pixels identified as MYI within the weekly ice age data set.Sea ice area was calculated from the NSIDC daily passive microwave sea ice concentration data set (Cavalieri et al., 1996;updated 2022).MYI area is characterized by a well-defined annual cycle from a maximum following replenishment to the minimum during September with the decrease in MYI area being the result of export during winter and the combination of export and melt during summer (Figure 1a; Figure S1 in Supporting Information S1).
Critical to the annual cycle and definition of MYI is that MYI is only created by replenishment from FYI that survives through the minimum.Replenishment is calculated as the area of second-year ice (MYI2) during the week after the minimum (Figure 1a).However, the time series of MYI area calculated from the Ice Age data set shows an erroneous increase in MYI area after replenishment, which is the result of concentration increasing within pixels containing at least some portion of MYI during freeze-up.To account for this error, we use a method similar to Kwok (2004a) and create an estimated annual record of MYI area by accounting for MYI export (Figure 1b).We use the maximum and minimum MYI area to bookend the annual record and then account for MYI export across all of the Arctic Oceans boundaries to create a time series of estimated MYI area (dashed line Figure 1b).At the time of the September minimum, we sum the net export for the ice season (blue line Figure 1b) and determine MYI melt as the difference between the estimated MYI area, which is based solely on export, and the calculated MYI area, which reflects MYI lost to export and melt (red line Figure 1b).Because MYI area is inherently overestimated within the Ice Age data set, MYI export and the MYI minimum are overestimated, meaning that MYI melt and MYI replenishment are underestimated.To constrain this error, we calculate the difference between the peak in the calculated MYI area and the estimated MYI area at that time (Figure 1b; Figure S1 in Supporting Information S1).On average 503,000 km 2 or 15% of the MYI area is erroneously created during freeze-up, most of which is expected to accrue in the marginal seas (Korosov et al., 2018) and therefore have limited effect on our estimates of MYI export through Fram Strait.However, as MYI area has declined this error has increased at a rate of 1.6% per decade.We ascribe this trend to the fact that declining MYI area is not only characterized by a reduction in MYI extent but also a reduction of sea ice concentration within MYI pixels at the end of summer, which agrees with results from Comiso ( 2012) and leaves a greater area for FYI to form in MYI pixels.As an example, the maximum error occurred in autumn 2012 (31%; 2013 ice season Figure S1 in Supporting Information S1), following a near-record MYI area minimum during which the MYI pack was dispersed across an area of low sea ice concentrations, leaving a large area within the MYI pack for FYI to form.
An additional source of error in determining MYI area stems from the convergence/divergence of the MYI pack and specifically how this is handled in the Ice Age data set.Theoretically, divergence has no impact on MYI area (area is conserved), whereas convergence leads to deformation which reduces MYI area but conserves MYI volume.Previous work on the annual MYI cycle has assumed that MYI does not deform (Kwok, 2004b), or has acknowledged that it may deform but does not consider deformation as a sink of MYI area (Kwok & Cunningham, 2010).Regan et al. (2023) calculated MYI deformation as convergence of modeled ice motion fields, yet they assumed that FYI was preferentially deformed and the MYI deformation only occurred once all FYI had been deformed.Mimicking this with ice motion fields and the Ice Age data set would introduce significant uncertainty and require additional tracking of each parcel of MYI to determine the actual MYI concentration and cumulative convergence over time.Given this uncertainty in quantifying MYI deformation, we do not account for this term within the MYI budget which may in turn lead to an overestimate of MYI melt.
Ice flux (F) across the boundaries of the Arctic Ocean is calculated at regular intervals using the following equation, where, c is the sea ice concentration, u is the ice velocity component normal to the gate and Δx is the interval.
For large channels like Fram Strait, and channels into the Kara and Barents Seas, F was calculated weekly using fields of sea ice drift and concentration from the NSIDC data sets Total ice export into the QEI has been quantified for the period from 1997 to 2002 (Kwok, 2006), 1997-2018(Howell & Brady, 2019), and more recently 2017-2021 (Howell et al., 2023).MYI flux was also determined during the latter period and revealed that MYI comprises 85% of the total ice flux into the QEI.To build a record of MYI flux into the QEI, we use the values of total ice export from Howell and Brady (2019) for the period 1997-2016, and the average export of 8,000 km 2 from Kwok (2006) for the period 1979-1996, then scale them by 85%.
MYI flux through Amundsen Gulf and M'Clure Strait are not considered in this budget.Amundsen Gulf is predominantly covered by seasonal ice and is therefore neither a source or sink of MYI (Babb et al., 2022).M'Clure Strait contains a mix of seasonal and MYI, but recent observations show that the oscillation between export and import averages out to a net seasonal ice flux of only 2 km 2 (Howell et al., 2023).
Collectively, the terms of MYI export, melt, and replenishment dictate the annual MYI budget (Figure 1b).The budget is summed for the annual ice season, which begins with replenishment after the minimum and runs to the following minimum, providing a net change in MYI area for each year.
Regional boundaries as defined by the NSIDC MASIE (Multisensor Analyzed Sea Ice Extent) mask (Figure 2) were used to quantify MYI transport between regions within the Arctic Ocean and to breakdown replenishment by region.

Ancillary Data
Monthly mean fields of 2 m air temperature (T) were retrieved from the ERA-5 reanalysis (Hersbach et al., 2020) and used to calculate the cumulative FDD (T < −1.8°C) from October to May, and MDD (T > 0°C) from June to September.MDD was tested for a correlation with MYI melt, while following Kwok (2007), the combination of FDD and MDD were tested for correlation with MYI replenishment.

MYI Area
Over the 43-year study period, the annual MYI minimum and maximum areas declined significantly (p < 0.05) at −72,500 km 2 year −1 and −61,000 km 2 year −1 , respectively (Figure 2a).The minimum MYI area declined at a higher rate than the decline in minimum total sea ice area within the Arctic Ocean (−59,000 km 2 year −1 ), indicating MYI is being lost at a greater rate than FYI.However, the reduction in the minimum MYI area has not occurred linearly, nor in eight to 9 year cycles as proposed by Comiso ( 2012), but rather through two stepwise reductions that interrupt three periods of relative stability in MYI area.The first stepwise reduction occurred between September 1988 and 1989, and coincides with the "flushing" of MYI through Fram Strait (Pfirman et al., 2004).The second stepwise reduction occurred between September 2005 and 2008, which is known to be a period of increased MYI loss (Kwok, 2009) that is thought to have been conditioned by the first reduction in 1989 (Lindsay et al., 2009) and corresponds to a shift toward thinner ice across the Arctic Ocean (Sumata et al., 2023).
The reduction in MYI area between the three periods was accompanied by a change in the spatial distribution of MYI in the Arctic Ocean with a retreat of the MYI edge toward the northern coast of Greenland and the CAA (Figure 2b).Furthermore, the reduction in MYI area coincides with an increase in ice drift speeds during each period (Figure 2b) as a younger ice pack is mechanically weaker and therefore more mobile (Kwok et al., 2013;Rampal et al., 2009).
The reduction in MYI area has been compounded by a dramatic loss of older MYI types (Figure 2).During the annual minimum, the area of MYI 3 years and older decreased 81% from 3.06 × 10 6 km 2 in the first period to 0.59 × 10 6 km 2 in the third period.The reduction is even more dramatic for MYI 5+ years old, which decreased 92% from 2.08 × 10 6 km 2 in the first period to 0.17 × 10 6 km 2 in the third period, and is likely even lower given that MYI area is skewed toward older ice types in the Ice Age data set.Over the 43-year study period, there are significant (p < 0.01) negative trends in the area of MYI 3 (−7,800 km 2 year −1 ), 4 (−9,400 km 2 year −1 ), and 5+ (−59,000 km 2 year −1 ) years old, but interestingly there is no trend in second-year ice area, which has remained stable around its mean minimum of 0.65 × 10 6 km 2 but now comprises a greater proportion of the MYI pack.

MYI Budget
To examine MYI loss during these two stepwise reductions and the equilibrium in MYI area that has existed during the three periods they separate, we now analyze the three terms and net annual balance of the MYI Budget.

MYI Export
On average 709,000 km 2 of MYI was exported from the Arctic Ocean annually over the record (Figure 3).A vast majority (648,300 km 2 ; 93%) of the export was through Fram Strait (Figure 3b) while the remaining 7% represents the balance of (a) export into Nares Strait and the QEI and (b) transport (either import or export) across the boundaries to the Barents and Kara Seas.
MYI export from the Arctic peaked at 1.4 × 10 6 km 2 in 1995 (Figure 3).This agrees with the observed peak in total ice export through Fram Strait presented by Kwok (2009), which the authors attributed to an increased sea level pressure gradient across the strait that enhanced ice drift speeds.Total MYI export has only surpassed 1 × 10 6 km 2 two other times, 1989 and 2007, both of which contributed to the two stepwise reductions.In 1989, a record amount of the oldest MYI (MYI 5+; 634,000 km 2 ) was exported through Fram Strait after it had been flushed out of the Beaufort Gyre by a change in the AO (Figure 3; Pfirman et al., 2004).In 2007, a strong Transpolar Drift Stream increased ice export through Fram Strait (Nghiem et al., 2007), while anomalous ice export into Nares Strait (Kwok et al., 2010) compounded the total MYI export (Figure 3).For comparison, the minimum MYI export through Fram Strait occurred in 2018 (340,000 km 2 ) which coincides with an anomalous drop in sea ice volume export (Sumata et al., 2022).
Following the second stepwise reduction from 2006 to 2008, the age distribution of MYI being exported through Fram Strait was much younger, with the proportion of MYI 4+ years declining from 57% of the ice pack prior to 2007 to only 15% after 2007 (Figure 3b).Additionally, since 2007, both MYI and total ice export through Fram Strait declined significantly (p < 0.05) with respective rates of −19,600 and −15,900 km 2 year −1 (Figure 3b).
The discrepancy in these rates has reduced the MYI proportion of the total ice export through Fram Strait from an average of 83% prior to 2007 to 69% since 2007, with the proportion never exceeding 75% since 2007 and reaching a minimum of 56% in 2016.The shift agrees with the transition toward younger thinner ice in Fram Strait identified by Sumata et al. (2023), while the variability in the proportion of MYI highlights the issue with estimating MYI export as a constant proportion of the total ice export (i.e., Babb et al., 2022;Kwok & Cunningham, 2015).Over the full study period, the MYI proportion of the total ice export through Fram Strait has significantly (p < 0.01) declined at a rate of −6% per decade.Overall ice export through Fram Strait has shifted to more FYI and younger MYI, a change which is due to younger ice within the Transpolar Drift Stream (Figure 2; Comiso, 2012;Haas et al., 2008;Krumpen et al., 2019), and has undoubtedly contributed to the longterm reduction in sea ice volume export through Fram Strait (Kwok, 2009;Sumata et al., 2022).Decreasing MYI export through Fram Strait has been partially offset by increasing MYI export into Nares Strait and the QEI, though the magnitudes of these increases are substantially lower than the trend in Fram Strait (Figure 3a).Historically, a small amount of MYI was imported into the Arctic Ocean from the Kara Sea; however, this source of MYI has been null since 2007 (Figure 3a).MYI export into the Barents Sea peaked at 160,000 km 2 in 2003, which corresponds to the peak observed by Kwok et al. (2005), but has a long-term mean of only 12,900 km 2 year −1 with no long-term trend.Following the second stepwise reduction, MYI export into the Barents Sea has been null during half of the years.
Overall, following the second stepwise reduction a significant (p < 0.05) negative trend in MYI export through Fram Strait has been slightly offset by increasing MYI export into Nares Strait and the QEI, but overall the net annual MYI export from the Arctic has decreased at a rate of 19,200 km 2 year −1 (Figure 3b).While on average 93% of the MYI export was through Fram Strait, this proportion declined from 95% prior to 2007 to 87% since 2007, as the consolidation of MYI in the central Arctic and decreases in ice arch duration within Nares Strait and the QEI (Howell & Brady, 2019;Moore, Howell, Brady, et al., 2021) has altered the balance of MYI export.

MYI Melt
Across the Arctic Ocean, an average of 481,000 km 2 of MYI was lost to melt annually between 1980 and 2021 (Figure 4).MYI melt peaked at 1.15 × 10 6 km 2 in 2016 and was near 0 km 2 in 1994.There is no significant trend over the full 43-year record, though there is a significant (p < 0.01) negative trend of ∼17,200 km 2 year −1 since the first stepwise reduction.Based on the results of Babb et al. (2022), approximately one-third of this increase has occurred in the Beaufort Sea, where MYI melt increased at a rate of 6,000 km 2 year −1 between 1997 and 2021, causing MYI transport through the Beaufort Gyre to be interrupted.Coincident to the increase in MYI melt has been a significant increase in MDD over the Arctic Ocean of 2 degree-days year −1 , that is, 82 degree-days total over the study period (Figure 5).MYI melt and MDD are significantly correlated (r = 0.38, p < 0.01) with melt increasing by 3,300 km 2 for every additional degree-day increase in MDD.

MYI Replenishment and Retention
MYI replenishment is the largest term in the MYI budget, averaging 1.11 × 10 6 km 2 per year (Figure 6a).However, as the sole source of MYI it must offset export and melt if the MYI budget is to balance annually.Over the study period, MYI replenishment significantly (p < 0.05) increased at a rate of +11,000 km 2 year −1 .The peak in MYI replenishment occurred in 1996 (1.8 × 10 6 km 2 ), yet the next six largest years of replenishment have all occurred since 2005.The minimum replenishment occurred in 1987 (700,000 km 2 ) and may have helped to condition the first stepwise reduction in 1989, while the largest negative anomalies relative to the positive trend occurred during years of record sea ice minima (1998, 2007, and 2012) and coincide with increased melt (Figure 4) during particularly warm years (Figure 5).However, over the study period replenishment and melt from the same year are not correlated, meaning increased MYI melt does not necessarily correspond to increased FYI melt and thereby reduced MYI replenishment.Although replenishment and melt are not correlated for the same summer, replenishment is negatively correlated (r = 0.46, p < 0.01) with melt during the following summer.This relationship is important; increasing replenishment creates a thinner MYI pack during the following melt season, increasing the area of MYI that melts.
Our values of MYI replenishment are significantly higher than those previously presented by Kwok (2004aKwok ( , 2007) ) and Kwok et al. (2009).Particularly in 2005 and 2007 when those studies showed near-zero replenishment (<0.1 × 10 6 km 2 ), and we calculated replenishment of 0.93 × 10 6 km 2 and 0.83 × 10 6 km 2 , respectively.The reason for this discrepancy is the different methods used to calculate replenishment.We calculate the area of second-year ice 1 week after the minimum from the Ice Age data set, which accounts for the reduction in MYI area not just through export but also through melt.The method developed by Kwok (2004a) only accounts for MYI export through Fram Strait and assumes that no MYI is lost to melt.As a result, their method overestimated the MYI area in September, which led to an underestimate of MYI replenishment.Our method also underestimates replenishment as it does not account for surviving FYI within MYI pixels.
Replenishment primarily occurs along the fringe of the summer ice pack where FYI buttresses up against the MYI pack, though a portion does occur within the MYI pack in areas of divergence where FYI has formed (Figure 7).Spatially, replenishment primarily occurs along the eastern side of the ice pack (Figure 7), where FYI that originally formed on the Russian shelves has been advected far enough north to tip the balance of seasonal growth and melt to the point where the ice survives summer.The fact that MYI is replenished on the eastern side and primarily melts in the Beaufort Sea, emphasizes why the two are not correlated, they are spatially disconnected and subject to different forcing during the melt season.
Historically, replenishment was approximately split evenly between the marginal seas and the central Arctic (Figure 6b).That changed during the second stepwise reduction as the summer ice edge retreated north of the regional boundaries and reduced the survival of FYI in the marginal seas.Concurrently, the consolidation of the MYI edge exposed a greater area of the central Arctic to FYI that-protected by colder temperatures at northern latitudes-could persist through the melt season (Figure 7e).As a result, since 2007, MYI replenishment in the Chukchi, East Siberian, and Laptev Seas has decreased by over 50% while MYI replenishment in the central Arctic has doubled.Meanwhile, there has been no change in MYI replenishment in the Beaufort Sea despite an increase in FYI area during winter (Galley et al., 2016).The fact that increasing FYI area during winter has not translated to an increase in MYI replenishment indicates that FYI in the Beaufort Sea is typically not thick enough to survive through the melt season and replenish the MYI pack (i.e., Galley et al., 2013), and further highlights the regional variability and importance of latitude for replenishment.Examining the distribution of replenishment area by latitude during the three periods of MYI stability, we find a clear northward transition over time that coincides with the poleward decrease in air temperatures during the melt season (May-September; Figure 7e).The dramatic reduction in replenishment in the marginal seas has transitioned replenishment from a bimodal distribution with peaks at ∼72°N and ∼82°N to a unimodal distribution around a peak at ∼83°N with very little replenishment occurring south of 75°N since 2008.
Warming between the three periods is also evident, with an increase of ∼2°C at 70°N and ∼0.5°C at the pole (Figure 7e).Significant (p < 0.05) trends toward fewer FDD (−23 degree-days year −1 ) and more MDD (+2 degree-days year −1 ; Figure 5) would intuitively reduce MYI replenishment as there is less FYI growth during winter and more FYI melt during summer.However, we find a clear increase in MYI replenishment that shows no relationship with pan-Arctic MDD and surprisingly a significant inverse relationship with pan-Arctic FDD (r = −0.45,p < 0.01) that indicates other factors must be driving the observed increase in replenishment.Based on the regional changes in MYI replenishment, it is clear that the increase has primarily been driven by the northward migration of FYI into the central Arctic where it is subject to cooler temperatures and less incident solar radiation facilitating less melt.To support this, we find that the area of both FYI and MYI at the end of winter (the last week of April) are significantly (p < 0.01) correlated with MYI replenishment.FYI area has a positive relationship (r = 0.61) while MYI area has a negative relationship (r = −0.61)implying that more FYI and less MYI at the start of the melt season leads to more MYI replenishment.This highlights a negative feedback in the Arctic system that stabilizes the MYI area by compensating for MYI loss through increased MYI replenishment.However, this MYI feedback requires that FYI grow thick enough during winter to survive the melt season, which is part of the negative conductive feedback (Bitz & Roe, 2004).There is already evidence that the current BABB ET AL. 10.1029/2023JC020157 13 of 19 level of warming has weakened the negative conductive feedback (Ricker et al., 2021;Stroeve et al., 2018) and projections that it will eventually be overwhelmed by warming (Petty et al., 2018).Yet in the near term, the MYI feedback may continue to provide some stability to the MYI pack.
A limitation to the stability that results from the MYI feedback is that MYI replenishment only reflects the retention of FYI into second-year ice, while MYI of all ages are lost to export and melt.This imbalance highlights an underlying transition in the MYI pack toward younger and therefore thinner MYI that is undercutting the stability that the positive trend in replenishment is facilitating.Hence, the continued retention of sea ice into progressively older and thicker MYI is key to maintaining the MYI pack.Over the 43-year study period, the retention of second-year ice significantly increased and the retention of MYI 3 years old was fairly stable, while retention of MYI 4 and 5+ years old significantly declined (Figure 6c).The reduced retention of older MYI types is primarily due to the increase in MYI melt in the Beaufort Sea (Babb et al., 2022) which has interrupted MYI transport through the Beaufort Gyre and therefore precludes ice from aging while being retained within the Gyre.As it is now, MYI is only able to age for as long as it can remain in the Central Arctic before it is either siphoned off into the Beaufort Sea, exported into Nares Strait or the QEI, or advected toward Fram Strait.

MYI Budget of the Arctic Ocean
With each of the three MYI terms calculated, we now close the annual MYI budget of the Arctic Ocean for the ice seasons from 1980 to 2021 and determine the net balance for each year (Figure 8a).The net balance shows very close agreement with the change in MYI area calculated from one minimum to the next, indicating our budget captures the vast majority of the changes in MYI area within the Arctic Ocean (Figure 8b).The average annual terms of the MYI budget are; (a) export: −709,000 km 2 , (b) melt: −463,000 km 2 , and (c) replenishment: 1,106,000 km 2 , for an average annual loss of 65,000 km 2 year −1 over the 43 years study period.However, there is considerable variability between years of MYI loss and MYI gain.The greatest MYI loss occurred in 1989 (−719,000 km 2 ), driving the first stepwise reduction in MYI area.The record loss in 1989 was the result of positive anomalies in export (+56%; +387,140 km 2 ) and melt (+19%; +92,450 km 2 ) coupled with a negative anomaly in replenishment (−16%; −174,590 km 2 ).Conversely, the highest MYI gain occurred in 2018 (490,000 km 2 ), due to a negative anomaly in export (−43%; −295,870 km 2 ) and positive anomaly in replenishment (+39%; +434,200 km 2 ), and despite a positive anomaly in melt (+36%; +175,180 km 2 ).Contrasting between years of MYI loss and gain against the mean magnitude of each term, reveals that a net loss corresponds to greater export (+57,000 km 2 ) and melt (+26,000 km 2 ) and much less replenishment (−95,000 km 2 ), while a net gain corresponds to reduced export (−93,000 km 2 ) and melt (−42,000 km 2 ) and much more replenishment (+155,000 km 2 ).While all three terms contribute to the direction of the net balance, replenishment has the greatest magnitude and even exceeds the combined anomaly of export and melt during years with a net gain or net loss; hence replenishment has the greatest influence on the overall net MYI balance.
Beyond the MYI balance of an individual year, it is important to look at the balance over a few years as individual years of MYI loss or gain can often be offset by a contrasting swing in subsequent years that can either stabilize the MYI pack or dramatically (and permanently) change it.For example, between 1995 and 2001 the MYI budget oscillated between large losses and gains, with the peak export (1995) and replenishment terms (1996) terms occurring during this period, but overall they offset each other and the MYI area remained relatively stable through this time (Figure 8).Similarly, the loss of MYI in 2012, which was primarily due to anomalously high melt (+60%; 290,870 km 2 ), was immediately offset by MYI gains in 2013 and 2014.This recovery was the result of cooler temperatures and a consolidated ice pack through the 2013 melt season (Kwok, 2015;Tilling et al., 2015) which reduced melt in 2013 (−84%; −405,550 km 2 ) and led to record replenishment in 2014 (+51%; +562,690 km 2 ; occurring during fall 2013).However, losses are not always offset in subsequent years.For example, the second stepwise reduction in MYI area occurred between 2006 and 2008 when approximately 1.4 × 10 6 km 2 of MYI was lost, which is slightly less than the MYI area loss of 1.54 × 10 6 km 2 reported by Kwok et al. (2009).Focusing on this period of MYI loss, we find that 2006 was characterized by increased melt (+21%; +99,000 km 2 ) and reduced replenishment (−16%; −174,850 km 2 ) with near average export (+9%; +58,821 km 2 ).2007 was characterized by increased export (+45%; +312,930 km 2 ) and melt (+55%; +265,700 km 2 ), and actually experienced increased replenishment relative to the long-term mean (+18%; +201,890 km 2 ; opposite to what Kwok et al., 2009 showed).2008 had the second greatest annual loss of MYI on record and was primarily the result of increased export (+33%; +227,950 km 2 ) and reduced replenishment (−25%; −275,400 km 2 ; from autumn 2007) with near-average melt (0%).Clearly it was not just one term that facilitated the second stepwise reduction in MYI area but rather anomalous export, melt, and replenishment over consecutive years steadily compounding the overall decline and driving a significant change in the MYI pack.
During the three periods of stability in the minimum MYI area, melt and export were in equilibrium with replenishment (Figure 8b).However, the proportion of export and melt changed between periods.During the first period export and melt were similar in magnitude, whereas during the second period export was more than twice as great as melt.During the third period, the two returned to being approximately equal in magnitude, cleanly breaking the budget down between approximately one-quarter melt, one-quarter export, and one-half replenishment.With trends toward declining export and increasing melt, the role of each term in the MYI budget is likely to continue swinging toward MYI melt exceeding MYI export.For reference, MYI melt exceeded MYI export during only nine of the 43 years analyzed here, though five of these have occurred since 2010, highlighting the increasing role of MYI melt in the MYI budget of the Arctic Ocean.

The Future of MYI
The Arctic is projected to be seasonally ice-free (<1 × 10 6 km 2 ) as soon as the 2030s or 2050s (Kim et al., 2023;Notz & SIMIP Community, 2020), at which point the Arctic Ocean will only be seasonally covered by FYI while a small area of MYI will be confined to the northern regions of CAA and Greenland known as the Last Ice Area.The projected near-complete loss of MYI in the not-too-distant future indicates the MYI budget of the Arctic Ocean will continue to be in a deficit.Based on our results, we can expect that future MYI loss will likely occur through a series of stepwise reductions with periods of relative stability in between.Using the MYI budget, we speculate on the contribution of each term to the future loss of MYI.
First, it is worth noting that any appreciable recovery of MYI is highly unlikely in the foreseeable future as that would require several years of reduced MYI loss (export and melt) coupled with increased replenishment and further retention of MYI into older and thicker MYI.Individual years of recovery do continue to occur (i.e., 2013 and 2018; Figure 8) and maintain the current state of equilibrium, yet a stepwise increase in MYI area would require several consecutive years with a net gain in MYI area and most importantly retention into older MYI that is thicker and therefore more resilient against melt.This has not happened at any point over the satellite era.
Export drove the first stepwise reduction in 1989 and contributed to the second reduction between 2006 and 2008.However, the consolidation of the MYI pack away from the area upstream of Fram Strait has led to a negative trend in MYI export since 2008 that has reduced the overall impact of export on the MYI budget and leads us to suggest that export will not be a main driver of future MYI loss.Instead, we speculate that the future loss of MYI will be driven by the combination of high melt and low replenishment, reinforced over several consecutive years.
Given that these two terms are related to ice melt, it is intuitive that a particularly warm summer would increase both FYI and MYI melt, with the former limiting replenishment.Conditioning during the preceding winter is also critical to these terms as a strong Beaufort Gyre would expose more MYI to increased melt rates in the Beaufort Sea (i.e., 2021; Babb et al., 2022;Mallett et al., 2021) while a warm winter would limit FYI growth and therefore replenishment (i.e., 2015;Ricker et al., 2017).Considerable MYI replenishment is already occurring in the Central Arctic (Figure 7), where surface air temperatures in the Arctic are coldest, enabling a long-term positive trend in replenishment.However, with further reductions in September sea ice extent, the area available for FYI to survive and replenish MYI will dwindle, causing the positive trend in replenishment to level off and eventually decline.
MYI area melt is likely to continue increasing in the coming years as air temperatures increase (greater MDD, lower FDD), while a transition of the MYI pack itself toward younger thinner MYI makes it less resilient and more susceptible to melt.The transition to younger ice types is being driven by an imbalance between ice of all ages being lost to export and melt, whereas only the replenishment of second-year ice is increasing in contrast to reduced retention of older MYI ages.As a result, the MYI cover continues to thin (Kacimi & Kwok, 2022;Krishfield et al., 2014;Kwok & Rothrock, 2009;Petty et al., 2023), making it more mobile and facilitating the formation of large polynyas within the Last Ice Area during recent years (Moore, Howell, & Brady, 2021;Schweiger et al., 2021).As a result, Schweiger et al. (2021) suggest that the remaining MYI pack is proving to be less resilient to warming than previously expected.
Ultimately, we speculate that the future loss of MYI is likely to be driven by gradually increasing melt and reduced replenishment, but conditioned by the transition toward a younger thinner MYI pack.With each reduction, the MYI pack will retreat even further toward the Last Ice Area along the coast of the CAA.Eventually, the Arctic Ocean is projected to become seasonally ice-free, at which time the remaining MYI will be confined to the narrow channels of the CAA, and there will be no replenishment within the Arctic Ocean.

Conclusions
The loss of MYI and transition to a predominantly seasonal ice cover in the Arctic Ocean has been one of the greatest changes to take place in the Arctic.Using a 43-year data set on sea ice age, we have examined the loss of MYI area and the relative contribution of melt, export, and replenishment to this loss.Overall, MYI area during the annual September sea ice minimum has significantly declined at a rate of −72,500 km 2 year −1 ; however, MYI loss has not occurred continuously but rather through two stepwise reductions that separated three prolonged periods of relative stability.During these stable periods, MYI loss through export and melt was wholly offset by replenishment, maintaining equilibrium within the MYI pack.While there is no long-term trend in MYI export, MYI melt has significantly increased since 1989 while MYI replenishment has significantly increased over the full 43-year study period.The trend in MYI melt is the result of warming temperatures and a transition to younger and thinner MYI that is less resilient to warmer temperatures and the associated ice-albedo feedback.MYI area melt is found to be correlated with MDD and increases 3,300 km 2 for every additional degree-day above 0°C.The trend in replenishment is not correlated with MDD, even though replenishment should reflect FYI melt, or FDD, which reflects FYI growth during the preceding winter.Instead, we suggest that the increase in replenishment has been driven by the northward contraction of the MYI edge which in turn provides greater space for FYI to survive through the melt season at higher latitudes; highlighting a negative feedback that serves to stabilize the MYI pack.While the increase in replenishment has dampened MYI loss and fostered three periods of stability, there is an underlying transition toward younger MYI as the retention of MYI to older ice types has declined.This is a change dominated by increasing melt in the Beaufort Sea interrupting the transport of MYI through the Beaufort Gyre which precludes the ice from aging as it had historically.Additionally, replenishment is found to be correlated with melt during the following summer, meaning that increased replenishment promotes a younger thinner MYI pack that is more susceptible to melt.
Overall, the MYI pack has been stable around a minimum area of 1.2 × 10 6 km 2 since 2008.However, this stability has been undercut by the continued transition to younger and thinner MYI, with the recent occurrence of large polynyas within the MYI pack suggesting it is not as resilient as previously expected and may be poised for another stepwise reduction.Eventually, the Arctic is projected to be seasonally ice-free, at which point MYI will be confined to the narrow channels of the CAA.In the meantime, we expect MYI loss to continue to occur episodically rather than continuously.The two previous stepwise changes reduced Arctic MYI area by 0.9 and 1.5 × 10 6 km 2 , meaning that a future reduction of similar magnitude would render the Arctic Ocean essentially MYI free.Based on the budget, we do not expect MYI to recover, and we expect future loss to mainly be driven by the combination of increased melt and reduced replenishment.Both of these mechanisms are promoted by warming trends during summer and conditioned by a combination of MYI transport and FYI growth during the preceding winter.Ultimately, the MYI budget of the Arctic Ocean reflects a balance of several factors that have generally been in equilibrium through much of our 43-year study period.However, occasionally MYI loss has greatly exceeded replenishment, leading to a dramatic reduction and, within the timescale of this study, unrecoverable change in the MYI pack.While a negative feedback in MYI replenishment has so far dampened MYI loss, continued warming that both increases MYI melt and limits MYI replenishment will eventually lead to the complete loss of MYI and transition to a seasonally ice-free Arctic Ocean.

Figure 1 .
Figure 1.The expected (a), and calculated and estimated (b), annual cycles of multiyear sea ice (MYI) area in the Arctic Ocean, in weeks after the September minimum.Terms of the presented MYI budget are bolded in (b).

Figure 2 .
Figure 2. Top: Time series of the weekly multiyear sea ice (MYI) area in the Arctic Ocean beginning the week after the minimum of 1979 and running to the minimum of 2021.The MYI age distribution during the September minimum is presented by colored bars for 1984-2021.Dots denote the MYI area during the minimum and maximum, with associated trend lines shown by dashed lines.The mean MYI minimum during the three periods are overlaid.Bottom: Maps of the median ice age during the minima of each period.The mean annual fields of ice drift are overlaid, and the regional boundaries are also presented.
, and used to calculate MYI flux by summing points along the flux gate identified as MYI by the Ice Age data set.Negative fluxes represent MYI export from the Arctic Ocean, while positive fluxes represent MYI import.For the narrower channels, such as Nares Strait and the QEI, passive microwave products are too coarse, so we rely on previously published values of ice flux that utilize higher-resolution ice drift data.Total ice export into Nares Strait was determined from 1998 to 2009 byKwok et al. (2010), whileHowell et al. (2023) determined total and MYI flux into Nares Strait from 2017 to 2021.To estimate MYI flux prior to 2017 we first estimate total ice flux using the relationship thatKwok et al. (2010)  found between the duration of the period when ice drift was unobstructed by ice arches and total ice export.This relationship is approximated to be F = 285.74× duration − 19,577, where duration is the number of days during each ice season (September minimum to September minimum) when the arch was not in place.To determine duration, we use the timing of ice arch formation and collapse presented byVincent (2019) for 1979-2019, while for 2020 and 2021, we use the dates of formation presented byKirillov et al. (2021) and estimate the date of breakup from daily MODIS imagery.The record of total ice flux into Nares Strait is presented in FigureS2in Supporting Information S1.Finally, we estimate MYI flux from total ice flux by assuming an MYI proportion of 88%, which is based on the data presented byHowell et al. (2023).
From 1980From   to 1988, MYI covered much of the Arctic Ocean, with older ice types being advected through the Beaufort Gyre and remnant FYI being confined to the perimeter of the summer ice edge.From 1989 to 2005, a wide band of the oldest MYI was present along the coasts of the CAA and Greenland, stretching from the Beaufort Sea to Fram Strait, while FYI remained intact in the central Arctic and spanned across the eastern face of the ice pack.Following the collapse ofMYI between 2006 and 2008, MYI coverage between  2008 and 2021  was dramatically altered compared to the previous periods.The oldest MYI types were typically only present immediately along the CAA with a portion extending into the Beaufort Sea and none of the oldest ice reaching Fram Strait.

Figure 3 .
Figure 3. Annual record of multiyear sea ice (MYI) export across the boundaries of the Arctic Ocean from the ice season of 1980-2021.Top: MYI transport into Nares Strait and the QEI, Barents Sea, and Kara Sea.Bottom: MYI and total ice transport through Fram Strait, along with the net MYI export for each year and the MYI age distribution of MYI export through Fram Strait (bars).Positive values indicate import, while negative values indicate export.Significant trends are presented with dashed lines.

Figure 4 .
Figure 4. Annual area of multiyear sea ice (MYI) melt for the Arctic Ocean.The dashed line shows the negative trend from 1990 to 2021.The significant trend is presented as a dashed line.

Figure 5 .
Figure 5.Time series of the spatially averaged freezing-degree-day (FDD) and melting-degree-day (MDD) over the Arctic Ocean from October to May and June to September, respectively.Significant trends are presented by dashed lines.

Figure 6 .
Figure 6.Annual area of multiyear sea ice (MYI) replenishment for (a) each of the marginal seas and (b) the central Arctic and sum of the marginal seas for the total MYI replenishment.(c) MYI retention by age.Note that retention of MYI 2, 3, and 4 are calculated as their area during the week after the minimum, while MYI5+ is calculated as the change in MYI5+ area from them minimum to the week after, representing the increase in area of MYI 5+ and therefore the retention of that age of ice.Significant trends are presented with dashed lines.

Figure 7 .
Figure 7. Areas of multiyear sea ice (MYI) replenishment during (a) 1987, (b) 1996, (c) 2007, and (d) 2013.Areas of MYI replenishment are presented in red, while the rest of the ice pack is presented in light blue.Regional boundaries are overlaid in black.(e) Latitudinal distributions of replenishment area (solid lines) and mean air temperature during the melt season (May-September; dashed lines) for the three stable periods of MYI.Note that latitudinal distributions are based solely on data within the boundaries of the Arctic Ocean.

Figure 8 .
Figure 8. Top: Stacked bar plots of the annual multiyear sea ice (MYI) budget with the net overall results presented in black.Bottom: Time series of the cumulative annual result of the MYI budget (blue) and the MYI area minimum (red).Pie charts of the average contribution of each term to the overall budget are presented for each of the three periods.The three periods of MYI stability are highlighted by shading.
Conversely, during the two stepwise reductions, MYI loss greatly exceeded replenishment, driving a dramatic reduction in MYI area and a concurrent northward contraction of the MYI pack toward the coast of the CAA.The first reduction occurred in 1989 after a change in the AO flushed MYI out of the Beaufort Gyre into the Transpolar Drift Stream and subsequently led to anomalously high MYI export through Fram Strait, with a peak in the export of the oldest MYI types.The second reduction occurred between 2006 and 2008 and was the result of anomalously high melt and export, coupled with anomalously low replenishment.The consolidation of the MYI pack during the second reduction reduced the presence of MYI upstream of Fram Strait, leading to a significant decline in MYI export and transition toward younger ice being exported through Fram Strait.At the same time, MYI export into Nares Strait and the QEI has increased, albeit at a much smaller magnitude; however, MYI export through these pathways is important because it is the oldest MYI that is lost.