The evolution of the Fram Strait sea ice volume export decomposed by age: estimating with parameter-optimized sea ice-ocean model outputs

Sea ice export through the Fram Strait is crucial in the dynamic evolution of Arctic sea ice and can further modulate Arctic sea ice mass balance as well as the ocean thermohaline circulation. In this study, based on outputs from a parameter-optimized and fully physical ocean–sea ice coupled model and sea ice age observation, we estimate sea ice volume (SIV) flux and its age evolution via the Fram Strait. The estimate of mean annual SIV flux is about 1605 ± 315 km3 yr−1 without a significant trend for 1979–2021. Combining with sea ice age data, the variation of the sea ice age and its corresponding SIV flux are obtained for 1984–2020. The SIV flux of 1st-year ice significantly increases as expected, but it still contributes very little to the total flux in the 2010s with a proportion of 3.5%. SIV fluxes of different ages in multi-year ice present diverse variations. The proportions of 2nd-year ice and 3rd-year ice in the annual SIV flux show an extreme increase from 6.8% and 25.0% in the 1980s to 49.0% and 38.8% in the 2010s, respectively, while the proportions of 4th-year ice and 5th-year and older (5+ year) ice significantly decrease from 22.8% and 45.0% in the 1980s to 7.1% and 1.6% in the 2010s, respectively. Meanwhile, the prevailing age of annual volume export via Fram Strait shifts from 4th-year and 5+ year ice to 2nd-year and 3rd-year ice around 2007/2008. It is worth noticing that the variation in Fram Strait ice export modulates the variation in Arctic SIV prior to 2008, but the reverse is true after 2008, indicating a decreasing influence of Fram Strait SIV export on Artic SIV variability with decreasing sea ice age. The results are beneficial to promote the understanding of the evolution of Fram Strait SIV export under the warming Arctic.


Introduction
With the accelerated Arctic warming, the Arctic sea ice dramatically retreated during the last decades. In particular, the Arctic sea ice extent (SIE) in September retreated 12.8 ± 2.3% per decade from 1979 to 2018 (Meredith et al 2019). Bi et al (2018a) reported that compared with the period from 2003 to 2008, the autumn Arctic sea ice volume (SIV) decreased in the period from 2011 to 2015 and about 87% of this change could be attributed to the depletion of multiyear ice (MYI). Thus, thinner and younger sea ice is increasingly present in the Arctic (Maslanik et al 2007, Kwok and Rothrock 2009, Kwok 2018. These changes are reflected in spatial SIV anomalies that are the results of the interaction between dynamics and thermodynamics (Ricker et al 2021). Quantifying SIV fluxes is crucial to estimate the impact of sea ice dynamics on sea ice mass balance changes in the Arctic.
The Fram Strait, located between Greenland and the Svalbard Archipelago (figure 1(a)), is a major outlet for Arctic sea ice and an important passage connecting the Arctic and the Atlantic. Sea ice export through the Fram Strait accounts for 90% of the Arctic sea ice outflow and the annual export is about 13% of total Arctic sea ice mass on average   (Serreze et al 2006, Haine et al 2015. Considering the dramatical changes in the oldest ice type of the Arctic sea ice during the past few decades (Maslanik et al 2011, Kwok 2018, sea ice export through the Fram Strait may have potential influences on the variability of the Arctic MYI (Ricker et al 2018).
Previously, observations and model datasets have all been used to estimate the Fram Strait SIV flux. For instance, based on sea ice thickness (SIT) from upward looking sonars (ULS), Spreen et al (2020) calculated the long-term variability of SIV export from 1992 to 2014. With the availability of SIT retrievals from ICESat and CryoSat-2, several studies provided SIV flux estimations in freezing seasons (e.g. Spreen et al 2009, Bi et al 2018b, Ricker et al 2018. Nevertheless, gaps remain because of the spatial scarcity of the in-situ observations and the challenges of retrieving SIT from satellites during melting seasons. Recently long-term estimates based on non-assimilated model outputs (e.g. Wei et al 2019, Zamani et al 2019 showed overestimation compared with satellite-derived results due to overestimations of simulated SIT and sea ice drift (SID) on the gate. The Fram Strait SIV flux was also estimated by applying reanalyzes of SIT (e.g. Zhang et al 2017, Min et al 2019. It is also worth noting that these reanalyzes only adjust the specified model variables during assimilation, which is not dynamically consistent (Balmaseda et al 2015). Furthermore, given the ability to preserve the model's conservation compared to reanalyzes and the fact that they are closer to observations than the output from the model free run, outputs of parametersoptimized models are also valuable data sources for studies of the Arctic sea ice. For instance, Ricker et al (2021) pointed out that the North Atlantic/Arctic Ocean Sea Ice Model (NAOSIM) optimized by the micro-genetic algorithm outperforms the Pan-Arctic Ice Ocean Modeling and Assimilation System (PIO-MAS) in reproducing the stabilizing mechanism for negative ice growth feedback in the marginal seas bordering North America and Asia. The Fram Strait SIV export should therefore be reevaluated in light of NAOSIM data.
In addition, the changes in the Arctic sea ice age featuring first-year ice (FYI) advance and MYI depletion during the past few decades (Maslanik et al 2011, Bi et al 2018a also have influences on sea ice outflow through the Fram Strait. However, whether the FYI has already become the main part of sea ice outflow is unclear. Moreover, sea ice over the Fram Strait is typically divided into FYI and MYI in previous studies, and conclusions about MYI are mainly drawn regarding MYI as a whole. For example, Wang et al (2022) indicated a large decline in the proportion of MYI in the area exported via the Fram Strait, which decreased from 72% in 200272% in /200372% in -201072% in /201172% in to 59% in 201272% in /201372% in -201972% in /202072% in . Ricker et al (2018 illustrated that the variation of MYI volume export through the Fram Strait contributes 54% of the Arctic MYI volume variability in freezing seasons. While, MYI is still not further classified in accordance with the sea ice age. However, as MYI is made up of different ice ages that exhibit different characteristics (Bi et al 2016, Tschudi et al 2016, it is necessary to examine whether the evolution of MYI at various ice ages is compatible with the evolution of MYI as a whole and whether the relation between SIV export and Arctic SIV has changed when the age composites in SIV outflow change. Therefore, it is crucial to fill the gap in the distinguishment of SIV export through the Fram Strait by sea ice age groups combined with a continuous sea ice age dataset.

NAOSIM sea ice data
NAOSIM is a regional sea ice-ocean model developed by the Alfred Wegener Institute (Gerdes et al 2003, Kauker et al 2005, Karcher et al 2007. The model grid covers the whole Arctic and the northern North Atlantic Ocean (north of approximately 50 • N) by a spherical rotated grid. The model is driven by atmospheric forcing's from the NCEP Climate Forecast System Reanalysis Climate Forecast System version 2 (NCEP-CFSR-CFSv2, Saha et al 2014). Sumata et al (2019aSumata et al ( , 2019b developed the sea ice model by optimizing fifteen sea ice and ocean model parameters simultaneously using a micro genetic algorithm (mGA). Compared to the adjoint approach which linearizes the physical model and results in exponentially growing perturbations, the mGA approach applies the full nonlinear original physical model system, which is more physically reasonable (Sumata et al 2019a). In addition, the usefulness of mGA and the robustness of the simulated sea ice climatology, trend, and interannual variability were verified by testing 11 optimization experiments (Sumata et al 2019a). The modeled sea ice data used in this study is the mediumresolution version (28 km × 28 km) of NAOSIM daily effective SIT and SID data from January 1979 to October 2021. The simulated SIT and SID we used are from the third optimization version (Sumata et al 2019a). For more details can refer to Sumata et al (2019aSumata et al ( , 2019b.

NSIDC sea ice age data
The 'EASE-Grid Sea Ice Age (Version 4)' product (Tschudi et al 2019b) provides weekly sea ice age from 1984 to 2020 with a spatial resolution of 12.5 km. The ice parcels are marked as FYI firstly in 1978 and then tracked as Lagrangian parcels following the weekly  (1979-1990, 1991-2000, 2001-2010, and 2011-2020). Note that solid black lines in figures (b) and (c) are 1-1 lines, the error bar in figure (b) represents the uncertainty of CS2SMOS.
'Polar Pathfinder Daily 25 km EASE-Grid Sea Ice Motion Vectors (version 4.1)' (Tschudi et al 2019a). All parcels age one year during the week of Arctic sea ice minimum extent and will no longer be considered up to 16 yr or the SIC of a grid cell is less than 15%. The age of a certain grid cell is always assigned as the oldest parcel within the grid, therefore this product could effectively estimate the oldest ice parcels. Tschudi et al (2020) evaluated the version 4 age product compared with the preceding version and indicated its improvement in the continuity of the age field and performance in MYI. More details can be found in Tschudi et al (2020).

Methods
Following Krumpen et al (2016) and Ricker et al (2018), we define the Fram Strait as a composite gate that consists of zonal and meridional gates, which have been chosen for lower errors and bias in satellite SIT and SID data. The zonal gate is defined as the passage between 12 • W and 20 • E along 82 • N, while the meridional gate is defined as the passage between 80.5 • N and 82 • N along 20 • E (figure 1(a)). For the calculation of SIV fluxes, daily NAOSIM SIT and SID data are interpolated onto the zonal and meridional gates firstly with the grid spatial resolutions of 1 • and 0.15 • , respectively, which is to get similar grid lengths on the zonal and meridional gates. Then SIV fluxes could be derived by following Ricker et al (2018) and Min et al (2019): where Q is SIV flux, L represents length of the grids, H represents the modeled effective SIT, and the subscript x and y correspond to variables on the zonal gate and meridional gate, respectively. Moreover, v and u represent sea ice velocities perpendicular to the zonal gate and meridional gate, respectively. SIV flux of each gate is obtained by summing up fluxes of all grids on that gate, then the total volume flux through the Fram Strait is the aggregate of the fluxes on the zonal and meridional gates. The southward (westward) flux through the zonal (meridional) gate is defined as positive flux (Selyuzhenok et al 2020).
We further calculate the volume flux differentiated by sea ice ages. The weekly sea ice age data are averaged to monthly data and interpolated onto the Fram strait as methods introduced above. Then we sum the monthly fluxes of grids that have the same age to calculate the annual total flux of different sea ice ages. In this study, the annual period is considered from October to September following previous studies (e.g. Kwok et al 2004, Wei et al 2019, and the cold (warm) season is specified from October (May) to April (September) (Spreen et al 2009, Ricker et al 2018. Generally, the investigation period for SIV flux is from October 1979 to September 2021 according to the availability of NAOSIM and the annual time window. The study period is from October 1984 to September 2020 when combining SIV flux with the sea ice age data. Throughout the study, trends and correlation coefficients are statistically significant when the confidence level of the Student t-test exceeds 95%.

Model validation
To validate the performance of NAOSIM sea ice data at the Fram Strait, we show scatter plots between monthly NAOSIM and satellite SIT also SID at the Fram Strait in figures 1(b) and (c), respectively. The satellite SIT data is the weekly CS2SMOS (v204) data generated at the Alfred Wegener Institute Helmholtz Center for Polar and Marine Research (AWI), which merges CryoSat-2 (CS2) and Soil Moisture and Ocean Salinity (SMOS) satellite data (Ricker et al 2017). The CS2SMOS product is a good reference for SIT validation in the Fram Strait, where mixed ice types can often be found. In figure 1(b), generally, scatters distribute closely to the 1-1 line and the 1-1 line is typically within the uncertainty of CS2SMOS SIT. Thus, NAOSIM SIT is comparable with CS2SMOS in cold seasons from 2010 to 2021. NAOSIM performs well at the correlation (CC = 0.88) and rootmean-square error (RMSE = 0.24 m) compared with CS2SMOS, although NAOSIM shows a little overestimation of thin ice and underestimation of thick ice. NAOSIM SID from 1979 to 2020 is compared with the daily 'Polar Pathfinder Daily 25 km EASE-Grid Sea Ice Motion Vectors (version 4.1)' (Tschudi et al 2019a) distributed by the National Snow and Ice Data Center (NSIDC). The significantly high CC values between NAOSIM and NSIDC SID for four periods show reliable variability of NAOSIM SID on the gate ( figure 1(c)). Before the 1990s, the scatters are mostly above a 1-1 line, indicating that NAOSIM SID is a little faster than NSIDC SID. However, NSIDC SID is slower and less variable in the 1980s owing to the lack of buoys (Zamani et al 2019, Tschudi et al 2020. Since the 1990s (i.e. 1991Since the 1990s (i.e. -2000Since the 1990s (i.e. , 2001Since the 1990s (i.e. -2010Since the 1990s (i.e. , and 2011Since the 1990s (i.e. -2020, scatters are mainly surrounding the 1-1 line, therefore NAOSIM SID is more consistent with NSIDC SID. The RMSE values also become smaller in 1991-2000, 2001-2010, and 2011-2020 compared to 1979-1990. In summary, NAOSIM data can well reproduce the Fram Strait sea ice parameters and provide reliable sea ice estimations for quantifying SIV fluxes through the Fram Strait.

SIV export through the Fram Strait
Combining NAOSIM SIT and SID, we estimate the variabilities of annual, cold-season, and warm-season SIV fluxes through the Fram Strait ( figure 2(a)). The mean annual SIV flux from 1979/1980-2020/2021 is about 1605 ± 315 km 3 yr −1 . On average, 71 ± 4% of the interannual variability of annual flux comes from the cold-season flux (1146 ± 240 km 3 yr −1 ), which is nearly 2.5 times of the warm-season flux (459 ± 108 km 3 yr −1 ). The annual SIV flux peaks in 1994/1995 (2321 km 3 yr −1 ) while the minimum SIV fluxes occur in 2017/2018 (999 km 3 yr −1 ). The peak value in 1994/1995 was also reported by previous studies (e.g. Kwok et al 2004, Zhang et al 2017, Wei et al 2019, which may have been caused by a significant anomalous southward SID at the Fram Strait (Arfeuille et al 2000). While the minimum value in 2017/2018 can be attributed to regional sea ice-ocean processes driven by abnormally atmospheric circulation over the Atlantic Arctic Ocean (Sumata et al 2022). Meanwhile, linear regressions indicate that none of the annual, cold-season, and warm-season SIV fluxes has an obvious trend from 1979 to 2021. Figure 2(b) shows the annual cycle of monthly SIV flux, SID, and SIT through the Fram Strait. Annually, more than 84% of SIV flux is from the zonal gate, even occupying more than 97% from July to September. The annual cycle of SIV flux (zonal gate plus meridional gate) amounts between 198.5 km 3 month −1 (March) and 42.1 km 3 month −1 (August). The annual cycle of SID is the fastest (5.11 km d −1 ) in March and the slowest (1.81 km d −1 ) in August, which is in phase with the annual cycle of volume flux. While SIT is the thickest in May (2.16 m), and the thinnest in September (0.93 m) and lags behind SIV. The coefficient of determinations (R 2 ) between the standardized monthly SIV flux and SIT/SID from 1979 to 2021 is calculated to figure out the determinative factor that influences SIV flux variability (Ricker et al 2018, Min et al 2019. The result shows that SID is the main factor that regulates the variation of monthly SIV flux with R 2 of 0.74, which is more than twice the R 2 between SIT and SIV flux (0.30).
The spatial distribution of the long-term trend and the long-term mean of the annual SIV flux on the Fram Strait is shown in figure 2(c). Spatial differences can be found both in the tendency and Greenland is mainly contributed by variation in SID. The magnitude of fluxes is similar among points of the meridional gate and shows a tiny decrease from 82 • N to 80.5 • N. Trends on the meridional gate are consistently negative and are statistically significant in higher latitudes. The decreasing trends in fluxes on the meridional gate may link to the shrinking sea ice north of the Svalbard which is induced by the enhanced inflow of the Atlantic water (Shu et al 2021).

Variabilities of the sea ice age and its corresponding fluxes
The evolution of the annual mean sea ice age at the Fram Strait from 1984/1985-2019/2020 is shown in figure 3(a). The annual mean ice age decreases along the zonal gate from Greenland to Svalbard, and older at higher latitudes along the meridional gate. Generally, the annual mean sea ice age at the Fram Strait becomes younger but displays interannual variability. An obvious shift in the sea ice age on the Fram Strait shows around 2007/2008, which could be attributed to the sea ice retreat in 2007 (Maslanik et al 2011, Kwok 2018. Before 2008, the zonal gate is covered by a large amount of 3rd-year and 3+ year ice but is mainly 2nd-year ice and 3rd-year ice after 2008. While, an increase in annual mean sea ice age to 4th-year ice shows near Greenland in 2016/2017, which is accounted for a reversal event of Beaufort Gyre in 2016/2017 winter so that the abnormally enhanced SID along the northeast of the Canadian Arctic Archipelago transported more MYI away from the Beaufort Sea to the Fram Strait (Babb et al 2020). Figure 3(b) shows the annual volume flux of different sea ice ages through the Fram Strait from 1984/1985-2019/2020. The annual volume fluxes of different ages show different trends while the trend of total volume flux through the Fram Strait is statistically insignificant. The volume flux of 1st-year significantly increases with the trend of 1.16 km 3 yr −2 , but the flux is still a small amount that only occupies 3.5% of the annual SIV flux in the 2010s. While the SIV flux of diverse compositions in MYI varies differently. The volume fluxes of 2nd-year and 3rd-year ice show statistically significant increasing trends of 24.22 km 3 yr −2 and 7.99 km 3 yr −2 , respectively, and their proportions in the annual SIV flux increased from 6.8% and 25.0% in the 1980s to 49.0% and 38.8% in the 2010s, respectively. However, volume fluxes of 4th-year ice and 5th-year and older (5+ year) ice significantly decreased with the trends of −9.74 km 3 yr −2 and −18.28 km 3 yr −2 , respectively, and their contribution to the total SIV flux decreased from 22.8% and 45.0% in the 1980s to 7.1% and 1.6% in the 2010s, respectively. Consistent with the evolution of the sea ice age on the Fram Strait, the age composition of annual SIV flux changed dramatically in 2007/2008. Since 2007/2008, almost no 4th-year and 5+ year ice but a large amount of 2nd-year and 3rd-year ice is transported through the Fram Strait, implying a new state of SIV export through the Fram Strait.

Conclusions and discussion
SIV export through the Fram Strait is an important dynamic process for regulating sea ice mass and freshwater balance of the Arctic (Lind et al 2018, Spreen et al 2020, Li et al 2022. However, disagreements still surround the magnitude and also trend estimates of the SIV flux across the strait, and analysis is still short of the detailed decomposition of SIV flux according to sea ice age especially the decomposition for MYI. Recent advances in Arctic sea ice data provide a unique opportunity to clarify these issues. NAOSIM can generate more accurate state estimates of Arctic sea ice and preserve the model's conservation by optimizing model parameters with mGA. Additionally, the continuous, complete, and long-term sea ice age record from NSIDC detailed distinguishes sea ice age from 1st-year ice to 5+ year ice. Thus, it is essential to reexamine the above issues by applying the NAOSIM model data and NSIDC sea ice age data. The mean annual SIV export through the Fram Strait is 1605 ± 315 km 3 yr −1 for 1979/1980-2020/2021. Additionally, the insignificant trend of the Fram Strait SIV flux for 1979-2021 by our study confirms the finding in previous studies (e.g. Spreen et al 2009, Zhang et al 2017, Zamani et al 2019. Combining the NSIDC age product with SIV export, we illustrate that although the amount of volume flux changes inconspicuously, the evolution of SIV export at various ages is diverse. As 1st-year ice plays a more important role in the warming Arctic (Kwok 2018), the statistically significant increasing trend of 1st-year ice SIV flux (+1.16 km 3 yr −2 ) is within our expectation, but it still shows less importance in the total flux with the proportion of 3.5% in the 2010s. For composites in MYI, SIV flux of 2nd-year ice (+24.22 km 3 yr −2 ) and 3rd-year ice (+7.99 km 3 yr −2 ) increase significantly, but SIV fluxes of 4th-year ice (−9.74 km 3 yr −2 ) and 5+ year ice (−18.28 km 3 yr −2 ) display statistically significant decreasing trends. In addition, the prevailing age of the annual MYI volume export changed obviously since 2007/2008, which could be connected with the extreme SIE retreat and MYI melt in 2007 summer (Maslanik et al 2011).
Since our finding reveals an obvious transformation of the predominant age in sea ice outflow via the Fram Strait around 2007/2008 without obvious changes in the amount of volume export, it is necessary to investigate whether the connection between the Fram Strait volume flux and Arctic SIV has changed before and after this time node. The lagged correlation between the monthly anomaly of volume The correlation coefficients indicate that the variability of the Fram Strait ice export modulates the variation in Arctic SIV. For 2008-2020, the anomalous Arctic SIV exhibits a significantly positive correlation with the SIV flux anomaly when Arctic SIV leads the SIV flux, which is not shown before 2008, and it is most correlated when the Arctic SIV leads the SIV flux by 14 months (CC = 0.47). The result illustrates that the variability of volume export becomes the response of variation in Arctic SIV when sea ice outflow becomes younger. Meanwhile, the negative correlation when Arctic SIV lags the volume flux decreases compared with 1979-2007. Thus, the preceding effect of the anomalous Fram Strait SIV export on Arctic SIV variability declines with the change of sea ice age in SIV export, which implies that local thermodynamic and dynamic processes in the Arctic rather than sea ice export might be responsible for the anomaly of Arctic SIV in recent years (Wei et al 2019).
The Fram Strait and northern Svalbard are key regions for oceanic heat supply to the Arctic Ocean by the warm Atlantic Water and are the place of oceansea ice interaction (Wang et al 2020). Under the situation of younger sea ice outflow and inconspicuous change in the amount of SIV flux, the larger mass of freshwater flux brought by sea ice can be transported to the Atlantic through the Fram Strait considering the larger density of younger sea ice than older sea ice (Zygmuntowska et al 2014), which may further influence the dense water formation in the North Atlantic Ocean (Ionita et al 2016, Sumata et al 2022. However, further comprehensive investigations are still needed on this subject. Meanwhile, uncertainties still exist within NAOSIM model data and NSIDC sea ice age product which may cause bias in our estimation. Compared with ULS-thickness based estimates near 79 • N (Vinje et al 1998, Kwok and Rothrock 1999, Kwok et al 2004, Spreen et al 2020, the NAOSIM derived SIV flux at 79 • N (figure not shown) is basically within the uncertainties of estimations obtained by in-situ observation of SIT although NAOSIM underestimates SIV flux in the freezing season. It is also worth noting that the spatial scarcity of in-situ observations may cause uncertainties in SIV flux estimation. Meanwhile, large discrepancies in SIV flux estimations can be induced by using different sources of SID data, even if the same SIT data is adopted (Vinje et al 1998, Kwok and Rothrock 1999, Spreen et al 2020. Moreover, results combining the sea ice age data in this study may overestimate the sea ice age, which is induced through the derivation of NSIDC age product (Tschudi et al 2020). In the future, we plan to further examine the causes and impacts of the reversal relation between sea ice export via the Fram Strait and Arctic SIV under the dramatically changing Arctic. The effect of the Fram Strait SIV outflow on ocean processes is also considered in our future investigations.

Data availability statement
The sea ice age product (10.5067/UTAV7490FEPB) and sea ice motion vectors (10.5067/INAWUWO7Q H7B) are accessible from the National Snow and Ice Data Center. The CS2SMOS data is available from ftp://ftp.awi.de/sea_ice/product/cryosat2/v2p4/.
All data that support the findings of this study are included within the article (and any supplementary files).