Sea-ice transport driving Southern Ocean salinity and its recent trends

Multiple lines of evidence indicate that the northward transport of sea ice from Antarctica can explain the bulk of the observed freshening in the Southern Ocean. The Southern Ocean has freshened over the past few decades, but the underlying mechanisms involved have remained unclear. Alex Haumann and colleagues bring together multiple lines of evidence and — despite large uncertainties in the underlying datasets — they find that northward transport of sea ice formed around the Antarctic coast can explain the bulk of the observed freshening. Recent salinity changes in the Southern Ocean1,2,3,4,5,6,7 are among the most prominent signals of climate change in the global ocean, yet their underlying causes have not been firmly established1,3,4,6. Here we propose that trends in the northward transport of Antarctic sea ice are a major contributor to these changes. Using satellite observations supplemented by sea-ice reconstructions, we estimate that wind-driven8,9 northward freshwater transport by sea ice increased by 20 ± 10 per cent between 1982 and 2008. The strongest and most robust increase occurred in the Pacific sector, coinciding with the largest observed salinity changes4,5. We estimate that the additional freshwater for the entire northern sea-ice edge entails a freshening rate of −0.02 ± 0.01 grams per kilogram per decade in the surface and intermediate waters of the open ocean, similar to the observed freshening1,2,3,4,5. The enhanced rejection of salt near the coast of Antarctica associated with stronger sea-ice export counteracts the freshening of both continental shelf2,10,11 and newly formed bottom waters6 due to increases in glacial meltwater12. Although the data sources underlying our results have substantial uncertainties, regional analyses13 and independent data from an atmospheric reanalysis support our conclusions. Our finding that northward sea-ice freshwater transport is also a key determinant of the mean salinity distribution in the Southern Ocean further underpins the importance of the sea-ice-induced freshwater flux. Through its influence on the density structure of the ocean, this process has critical consequences for the global climate by affecting the exchange of heat, carbon and nutrients between the deep ocean and surface waters14,15,16,17.

either from enhanced Antarctic glacial melt 2,6,10-12 or from increased atmospheric freshwater fluxes, as a result of an excess of precipitation over evaporation 1,5 . Glacial meltwater 12 is the most likely cause of the freshened coastal waters in the Amundsen and Ross seas 2,10,11 , but the freshening signal in the AABW, which is formed in this region, is much smaller than expected 6 . In contrast, the recent freshening of the AAIW seems to be much larger than can be explained by the simulated increases in the atmospheric freshwater flux by global climate models in the open Southern Ocean 1,4 .
Changes in northward sea-ice transport could possibly contribute to the widespread salinity changes in the Southern Ocean 8 . This process acts as a lateral conveyor of freshwater by extracting freshwater from the coastal regions around Antarctica where the sea ice forms and releasing it at the northern edge of the sea ice where the sea ice melts [19][20][21] (Fig. 1a). Despite substantial wind-driven changes in sea-ice drift over the past few decades 8,9 , this contribution has not yet been quantified. Here we suggest that surface freshwater fluxes induced by stronger northward sea-ice transport are a major cause of the observed salinity changes in recent decades; this is corroborated by our finding that the transport process plays a key role in the long-term mean salinity distribution in the Southern Ocean.
Our conclusions are based on basin-scale estimates of annual net sea-ice-ocean freshwater fluxes and the annual northward transport of freshwater by sea ice over the period 1982-2008. Further evidence is provided by our assessment of atmospheric reanalysis data 22 and the results from a regional study 13 . We derived the sea-ice-related freshwater fluxes by combining sea-ice concentration, drift and thickness data and by using a mass balance approach to determine the volume divergence and local change in sea ice (Methods). The sea-ice concentration is derived from satellite observations 23 (Extended Data Fig. 1) and its thickness from a combination of satellite data 24 and a modelbased sea-ice reconstruction that assimilates satellite data 25 (Extended Data Fig. 2). The sea-ice volume divergence was computed from satellite-based sea-ice drift vectors 26 (Extended Data Figs 3,4) and seaice volume. From the resulting sea-ice volume budget, we estimated the freshwater equivalents of local annual sea-ice-ocean fluxes due to freezing and melting and annual lateral sea-ice transport (Methods).
Uncertainties in these derived freshwater flux products are substantial (Methods). A major challenge arises from the need to combine sea-ice drift estimates from different satellites to estimate the trends. We addressed potential inhomogeneities and biases by vigorous data quality control, implementing several corrections and considering different time periods (Methods). A second challenge is associated with the relatively limited number of observations of sea-ice thickness. These uncertainties plus the observationally constrained range of the other input quantities were incorporated into our error estimates of the final freshwater flux product (Extended Data Tables 1, 2). In the Atlantic sector, uncertainties associated with the mean sea-ice thickness distribution dominate the uncertainty, while in the Pacific sector uncertainties are mostly caused by uncertainties in sea-ice drift.
Our analysis reveals large trends in the meridional sea-ice freshwater transport in the Southern Ocean between 1982 and 2008 (Figs 1b and 2c) that affect the regional sea-ice-ocean freshwater fluxes (Fig. 2d). The annual northward sea-ice freshwater transport of 130 ± 30 mSv (1 mSv = 1,000 m 3 s −1 ≈ 31.6 Gt yr −1 ; Fig. 2a; Extended Data Table 1) from the coastal region to the open ocean strengthened by + 9 ± 5 mSv per decade (Extended Data Table 2). Here, the coastal ocean refers to the region between the Antarctic coast and the zero sea-ice-ocean freshwater flux line and the open ocean is the region between the zero sea-ice-ocean freshwater flux line and the sea-ice edge (Fig. 2b). The increased northward transport caused, on average, an additional extraction of freshwater from the coastal ocean of − 40 ± 20 mm yr −1 per decade and an increased addition to the open ocean region of + 20 ± 10 mm yr −1 per decade.
The overall intensification occurred primarily in the Pacific sector where we find a vigorous northward freshwater transport trend of + 14 ± 5 mSv per decade. The trends in this sector are the most robust (Extended Data Table 3). Over the whole period, this change in the Pacific sector corresponds to an increase of about 30% with respect to the climatological mean in the entire Southern Ocean (Extended Data Table 1). The largest trends occurred locally in the high-latitude Ross Sea (Fig. 2c, d), where our estimated trends agree well with a previous study 13 (Methods). The increase in the Pacific sector is partly compensated for by small decreases in the Atlantic and Indian ocean sectors. We reach similar conclusions when we consider only the satellite data from 1992 to 2004, that is, the period when they are least affected by potential inhomogeneities (Extended Data Table 3).
The reason for the observed northward sea-ice freshwater transport and its recent trends is the strong southerly winds over the Ross and Weddell seas, which persistently blow cold air from Antarctica over the ocean, pushing sea ice northwards 9 . The winds over the Ross Sea considerably strengthened in recent decades, possibly owing to a combination of natural variability, changes in greenhouse gas concentrations and stratospheric ozone depletion 9 . These changes in the southerly winds induced regional changes in northward sea-ice drift 8,9 , which are responsible for the sea-ice freshwater transport trends (Methods). This relation between the atmospheric circulation and sea-ice drift changes enabled us to independently estimate the sea-ice c, d, Linear trends of northward sea-ice freshwater transport (c) and net sea-ice-ocean freshwater flux from freezing and melting (d). Stippled areas are significant at the 90% confidence level using Student's t-test (see Methods). The arrows show the mean (a) and trend (c) of the annual transport vectors. The thick black lines indicate the zero sea-ice-ocean freshwater flux line that divides the coastal from the open ocean regions, the thin black lines show the continental shelf (1,000 m isobath). The grey lines represent the edge of the sea ice (1% sea-ice concentration) and the green lines show the boundaries of the ocean basins labelled. drift anomalies using sea-surface pressure gradients along latitude bands from atmospheric reanalysis data 22 (Methods). Comparing the resulting northward sea-ice transport anomalies to the satellite-based estimates across the same latitude bands results in a similar overall trend (Fig. 3). Thus, this alternative approach not only corroborates our estimated long-term trend, but also suggests that any remaining inhomogeneities in the sea-ice drift data that are due to changes in the satellite instruments are comparably small after applying multiple corrections (Methods).
To assess how the changing sea-ice-ocean freshwater flux (Fig. 2d) affected the salinity in the Southern Ocean we assumed that the additional freshwater in the open ocean region entered the AAIW and the SAMW formed from upwelling Circumpolar Deep Waters (CDW) 27,28 (Methods). We find that our freshwater flux trends imply a freshening at a rate of − 0.02 ± 0.01 g kg −1 per decade in the surface waters that are transported northwards and form the AAIW and SAMW (Fig. 1b). Thus, the sea-ice freshwater flux trend could account for a substantial fraction of the observed long-term freshening in these water masses 1,3,4 . The strong sea-ice-ocean freshwater flux trends in the Pacific sector ( Fig. 2d) spatially coincide with the region of largest observed surface freshening 2,5 (Extended Data Fig. 7) and can explain also the stronger freshening of the Pacific AAIW compared with that of the Atlantic 1,4 . A more quantitative attribution of the observed salinity trends to the freshwater transport trends is beyond the scope of our study because the observed freshening trends stem from different time periods, and have strong regional variations and large uncertainties themselves 1,3,4 . However, our data show that changes in northward sea-ice freshwater transport induce salinity changes of comparable magnitude to the observed trends.
Our estimates in coastal regions (Fig. 2d) also help to explain the observed salinity changes in the AABW 6 , which is sourced from this region. Additional glacial meltwater from West Antarctica 12 strongly freshened the continental shelf in the Ross and Amundsen seas over recent decades 2,10,11 (Fig. 1b). However, the observed freshening in Pacific and Indian Ocean AABW was found to be much smaller than expected from this additional glacial meltwater 6 . Our data suggests that the freshening induced by the increasing glacial meltwater is substantially reduced by a salinification from an increased sea-ice to ocean salt flux over the continental shelf in the Pacific sector. This salt flux trend corresponds to a freshwater equivalent of − 10 ± 3 mSv per decade, resulting from increasing northward sea-ice export from this region of enhanced sea-ice formation (Fig. 2c, d). In contrast, over the continental shelf in the Atlantic sector our data suggest a decreasing sea-ice to ocean salt flux, corresponding to a freshwater equivalent of + 6 ± 3 mSv per decade, which may have contributed to the observed freshening of the newly formed Atlantic AABW 6 and the north-western continental shelf waters 18 .
The large contribution of the trends in sea-ice freshwater transport to recent salinity changes in the Southern Ocean is in line with the dominant role that sea ice plays in the surface freshwater budget in the seasonal sea-ice zone 29 and in the global overturning circulation [19][20][21]27 in the mean state. The freshwater equivalent of the total Southern Ocean sea-ice melting flux (Fig. 4a) is as large as 460 ± 100 mSv (Extended Data Table 1). On an annual basis, the vast majority of this melting flux is supplied by the freezing of seawater of − 410 ± 110 mSv, with the remaining flux arising from snow-ice formation 30 (Methods; Fig. 4b). Most of the sea ice is produced in the coastal region (− 320 ± 70 mSv), but only about 60% of the sea ice also melts there. The rest, that is, 130 ± 30 mSv, is exported to the open ocean (Fig. 4c). These mean estimates agree well with an independent parallel study 27 , which is based on the assimilation of Southern Ocean salinity and temperature observations (Methods).
The process of northward freshwater transport by sea ice effectively removes freshwater from waters that enter the lower oceanic overturning cell, in particular the AABW, and adds it to the upper circulation cell, especially the AAIW (Fig. 1a). Through this process, the salinity difference between these two water masses, and thus the meridional and vertical salinity gradients, increase. In a steady state, the northward sea-ice freshwater transport of 130 ± 30 mSv implies a salinity modification of + 0.15 ± 0.06 g kg −1 and − 0.33 ± 0.09 g kg −1 Satellite-based (+8 mSv per decade) ERA-Interim-based (+8 mSv per decade) in waters that are entering the lower and upper cell, respectively (Methods). The latter suggests that sea-ice freshwater transport accounts for the majority of the salinity difference between the upwelling CDW and the exiting AAIW. We estimated that the salinification from sea ice in waters entering the lower circulation cell is compensated by glacial meltwater and excess precipitation over evaporation in this region in about equal parts, agreeing with the very small salinity difference between the CDW and AABW (Methods).
Because salinity dominates the density structure in polar oceans 14 , our findings imply that sea-ice transport is a key factor for the vertical and meridional density gradients in the Southern Ocean and their recent changes (Fig. 1). This interpretation is consistent with the observation that large areas of the upper Southern Ocean not only freshened but also stratified in recent decades 7 . Increased stratification potentially hampers the mixing of deeper, warmer and carbon-rich waters into the surface layer and thus could increase the net uptake of CO 2 14,16,17 . Consequently, our results suggest that Antarctic sea-ice freshwater transport, through its influence on ocean stratification and the carbon cycle, is more important for changes in global climate 14,15 than has been appreciated so far. This implication of our findings for the climate system stresses the need to better constrain spatial patterns as well as temporal variations in sea-ice-ocean fluxes by reducing the uncertainties in the observations of drift, thickness and snow cover of Antarctic sea ice.
Online Content Methods, along with any additional Extended Data display items and Source Data, are available in the online version of the paper; references unique to these sections appear only in the online paper. Letter reSeArCH MethOds Data. The satellite-derived sea-ice concentration is drawn from the Climate Data Record (CDR) 23 , which comprises data from the NASA Team algorithm (NTA) 31 and the Bootstrap algorithm (BA) 32 , as well as a merged data set. Sea-ice thickness data are taken from a reconstruction with the ocean-sea-ice model NEMO-LIM2 (1980-2009 25 , from the laser altimeter ICESat-1 (2003-2008; http://seaice.gsfc. nasa.gov) 24 , as well as from ship-based observations (ASPeCt; 1980-2005; http:// aspect.antarctica.gov.au) 33 . Satellite-derived sea-ice drift data originates from the National Snow and Ice Data Center (NSIDC) 26 , is provided in NetCDF-format by the Integrated Climate Data Center (University of Hamburg) and is corrected by drifting buoy data (1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005) 34 . We used an alternative sea-ice drift product for the uncertainty estimation (1992-2003; http://rkwok.jpl.nasa.gov; hereafter referred to as Kwok et al.) 35,36 . Additionally, we used daily atmospheric sea-level pressure, surface air temperature and 10 m wind speed values from the ERA-Interim reanalysis (1980-2009, http://apps.ecmwf.int) 22 . We provide a detailed description of the data processing in the corresponding sections below. Sea-ice concentration. We used all three sea-ice concentration products available from the CDR 23 . If any of the grid points in either the merged, NTA or BA products show a sea-ice concentration of 0%, all of the products are set to 0%. We used a first-order conservative remapping method from the Climate Data Operators (CDO) 37 to interpolate the sea-ice concentration to the sea-ice drift grid. The BA performs better than the NTA around Antarctica as the NTA underestimates seaice concentrations by 10% or more 23,38 (Extended Data Fig. 1a, b). Therefore, we primarily used the BA product. However, the BA potentially underestimates the concentration of sea ice in the presence of thin ice and leads 23,38 . Therefore, we used the merged product, which should be more accurate in these regions 23 , to estimate the uncertainties. Generally, sea-ice concentration is the best constrained of the three sea-ice variables. Its contribution to the climatological mean flux uncertainty is below 1% (Extended Data Table 1). To obtain the uncertainty in the freshwater flux trends, we also used the NTA because differences in the trends in Antarctic sea-ice area between the BA and NTA have been reported 39 . Differences between the BA and NTA sea-ice concentration trends range from 10% to 20% relative to the actual trend (Extended Data Fig. 1c, d). The associated uncertainties in the spatially integrated sea-ice freshwater flux trends are about 10% (Extended Data Table 2). Sea-ice thickness. Sea-ice thickness data spanning our entire analysis period do not exist, mostly owing to challenges in remote sensing of Antarctic sea-ice thickness 40 . We therefore used a sea-ice thickness reconstruction 25 from a model that assimilated the observed sea-ice concentration. Through this assimilation, the model constrained air-sea heat fluxes, improving the spatial and temporal variability of the sea-ice thickness. The model did not assimilate sea-ice thickness observations themselves. Sea-ice thickness, as we use it here, is not weighted with sea-ice concentration and does not include the snow layer.
The reconstruction overestimates the sea-ice thickness in the central Weddell and Ross seas and underestimates it in some coastal regions compared to the ICESat-1 24 and ASPeCt 33 data sets (Extended Data Fig. 2). To compare the different sea-ice thickness data sets, we interpolated the reconstruction, ICESat-1 and ASPeCt data to the sea-ice drift grid using CDO 37 distance-weighted averaging. For our best estimate of the sea-ice freshwater fluxes, we applied a weighted bias correction to the reconstruction using the spatially gridded version of the ICESat-1 data (see the following paragraph). Both the ICESat-1 and ASPeCt data sets are potentially biased low, particularly in areas with thick or deformed sea ice 33,40-42 , where we found the largest differences between these two data sets and the uncorrected reconstruction. Thus, the thicker sea ice in the Weddell Sea in the uncorrected reconstruction might be realistic, especially when considering alternative ICESat-1 derived estimates for this region 40,43,44 . To capture the full uncertainty range associated with the mean sea-ice thickness distribution, we used the difference between the uncorrected reconstruction and the ICESat-1 data. Uncertainties in sea-ice thickness dominate the climatological freshwater flux uncertainties in the Atlantic and Indian Ocean sectors, ranging from 10% to 35%, and are also substantial in all other regions and for the overall trends (Extended Data Tables 1, 2).
For the correction of the mean sea-ice thickness distribution, we first calculated relative differences to ICESat-1 whenever data were available. Then, we averaged all of the differences that were within two standard deviations over time. We applied this average relative bias correction map to the data at each time step. To ensure that local extremes were not exaggerated, we used weights. Weights were one for a sea-ice thickness of 1.2 m, that is, the full bias correction was applied, and decreased to zero for sea-ice thicknesses of 0.2 m and 2.2 m, that is, no bias correction was applied. We derived these thresholds empirically to reduce biases with respect to the non-gridded ICESat-1 and ASPeCt data (Extended Data Fig. 2). Trends in the reconstruction remain largely unaffected by the bias correction (comparing Extended Data Fig. 2a and the original trend 25 ).
Local extremes in the sea-ice thickness reconstruction, caused by ridging events, are probably inconsistent with the observed sea-ice drift and would lead to unrealistic short-term variations in our final fluxes. However, when considering the net annual melting and freezing fluxes and averages over large areas these variations cancel out. To reduce the noise in our data set, we filtered extremes with a daily sea-ice thickness anomaly larger than 2 m with respect to the climatological seasonal cycle, representing only 0.1% of all data points. These and other missing grid points (in total 2.6%) were interpolated by averaging the neighbouring grid points. We also calculated our sea-ice freshwater fluxes on the basis of the unfiltered data and included these fluxes in our uncertainty estimate.
Snow-ice formation due to flooding and refreezing 30,45 is part of the estimated sea-ice thickness. As snow-ice forms partly from the atmospheric freshwater flux and not from the ocean alone, it could lead to an overestimation of the total ocean to sea-ice freshwater flux due to freezing. The amount of snow-ice formation is highly uncertain 30,45 but lies within the uncertainty of the sea-ice thickness. To account for this process, we reduced the freezing fluxes according to snow-ice formation estimates from the literature 30 . In the Atlantic, Indian Ocean and Pacific sectors we applied approximate snow-ice formation rates of 8 ± 8%, 15 ± 15%, and 12 ± 12% of the freezing flux, respectively 30 . In the entire Southern Ocean, the amount of snow that is transformed to ice would thus amount to about 50 mSv, or about 35% of the suggested atmospheric freshwater flux onto Antarctic sea ice 27 .
Trends in sea-ice thickness (Extended Data Fig. 2a) are highly uncertain but broadly agree among different modelling studies 25,46,47 . To show that our results are robust with respect to the less certain trends or short-term variations in sea-ice thickness, we compared our estimated transport trends across the latitude bands (equation (3)) with a sensitivity analysis, where we kept the sea-ice thickness constant. The resulting transport trends across the latitude bands of about − 6 mSv per decade in the Atlantic sector and about + 11 mSv per decade in the Pacific sector are still within our estimated uncertainty (Extended Data Table 2). Most of the sea-ice thickness trends (Extended Data Fig. 2a) occur either north (in the Pacific sector) or south (in the Atlantic sector) of the zero freshwater flux line or latitude bands. Thus, the trend in sea-ice thickness does not considerably affect the northward sea-ice freshwater transport trend. However, the mean sea-ice thickness uncertainty at the zero freshwater flux line is the largest contributor to the overall northward sea-ice freshwater transport trend (Extended Data Table 2). Sea-ice drift. We used the gridded version of the NSIDC 26 sea-ice drift data set. In the Antarctic, it is based on five passive microwave sensors 48,49 and data from the Advanced Very High Resolution Radiometer (AVHRR) 50 (Extended Data Fig. 4). Two studies validated this data set with buoy data in the Weddell Sea (1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005) 34 and around East Antarctica (1985)(1986)(1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997) 51 . There is a very high correlation between the buoy and the satellite data on large temporal and spatial scales (that is, monthly and regional) and a strongly reduced agreement on smaller scales (that is, daily and local) 34,51 . The satellite-derived sea-ice drift underestimates the sea-ice velocity given by the buoys by 34.5% 34 , that is, faster drift velocities have a larger bias 52 . The bias is smaller for the meridional (26.3%) than for the zonal drift 34 . We corrected for these low biases by multiplying the drift velocity by the correction factor (1.357) that corresponds to the meridional drift bias 34 . We argue that the meridional component of the bias is the better estimate in the central sea-ice region, which is the key region for our results. Here, the drift is mainly meridional. The larger biases are observed in the swift, mostly zonal drift along the sea-ice edge that causes the larger zonal biases. The spatial dependence of the bias and our correction imply that larger biases and uncertainties remain in our final product around the sea-ice edge.
We processed this bias-corrected drift data further: first we removed all of the data that were flagged as close to the coast or interpolated over large distances in the product; second, we removed any data with sea-ice concentrations below 50%, closer than 75 km to the coast 34 , or with a spurious, exact value of zero. Our results are not sensitive to this filtering but it reduces the spatial and temporal noise. After these modifications, about 75% of all of the grid cells covered by sea ice had an associated drift vector.
We compared both the original and the bias-corrected data to a partly independent product by Kwok et al. 35,36 . We interpolated these data onto our grid using CDO 37 distance-weighted averaging and applied the same 21-d running mean as for the NSIDC sea-ice drift data. We compared sea-ice drift vectors whenever both data sets were available and sea-ice concentrations were larger than 50%. Extended Data Fig. 3 shows the meridional drift components before and after applying the bias correction factor from the buoy data (Extended Data Fig. 3a and b, respectively). We find that the agreement between the two data sets is much higher after the corrections. Compared with the original NSIDC sea-ice drift data set, the largest improvement occurs in the slope: 1.06 compared with 1.55. Root-mean-square (r.m.s.) differences and the linear correlation coefficient remain identical and the absolute bias is reduced by 0.2 km d −1 . The correlation Letter reSeArCH coefficients between the two data sets are 0.8 for both the zonal and meridional drift components. The spatial patterns of the mean annual sea-ice drift speed (Extended Data Fig. 3c-e) illustrate the improvement in agreement between the two data sets after the application of the bias correction but confirm that considerable differences remain at the sea-ice edge. These differences lead to a relatively high r.m.s. difference in the annual mean sea-ice drift speed in these regions (Extended Data Fig. 3f). However, in the central sea-ice pack-the region that is crucial for our results-the r.m.s. differences are much smaller.
Our bias-corrected sea-ice drift speeds are typically slightly lower (by about 9-19%) than those by Kwok et al. but considerably higher than in the uncorrected NSIDC data (about 26%, see above). We used these differences between the data sets to estimate the uncertainties induced by sea-ice drift on the sea-ice freshwater transport (Δ u; Extended Data Tables 1, 2). First, we recomputed all of the fluxes by correcting the original NSIDC data with correction factors derived from the Kwok et al. data (1.82 or 45% for the zonal drift, and 1.55 or 35% for the meridional drift) instead of the buoy-derived correction factor. In this way, we also accounted for an uncertainty in the drift direction. Then we averaged the deviations between our best estimate and the estimate based on Kwok et al. 35,36 with those between our best estimate and using the uncorrected and unfiltered NSIDC data. Uncertainties from sea-ice drift in the freshwater fluxes are about 20%. They contribute considerably to the final freshwater flux uncertainty and our trend uncertainties in all regions. Sea-ice-ocean freshwater flux. We estimated annual net sea-ice-ocean freshwater fluxes over the period 1982-2008 by calculating the local sea-ice volume change and divergence 8,53 . From this we derived the local freshwater fluxes F (m 3 s −1 ) from the sea ice to the ocean due to freezing and melting on a daily basis through a mass balance: where the four variables c, h, u and A denote the sea-ice concentration, thickness, drift velocity and grid-cell area, respectively. The factor C fw converts the sea-ice volume flux to a freshwater equivalent 54 : Here, ρ ice , s ice , s sw and ρ fw are the sea-ice density (925 kg m −3 ) 55 , the sea-ice salinity (6 g kg −1 ) 56 , the reference seawater salinity (34.7 g kg −1 ) 28 and the freshwater density (1,000 kg m −3 ), respectively. The annual sea-ice freshwater fluxes were computed from the daily fluxes from March to February of the next year (that is, March 1982 to February 2009), which correspond to the annual freezing and melting cycle of sea ice in the Southern Ocean 53 . Remaining imbalances between, for example, the open and coastal ocean of the Atlantic sector (Extended Data Tables 1, 2) are due to multiyear sea ice in the coastal region. We performed all of the calculations on the grid of the sea-ice drift data 26 and averaged all data products over 3 × 3 grid boxes, resulting in a nominal resolution of 75 km. To obtain the zero freshwater flux contour line, we averaged the climatological fluxes over 9 × 9 grid boxes. To estimate the melting and freezing fluxes, we separately summed up the positive and negative daily fluxes over a year (Fig. 4a, b). As temporal fluctuations accumulate when only adding positive or negative values, noise can lead to an overestimation of these fluxes. Each of the sea-ice variables (c, h and u) were therefore low-pass filtered using a 21-d running mean. Sea-ice freshwater transport. The total northward sea-ice volume transport (in m 3 s −1 ) between the coastal and open ocean regions equals the spatial integral of the divergence term in equation (1) in either of the two regions (by Gauss's theorem). We chose the open ocean region because there is considerable zonal exchange between the Indian Ocean and Atlantic sectors (Fig. 2a) in the coastal region, influencing the sector-based estimates. In the open ocean, this effect is negligible. We used this approach for the reported transport estimates (Extended Data Tables 1-3 and Extended Data Fig. 5a-c).
To demonstrate that our main findings are robust on the basin scale, and not influenced by small-scale noise and local uncertainties, we also calculated the northward sea-ice freshwater transport across latitude bands at 69.5° S in the Atlantic sector and 71° S in the Pacific sector (Fig. 3). To this end, we averaged c n , h n and meridional drift (v n ) in 1° longitude segments (n) along these latitudes and calculated the local freshwater transport T n (m 3 s −1 ): n nn n n fw where Δ l n denotes the length of sectors n along the latitude bands. The combined annual northward freshwater transport of both sectors is 100 ± 30 mSv with an increase of 8 ± 5 mSv per decade over the period 1982-2008 (Extended Data Fig. 5d and Fig. 3). This compares well with the mean (120 ± 30 mSv) and trend (9 ± 5 mSv per decade) of our spatially integrated sea-ice-ocean fluxes in the Pacific and Atlantic (Extended Data Fig. 5b, c).
We calculated the spatial pattern of the sea-ice freshwater transport f (m 2 s −1 ) as displayed in Fig. 2a, c, according to: Time-series homogenization. Our analysis and earlier studies 9,57 revealed major temporal inhomogeneities in the NSIDC sea-ice drift data set at the transitions between satellite sensors (Extended Data Fig. 4). We argue that these temporal inhomogeneities are linked to the unavailability of the 85 GHz and 91 GHz channels and sparser data coverage in the earlier years. The drift speed before 1982 seems to be underestimated, which is to some extent mitigated by AVHRR data thereafter. From 1982 to 1986, the drift speed is consistent but has a low bias. The drift ramps up in 1987, when the 85 GHz channels became available, and decreases again between 1989 and 1991, when these channels degraded 58 . A final sudden decrease occurs from 2005 to 2006 when 85 GHz data were not used. We used wind speed data over the sea ice from ERA-Interim 22 as an independent data source and scaled it to the sea-ice drift velocity for comparison (Extended Data Figs 4b). The scaling factor stems from the consistent years in the period 1988-2008 and varies in space and with the season 59,60 . This analysis supports our argument that the sea-ice drift speed is underestimated when the higher resolution 85/91 GHz channels were not available. We note that the meridional drift seems less sensitive to these inhomogeneities than the total drift, which might be related to higher data availability in the central sea-ice pack and is consistent with the lower biases found in the meridional sea-ice drift. Spurious increases in the sea-ice velocity would affect our estimated trends if they were not taken into account (Extended Data Figs 5, 6). Thus, we corrected the annual divergence (equation (1)) and lateral transport (equations (3), (4)) for the sensor-related temporal inconsistencies as follows. We excluded the inconsistent years (1980, 1981, 1987, 1989-1991, 2005 and 2006) from the analysis. To homogenize the years 1982-1986 with the years 1988-2008, that is, to remove the spurious trend in 1987, we first calculated linear regression lines before and after 1987 at each grid point. Then we added the differences between the end (1986) and start (1988) points of the regression lines to all years before 1987, that is, assuming a zero change in 1987. Fitting regressions before and after spurious jumps is a common procedure to homogenize climate data 61,62 . Here, we used a linear regression that serves the purpose of computing long-term trends in the time series.
To estimate the sensitivity of the trends in northwards sea-ice freshwater transport to the uncertainties associated with the offset correction before 1987 (shown in orange and green in Extended Data Fig. 5), we performed a Monte Carlo analysis by varying the offset and estimating the resulting trends. We generated 10,000 normally distributed offsets around our best guess (about 19 ± 5 mSv for the entire Southern Ocean; Extended Data Table 3). The standard deviation of this distribution was chosen to match the offset uncertainty that arises from the r.m.s. errors of the trends in each of the two time intervals : 1982-1986 and 1988-2008. For each of these generated offsets, we then estimated the trends and their significance (Extended Data Table 3). For both the entire Southern Ocean and the Pacific sector, all of the sampled offsets yield a positive northward sea-ice freshwater transport trend. All trends for the Pacific sector and 92% of those for the entire Southern Ocean are positive and at the same time significant at least at a 90% confidence level using Student's t-test. Thus, our trend results are insensitive to uncertainties in the applied homogenization at the 90% confidence level. The posterior uncertainty shows that the uncertainty associated with the offset has no noticeable effect on the total uncertainty range, that is, is smaller than ± 1 mSv per decade. Uncertainty estimation. The uncertainties of the local (grid-point-based) fluxes and timescales shorter than one year are probably large due to potential inconsistencies between the data sets on such scales and an amplification of the uncertainties by the spatial and temporal differentiations in equation (1). Integrating these terms in space and time greatly reduces these uncertainties (Extended Data Tables 1, 2). We estimated the uncertainties in our product that are associated with the underlying input variables c, h and u by using their observationally constrained ranges from different data sources, including the applied corrections and filtering as described. Additionally, we used an averaging period of 31 d (instead of 21 d) and, for trends only, an estimate without a running-mean filter, to obtain uncertainty estimates associated with temporal noise (Δ t). The results confirmed that the annual melting or freezing fluxes, are sensitive to the low-pass filtering, but not the net annual fluxes, as in the latter product the noise is averaged out. The sensitivity of the spatially integrated values to variations of the zero freshwater flux line is estimated by varying the smoothing radius from two to six grid boxes (Δ A). The uncertainty associated with the constant conversion factor (Δ C fw ; equation (2)) Letter reSeArCH is about 5% when using a realistic range of values 28,55,56 . For the trends only we computed the standard error of the slope from the variance of the residuals around the regression line (Δ s e ) 63 . The total uncertainty for both the climatological mean and the trends was estimated by calculating the r.m.s. of the individual contributions. This analysis shows that in the Atlantic and Indian Ocean sectors both the uncertainties in the climatology and trends (Extended Data Tables 1, 2) are dominated by uncertainties in the sea-ice thickness. In contrast, the uncertainty in the sea-ice drift dominates the uncertainty in the Pacific sector. We tested the significance of the trends with Student's t-test, accounting for the fact that only 21 out of 27 years were used and for a lag-1 autocorrelation 63 . To indicate the significance of the trends at grid-point level (Fig. 2c, d and Extended Data Fig. 6), at which the data uncertainties are unknown, the local r.m.s. of the variance of the residuals was artificially increased by 40%, approximately corresponding to our data uncertainty estimate in Extended Data Table 2. The quality of our data directly at the coastline and around the sea-ice edge is reduced due to the limited quality and quantity of the underlying observations in these regions. Sea-ice freshwater flux evaluation. A modelling study 27 carried out in parallel to this study calculated freshwater fluxes associated with sea-ice formation, melting and transport in the Southern Ocean State Estimate (SOSE). This model assimilates a large amount of observational data and optimizes the surface fluxes. They estimated an annual sea-ice-ocean freshwater flux due to sea-ice formation of − 360 mSv over the entire Southern Ocean, which is within our estimated range of − 410 ± 110 mSv. Moreover, they estimated that the combined annual sea-iceocean freshwater flux due to sea-ice and snow melting is about 500 mSv. Thus, in their estimate a total of 140 mSv of snow accumulated on the sea ice. Our estimates partly include snow accumulation on sea ice, because part of the sea-ice thickness results from snow-ice formation, which we estimated to be about − 50 mSv (section on sea-ice thickness). However, the snow layer on top of the sea ice is not included in our estimate of the freshwater flux due to sea-ice melting of 460 ± 100 mSv. In that study 27 , the authors estimate that the lateral sea-ice freshwater transport from the density class of the CDW to the AAIW and the SAMW amounts to 200 mSv in the period between 2005 and 2010. Their estimate slightly differs from our estimated transport from the coastal to the open ocean, which ranges between about 140 mSv and 160 mSv in 2007 and 2008 (Extended Data Fig. 5). The reasons might be the slightly different regions and that their estimate also includes the transport of the snow layer on top of the sea ice.
Given the reduced confidence in the local fluxes (for example, sea-ice production in coastal polynyas), it is reassuring that our data agree within our estimated range of uncertainty with previous estimates of mean fluxes for some larger coastal polynya regions 64,65 . Our confidence is higher for fluxes integrated over larger regions, such as the high-latitude Ross and Weddell seas (Extended Data Fig. 5e). Here our estimates are in close agreement with previous studies.
In the Ross Sea, we estimated that the northward transport from the coastal region across a flux gate between Land Bay and Cape Adare 36 (the turquoise area in Extended Data Fig. 5e) is 23 ± 5 mSv, increasing by about 30% (or + 7 ± 4 mSv) per decade in the period 1992-2008. On the basis of the same passive microwave data, but using a different algorithm for retrieving the sea-ice motion data, two studies 36,66 found a mean sea-ice area flux across this flux gate of about 1,000,000 km 2 between March and November in the periods 1992-2003 (ref. 36) and 1992-2008 (ref. 66), respectively. Using an approximated mean sea-ice thickness (0.6 m) 13,66 and the conversion factor (equation (2)), this corresponds to a mean northward freshwater transport of about 19 mSv. In close agreement with our estimate, these studies found an increase of 30% per decade (about + 6 mSv per decade). Another study 13 , using sea-ice motion from the Advanced Microwave Scanning Radiometer-EOS (AMSR-E), estimated that the mean seaice area flux between April and October (2003-2008) across the same flux gate is about 9.3 × 10 5 km 2 corresponding to a freshwater transport of about 23 mSv. Using the same data, but an alternative approach 67 , they found that the total sea-ice production in all of the Ross Sea polynyas together was about 737 km 3 between April and October (2003)(2004)(2005)(2006)(2007)(2008), corresponding to a sea-ice-ocean freshwater flux of − 31 mSv. This estimate is similar to the total production of about − 36 ± 7 mSv south of the flux gate in our data set, because most of the sea-ice production in this region occurs in the polynyas 13 . Using passive microwave data, the same study 13 found an increase of the production in the Ross Sea polynyas of 28% per decade between 1992 and 2008. A modelling study 68 found a net annual sea-ice-ocean freshwater flux due to melting and freezing of − 27 mSv on the continental shelf in the Ross Sea, which is in agreement with our estimate of − 23 ± 5 mSv. They also found a long-term (unquantified, see figure 9b in ref. 68) decrease in the net annual sea-ice-ocean freshwater flux over the Ross Sea continental shelf in the period 1963-2000, which is qualitatively in line with our results.
In the Weddell Sea, the northward sea-ice area flux across a flux gate close to the 1,000 m isobath (blue area in Extended Data Fig. 5e) has been found to be 5.2 × 10 5 km 2 on the basis of AMSR-E data between April and October (2003)(2004)(2005)(2006)(2007)(2008) 13 . Using an approximated mean sea-ice thickness (0.75 m) 13 and the conversion factor (2), this corresponds to a mean northward freshwater transport of about 16 mSv. This agrees well with our estimate of an annual northward transport of 16 ± 4 mSv for the same years and the same region. Similar to the Ross Sea, production in the major polynyas of the Weddell Sea was estimated 13 . However, in the Weddell Sea, a large fraction of the sea-ice transported across the flux gate is not produced in the coastal polynyas 13 ; thus we cannot directly compare our large-scale estimate to the sea-ice production in the polynyas. In the same study 13 , based on passive microwave data, they found a small, but insignificant long-term decrease in the sea-ice production in the Weddell Sea polynyas between 1992 and 2008, which is qualitatively consistent with our findings in the Atlantic sector. For a much larger area in the Weddell Sea, a modelling study 69 estimated an annual northward sea-ice freshwater transport of about 34 mSv and another observational study 70 , mostly based on moorings and wind speed, estimated that this flux is as large as about 38 ± 15 mSv. These estimates agree well with our finding of an annual northward freshwater transport of 41 ± 18 mSv across the 69.5° S latitude band, which is approximately their considered transect. Sea-ice freshwater transport based on ERA-Interim data. To support our findings, we quantified the changes in sea-ice motion that are induced by changes in geostrophic winds 59,60,70,71 from daily ERA-Interim 22 sea-level pressure and surface air temperature data. We averaged the data over 1° longitudinal segments along the previously defined latitude bands (Fig. 3), computed 21-d running means, and smoothed the data spatially over seven longitudinal bins. Then we calculated the sea-level pressure gradients along the latitude bands and used these together with the atmospheric surface density to estimate geostrophic winds normal to the latitude bands 59,71 . From these, we calculated the sea-ice drift speed using a drift-to-wind-speed ratio of 0.016, derived from drifting buoys in the central Weddell Sea 59,71 . This parameter is strongly variable in space and time, which is a major uncertainty in the resulting sea-ice drift. Nevertheless, it provides an average estimate for the mostly free drifting sea ice in the central Antarctic sea-ice pack 59,71 .
The resulting northward sea-ice freshwater transport (equation (3)) is independent in terms of the sea-ice drift but not in terms of the sea-ice concentration and thickness. We used anomalies (at each 1° increment) because the absolute values of the local transport are likely to be biased by the local influences of ocean currents and sea-ice properties. The resulting total annual anomalies of the northward sea-ice freshwater transport agree well in terms of the variability and longterm trend with the transport anomalies based on the satellite sea-ice drift data (+ 8 mSv per decade; Fig. 3). These estimates do not suffer from the temporal inhomogeneities that we identified in the satellite sea-ice drift data (see Methods section 'Time-series homogenization'). Sea-ice contribution to ocean salinity. We determined the evolution of ocean salinity s (g kg −1 ) in response to a given value of F (m 3 s −1 ) from a combination of mass and salt balances. The mass balance for a given well-mixed ocean surface box of volume V and density ρ reads: (5) in in fw out where Q in and Q out (m 3 s −1 ) are the volume fluxes of seawater in and out of the box, ρ in (kg m −3 ) is the respective density. In a steady state, equation (5) yields: in in out fw The corresponding salt balance reads: in in in out We assumed the same constant source water salinity s in = s sw and ρ fw as in equation (2) and used a constant reference density (ρ = 1,027 kg m −3 ). Moreover, we used the formation rate of the modified water mass as the volume flux of seawater out of the surface box (Q out = Q). Then, substituting equation (6) into equation (7) yields: In a steady state, this results in an equation that describes the modified salinity s as follows: fw sw Using s = s sw + Δ s, where Δ s is the difference in salinity between the source and modified water masses, equation (9) reduces to: fw sw

Letter reSeArCH
We used net water-mass formation rates (Q) of 29 Sv for formation of the AABW from the CDW and 13 Sv for the formation of the AAIW/SAMW from the CDW 28 . Figure 1a illustrates the results and shows the zonal mean ocean salinity and density distribution 72 for comparison.
Assuming that + 130 ± 30 mSv of freshwater enter the CDW through northward sea-ice freshwater transport, the salinity modification between the CDW and AAIW/SAMW (using equation (10)) is − 0.33 ± 0.09 g kg −1 . The uncertainty includes a ± 2 Sv uncertainty in the water-mass formation rate. In observations, the salinity difference between the CDW and the AAIW and SAMW ranges from about − 0.3 g kg −1 to − 0.5 g kg −1 (ref. 28). Thus, northward freshwater transport by sea-ice could explain the majority of the salinity modification, consistent with very recent findings 27 and a mixed-layer salinity budget 73 .
Similarly, we calculated the contribution of − 130 ± 30 mSv of freshwater removed from coastal regions due to northward sea-ice transport to the salinity modification (using equation (10)) between the CDW and AABW, obtaining an increase of + 0.15 ± 0.06 g kg −1 . The uncertainty includes a ± 7 Sv uncertainty in the AABW formation. However, the observed salinity differences between the CDW and AABW are generally small or even of opposite sign 74 . This is the result of a compensating effect between a sea-ice-driven salinification and a freshening from glacial and atmospheric freshwater. The freshwater fluxes from land ice through basal and iceberg melting are about + 46 ± 6 mSv and + 42 ± 5 mSv, respectively 75 . Assuming that roughly 60% of the icebergs melt in the coastal regions 76 , a total of about + 70 mSv are added from the land ice to the coastal ocean, corresponding to a freshening of about − 0.08 g kg −1 or a compensation of the sea-ice freshwater flux of about 55% in the AABW. We estimated from the ERA-Interim atmospheric reanalysis data 22 that the net atmospheric freshwater flux in the coastal region is about + 80 mSv, corresponding to a freshening of about − 0.09 g kg −1 . The resulting net salinity change in coastal waters from sea-ice, atmospheric and land-ice freshwater fluxes is almost zero (− 0.02 g kg −1 ). Such a compensation of the freshwater fluxes in coastal regions was noticed previously 69,77 . We note that large regional variations of these fluxes have been reported 75,78 .
To estimate the temporal salinity changes at the surface and in the newly formed AAIW and SAMW, we assumed a constant value of Q and that the freshwater flux and ocean salinity consist of a climatological value plus a time-dependent perturbation ( + ′ F F and + ′ s s , respectively). Equation (8)  As the climatological fluxes are in steady state, the first three terms on the right side in equation (11) cancel according to equation (9), resulting in: fw sw We approximated the freshwater flux perturbation (F' = at) using our estimated trend a, and rearranged the terms resulting in a first-order linear differential equation: fw sw Integration in time yields an expression for the time-dependent evolution of the salinity perturbation: To obtain an estimate of the salinity trend at a given time t, we substituted equation (14) into equation (13) as follows: The equilibrium response of the system, that is, the long-term trend after several years of perturbation, is: Using our estimated sea-ice freshwater transport trend (a) of + 9 ± 5 mSv per decade and an AAIW/SAMW water-mass formation rate as above, we obtained an equilibrium freshening rate of − 0.023 ± 0.014 g kg −1 per decade (green in Extended Data Fig. 7b), which is valid for sufficiently large values of Qt/V. Fig. 7b (in purple and blue; using equation (14)) shows that if we assumed that the trend started in 1982, there would be a delayed response lowering the mean salinity trend estimate depending on V. We thus tested the sensitivity of the trend to V, which corresponds to the upper 150 m between the zero sea-iceocean freshwater flux line and the Subantarctic Front 79 (Extended Data Fig. 7a), which is the source region of the AAIW. The circumpolar V of about 5 × 10 6 km 3 results in a mean salinity trend (using equation (14)) of − 0.014 ± 0.008 g kg −1 per decade between 1982 and 2008 (purple). However, the AAIW formation does not occur in a circumpolar belt but mostly in the south-eastern Pacific and north-western Atlantic, that is, on either side of Drake Passage [80][81][82][83][84] . Assuming that most of the water is modified in this region and further downstream in the South Pacific 80,82,84 , we estimated a second, somewhat smaller V of about 2 × 10 6 km 3 (shown in blue). The sea-ice freshwater transport trend into this reference volume is about + 8 ± 5 mSv per decade (Figs 2c, d), resulting in a mean salinity trend (using equation (14)) of − 0.018 ± 0.010 g kg −1 per decade (blue); because a certain amount of freshwater is transported eastwards out of this sector (blue), the mean trend of the delayed response lies somewhere in between the estimates based on the two different reference volumes (blue and purple).

Extended Data
It is unlikely that the trend started exactly in 1982. Thus, the actual salinity response will fall between our estimated delayed response and the equilibrium response. For the range of values above, the deviations in the freshening rate due to effects of a delay and variations in the reference volume are much smaller than the actual magnitude of the trend itself. We thus conclude that the overall mean freshening rate of the newly formed AAIW and the surface waters advected northwards across the Subantarctic Front into the SAMW due to the changes in sea-ice freshwater transport is about − 0.02 ± 0.01 g kg −1 per decade (Fig. 1b). Data deposition. Sea-ice freshwater fluxes leading to the main conclusions are publicly available (http://dx.doi.org/10.16904/8). Other presented data are available from the corresponding author upon request. Code availability. Climate Data Operators (CDO; version 1.6.8) used for part of the analysis is publicly available (http://www.mpimet.mpg.de/cdo). Other analytical scripts are available upon request from the corresponding author.