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### Data source

We used high-quality top-to-bottom hydrographic observations in the AAB from the 1990s until 2019. The continental slopes of five sections at 170° E, 150° E, 140° E, 115° E, and 80° E were studied (Supplementary Table S1). The R/V Kaiyo-maru, Fisheries Agency of Japan, conducted a research cruise over 80°–150° E in the AAB, in the proximity of its seasonal ice edge, from December 2018 to March 2019. Previously in 1996, this part of the AAB was observed simultaneously by the R/V Aurora Australis^{21}. Data from the section 115° E is supplemented by data obtained by the Training and Research Vessel Umitaka-maru, Tokyo University of Marine Science and Technology, obtained in 2015. CTD data from the WOCE Hydrographic Program (WHP) repeat and nearby sections from the 1990s are also compiled. A total of 20 cruises in the austral summer from December to March were used. The year in the text denotes the new year of the season (i.e. the cruise that took place during December 2018–March 2019 is treated as 2019). The data were collected according to the WHP/GO-SHIP standards^{30}.

Data were selected for the five sections on the continental slope with a depth range of 2,500–4,000 m. Since the deepest depth was around 3,000 m along the 170° E section, data were selected from the depth range of 2,500–3,000 m.

Although the overall sampling interval is not homogeneous, all sections (except 80° E and 170° E) covered CTD data in the 1990s, 2000s and former/latter pentads of the 2010s. Data along 170° E separate the former and latter half of the 2010s, although the section was visited only three times in total. Data along 80° E were not sampled in the early 2010s. In the 1970s, historical cruises by R/V Eltanin are supplemented for the four sections spanning from 80° E to 150° E.

### Data processing

We constructed time series for AABW properties for the five sections. The temporal sampling interval was not homogeneous among the sections as described above. To filter out the variability with time scales of a few years, station data were averaged within five periods (I. 1969–1971, II. 1990–1999, III. 2000–2009, IV. 2010–2015, and V. 2016–2019) in calculating the density layer thickness (Fig. 4) and freshwater content change (Fig. 5). The duration is represented by the central time in each period.

We estimated the freshwater flux per unit area *V*_{fw} by a standard method^{5}. Initially, a water column on a unit area and a height *H*_{1} has a salinity *S*_{1}. After adding a freshwater *V*_{fw} over a period *dt* at the surface and mixing, the column increased in height to become *H*_{2} and a salinity *S*_{2}. Since the salt content is conserved,

$$ V_{fw} = (H_{2} – H_{1} ) / dt = left( {frac{{S_{1} }}{{S_{2} }} – 1} right)H_{1} / dt, $$

where we neglected the small change in density. In Fig. 5, *V*_{fw} for 1990–2015 was calculated by the salinity trend between the second and fourth periods, and *V*_{fw} for 2010–2019 was calculated by the trend between the fourth and fifth periods (for 80° E, the lacking fourth period was substituted by the third period).

The estimate was derived for the layer thickness *H*_{1} (300 dbar) at the bottom. Using the mean and standard deviation of salinity estimate in each period, 1,000 random sets of salinity time series were artificially generated. The mean and standard deviation of V_{fw} was then estimated from the 1,000 datasets. An estimate of total freshwater flux over the domain was calculated by integrating V_{fw} in zonal direction and then multiplied by 200 km, which roughly corresponds to the meridional distance between the 2,500 and 4,000 m isobaths on the continental slope.

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