Ventilation of the abyss in the Atlantic sector of the Southern Ocean

The Atlantic sector of the Southern Ocean is the world’s main production site of Antarctic Bottom Water, a water-mass that is ventilated at the ocean surface before sinking and entraining older water-masses—ultimately replenishing the abyssal global ocean. In recent decades, numerous attempts at estimating the rates of ventilation and overturning of Antarctic Bottom Water in this region have led to a strikingly broad range of results, with water transport-based calculations (8.4–9.7 Sv) yielding larger rates than tracer-based estimates (3.7–4.9 Sv). Here, we reconcile these conflicting views by integrating transport- and tracer-based estimates within a common analytical framework, in which bottom water formation processes are explicitly quantified. We show that the layer of Antarctic Bottom Water denser than 28.36 kg m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-3}$$\end{document}-3 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma _{n}$$\end{document}γn is exported northward at a rate of 8.4 ± 0.7 Sv, composed of 4.5 ± 0.3 Sv of well-ventilated Dense Shelf Water, and 3.9 ± 0.5 Sv of old Circumpolar Deep Water entrained into cascading plumes. The majority, but not all, of the Dense Shelf Water (3.4 ± 0.6 Sv) is generated on the continental shelves of the Weddell Sea. Only 55% of AABW exported from the region is well ventilated and thus draws down heat and carbon into the deep ocean. Our findings unify traditionally contrasting views of Antarctic Bottom Water production in the Atlantic sector, and define a baseline, process-discerning target for its realistic representation in climate models.

saturation level from other works 4,5 ). This is in agreement with our estimate of local Weddell-sourced AABW production of 7.3 ± 0.9 Sv, which is itself consistent with previous estimates from mass-balance calculations.

Supplementary Note 2: Comparison of DSW characteristics from the Larsen continental shelf and Filchner Depression
Multiple lines of evidence obtained downstream of the Larsen continental shelf show DSW formation that contributes to the Weddell-sourced AABW 5,9,10 . In this paper, we assume that the characteristics of DSW acquired in the Filchner Depression sector of the Weddell Sea are a good representation of all DSW of the southern and western shelves of the Weddell Sea. This assumption appears rasonable when gathering the limited DSW characteristics abtained from observations (available from: https://doi.pangaea.de/10.1594/PANGAEA.729699) on the continental slope directly downstream of the Larsen continental shelf 11 (Suppl. Fig. 1A). The Θ-S A observations (Suppl. Fig. 1B) suggests that their characteristics are consistent with the observations of very cold water formed in interaction with Filchner-Ronne Ice Shelf, within the standard deviation of DSW found in the Filchner Depression.

Supplementary Note 3: Implications of interannual water-mass variability on our assumptions and results
Since the early 1990s to 2014, Antarctic Bottom Water (AABW) has freshened, warmed and declined in volume in the Atlantic sector of the Southern Ocean [12][13][14] . Abrahamsen et al. 15 indicate that the volume reduction reflects low-frequency variability in the Weddell system, with a recent increase of the AABW supply to the Atlantic Ocean. Here we assess the extent to which such temporal variability may impact our results, which implicitly adopt a steady-state assumption with respect to water-mass sources and production. Temporal variability could affect our results in three ways: (i) our definition of water-mass endmembers that uses invariant characteristics; (ii) our decomposition of the observed water-parcels into the percentage contributions of the different water-mass endmembers; (iii) our transport estimates which are computed for the period 2008 to 2010 rather than the period of the complete observational record.
Issues (i) and (ii) are both linked to our assumption of fixed water-mass endmember characteristics, applied to a decomposition of water-parcels observed over a large time span. To address this issue, we have ascribed conservatively large error bars on our water-mass endmembers properties, so that these error bars encompass the spatio-temporal variability identified over the region and period of our measurements. These error bars are computed from our dataset spanning more than 40 years. To address the possibility that the variability might be larger than that captured by the relatively sparse δ 18 O dataset, we compare our Θ-S A dataset. Suppl. Fig. 2A shows the locations of historical Θ and S A profiles in the region. Θ-S A diagrams per decade (Suppl. Fig.   2B-F) show that in each decade water-masses as defined in this full historical dataset consistently lie within the error bars of our specified water-mass endmember characteristics. We do not have access to further independent and reliable δ 18 O observations that we could use to cross-examine our water-mass definition procedure. Furthermore, using this available dataset to produce Θ-S A diagrams with δ 18 O in color per decades, Suppl. Fig. 3B-F show that while there is some variability within our specified water-mass endmember characteristics and associated error bars, the decadal variability in δ 18 O within each water-mass is much lower than the δ 18 O contrast between water-masses. The standard deviations of δ 18 O across five decadal means (representative of decadal-scale variability) is 0.02‰ for CDW, 0.06‰ for WW, and 0.03‰ for DSW; much lower than the mean δ 18 O

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contrast between the water masses isotopic composition (i.e. 0.04‰ for CDW, -0.35‰ for WW, and -0.51‰ for DSW; see Methods section). In addition, the standard deviation of δ 18 O across the five decadal means is encompassed by the δ 18 O standard deviation used in each water-mass definition (i.e. ± 0.03‰ for CDW, ± 0.07‰ for WW, and ± 0.08‰ for DSW; see Methods section). The slight variability of CDW properties for some decades is indicative of a sampling variability. However, the few observations lying outside of our determined error range of CDW properties (mostly saltier and warmer observations than our definition) remained sparse and the computed error bars cover the majority of this variability. We note nevertheless that bias in our defined CDW properties or on its associated error range caused by uneven sampling, could potentially affect our results on fractions. The sensitivity tests done over the relatively wide error range that we chose for each water-mass however demonstrate that our overall conclusions are robust to such kind of errors on water-mass definition.
Item (iii) directly links to the transport estimates, such that a long-term trend in transport could affect mass-balance diagnostics if a large time span is considered. However, any long-term change in the transport as described earlier 12,13,15 would not affect our estimates, because the inverse calculation is performed using observations spanning only the period 2008 to 2010. Our estimate is therefore not representative of a long-term mean (which would be affected by a long-term trend), but representative of a 2008-2010 mean, and the effects of temporal variability within that period are accounted for in the uncertainty estimates generated by the inversion. Further details on the transport estimates and their errors can be found in the previously published work of Jullion et al. 8 .
We are therefore confident that our water-mass definition approach provides a robust representation of the long-term climatological mean state of our study region, and that it is thereby appropriate to decompose observed water-parcel characteristics into endmember fractions.

Supplementary Note 4: Volumetric temperature-salitiny census of the Weddell gyre
We here investigate how much a simple linear combination of three endmembers can explain the full variety of water-masses temperature-salinity characteristics present in the Weddell Sea. To this end we produce a volumetric census of the Weddell gyre in temperature-salinity space using a state of the art ocean climatology (Suppl. Fig. 4A; source data available from: https://www.nodc.noaa.gov/OC5/woa18/woa18data.html). We then superimpose the polygon formed by our three endmembers characteristics and the error bars, which represent the temperature-salinity domain that is mathematically possible to explain from linear combination of our three endmembers (Suppl. Fig. 4B). This polygon covers about 96% of the total volume of the gyre domain. Further, the remaining 4% of waters that lay away from the polygon formed by our three endmembers characteristics and the error bars are mostly in the near-surface layer which is not investigated in our paper.

Supplementary Note 5: Diapycnal mixing deduction in the deep-ocean water-masses
Diapycnal entrainment of CDW into the DSW plumes is expressed in this paper as a volume flux. Assuming that this entrainment occurs evenly over the continental slope, between the 600 m and 3000 m bathymetry contours from the Filchner Depression to the Antarctic Peninsula (Suppl. Fig. 5A), we can estimate a mean diapyncal velocity w, by dividing the volume flux by the total area of 240 x 10 3 km 2 , represented as the red area in Suppl. Fig. 5A. On a one-dimensional assumption where we would only consider the vertical dimension, the diapycnal velocity relates the vertical diffusivity, κ, through the simple advection-diffusion 4/18 equation: We can therefore further estimate a mean vertical diffusivity associated with our estimated diapycnal entrainment of CDW.
We do that by computing the gradient and curvature of a mean neutral density profile (γ n ) over the western continental slope of the Weddell Sea 9 at 28.36 kg m −3 γ n (Suppl. Fig. 5B). κ is then derived from Eq. 1. The seawater samples at BGS are analyzed using an IRMS and equilibration method for oxygen isotopes, and do not include analyzer-dependent "sea salt effect" correction. An inter-laboratory comparison between BGS and LOCEAN 16 evaluated the effect of the sea salt on the measurements using equilibration method with IRMS and CRDS techniques. They reveal that the correction associated to measurements carried out with IRMS can differ between labs and estimate that a correction of -0.07‰ for δ 18 O should be applied for a seawater at salinity ∼35 g kg −1 for BGS.

Supplementary
During the 2017 WAPITI expedition in the Weddell Sea, samples for water isotopes along the repeated A23 section, located at 30 • W across the western Weddell gyre between Orkney Passage and the South Sandwich Trench, were duplicated (Suppl.  Fig. 6B). We however do observe a mean offset of about 0.09 ± 0.04‰ (Suppl. Fig. 6C, BGS being higher than LOCEAN). The standard deviation of the differences between the two datasets is ∼0.04‰, which seems reasonable given the errors associated with both datasets (∼0.04‰ for BGS; ∼0.04-0.06‰ for LOCEAN). Given the offset and the comparison study of Benetti et al. 16 , we applied an offset of -0.07‰ to the BGS dataset to homogenize the δ 18 O datasets between LOCEAN and BGS.
In addition to this general offset, we applied further quality control to the BGS datasets. In particular, we identified an offset (Suppl. Fig. 7A,B) between the most recent analysis performed at BGS (post 2016), and the previous ones (2008-2010) run on a different mass spectrometer. When restricting the comparison to overlapping regions (Suppl. Fig. 7C), therefore minimizing the potential influence of regional variability, the offset is still present. Now, looking at this difference in δ 18 O-γ n space (Suppl. Fig. 7D), the offset appears very consistent over a wide range of densities greater than 28 kg m −3 γ n (Suppl. Fig. 7D). Neutral densities greater than 28 kg m −3 γ n encompass water-masses with very different time-scales of ventilation going from tens of years (bottom waters), to hundred of years (CDW). Therefore, if the observed offset in δ 18 O was physical and due to temporal variability, we would expect that the difference of δ  Fig. 8A). Suppl. Fig. 8B represents the observations limited in neutral densities greater than 28 kg m −3 γ n where slight variabilities have likely a spatial explanation due to a high mixing behavior of water-masses flowing along the continental slope. Furthermore, in the δ 18 O-γ n space all datasets appear to be consistent (Suppl. Fig. 8C).

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The mean difference for each historical dataset related to 2017 is reported in Suppl. Fig. 8D and then each offset in the neutral density range 28.15-28.3 kg m −3 γ n (as well as dashed lines in Suppl. Fig. 8D), as it corresponds to a water-mass layer that is least variable on timescales of hundreds of years (CDW). Based on the calculation, each offset falls within the instrumental error (i.e for LOCEAN ∼0.06‰). We therefore applied no offset correction to these historical datasets, before using them in combination with the other observations.

Supplementary Note 7: Accuracy of tracer characteristics prediction using our source constituents decomposition
In order to evaluate the overall accuracy of our decomposition method, we examine what would be the prediction of the decomposition used in this study in terms of the conservative temperature and dissolved oxygen content. The prediction is then compared to the actual measurements of both tracers. Suppl. Fig. 9 shows histograms of calculated values minus measured ones as well as percentages for dissolved oxygen (Suppl. Fig. 9A-C) and conservative temperature (Suppl. Fig.   9B-D). The comparison is only done for water-masses denser than 28 kg m −3 γ n , which is the focus of this study. Dissolved oxygen prediction is within 15 µmol kg −1 (red line as median value on Suppl. Fig. 9A) of the observed value. Given observed dissolved oxygen ranges from ∼184 to 328 µmol kg −1 , the decomposition allows for a prediction with an accuracy of 10% of this range (red line as median value on Suppl. Fig. 9C). Conservative temperature prediction is within 0.2 • C (red line as median value on Suppl. Fig. 9B) of the observed value. Given observed conservative temperature ranges from ∼ -2.3 to 1.93 • C, the decomposition allows for a prediction with an accuracy of 5% this range (red line as median value on Suppl. Fig. 9D).

Supplementary Note 8: Error estimation of the transport calculation
Error estimation of the transport calculation is from the 80% confidence range of a Monte-Carlo experiment repeating 1000 times of the transport calculation in the main text. In addition, here we examine the error propagated mathematically. From error propagation theory, one can write the covariance of transport T across the ANDREX/I06S section in terms of covariance 6/18 of f k, j the fraction of the "source" water mass estimated at station j, level k and u k, j the corresponding adjusted geostrophic velocity from Jullion et al. 8 (A k, j , the area defined by vertical spacing and station spacing, has no associated error): cov(T ) = J cov(C) J T (2) with: Assuming that errors in fractions and velocity have no spatial correlation, one can write: cov( f k, j ) = Diag(ε 2 f k, j ), and cov(u k, j ) = Diag(ε 2 u k, j ), where Diag is a diagonal matrix. By combining these terms in Eq. 2, we find that the error on the Transport T (total and for each water-mass endmember, Suppl. Fig. 10), expressed as its standard deviation, std(T), is: with: cov(T ) = n ∑ k m ∑ j ε f k, j × u k, j × A k, j 2 + f k, j × ε u k, j × A k, j 2 (4)