Three-dimensional reconstruction of glacier-derived freshwater in East Antarctica using an end-member-independent hydrographic parameterization

Abstract

The melting of the Antarctic Ice Sheet contributes to global sea-level rise and widespread ocean freshening. A major driver of this process is the intrusion of warm deep water onto the continental shelf, which enhances basal melting of ice shelves and weakens their buttressing of inland ice. However, the three-dimensional distribution of glacier-derived freshwater remains poorly constrained in East Antarctica. Here we present a hybrid multiple linear regression–neural network (MLR–NN) framework that reconstructs glacier-derived freshwater from dissolved inorganic carbon (DIC) residuals without prescribing fixed freshwater end-member compositions. Applying this framework to hydrographic observations around the Totten and Moscow University Ice Shelves, we estimate freshwater discharge rates of 70 ± 7 and 53 ± 9 Gt yr⁻¹, respectively. The reconstructed freshwater signal extends across the continental shelf to approximately 64°S. We also identify differences in freshwater discharge between observations collected during the 2010s and the 2020 s, although sparse temporal sampling prevents these differences from being interpreted as a robust long-term trend. Our results provide a three-dimensional observational reconstruction of glacier-derived freshwater in this sector of East Antarctica and demonstrate the potential of an end-member-independent hydrographic parameterization for investigating glacier–ocean interactions in data-limited polar environments.

Glacier-derived freshwater in East Antarctica is reconstructed using an end-member-independent approach, revealing its three-dimensional distribution and estimating freshwater discharge from two major ice shelves.

Introduction

The Antarctic Ice Sheet contains approximately 70% of Earth’s freshwater, equivalent to about 58 m of global mean sea-level rise if fully melted¹. Under ongoing global warming, the Antarctic Ice Sheet has been losing mass at an accelerating rate². Recent studies have documented substantial mass loss, particularly in West Antarctica and the Antarctic Peninsula, driven largely by the thinning and retreat of outlet glaciers and ice shelves in response to oceanic and atmospheric warming^2–4. Consequently, Antarctica’s contribution to global sea-level rise has increased markedly since the 2010s, highlighting its growing importance in future sea-level projections^3,5–7.

A key focus of recent research has been the direct interaction between the Antarctic Ice Sheet and the surrounding ocean, particularly the intrusion of warm Circumpolar Deep Water (CDW) onto the continental shelf and its role in enhancing basal melting beneath ice shelves^8–13 (Fig. 1). Ocean-driven ice-shelf thinning can reduce buttressing and promote grounding-line retreat, thereby accelerating ice discharge from the ice sheet. Although recent advances in high-resolution, physics-based ice-sheet models coupled with climate models have improved the representation of observed Antarctic ice-sheet changes, substantial uncertainties remain in projections beyond the mid-twenty-first century¹⁴.

Fig. 1. Conceptual schematic illustrating the framework used to estimate glacier-derived freshwater from dissolved inorganic carbon (DIC).

In the Southern Ocean (south of 30°S), the region south of 60°S with a seafloor depth shallower than 1500 m is defined as the coastal Southern Ocean (SO_coastal), whereas the remaining area is defined as the open Southern Ocean (SO_open). In the absence of glacier-derived freshwater input, seawater in SO_coastal is assumed to originate from SO_open, such that DIC_int = DIC_open. Warm modified Circumpolar Deep Water (mCDW) flows southward from SO_open into ice-shelf cavities within SO_coastal, where it induces basal melting and releases glacier-derived freshwater. The resulting freshwater-enriched mCDW becomes more buoyant and rises toward the ocean surface, while freshwater derived from glacier surface melting is simultaneously incorporated into the water column (DIC_fw; light-blue arrows). Mixing between glacier-derived freshwater and the initial seawater modifies the DIC concentration to DIC_coastal, which represents the mixture of DIC_int and DIC_fw. Following Pan et al.⁷, DIC variations within the subsurface mCDW layer are assumed to be unaffected by sea-ice formation and melting. In the surface layer, where sea-ice formation/melting (SI) and evaporation/precipitation (EP) occur, their net effects are assumed to be equivalent between SO_open and SO_coastal and therefore cancel when estimating glacier-derived freshwater.

A major unresolved issue is the uncertainty in the mass balance of East Antarctica. East Antarctica, which contains most of the Antarctic ice, exhibits substantial regional variability in ice-sheet change, and uncertainties remain in estimates of its overall mass balance^15,16. Sparse observations, uncertainties in subglacial bedrock topography, and complex glaciological processes hinder accurate quantification, particularly because incomplete mapping beneath ice shelves and limited in situ ocean observations constrain model forcing and validation^7,17–20.

Totten and Moscow University Ice Shelves are major marine-based outlet glaciers draining the Aurora Subglacial Basin. Together, they contain ice equivalent to approximately 5.1 m of global mean sea-level rise and have experienced substantial ice-shelf thinning and enhanced basal melting associated with the intrusion of warm ocean waters^21–26. Their grounding lines are located well below sea level, making them susceptible to ocean-driven basal melting associated with intrusions of warm modified Circumpolar Deep Water (mCDW; neutral density range γⁿ = 28.00–28.27^27,28)^11,24,29,30. Satellite remote sensing and oceanographic observations have revealed thinning of the Totten Ice Shelf, grounding-line retreat, and enhanced basal melting associated with mCDW inflow^15,24,25. Numerical models have also advanced our understanding of ice-sheet–ocean interactions in this region, although uncertainties in basal topography and ocean heat transport remain substantial²⁰.

Quantifying glacier-derived ocean freshening remains challenging because of severe weather conditions in the Southern Ocean (SO; south of 30°S), limited observational coverage, and the lack of a systematic method for resolving the three-dimensional distribution of freshwater derived from glacier melting. Existing approaches have important limitations. Satellite observations are widely used to monitor ice-sheet mass balance and sea-level contribution^5,15,31, and basal melt rates can be inferred by subtracting surface ice discharge from total ice-sheet mass change³². However, satellite observations cannot directly resolve the spatial distribution of glacier-derived freshwater in the ocean. Numerical simulations of coupled ocean–sea ice–ice shelf systems provide valuable insight into ice–ocean interactions^20,29,33, but their ability to reconstruct ocean freshening is limited by uncertainties in physical and chemical observations, bathymetry, and model forcing¹¹. In situ observations using tracers such as salinity and oxygen isotopes (δ¹⁸O) can detect freshwater signals^16,34,35, and endmember approaches are commonly used to separate freshwater sources^13,29,36. However, water-mass endmembers vary in space and time, making them difficult to constrain and introducing substantial uncertainty. Repeated in situ observations are also logistically difficult in Antarctic environments and generally provide limited spatial and temporal coverage.

To address these limitations, recent studies have employed parameterization techniques that reconstruct biogeochemical properties from routinely observed hydrographic variables^7,37,38. In this framework, a target chemical property is statistically predicted from hydrographic parameters such as temperature (T), salinity (S), dissolved oxygen (DO), and pressure (Pr), which collectively reflect water-mass transport, mixing, and biogeochemical processes. Because these hydrographic variables capture dominant internal ocean processes, the parameterized concentration represents the component of the chemical property that can be explained by internal ocean dynamics. Any systematic difference between observed and parameterized concentrations can therefore be interpreted as the influence of external processes that are not explicitly represented by the hydrographic relationships.

In the Southern Ocean coastal region, glacier-derived freshwater input modifies seawater properties and carbon concentrations but is not directly represented by hydrographic parameterization. Consequently, by quantifying the residual between observed and parameterized dissolved inorganic carbon (DIC), the contribution of glacier-derived freshwater can be estimated without defining water-mass endmembers or imposing spatial constraints.

The fundamental concept of this parameterization framework is that the DIC concentrations can be represented as the sum of a component explained by hydrographic variables and a residual associated with external processes. Accordingly, the predicted DIC concentration (DIC_pred) is expressed as

$${\mathrm{DIC}}_{\mathrm{p}\mathrm{red}}\left(\mathrm{T},\mathrm{S},\mathrm{DO},\mathrm{Pr},\dots \right)={\mathrm{DIC}}_{\mathrm{in}}\left(\mathrm{T},\mathrm{S},\mathrm{DO},\mathrm{Pr},\dots .\right)+{\mathrm{DIC}}_{\mathrm{ex}}$$ 1

where DIC_in represents the component of DIC explained by internal ocean processes captured by the hydrographic variables, and DIC_ex represents the component associated with external processes that are not explicitly described by the parameterization. In this study, glacier-derived freshwater input is treated as the dominant external process contributing to DIC_ex in subsurface and deep waters influenced by mCDW. In surface waters, additional effects from sea-ice formation/melting and evaporation/precipitation are considered separately. The estimated DIC_ex is subsequently used to derive the glacier-derived freshwater fraction (F_g) through Eqs. (2)–(4).

In the present study, DIC is parameterized from hydrographic variables using a hybrid multiple linear regression–neural network (MLR–NN) framework. DIC was selected because it exhibits large spatial variability, high analytical precision, and strong sensitivity to freshwater inputs, allowing external perturbations to be detected from deviations between observed and parameterized concentrations. We applied this framework to hydrographic and biogeochemical observations from GLODAPv2.2023 and the Japan Antarctic Research Expedition (JARE) around the Totten and Moscow University Ice Shelves. Using this approach, we reconstructed the three-dimensional distribution of glacier-derived freshwater, estimated meltwater discharge rates, and evaluated recent changes in freshwater input to this sector of East Antarctica. Unlike conventional end-member mixing analyses, this framework estimates glacier-derived freshwater from DIC residuals without prescribing fixed freshwater end-member compositions or their spatial and temporal variability. This enables three-dimensional reconstruction of glacier-derived freshwater over broad regions of the Southern Ocean using routinely observed hydrographic variables.

Results

Freshwater from glacier melting in East Antarctica

We developed hybrid multiple linear regression–neural network (MLR–NN) parameterizations of dissolved inorganic carbon (DIC) for the open Southern Ocean (SO_open) and coastal Southern Ocean (SO_coastal) using temperature (T), salinity (S), pressure (Pr), and apparent oxygen utilization (AOU), defined as the difference between the dissolved oxygen concentration at air–sea equilibrium (DO_sat) and the observed dissolved oxygen concentration (DO_obs); that is, AOU = DO_sat − DO_obs.

The resulting analytical equations are presented below.

For the open Southern Ocean (SO_open; south of 30°S, bottom depth >1,500 m), the parameterization is expressed as

$${\mathrm{DIC}}_{\mathrm{open}}=2229+110.6\cdot {\mathrm{H}}_{\mathrm{o1}}+108.6\cdot {\mathrm{H}}_{\mathrm{o2}}+61.85\cdot {\mathrm{H}}_{\mathrm{o3}}{\mathrm{H}}_{\mathrm{o}1}=\tanh \left[0.5\left(\mathrm{-}6.808\times {10}^0\mathrm{-}1.432\times {10}^{-1}\cdot {\mathrm{T}}_{\mathrm{o}}+4.261\times {10}^{-2}\cdot {\mathrm{S}}_{\mathrm{o}}+2.317\times {10}^{-2}\cdot {\mathrm{AOU}}_{\mathrm{o}}+2.762\times {10}^{-4}\cdot {\mathrm{Pr}}_{\mathrm{o}}\right)\right]{\mathrm{H}}_{\mathrm{o}2}=\tanh \left[0.5\left(\mathrm{-}4.223\times {10}^1\mathrm{-}1.069\times {10}^{-1}\cdot {\mathrm{T}}_{\mathrm{o}}+1.241\times {10}^0\cdot {\mathrm{S}}_{\mathrm{o}}+6.598\times {10}^{-3}\cdot {\mathrm{AOU}}_{\mathrm{o}}+1.213\times {10}^{-4}\cdot {\mathrm{Pr}}_{\mathrm{o}}\right)\right]{\mathrm{H}}_{\mathrm{o}3}=\tanh \left[0.5\left(\mathrm{-}3.735\times {10}^1\mathrm{-}1.560\times {10}^{-1}\cdot {\mathrm{T}}_{\mathrm{o}}\mathrm{-}1.034\times {10}^0\cdot {\mathrm{S}}_{\mathrm{o}}+2.275\times {10}^{-3}\cdot {\mathrm{AOU}}_{\mathrm{o}}\mathrm{-}3.468\times {10}^{-4}\cdot {\mathrm{Pr}}_{\mathrm{o}}\right)\right]$$ 2

where H_o1, H_o2, H_o3 are the outputs of the three hidden nodes, and tanh(x) = (e^x – e^−x)/(e^x + e^−x) is the hyperbolic tangent activation function. The parameterization was developed using 53,565 observations and reproduced the observed DIC concentrations with high accuracy (R² = 0.99; mean absolute deviation (MAD) = 3.81 µmol kg⁻¹). Model performance was evaluated using independent testing data and five-fold cross-validation. The agreement between predicted and observed DIC concentrations is shown in Supplementary Fig. S2.

For the coastal Southern Ocean (SO_coastal; south of 60°S, bottom depth ≤1500 m), the parameterization is expressed as

$${\mathrm{DIC}}_{\mathrm{coastal}}=2175+31.66\mathrm{\cdot }{\mathrm{H}}_{\mathrm{c}1}\mathrm{-}122.9\mathrm{\cdot }{\mathrm{H}}_{\mathrm{c}2}+34.27\mathrm{\cdot }{\mathrm{H}}_{\mathrm{c}3}{\mathrm{H}}_{\mathrm{c}1}=\tanh \left[0.5\left(2.644\times {10}^1+6.317\times {10}^{-1}\mathrm{\cdot }{\mathrm{T}}_{\mathrm{c}}\mathrm{-}6.873\times {10}^{-1}\mathrm{\cdot }{\mathrm{S}}_{\mathrm{c}}\mathrm{-}4.219\times {10}^{-2}\mathrm{\cdot }{\mathrm{AOU}}_{\mathrm{c}}+4.185\times {10}^{-4}\mathrm{\cdot }{\mathrm{Pr}}_{\mathrm{c}}\right)\right]{\mathrm{H}}_{\mathrm{c}2}=\tanh \left[0.5\left(4.137\times {10}^1+1.935\times {10}^{-1}\mathrm{\cdot }{\mathrm{T}}_{\mathrm{c}}\mathrm{-}1.180\times {10}^0\mathrm{\cdot }{\mathrm{S}}_{\mathrm{c}}\mathrm{-}1.454\times {10}^{-2}\mathrm{\cdot }{\mathrm{AOU}}_{\mathrm{c}}+1.404\times {10}^{-5}\mathrm{\cdot }{\mathrm{Pr}}_{\mathrm{c}}\right)\right]{\mathrm{H}}_{\mathrm{c}3}=\tanh \left[0.5\left(\mathrm{-}6.357\times {10}^1+1.684\times {10}^0\mathrm{\cdot }{\mathrm{T}}_{\mathrm{c}}+1.964\times {10}^0\mathrm{\cdot }{\mathrm{S}}_{\mathrm{c}}+7.100\times {10}^{-2}\mathrm{\cdot }{\mathrm{AOU}}_{\mathrm{c}}\mathrm{-}7.499\times {10}^{-4}\mathrm{\cdot }{\mathrm{Pr}}_{\mathrm{c}}\right)\right]$$ 3

where H_c1, H_c2, H_c3 are the outputs of the three hidden nodes. The coastal parameterization was developed using 3683 observations and also reproduced the observations with high accuracy (R² = 0.97; MAD = 3.71 µmol kg⁻¹). The agreement between predicted and observed DIC concentrations is likewise shown in Supplementary Fig. S2.

A similar framework was evaluated for total alkalinity (TA); however, DIC provided a wider applicable concentration range and higher predictive accuracy (Supplementary Fig. S3). DIC was therefore adopted for subsequent estimation of glacier-derived freshwater.

Using the parameterized DIC fields, the glacier-derived freshwater fraction (F_g) was estimated as

$${\mathrm{F}}_{\mathrm{g}}=\left({\mathrm{DIC}}_{\mathrm{int}}\mathrm{-}{\mathrm{DIC}}_{\mathrm{coastal}}\right)/{\mathrm{DIC}}_{\mathrm{int}}=\left({\mathrm{DIC}}_{\mathrm{open}}\mathrm{-}\left({\mathrm{DIC}}_{\mathrm{open}}+{\mathrm{DIC}}_{\mathrm{fw}}\right)\right)/{\mathrm{DIC}}_{\mathrm{open}}=-{\mathrm{DIC}}_{\mathrm{fw}}/{\mathrm{DIC}}_{\mathrm{open}}$$ 4

where DIC_int represents the initial DIC concentration of coastal seawater in the absence of glacier-derived freshwater input, approximated by DIC_open, and DIC_fw represents the DIC anomaly associated with glacier-derived freshwater. A positive F_g indicates glacier-derived freshwater input, whereas values close to zero or negative indicate little or no detectable glacier-derived freshwater signal within the uncertainty of the parameterization (Supplementary Fig. S4). Propagation of the DIC parameterization errors yielded an estimated uncertainty of approximately 24% in F_g.

Spatial distributions of freshwater from glacier melting in East Antarctica

We applied our parameterization framework to observational hydrographic data collected around the ice-shelf fronts of the Totten and Moscow University Ice Shelves in East Antarctica to reconstruct the spatiotemporal distribution of F_g during 2012–2024 (Figs. 2–4 and Supplementary Data 1).

Fig. 2. Representative vertical sections of the glacier-derived freshwater fraction (F_g) across East Antarctica.

Blue circles on the map indicate hydrographic observation stations occupied during 2012–2024 (Supplementary Data 1), and the yellow star indicates Mooring Station TM1, where the time-series observations shown in Fig. 4 were conducted. The common color scale is shown in the upper left. Black and blue symbols denote the uncorrected glacier-derived freshwater fraction (F_g) and the sea ice-corrected freshwater fraction [F_g(c)], respectively. The sea ice correction accounts for differences in sea-ice formation and melting (SI) between the open Southern Ocean (SO_open) and the coastal Southern Ocean (SO_coastal), assuming an annual SI ratio of 1:2^40,41. The correction is applied only to surface waters shallower than approximately 100 dbar, where low salinity and low temperature indicate the dominant influence of sea-ice melt³⁹.

Fig. 4. Time series of the glacier-derived freshwater fraction (F_g) and corresponding hydrographic properties at the front of the Totten Ice Shelf.

Time series of F_g together with pressure (Pr; dbar), temperature (T; °C), salinity (S; psu), and dissolved oxygen (DO; µmol kg⁻¹) measured at Mooring Station TM1 (116.5°E, 66.6°S) during 2022–2024. F_g was estimated by applying the hybrid MLR–NN DIC parameterization to the observed hydrographic properties. Data are shown for mooring depths of (a) 500 dbar, (b) 880 dbar, and (c) 1000 dbar.

In SO_coastal at the fronts of the Totten and Moscow University Ice Shelves within the Sabrina Depression, south of approximately 66°S, F_g generally exceeded 10‰ in surface waters shallower than approximately 100 dbar (Fig. 2; representative stations TN9, TN5, and TN26). This layer is characterized by low salinity and low temperature, reflecting freshwater input from sea-ice melt and icebergs³⁶, and is consistent with previous estimates of glacier-derived meltwater mixed with sea-ice-derived freshwater based on δ¹⁸O endmember calculations³⁹.

Between approximately 100 and 500 dbar, F_g was generally maintained at approximately 2‰, comparable to previous tracer-based estimates of glacier-derived meltwater in SO_coastal^34,39 (Fig. 3). In Vincennes Bay (~107°E, ~66°S), located west of the Sabrina Depression, vertical profiles of F_g below the surface layer were close to zero, differing from those observed near the Totten and Moscow University Ice Shelf fronts (Fig. 3, S5, S6, and Supplementary Data 1). In SO_open north of approximately 65°S, F_g showed only slightly positive values in surface waters shallower than 100 dbar and remained nearly zero below 100 dbar (Figs. 2, 3, and S5). The mean deep-water anomaly from zero in this region was 0.3‰ (Table S2), and the negligible F_g signals in regions and depth ranges with little direct glacier influence provide independent support for the validity of the parameterization-based F_g estimates.

Fig. 3. Horizontal distributions of the glacier-derived freshwater fraction (F_g, ‰) across East Antarctica reconstructed from hydrographic observations collected between 2012 and 2024.

a 0 dbar, b 50 dbar, c 100 dbar, d 200 dbar, e 300 dbar, f 400 dbar, g 500 dbar, h 600 dbar, i 700 dbar, and j 800 dbar. k Water-column-averaged sea ice-corrected freshwater fraction F_{g(c) ave}. (l) Ratio of F_{g(c) ave} to F_{g ave}, where the subscript “ave” denotes the average over the upper 1000 dbar of the water column. m Basal meltwater flux (R_m; Gt yr⁻¹). F_g in surface waters shallower than the layer of maximum temperature within the upper 100 dbar [(a)–(c)] was corrected for the influence of sea-ice formation and melting to derive F_g(c); the corresponding uncorrected F_g distributions are shown in Supplementary Fig. S5. R_m was estimated by multiplying F_{g(c) ave} by a representative transport of 1.0 Sv, corresponding to the median of the climatological transport range of 0.8–1.2 Sv for the clockwise on-shelf circulation associated with the westward-flowing Antarctic Slope Current, as derived from observation-constrained numerical simulations. This circulation transports warm modified Circumpolar Deep Water (mCDW) toward the Totten and Moscow University Ice Shelf fronts^20,29,30,42. n Locations of the hydrographic observation stations used in this study. These figures were generated using Ocean Data View version 5.8.3⁵⁷.

At mooring station TM1 (116.51°E, 66.60°S; bottom depth 1020 m), located near the front of the Totten Ice Shelf, mooring systems were deployed at 500, 880, and 1000 dbar from February 2022 to March 2024 to collect T, S, DO, and Pr data (Fig. 4). This mooring station is close to sampling stations TN9 and TN5 (Fig. 2 and Supplementary Data 1). Applying the hybrid MLR–NN DIC parameterizations to the TM1 mooring data yielded time series of F_g at the Totten Ice Shelf front (Fig. 4). Annual mean F_g values were 2.1 ± 0.4‰ at 1,000 dbar, 2.8 ± 0.4‰ at 880 dbar, and 2.0 ± 0.6‰ at 500 dbar, where uncertainties represent one standard deviation. Taken together, the hydrographic and mooring observations indicate that F_g increases toward shallower depths. These results are consistent with a pathway in which warm mCDW enters the cavity beneath the Totten Ice Shelf, induces basal melting, and produces meltwater-enriched seawater that becomes more buoyant and rises toward the surface through mixing^11,24,29 (Fig. 1, S7, and S8).

A caveat is that the hydrographic observations used here represent late-summer conditions, with offshore stations sampled in January and coastal stations sampled from late February to early March. These periods correspond to the end of the sea-ice melt season offshore and the period immediately before new sea-ice formation begins near the coast. Thus, shallow freshwater signals may include a peak seasonal contribution from sea-ice melt, particularly in low-salinity, low-temperature waters shallower than 100 dbar³⁶ (Fig. 2).

In this study, the initial estimate of F_g assumes that the net effects of sea-ice formation/melting (SI) and evaporation/precipitation (EP) are the same between SO_open and SO_coastal and therefore cancel in Eq. (4)⁷. However, if SI is larger in SO_coastal than in SO_open, F_g in the surface layer may be overestimated. Satellite-based estimates from the 2000s indicate that the annual ratio of SI between SO_open and SO_coastal is approximately 1:2, with longitudinal variability across East Antarctica reaching ~50%⁴⁰. A comparable ratio was independently derived within the Sabrina Depression from salinity deficits associated with sea-ice melt using approximately 25,000 spring hydrographic profiles collected between the mid-2000s and the 2020s, covering the same period as the observations analyzed in this study⁴¹. Based on this annual SO_open-to-SO_coastal SI ratio of approximately 1:2, we corrected F_g in surface waters shallower than the layer of maximum temperature within the upper 100 dbar by multiplying it by 0.5. The corrected freshwater fraction, F_g(c), is therefore defined as

$${\mathrm{F}}_{\mathrm{g}\left(\mathrm{c}\right)}={\mathrm{F}}_{\mathrm{g}}\times \left({\mathrm{SI}}_{\mathrm{open}}/{\mathrm{SI}}_{\mathrm{coastal}}\right),$$ 5

where SI_open/SI_coastal = 0.5. The corrected value, F_g(c), is interpreted as a conservative estimate of the glacier-derived freshwater fraction in the surface layer (Figs. 2, 3a–c, and S5; see Methods).

After this correction, F_g(c) in the surface layer of SO_coastal decreased to approximately half of F_g, reaching ~5‰ in waters characterized by low salinity and low temperature above ~100 dbar. The ratio of water-column-averaged F_g(c) to water-column-averaged F_g over 0–1000 dbar [F_{g(c) ave}/F_{g ave}] was 0.89 ± 0.11 in SO_coastal. In contrast, F_g(c) differed little from F_g in SO_open because no pronounced low-salinity, low-temperature layer was observed in the upper 100 dbar; the corresponding F_{g(c) ave}/F_{g ave} ratio was 0.97 ± 0.07 (Fig. 3l and Supplementary Data 1).

Discussion

Changes in freshwater input from the Totten and Moscow University Ice Shelves in East Antarctica

Water-column-averaged, sea ice-corrected F_g [F_{g(c) ave}] exceeded 2‰ at the fronts of the Totten and Moscow University Ice Shelves, decreased gradually offshore, and approached 0‰ near 64°S (Fig. 3k). This offshore decrease likely reflects dilution by mixing with surrounding seawater and/or the diminishing influence of meltwater and icebergs (Fig. 3a–g).

Observation-constrained numerical simulations²⁹, validated against hydrographic observations, satellite-derived circulation, and independent numerical models^20,30,42,43, indicate that the clockwise on-shelf circulation associated with the westward-flowing Antarctic Slope Current has a climatological transport of 0.8–1.2 Sv during 1991–2020. This circulation supplies warm modified Circumpolar Deep Water (mCDW) to the Totten and Moscow University Ice Shelf fronts. We therefore adopted the median value (1.0 Sv) as the representative climatological transport of this circulation for estimating glacier-derived freshwater discharge rates in the present study. Using the median transport rate of 1.0 Sv and multiplying it by mean F_{g(c) ave} values of 2.23 ± 0.21‰ in the Totten Ice Shelf region and 1.67 ± 0.28‰ in the Moscow University Ice Shelf region (Fig. 3 and Supplementary Data 1), we estimated freshwater formation rates from glacier melting, here defined as basal meltwater flux R_m, for the two ice-shelf front regions (Tables 1, 2).

Table 1.

Comparison of glacier-derived freshwater formation rates near the Totten and Moscow University Ice Shelves estimated in this study and previous studies

References	Method	Period	Location	Ice discharge (G-ton yr−1)
Totten Ice Shelf
This studya	MLR-NN based parametrization of DIC	2014–2022	Totten	70 ± 7
Rignot et al.44	Satellite data (steady state)		Totten	63 ± 4
Depoorter et al.45	Satellite data (steady state)		Totten	64 ± 12
Liu et al.46	Satellite data (unsteady state)	2005–2011	Totten	80 ± 5
Li et al.15	Satellite data and model	1979–2014	Totten	65 ± 4
Rignot et al.5	Satellite data (unsteady state)	2009–2017	Totten	71 ± 3
Adusumilli et al.31	Satellite data and model	1994–2018	Totten	64 ± 11
Davison et al.56	Satellite data and model	1997–2021	Totten	126 ± 242
Pelle et al.18	Ice sheet-ocean circulation coupling model	2017–2020	Totten	100 ± 20
Moscow University Ice Shelf
This studya	MLR-NN based parametrization of DIC	2014–2020	Moscow U.	53 ± 9
Rignot et al.5	Satellite data (unsteady state)	2009–2017	Moscow U.	47 ± 2
Davison et al.56	Satellite data and model	1997–2021	Moscow U.	61 ± 185

^aCalculated by multiplying the water-column-averaged sea ice-corrected freshwater fraction [F_{g(c) ave}] at the fronts of the Totten and Moscow University Ice Shelves by a representative transport of 1.0 Sv, corresponding to the median of the climatological transport range (0.8–1.2 Sv) of the clockwise on-shelf circulation associated with the westward-flowing Antarctic Slope Current, as derived from observation-constrained numerical simulations²⁹.

Table 2.

Comparison of water-column-averaged glacier-derived freshwater fractions (F_{g ave}, ‰) and basal meltwater fluxes (R_m) between the 2010s and the 2020s at the fronts of the Totten and Moscow University Ice Shelves in East Antarctica

Area	Station	Date	Fg (c) ave (‰)	Rm (G-ton yr−1)	Station	Date	Fg (c) ave (‰)	Rm (G-ton yr−1)	interval (yr)	Increase ratio (%)
Totten	0227947_34	2014/12/31	1.61	51	JARE_TN2	2018/03/07a	3.18a	100
	0227947_35	2015/01/01	1.05	33	JARE_TN5	2022/03/05	1.92	60
	0227947_36	2015/01/01	2.37	75	JARE_TN6	2022/03/05	1.82	57
	0227947_37	2015/01/01	2.45	77	JARE_TN7	2022/03/02	1.53	48
					JARE_TN9	2022/03/01	3.12	98
					JARE_TN10	2022/03/01	2.80	88
					JARE_TN34	2020/03/03	2.68	85
	average	2014/12/31	1.87	59		2021/04/24	2.44 (2.31)a	77 (73)	6.3	130 (108)a
	error		0.33	10			0.25	8		26
Moscow U.	0227947_12	2014/12/27	0.71	22	JARE_TN25	2019/12/19	2.13	67
	0227947_19	2014/12/27	1.55	49	JARE_TN26	2019/12/19	1.95	61
	0227947_53	2015/01/05	0.80	25	JARE_TN108	2020/03/05b	3.08b	97
	0227947_71	2015/01/05	1.15	36	JARE_TN109	2020/03/05b	2.00b	63
	average	2014/12/31	1.05	33		2020/01/26	2.29 (2.04)b	72	5.1	218(194)b
	error						0.27	8		46

Values are based on hydrographic observations collected during each period. R_m was estimated by multiplying the water-column-averaged sea ice-corrected freshwater fraction [F_{g(c) ave}] by a representative transport of 1.0 Sv, corresponding to the median of the climatological transport range (0.8–1.2 Sv) of the clockwise on-shelf circulation associated with the westward-flowing Antarctic Slope Current, as derived from observation-constrained numerical simulations²⁹. Errors represent standard errors.

^aValues in parentheses for the Totten Ice Shelf were obtained by reassigning station JARE_TN2 from the 2020s group to the 2010s group.

^bValues in parentheses for the Moscow University Ice Shelf were obtained after excluding stations JARE_TN108 and JARE_TN109, sampled in March, from the 2020s group.

The resulting R_m estimates are 70 ± 7 Gt yr⁻¹ for the Totten Ice Shelf front and 53 ± 9 Gt yr⁻¹ for the Moscow University Ice Shelf front. When the ±20% range in the climatological mean transport rate of the westward-flowing current is included (1.0 ± 0.2 Sv)^20,29,30,42, the corresponding uncertainties increase to 70 ± 16 Gt yr⁻¹ and 53 ± 14 Gt yr⁻¹, respectively. Within these uncertainties, our estimates are broadly consistent with previous satellite-based estimates of basal melt rates^{5,15,31,44–46} (Table 1). This agreement provides independent observational support for the applicability of our parameterization-based approach for estimating glacier-derived freshwater. Importantly, our method also resolves the spatial distribution of meltwater-derived ocean freshening, which extends offshore to around 64°S in East Antarctica (Fig. 3), a feature that is difficult to constrain directly using satellite observations or conventional tracer-based approaches.

We also compared temporal changes in R_m at the Totten and Moscow University Ice Shelf fronts (Fig. 5 and Table 2). Between the 2010s and the 2020s, R_m was estimated to be 130 ± 26% higher in the Totten region and 218 ± 46% higher in the Moscow University region. These differences may indicate enhanced ice-shelf melting associated with increased mCDW inflow into these regions. This interpretation is further supported by differences in the spatial distribution of F_g between the 2010s and the 2020 s, which suggest increased freshwater release from ice-shelf melting in the vicinity of the ice-shelf fronts during the later period (Figs. S9 and S10). However, these estimated differences are sensitive to the treatment of a limited number of observations and should therefore be interpreted with caution (see Table 2 footnotes). Alternative grouping and filtering of the available datasets yield different estimates of the magnitude of change, highlighting the uncertainty associated with sparse temporal sampling. The currently available observations are insufficient to determine whether these differences represent a persistent long-term trend or reflect natural temporal variability in mCDW transport to the ice-shelf fronts²⁹.

Fig. 5. Comparison of horizontal distributions of the glacier-derived freshwater fraction (F_g, ‰) at the fronts of the Totten and Moscow University Ice Shelves in East Antarctica between the 2010s and the 2020s.

The distributions are reconstructed from hydrographic observations collected during each period. The left and right columns show the distributions for the 2010s and the 2020 s, respectively. The freshwater fractions shown in (a), (b), (g), and (h), corresponding to surface waters shallower than the layer of maximum temperature within the upper 100 dbar, are the sea ice-corrected freshwater fractions [F_g(c)], whereas those shown in (c–e) and (i–k) are the uncorrected freshwater fractions [F_g]. f and l show the basal meltwater flux (R_m; Gt yr⁻¹). The corresponding R_m estimates are summarized in Table 2. These figures were generated using Ocean Data View version 5.8.3⁵⁷.

Our results are also insufficient to resolve detailed spatiotemporal variability because repeated CTD observations and mooring measurements remain limited in the coastal Southern Ocean. In addition, our R_m estimates depend on the transport rate of the westward-flowing Antarctic Slope Current reaching the Totten and Moscow University Ice Shelf fronts, for which direct current-meter observations remain sparse in both space and time. Future improvements will require application of this framework to the expanding Southern Ocean Argo observing system, which provides autonomous vertical measurements of hydrographic properties such as T, S, DO, and Pr. Additional long-term current-meter observations across the coastal Southern Ocean will also be needed to better constrain ocean transport and its temporal variability. Combined with these expanding observational capabilities, the proposed end-member-independent hydrographic parameterization framework provides a practical approach for sustained monitoring of glacier-derived freshwater and its long-term variability across East Antarctica.

Methods

Overview of the parameterization framework

In this study, hydrographic variables (temperature, salinity, dissolved oxygen, and pressure) are first used to parameterize dissolved inorganic carbon (DIC) using a hybrid multiple linear regression–neural network (MLR–NN) framework. The residual DIC component associated with glacier-derived freshwater is then used to estimate the glacier-derived freshwater fraction (F_g) through Eqs. (2)–(4). Finally, the estimated F_g is combined with the climatological transport of the clockwise on-shelf circulation associated with the westward-flowing Antarctic Slope Current to estimate glacier-derived freshwater discharge rates. Unlike conventional end-member mixing analyses, the proposed framework estimates glacier-derived freshwater from DIC residuals without prescribing fixed freshwater end-member compositions, thereby avoiding the need to define spatially and temporally varying end-member properties. This enables robust estimation of glacier-derived freshwater over broad spatial and temporal scales (see also Supplementary Fig. S1).

Data used in this study

The observational hydrographic data used to develop the DIC parameterizations, including DIC, T, S, DO, Pr, and related variables, were obtained from the Global Ocean Data Analysis Project version 2 (GLODAPv2.2023)^47–51 for the Southern Ocean south of 30°S over the period 2000–2021. The quality of chemical measurements, including carbonate-system variables, has been maintained using certified reference materials since 2000⁵². We therefore used data collected from 2000 onward. Data quality was evaluated using World Ocean Circulation Experiment (WOCE) quality flags (https://learning.cchdo.io/submitting_data/quick_guide). Only observations with a WOCE flag of 2, indicating acceptable data quality, were used to construct the DIC_open and DIC_coastal parameterizations.

To estimate glacier-derived freshwater fractions in the Southern Ocean, we used hydrographic observations from the Japan Antarctic Research Expedition (JARE) 59-65 (https://ads.nipr.ac.jp/), together with GLODAPv2.2023 data^47–51. In the JARE dataset, hydrographic observations north of 66°S were mainly conducted aboard T/S Umitaka-Maru, operated by Tokyo University of Marine Science and Technology, using twenty-four 8-L X-Niskin bottles from the surface to 10 m above the seafloor. These data have quality comparable to WOCE flag 2. Hydrographic observations south of 66°S were conducted aboard the icebreaker R/V Shirase using twelve 4-L X-Niskin bottles from the surface to 1000 dbar, with quality also comparable to WOCE flag 2 (Fig. 2 and Supplementary Data 1). In addition, mooring systems were deployed near the front of the Totten Ice Shelf at Mooring Station TM1 (116.51°E, 66.60°S; bottom depth 1020 m) at depths of 500, 880, and 1000 dbar from February 2022 to March 2024 to collect T, S, DO, and Pr data (Fig. 4 and Supplementary Data 1). Cruise information is summarized in Supplementary Data 1.

Development and validation of hybrid MLR-NN parameterizations for DIC

Following the MLR framework of Pan et al.⁷, we developed hybrid MLR–NN parameterizations of DIC using the GLODAPv2.2023 dataset. The explanatory variables identified by the MLR analysis were then used to optimize nonlinear relationships with a neural network containing three hidden nodes. Model performance was evaluated using independent testing data and five-fold cross-validation.

To identify suitable explanatory variables for DIC parameterization in SO_open and SO_coastal, multiple linear regression analyses were performed using CTD-bottle data from 2000 onward in GLODAPv2.2023^47–51 (Fig. S2). Variables were considered significant when their F-value, a statistical index used to evaluate the significance of regression parameters, exceeded 2.4⁵³. Multicollinearity among explanatory variables was assessed using the variance inflation factor (VIF), with VIF < 10 indicating the absence of substantial multicollinearity^7,37,38. For both SO_open and SO_coastal DIC, T, S, AOU, and Pr satisfied these criteria and were selected as explanatory variables (Table S1). T and S primarily represent physical water-mass properties, Pr is related to pressure-dependent thermodynamic effects including CaCO₃ dissolution, and AOU reflects biological processes such as productivity and remineralization⁵⁴.

These variables were then used to develop NN-based DIC parameterizations for SO_open and SO_coastal using GLODAPv2.2023 CTD-bottle data collected from 2000 onward^47–51 (Figs. S1 and S2). Model performance was evaluated using five-fold cross-validation⁵⁵. In each fold, 80% of the observations were randomly used for training and the remaining 20% were used for testing (Fig. S2). The resulting hybrid MLR–NN DIC parameterizations had MAD values of approximately 4 µmol kg⁻¹ for both DIC_open and DIC_coastal (Eqs. 2 and 3), representing an improvement of nearly 40% relative to previous MLR-only parameterizations⁷. These results demonstrate that the hybrid MLR–NN framework substantially improves the predictive accuracy of DIC parameterization relative to the previous MLR-only approach, providing a more robust basis for estimating glacier-derived freshwater.

All observational data used in this study are publicly available. The DIC parameterizations were developed using GLODAPv2.2023, and the hydrographic observations used to estimate glacier-derived freshwater are archived in the Arctic Data archive System (ADS). Details and direct links to the datasets are provided in the Data Availability section.

Estimation of glacier-derived freshwater using hybrid MLR-NN parameterizations

Previous studies indicate that warm mCDW flows southward from SO_open to SO_coastal and into ice-shelf cavities in East Antarctica^7,11,24,29. In the absence of glacier-derived freshwater input, seawater reaching SO_coastal is assumed to originate primarily from SO_open, such that the initial DIC concentration in SO_coastal (DIC_int) can be approximated as

$${\mathrm{DIC}}_{\mathrm{int}}={\mathrm{DIC}}_{\mathrm{open}}$$ 6

When southward-flowing mCDW induces basal melting beneath an ice shelf, glacier-derived freshwater is incorporated into the mCDW. The freshwater-enriched seawater becomes more buoyant and rises through mixing. For DIC, this process can be expressed as

$${\mathrm{DIC}}_{\mathrm{coastal}}={\mathrm{DIC}}_{\mathrm{int}}+{\mathrm{DIC}}_{\mathrm{fw}}={\mathrm{DIC}}_{\mathrm{open}}+{\mathrm{DIC}}_{\mathrm{fw}}$$ 7

where DIC_fw represents the DIC anomaly associated with glacier-derived freshwater. The DIC difference between SO_open and SO_coastal, determined from the two hybrid MLR–NN parameterizations, can then be used to estimate the glacier-derived freshwater fraction F_g, as shown in Eq. (4).

A positive F_g value indicates freshwater input from glacier melting, whereas values close to zero or negative indicate little or no detectable glacier-derived freshwater signal within the uncertainty of the parameterization (Fig. S4). Equation (4) is most robust for subsurface and deep waters where mCDW occurs below the surface layer and where the effects of sea-ice formation and melting are limited. In regions and depth ranges not affected by glacier-derived freshwater or sea-ice processes, F_g should be close to zero. Consistent with this expectation, F_g in deep waters below 100;dbar in SO_open north of approximately 65°S was 0.3‰ (Table S2).

Caveat for correcting F_g in the surface layer

In surface waters shallower than approximately 100 dbar, the freshwater budget is also influenced by sea-ice formation/melting (SI) and evaporation/precipitation (EP). In the initial F_g estimate, we assumed that the net effects of SI and EP are the same between SO_open and SO_coastal and therefore cancel in Eq. (4). This assumption allows glacier-derived freshwater fractions to be estimated using available hydrographic data. However, any spatial or temporal differences in SI or EP between the two regions would be implicitly included in the residual term. Therefore, F_g in the surface layer should be interpreted as a combined signal of glacier-derived freshwater and any unaccounted differences in SI and EP. Surface-layer F_g may therefore have larger uncertainty when SI or EP differs substantially between SO_open and SO_coastal⁷ (Fig. 1). To reduce this uncertainty, we introduced a sea ice-corrected freshwater fraction, F_g(c), for the surface layer (Figs. 2 and 3).

Author contributions

Y.W.W. conceived and led the study. Y.W.W., D.H., Y.O., M.S., Y.N., R.M., and K.M. participated in the JARE expeditions used in this study and contributed to the associated observations. Y.W.W. performed the data analysis. Y.W.W., D.H., Y.O., M.S., Y.N., R.M., and K.M. contributed to the interpretation of the results and the writing of the manuscript.

Peer review

Peer review information

Nature Communications thanks Eric Rignot, Nicholas Golledge and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Funding

This work was supported by JSPS KAKENHI (Grant No. 22H05003) and the Science Program of the Japanese Antarctic Research Expedition (JARE) as a Prioritized Research Project (AJ1003).

Data availability

The observational hydrographic and dissolved inorganic carbon (DIC) data used to develop the DIC parameterizations are publicly available through GLODAPv2.2023 (https://glodap.info). The hydrographic observations from the Japan Antarctic Research Expedition (JARE) used in this study are publicly available through the Arctic Data Archive System (ADS) of the National Institute of Polar Research (https://ads.nipr.ac.jp/) under dataset IDs A20230206-001, A20230206-003, A20230131-005, A20230323-001, and A20240327-001.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at https://doi.org/10.1038/s41467-026-77441-z.