Deep learning based reconstructions of the Atlantic meridional overturning circulation confirm twenty-first century decline

LETTER • OPEN ACCESS Deep learning based reconstructions of the Atlantic meridional overturning circulation confirm twenty-first century decline To cite this article: Simon L L Michel et al 2025 Environ. Res. Lett. 20 064036 View the article online for updates and enhancements. You may also like Mutual stabilization of AMOC and GrIS due to different transient response to warming Frerk Pöppelmeier and Thomas F Stocker - Storm surge changes around the UK under a weakened Atlantic meridional overturning circulation Tom Howard, Matthew D Palmer, Laura C Jackson et al. - Comment on ‘On the relationship between Atlantic meridional overturning circulation slowdown and global surface warming’ Xianyao Chen and Ka-Kit Tung - This content was downloaded from IP address 163.1.18.115 on 23/10/2025 at 12:27 Environ. Res. Lett. 20 (2025) 064036 https://doi.org/10.1088/1748-9326/add7f0 OPEN ACCESS RECEIVED 25 February 2025 REVISED 9 May 2025 ACCEPTED FOR PUBLICATION 13 May 2025 PUBLISHED 23 May 2025 Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. LETTER Deep learning based reconstructions of the Atlantic meridional overturning circulation confirm twenty-first century decline Simon L L Michel1,2,∗, Henk A Dijkstra1, Francesco Guardamagna1, Valérian Jacques-Dumas1, René M van Westen1and Anna S von der Heydt1 1Institute for Marine and Atmospheric research Utrecht (IMAU), Utrecht University, Utrecht, The Netherlands 2Atmospheric Oceanic and Planetary Physics (AOPP), University of Oxford, Oxford, United Kingdom ∗Author to whom any correspondence should be addressed. E-mail: [email protected] Keywords: AMOC reconstruction, machine learning, climate models validation Supplementary material for this article is available online Abstract Gaining knowledge of the past and present variations of the Atlantic meridional overturning circulation (AMOC) is crucial for the development of accurate future climate projections. The short range covered by direct AMOC observations, inconsistent paleoclimate records, and scattered hydrographic data are insufficient to realistically reconstruct the AMOC strength since 1900. An AMOC proxy index based on sea surface temperatures suggests that the AMOC has declined by 15% since the late 19th century but this index received extensive scientific criticism. Here, we use a deep learning algorithm and climate model simulations to accurately reconstruct the AMOC strength between 20◦N and 60◦N since 1900. In contrast with the existing indices, our reconstructions are well in agreement with AMOC strength variations simulated by climate models and direct observations at 26.5◦N. Our novel set of AMOC reconstructions contribute to a larger confidence in 21st century AMOC decline projections from climate models. Modern earth system models (ESMs) from the Coupled Model Intercomparison Project phase 6 (CMIP6) (Eyring et al 2016) consistently project a decline in Atlantic meridional overturning circulation (AMOC) strength throughout the twenty-first century (Weijer et al 2020) due to anthropogenic climate change (Eyring et al 2021). However, there is substantial spread in projected AMOC decline among ESMs (Weijer et al 2020, Bellomo et al 2021), with a strong meridional dependency (Frajka Williams et al 2019, Zou et al 2020, Årthun et al 2023, Asbjørnsen et al 2024), leading to uncertainties in regional and global temperature and precipitation trends (Bellomo et al 2021). Given the implications for policymaking, robust validation of ESMs using historical observations is essential, particularly regarding AMOC strength (Bellomo et al 2021). The AMOC has been monitored at 26.5◦N since 2004 through the RAPID array (Cunningham et al 2007, Smeed et al 2014, McCarthy et al 2015,2018, Moat et al 2023), providing a valuable nearly 20 year observational record (Moat et al 2023). Although this dataset reveals significant variations in AMOC strength (Smeed et al 2014,2018), it is limited by measuring the large-scale circulation at only one latitude. To address this limitation, subsequent research projects such as SAMBA (Meinen et al 2013) and OSNAP (Lozier et al 2019) have begun measuring AMOC at other latitudes (34◦S and 60◦N, respectively), albeit with shorter time series of less than ten years. Nevertheless, the RAPID observations, referred to as AMOCRAPID, indicate an overall decline in AMOC strength since 2004 (Smeed et al 2014, 2018), though there has been a modest but consistent increase in the last twelve years of available data (Smeed et al 2018, Moat et al 2023) (i.e. from 2010 to 2021). However, due to their expense and complexity (Cunningham et al 2007, Smeed et al 2014, McCarthy et al 2015,2018, Moat et al 2023), the RAPID measurements cover too short a period to establish or dismiss any consistent long-term trend in AMOC intensity in response to anthropogenic climate change (Cunningham et al 2007, Smeed et al 2014, McCarthy et al 2015,2018, Frajka-Williams et al 2019, Moat et al 2023). Recent studies, incorporating direct deep ocean observations from various © 2025 The Author(s). Published by IOP Publishing Ltd Environ. Res. Lett. 20 (2025) 064036 S L L Michel et al Atlantic regions (Lozier et al 2019, Chafik et al 2022, Asbjørnsen et al 2024), hydrographic data (Rossby et al 2022), and ESMs (Zou et al 2020), have highlighted the latitudinal dependency of AMOC variability, thereby casting doubt on the robustness of trends observed in RAPID data (Moat et al 2023). Subsurface density measurements in coastal North Atlantic areas have been utilised to contextualise direct AMOC observations (Worthington et al 2021, Rossby et al 2022). However, due to their limited spatial and temporal coverage, these data are too noisy to effectively reconstruct monthly to annual AMOC strength using current aggregation methods (Rossby et al 2022). Given the constraints of usingAMOCRAPID and hydrographic observations for ESM validation, AMOC fingerprints based on North Atlantic sea surface temperature (SST) and salinity (SSS) fields have been developed to estimate 20thcentury AMOC variations (Knight et al 2005, Caesar et al 2018, Zhang et al 2019, Jackson and Wood 2020). Notably, the emergence of the ‘warming hole’ pattern in the North Atlantic subpolar gyre (SPG) surface has been identified as an indicator of declining AMOC strength since 1900 (Rahmstorf et al 2015, Caesar et al 2018). Using the SST average over the SPG (SSTSPG) minus the global mean SST signal as an AMOC proxy (AMOCSPG, see material and methods), it has been demonstrated that the AMOC decreased by 15% overall since the mid-19th century (Caesar et al 2018). However, salinity also significantly contributes to surface density fields and is thus critical for AMOC variations (Jackson and Wood 2020). In this regard, SSS indices instead reveal a century-long upward trend in AMOC strength (figure S1), raising doubts about the relevance of sea surface-based AMOC indices. Although an abnormally cold (resp. warm) SSTSPG can indicate a decreasing (resp. increasing) AMOC response to anthropogenic greenhouse gas (resp. aerosol) emissions, the respective timescales of SSTSPG and AMOC responses to overlapping and opposite radiative effects from different forcings differ considerably and are non-stationary (Little et al 2020). The AMOCSPG index also assumes that the AMOC fingerprint on SSTSPG over the strongly forced recent decades (Caesar et al 2018) was the same as during the mainly naturally driven AMOC over the 20th century (Latif et al 2022). This constitutes a strong assumption of stationarity in SPG and AMOC dynamics under constantly evolving radiative forcing (Little et al 2020). North Atlantic SST and SSTSPG are also driven by diverse factors and their interactions, including the AMOC (Knight et al 2005, Zhang et al 2019, Jackson and Wood 2020), but also stratospheric (Booth et al 2012, Mann et al 2021) and tropospheric (Booth et al 2012) aerosol concentrations, or atmospheric (Fan et al 2023) and oceanic (Buckley and Marshall 2016, Frajka-Williams et al 2019, Chafik et al 2022, Swingedouw et al 2022, Chafik and Lozier 2025) processes. Given the variety of processes affecting North Atlantic SST patterns, the AMOCSPG may be too simplistic as its calculation assumes an unrealistic in-phase and stationary relationship between SSTSPG, the AMOC, and the global warming signal (Chen and Tung 2021) (figure S2). Consequently, the Special Report on the Ocean and Cryosphere in a Changing Climate (2019) from the Intergovernmental Panel on Climate Change (Collins et al 2019) evaluated the claim that the AMOC strength has significantly decreased as a response to climate change (Caesar et al 2018) with only medium confidence. With respect to the AMOC validation of ESMs, the AMOCSPG indicates that the AMOC has declined over the second half of the 20th century (Caesar et al 2018), while the mean of the CMIP6 ESMs indicates that it would have increased (Menary et al 2020, Robson et al 2022). Are the CMIP6 ESMs, with their known biases, wrong here or is the AMOCSPG, often considered as extended AMOC observations (Caesar et al 2018, Boers 2021, Ditlevsen and Ditlevsen 2023), inadequate? Clearly, there is an urgency to obtain better reconstructions of the 20th-century AMOC strength (figure S1), using available observations. 1. A deep learning approach to AMOC reconstruction Here,weprovidea novel reconstruction of the AMOC strength using a deep learning algorithm trained to produce AMOC timeseries at different latitudes based on SST observations. The use of deep learning for this task is innovative, as is the production of several AMOC indices for different latitudes of the North Atlantic Ocean (figure 1(a)). This aligns with recent results indicating a strong spatial dependence of AMOC variability from interannual to decadal timescales (Zou et al 2020, Asbjørnsen et al 2024). These findings are confirmed for our North Atlantic study area (0◦N–80◦N, 80◦W–0◦, figure 1(a)) by a set of 51 historical climate simulations from 17 ESMs (3 simulations each, table S1). This extensive model intercomparison analysis indicates that AMOC trends (figure 1(b)) and covariances (figure 1(c)) in the North Atlantic meridional stream function time series vary greatly across latitudes (Zou et al 2020, Asbjørnsen et al 2024) and depth (figures 1(b) and (c)). This analysis further confirms that AMOC variations cannot be characterised by a single index, suggesting that former attempts to reconstruct the AMOC strength from surface data can potentially lead to misinterpretations regarding historical AMOC variability. The deep learning method we use here is a 3-layer (convolutional neural network (CNN), see materials and methods), a widely used approach in image analysis (Goodfellow et al 2016) that has proven itself in many climate research applications (Ham et al 2019, Jacques-Dumas et al 2022, Bˆ one et al 2024). To train 2 Environ. Res. Lett. 20 (2025) 064036 S L L Michel et al Figure 1. Area of study and model diversity of Atlantic meridional overturning circulation (AMOC) time series across latitudes in earth system models (ESMs) from CMIP6 (1). (a). Study area (light green), where sea surface temperature and (SST) and sea surface salinity (SSS) fields are used to train and validate convolutional neural networks (CNNs) to reconstruct AMOC time series for the 9 latitudes indicated by dashed lines (i.e. from 20◦N to 60◦N with an increment of 5◦). (b). Mean trends in North Atlantic meridional overturning stream function time series below 500 m of depth from an ensemble of 51 historical simulations from 17 CMIP6 ESMs (3 simulations each, table S1) expressed in Sverdrup (Sv) per decade, for the period 1900–2014. Green dots indicate where the ensemble mean from ESM simulations is significantly different from 0 at the 95% confidence level. The black dashed lines indicate where the maximum overturning is reached on average for the 51 ESM simulations. (c). Matrix of mean correlations (colours) of AMOC time series (each calculated within the same simulation) for the 9 latitudes studied here and indicated in a, for the same 51 historical simulations from b. The fraction of significant correlations is indicated by the size of dots for each couple of latitudes among the 51 simulations. CNN models, we selected the best ESM from the 17 listed in table S1 for representing the two main components of surface density fields: the SST and SSS fields (table S2). The model-observation comparison uses SST and SSS observations from the EN4 dataset (Good et al 2013). To comprehensively study ESMs’ ability to represent SST and SSS, we computed mean biases in simulated mean state, standard deviations, minima, and maxima over the overlapping period of historical CMIP6 simulations and the EN4 dataset (1900–2014, figure S3). These statistics were averaged over three historical simulations for each of the 17 ESMs (table S2). We focus on model biases calculated from annually averaged data (figure S3) and also provide similar analyses for monthly and seasonal averages for both SST (figure S4) and SSS (figure S5). Results indicate that ESMs can better represent SST only, SSS only, or both, in comparison to other ESMs (figures S3– S5 and table S2). We are interested in the ESM that bestreproducesstatisticsforbothSSTandSSS,asthey together determine surface density fields which is crucial for simulating the interplay between the ocean surface and the AMOC (Knight et al 2005, Zhang et al 2019, Jackson and Wood 2020, Swingedouw et al 2022). Accurately simulating SST and SSS statistical properties is fundamental for adequately training CNN models to reconstruct the AMOC from ocean surface properties within climate simulations, which we will then apply to observational data. Additionally, while mean and variability statistics are essential for training CNNs on realistic simulation data, we also evaluated how well ESMs reproduce SST and SSS trends over the historical period (figure S6 and table S3). 2. Novel AMOC reconstructions across latitudes The best-performing ESM identified through our bias analyses (figures S3–S6, Tabs. S2 and S3, see materials and methods) is HadGEM3-GC31-MM (hereafter HadGEM3), based on both mean-state statistics (figures S3–S5 and table S2) and trend performance (figure S6 and table S3). To train the CNNs, we use 4 historical HadGEM3 simulations, each covering 115 years (1900–2014). Additionally, we use one future simulation with low CO2emissions (SSP1-2.6, 86 years) and one piControl simulation (500 years) with constant pre-industrial CO2levels (280 ppm). Using SSP1-2.6 and piControl simulations has two 3 Environ. Res. Lett. 20 (2025) 064036 S L L Michel et al main advantages: i) it provides more data for training than the relatively short historical simulations, with greenhouse gas concentrations similar to late (SSP1-2.6)and early (piControl)historical levels; ii) it prevents CNNs from overfitting to historical climate simulations’ outputs, generated under similar radiative forcing (i.e. observed anthropogenic and natural forcings since 1900). In addition to validations for HadGEM3, we applied the same CNN approach to the six best ESMs from figures S3–S5 and table S2 to ensure our results are not model-specific. A detailed description of climate simulations used for CNN validations and training is given in table S4 (HadGEM3 only) and table S5 (six best ESMs). To quantify the efficiency of CNNs in reconstructing AMOC variations in HadGEM3 simulations across latitudes from 20◦N to 60◦N (figure 1(a)), we excluded one historical simulation from the training set at a time and trained CNNs with the remaining simulations (historical, piControl, and SSP1-2.6). The CNN’s ability to reconstruct historical AMOC variations was tested by reconstructing the AMOC time series of the excluded historical member and comparing it with the original AMOC time series from this simulation (see table S4). Similarly, in the six best ESMs experiment, we applied a leave-onemodel-out approach: all simulations from a single ESM are excluded from training, one ESM at a time, and the CNN’s reconstruction skill is evaluated by reconstructing the historical AMOC time series from the excluded ESM (see table S5). To ensure high performance for each CNN model trained for each excluded historical simulation and eachlatitudestudied,weused5-foldcross-validations (see materials and methods) to tune the CNNs’ hyperparameters. We trained and tuned 109 CNNs without optimising the number of epochs. Instead, we used a large number of epochs (i.e. 1000) with an early stopping criterion to ensure convergence of CNNs’ training losses. Therefore, we only optimised the batch sizes and initial learning rates. Each CNN was tested for three batch sizes and four initial learning rates (see supplementary materials), resulting in 12 hyperparameter combinations for each excluded historical member/latitude pair. The optimal batch size and initial learning rate for each case are provided in table S6 for HadGEM3 analyses and in table S7 for analyses based on the six best ESMs. In order to assess the generalisability of our approach, we conducted an additional sensitivity analysis on the input variables using the six best ESMs (table S5). Applying the validation setup for the six best ESMs described above and employing singleinput CNNs based on SST only, SSS only, and twoinput CNNs combining both SST and SSS, we find that CNN models perform better in reconstructing historical ESM-based AMOC time series using SST only (figure S7). This outcome might stem from significant biases and differences in ESM representations of North Atlantic SSS (Liu et al 2017). Moreover, utilising SST only for CNN training may yield more accurate reconstructions when applied to real data for practical reasons. Indeed, SST has been directly measured with better spatio-temporal coverage since 1900 (Good et al 2013) compared to SSS, making it less susceptible to measurement uncertainties and statistical approximations (Good et al 2013, Ben-Yami et al 2023). To further assess the performance of CNN models in reconstructing ESM-based AMOC variations across latitudes, we compared our outputs with existing AMOC indices (Boers 2021, Caesar et al 2018, Jackson and Wood 2020) (figure S1) computed from the same historical ESM simulations. These indices include AMOCSPG based on SST (Caesar et al 2018) and four SSS-based AMOC indices computed as averages over different Atlantic areas (Jackson and Wood 2020, Boers 2021), denoted here as AMOCSSS1 through AMOCSSS4 (see materials and methods). In figure 2, we demonstrate that AMOC time series generated from CNN models largely outperform other AMOC indices across all latitudes studied and for the four excluded members from training (figures 2(a)– (d)). While AMOCSSS3 and AMOCSSS4 exhibit low performance in estimating AMOC strength at any latitude for all four historical members (figures 2(a)– (d)), SPG-based SSS (AMOCSSS1 and AMOCSSS2) and SST (AMOCSPG) indices show relatively good abilities in estimating variations of southernmost AMOC time series for two members (members 2 and 4, figures 2(b) and (d)). However, they generally yield poor estimations of Atlantic overturning in northernmost areas for all members (figure 2). These varying reconstruction skills across latitudes, indices, and excluded HadGEM3 historical members (figure 2), highlight that basin-scale AMOC variations cannot be adequately characterised with a single index (figure 2). Producing a set of past century AMOC strength variations across several latitudes thus provides a more coherent and robust view of historical AMOC variability. Individual reconstructions and their comparison with other indices in the literature and the AMOC time series from HadGEM3 simulations are provided in figures S8–S11. We conducted a similar analysis using the six best ESMs instead of relying solely on HadGEM3, excluding all simulations from each of these ESMs (including piControl and SSP1-2.6) from training, one after the other (figure S12). Our conclusions mirror those drawn from the HadGEM3-only analyses (figure S12). From figures 2and S11, it is evident that ESMs’ AMOC time series generated from CNN models are significantly more accurate than previously suggested AMOC indices (Caesar et al 2018, 4 Environ. Res. Lett. 20 (2025) 064036 S L L Michel et al Figure 2. Performance of convolutional neural network (CNN) to reconstruct Atlantic meridional overturning circulation (AMOC) time series in HadGEM3 using sea surface temperature (SST) fields, and comparison with other AMOC indices. Reconstructions were performed for 9 different latitudes (from 20◦N to 60◦N with an increment of 5◦) with HadGEM3, the best ESM in terms of simulating observed SST and SSS statistics (figures S3–S6 and table S2). The training set used here is composed of 4 historical runs, and one SSP1-2.6 and piControl runs (table S4). For panels (a)–(d), green circles give the correlation of reconstructed AMOC time series for historical simulation members 1–4 and actual AMOC time series from this same simulation, when it was excluded from the training (materials and methods, table S4), one after the other, for each latitude. Blue circles, orange squares, red diamonds, pink triangles, and purple circles show the correlations between the AMOC time series from the given ESM simulation member with other existing surface-based indices of the AMOC proposed by other studies, i.e. AMOCSSS1 through AMOCSSS4 (Jackson and Wood 2020, Boers 2021) and AMOCSPG (Caesar et al 2018) (materials and methods), respectively. Jackson and Wood 2020), across all latitudes considered, with improvementsconsistentlysignificant at the 95% confidence level (figures 2and S11). 3. Comparison of AMOC reconstructions in historical ESM simulations To compare the performance of CNN and earlier suggested AMOC indices in historical ESM simulations, we retrained nine new CNN models (one for each latitude of interest, see figures 1and 2) using all simulations from HadGEM3 (i.e. the best ESM). We applied the same cross-validation scheme as for figure 2to tune these CNN models, and the optimal sets of batch sizes and initial learning rates were determined for each latitude (table S8). Comparisons were made between the CNN-based AMOC reconstructions and the AMOC results of 51 historical simulations from the 17 ESMs presented in table S1. For reference, we included SST (AMOCSPG) and SSS (AMOCSSS1) indices, with the latter chosen as it performed best among the studied SSS indices when computed within historical simulations (see figures 2 and S12). Figure 3illustrates that, for all AMOC time series, the reconstructions obtained by applying CNNs to real data (AMOCCNN) fall within the range of historical simulations. To quantify this, we calculated the number of years between 1900 and 2014 that fall outside of the range described by ESM simulations (table S1). We performed the same calculation for AMOCSPG and AMOCSSS1, as well as for each of the 51 simulations (table S1) where the ESM range for one model simulation is based on the 50 remaining ones (figure 3). Interestingly, lower latitude AMOCCNN reconstructions (20◦N to 30◦N) closely align with AMOCSPG, with the latter lagging the former by about 5–10 years. Both time series depict a downward trend from the 1950s (Caesar et al 2018), but CNN-based AMOC reconstructions suggest a slight recovery of the AMOC in recent years, consistent with direct RAPID observations (Moat et al 2023). This partial recovery is thus expected to continue over the coming years for AMOCSPG (figure 3). For middle latitudes (35◦N and 40◦N), the century-long downward trend appears to be less pronounced for 40◦N or non-discernible for 35◦N. Conversely, at higher latitudes (from 45◦N), a downward trend marked by recent record lows is observed, with no visible recovery yet in these regions (figure 3). 5 Environ. Res. Lett. 20 (2025) 064036 S L L Michel et al Figure 3. Atlantic meridional overturning circulation reconstructions with convolutional neural networks (CNNs) and comparison with other existing surface-based indices and earth system model (ESM) simulations. Reconstructed AMOC time series are provided for 9 different latitudes (from 20◦N to 60◦N with an increment of 5◦), each obtained with a CNN trained and tuned (materials and methods, table S8) using simulations from HadGEM3 (i.e. the less biased ESM from table S2) and applied to observed sea surface temperature (SST) from the HadISST dataset (Rayner et al 2003) For each latitude, the left panel gives the normalised and 10-year smoothed reconstructed AMOC time series from the CNN (AMOCCNN, green), and one SST (Caesar et al 2018) (AMOCSPG, purple lines) and one SSS (Jackson and Wood 2020, Boers 2021) (AMOCSSS1, orange lines) indices from previous studies (materials and methods), here computed from EN4. Grey shaded areas give the spread of normalised and 10-year smoothed AMOC time series for respective latitudes, computed for 51 historical simulations from 17 CMIP6 ESMs (3 simulation members each, table S1). The ensemble mean of the ESMs’ AMOC time series are given by black lines. Right panels give the number of years where AMOCCNN (green dots), AMOCSPG (purple dots), and AMOCSPG (orange dots) fall out of the range drawn by the 51 historical simulations from ESMs (table S1). Grey boxplots give the same out-of-range statistics, when each simulation member from the 51 ensemble is excluded, and where the ESM spread is recomputed from the 50 other simulations. Consistent with ESMs, the largest decrease at the centennial scale is generally observed for the highest latitudes (figures 1(b) and 3). The increase in subpolar salinity concentration (captured by AMOCSSS1) from 1950 to 1970, associated with enhanced ocean convection, is recorded in all our reconstructions, albeit with a slight delay at the highest latitudes (figure 3). The second salinity increase through the late 20th century is also associated with a local increase in both AMOCCNN and AMOCSPG time series. To assess the long-term behaviour of the AMOC across latitudes, we conducted a trend analysis using all 51 historical ESM simulations, the CNN-based reconstructions from observations (AMOCCNN), and the benchmark indices AMOCSPG and AMOCSSS1 (figure S13). At the lowest latitudes (20◦N–30◦N) and at 60◦N, AMOCCNN trends lie near the lower end of the ESM range, consistent with the marked decline seen in figure 3. At other latitudes, trends remain negative, though not statistically significant at 35◦N and 40◦N, and fall within the ensemble range (figure S13). The two reference indices, which do not vary with latitude, show contrasting behaviour: AMOCSPG lies consistently near the bottom of the ESM range, while AMOCSSS1 exhibits a positive trend (as in figure S1). The latter agrees with a subset of ESM simulations (figure S13) whose AMOC responds strongly to tropospheric aerosol forcing (Menary et al 2020, Robson et al 2022). Notably, AMOCCNN trends appear stronger than most ESMs at 20◦N–30◦N and 60◦N. This may reflect the earlier onset of AMOC strengthening in the reconstructions, around the 1950s, linked to increased salinity (as seen in AMOCSSS1), in contrast with the delayed (1980s– 1990s) aerosol-driven positive response in many ESM simulations (Menary et al 2020). Overall, the AMOCSPG and AMOCSSS1 indices often exhibit values outside the range of ESM simulations for most latitudes (figure 3), likely due to theirdelayed response and inability tocaptureAMOC variability across the entire North Atlantic (figures 2 and S12). In contrast, the AMOCCNN reconstructions consistently align better with the range of ESM results (figure 3). While reconstructions at the lowest latitudes may occasionally fall outside the ESM range, they still demonstrate improved agreement compared to previous indices (figure 3). This reconciliation addresses earlier discrepancies between existing estimations of historical AMOC strength and AMOC simulations from ESMs, marking a significant advancement. 4. Comparison with direct AMOC observations We did not proceed to comparisons of our reconstructions with too short records (less than ten years) from the SAMBA (Meinen et al 2013) and OSNAP (Lozier et al 2019) arrays. In addition, SAMBA measurements (at 34◦S) fall outside our trained CNN domain (0◦N–80◦N, 80◦W–0◦, 6 Environ. Res. Lett. 20 (2025) 064036 S L L Michel et al Figure 4. Comparison of Atlantic meridional overturning circulation (AMOC) timeseries with direct observations from RAPID (8) and HadISST (43). (a), (b). Green lines give the AMOC reconstructed from convolutional neural network (AMOCCNN) for latitudes 25◦N (a.) and 30◦N (b.). Purple line: AMOC reconstruction based on sea surface temperature (SST) in the subpolar gyre (AMOCSPG). Blue: AMOC reconstruction based on sea surface salinity averaged in the subpolar North Atlantic (AMOCSSS1). Red: direct AMOC measurements from the RAPID data array measuring overturning at 26.5◦N in the North Atlantic (Moat et al 2023). (c), (d). Correlation maps of SST from HadISST (43) against AMOC timeseries reconstructed at 25◦N and 30◦N from CNN. Stippled grid points indicate where the correlation is significant at the 90% confidence level using a student t-test for correlation with corrected degrees of freedom using time series autocorrelations (Michel et al. 2022). (e), (f). Ensemble mean correlation maps of SST against AMOC timeseries at 25◦N and 30◦N from the four historical HadGEM3 simulations. Stippled grid points indicate where correlations are of same sign in all four members. The purple surrounded area (panels c. through f.) depicts the region used for the AMOCSPG reconstruction (Caesar et al 2018). figure 1(a)). Thus, our analysis focuses on the RAPID time series, compared (figures 4(a) and (b)) with AMOCCNN reconstructions at adjacent latitudes (i.e. 25◦N and 30◦N). Remarkably, our reconstructions closely match RAPID measurements, capturing the 2009–2010 drop and subsequent partial recovery at the interannual scale (Moat et al 2023, figures 4(c) and (d)). Figures 4(c)–(f) shows the correlation between AMOC time series at 25◦N and 30◦N and SST fields, based on historical observations from HadISST (Rayner et al 2003) and HadGEM3 simulations. As expected,the(linear)relationshipbetweenourreconstructed AMOC and SST patterns closely matches that in HadGEM3, since the CNN was trained to infer AMOC variability from SST. This indicates that the physical relationship learned during training also applies to observational data. In line with earlier studies (Rahmstorf et al 2015, Caesar et al 2018), AMOCSST correlations under climate change are generally negative at low latitudes on interannual timescales, except in parts of the subpolar North Atlantic where correlations are positive (figures 4(c) and (e)). However, consistent with HadGEM3, the region of positive correlation is shifted southward compared to the AMOCSPG region defined by Caesar et al (2018) (figures 4(c)–(f)). Specifically, areas within the Labrador and Irminger seas (used in AMOCSPG) are anticorrelated with our AMOC reconstructions and with HadGEM3 AMOC at 25◦N and 30◦N (figures 4(c)–(f)). 5. Conclusions and discussions Recent findings have raised concerns that the AMOC may be nearing a tipping point, primarily based on surface AMOC indices (Boers 2021, Michel et al 2022, Ditlevsen and Ditlevsen 2023). In line with this, we performed an Early Warning Signal (EWS) analysis on our reconstructed AMOC time series (figure S14), using both AR (1) and variance metrics computed over 50 year sliding windows from detrended time series (as in Boers 2021). Significant trends in these indicators were found only for the two northernmost reconstructions (55◦N and 60◦N), potentially suggesting increased instability. However, the reliability of such metrics is limited when applied to relatively short time series (∼120 years). A recent study (Van Westen et al 2024) showed that, under such conditions, EWS indicators can yield false positives. This limitation was also highlighted in earlier work using an intermediate-complexity climate model (Boulton et al 2014), which found that at least 250 years of data are required for robust detection. While EWSs have been identified in observed surface-based AMOC indices (Boers 2021, Ditlevsen and Ditlevsen 2023) and in a last-millennium machine learning reconstruction (Michel et al 2022), the latter offering 7 Environ. Res. Lett. 20 (2025) 064036 S L L Michel et al greater statistical robustness according to Boulton et al (2014), we caution against overinterpreting short-term signals. Furthermore, the most recent and physically grounded assessment of a potential AMOC tipping point, based on South Atlantic salinity transport (Van Westen et al 2024), points to a mechanismbased framework not assessable from our reconstructions, which do not capture relevant oceanic transport. Thus, while our results offer limited evidence of EWSs, we consider physically based approaches a more reliable path for assessing AMOC tipping behaviour, in line with recent critiques of statistical EWS metrics (Rietkerk et al 2025). While climate change has already impacted many observables worldwide (Eyring et al 2021), the development of historical AMOC time series has long been very controversial (Frajka-Williams et al 2019). Disagreements between AMOC reconstructions based on surface indices, ESM simulations, and the direct, but very short, observations from the deep ocean (Cunningham et al 2007, Smeed et al 2014, McCarthy et al 2015,2018, Moat et al 2023), indicate that ESMs were not able to correctly simulate the AMOC, hence casting legitimate doubts on their projections of a future AMOC decline over the twentyfirst century. The present study employs advanced deep learning techniques to produce new AMOC indices that align with historical ESM simulations across latitudes from 20◦N to 60◦N. These results reconcile the longstanding mismatch between AMOC fingerprint proxies (Caesar et al 2018, Jackson and Wood 2020, Boers 2021) and ESM simulations (Jackson et al 2022), reinforcing confidence in future projections of 21st century AMOC decline (Weijer et al 2020). Data availability statement All data required to reproduce the study are available online on the following Zenodo link: https://zenodo. org/records/15368404. Output data from the study are available online on the same Zenodo link. Acknowledgment The analyses of all the model output were conducted on the Dutch National Supercomputer (Snellius) within NWO-SURF project∼17239. R.M.v.W. and H.A.D. are funded by the European Research Council through the ERC-AdG project TAOC (PI: Dijkstra, project∼101055096). V.J.-D. is funded by the European Union’s Horizon 2020 research and innovation program CriticalEarth under the Marie Sklodowska-Curie grant agreement (project∼956170). The work of F.G. was supported by the Netherlands Organization for Scientific Research (NWO) under grant OCENW.M20.277. S.L.L.M., H.A.D. and A.S.vdH. acknowledge funding from the European Union’s Horizon 2020 research and innovation program under Grant Agreement No. 820970 (TiPES contribution no. 255). S.L.L.M. also acknowledge funding from the UK research and Innovation under the UK government’s Horizon Europe funding guarantee, and European Union’s Horizon 2020 program under Grant Agreement No. 101081383 (EERIE). The work of A.S.vdH. was also funded by the Dutch Research Council (NWO) through the NWO-Vici project ‘Interacting climate tipping elements: When does tipping cause tipping?’ (Project VI.C.202.081). Data for CMIP6 ESM outputs are available on the different Earth System Grid Federation nodes, such as: https://esgfdata.dkrz.de/projects/esgf-dkrz/,https://esgf-index1. ceda.ac.uk/projects/esgf-ceda/,https://esgf-node.ipsl. upmc.fr/projects/esgf-ipsl/. Data from the RAPID AMOC monitoring project is funded by the Natural Environment Research Council and are freely available from www.rapid.ac.uk/rapidmoc. Authors contributions S.L.L.M. has led the study and was its main designer. S.L.L.M and H.A.D. have co-written the manuscript, managed its production, and determined its scope and purpose. F.G. and V.J.-D. have carried out the deep learning analyses of the study, with systematic contributions and assessments from S.L.L.M. and H.A.D. F.G. and V.J.-D. also contributed to the manuscript writing. R.M.v.W. and A.S.v.d.H. contributed to results’ assessments, interpretations, the design of the study, and significantly contributed to the manuscript writing. Code availability All codes required toreproduce the study are available online on the following Zenodo link: https://zenodo. org/records/15368404. ORCID iDs Simon L L Michel https://orcid.org/0000-00015709-4755 Henk A Dijkstra https://orcid.org/0000-00015817-7675 Francesco Guardamagna https://orcid.org/00090002-9501-9208 Valérian Jacques-Dumas https://orcid.org/00000002-8192-9051 René M van Westen https://orcid.org/0000-00028807-7269 Anna S von der Heydt https://orcid.org/00000002-5557-3282 8