## Introduction

Accurate knowledge of the temporal and regional distributions of ocean heat content change (ΔOHC) is key to monitoring the Earth energy imbalance and the anthropogenic climate perturbation1,2,3,4,5. Yet, ΔOHC is mainly assessed from the 1960s and for the upper 2000 m6,7,8,9 where temperature records are most numerous10,11,12. For the deep ocean, ΔOHC estimates have mostly relied on decadal hydrographic surveys whose sparse observational coverage9,11,13 makes estimates of the deep variability uncertain, particularly in the North Atlantic14. Historical reconstructions of ocean temperatures with the improved deep-sea resolution, such as those provided by recent studies15,16,17 and the present work, are therefore essential for a full account of ocean heat uptake. Long-term and well-resolved time series are also an asset to help disentangle long-term warming due to anthropogenic forcing of the climate system from regional deviation of ocean heat content trends18 due to internal variability such as the North Atlantic Oscillation (NAO)19 or the Atlantic Multidecadal Oscillation (AMO)20.

Besides accurate estimates of the full depth ΔOHC inventories in response to climate change, understanding how the ocean redistributes temperature anomalies (ΔT) absorbed at its surface is a prerequisite for improving the reconstruction of past climates and skillful climate projections21. Excess heat (taken as ΔOHC since a chosen reference period) redistribution from the Southern to the Northern hemisphere by the ocean circulation has been shown to balance the interhemispheric asymmetry in ocean surface heat uptake in CMIP5 historical simulations during 1861–200522. Yet, observations12,23 and models24 show that during the recent period (2005–2015), the southern hemisphere ocean was storing more heat than the northern hemisphere ocean, with Rathore et al.24 noting that the 2005–2015 hemispheric asymmetry in heat gain (0–2000 m) can be explained by internal climate variability. On a regional scale, most of the warming of the Arctic Mediterranean for 2002–2012 can be accounted for by an increase in northward ocean heat transport at the Greenland-Scotland Ridge25, with transport and temperature contributing by equal parts. As unabated warming is observed26, the role of the ocean in transporting excess heat and shaping regional patterns of heat gain is still an ongoing debate.

Here we present a new historical full-depth ΔOHC reconstruction, placing our focus on the 25°N trans-Atlantic hydrographic section, a benchmark for the quantification of the AMOC and associated heat transport27,28,29. The section benefits from frequent occupations and continuous AMOC monitoring since 200430,31 (Fig. 1a, Supplementary Table 1 and Supplementary Fig. 1). The reconstruction is based on time-varying sea surface temperatures (SST, monthly time series for years 0–2018) of the global ocean and Green’s functions. The latter represents the ocean circulation and, convolved under the assumption of a stationary state with SST observations, allows us to reconstruct the temporal evolution of the surface-bottom temperature at 25°N (‘Methods’). One advantage of the approach is that because space and time-varying history of SST is relatively well observed compared to the interior of the ocean, the reconstructed continuous and full-depth temperature time series at 25°N fill in for times when interior observations are missing. We determined the Green’s functions using a maximum entropy principle (MEP) constrained by measurements of temperature and 8 other independent tracers (transient tracers, salinity and preformed nutrients) along five full-depth surveys of the 25°N section and by the corresponding temperature and tracer sea surface climatologies (‘Methods’). The five sets of Green’s functions provide representations of the circulation as experienced by the tracers measured during the five corresponding surveys sampled between 1992 and 2015, and thus circulation outside this sampling period is not represented (‘Methods’). The MEP application assigns probability distributions on surface origins and transit times (also known as age spectrum or memory of the ocean)32,33 since last contact with the atmosphere to each sampling point of the 25°N hydrographic surveys, modelling a water sample as the mixture of surface water masses. Relating ocean interior to surface variability overtime, the method makes it possible to decipher the ocean interior excess heat spatiotemporal origins in response to regional climate fluctuations and thus provides unprecedented documentation of ocean heat content change.

We show that redistribution of excess heat by water masses in the lower limb of the AMOC from their region of formation in the Labrador, Irminger, and Nordic Seas to the subtropical North Atlantic contributed 62% of the full water column warming at 25°N for 1850–2018, sequestering excess heat in the deep ocean and outweighing the mitigation of global warming by the upper ocean. Analysis of the decadal variability of ΔOHC at 25°N in response to regional climate fluctuations, including the NAO phase shifts, highlights distinct responses from the Nordic versus the Labrador and Irminger Seas and stresses a resilient cooling to global warming from the northeast subpolar Atlantic relative to 1850. While a lot of attention has been given in the past to the warming from the Labrador Sea Water, the contribution from the Nordic Seas now deserves special attention as we forecast that the Nordic Seas will become the prominent contributor to the deep layer warming at 25°N during the next five decades in response to the late twentieth-century warming reinforced by strong positive phases of the North Atlantic Oscillation. Finally, by computing the transport of excess heat across the section, we determine that during 2012–2018, when warming accelerates in the upper ocean, the redistribution of excess heat by the upper branch of the AMOC, attributable for 24% to southern origin excess heat, can account for the rate of warming in the domain north of 25°N. These results point out that excess heat redistribution has become a key driver of the North Atlantic heat gain.

## Results

### History of the 25°N warming

Figure 1b–d depicts the long-term (2018–1850) and full-depth warming along the 25°N section. The highest values, up to 0.8 °C, are in the upper subtropical gyre, a hot spot of excess heat storage34,35,36 encompassing the upper branch of the AMOC. Below, the imprint of the AMOC lower limb stands out with the sequestration of excess heat enhanced in the deep western boundary current. It carries the ΔT of the North Atlantic deep water identified as two relative maxima up to 0.25 °C at 1500 m and 2500–3500 m. Minimum ΔT (<0.1 °C) at 800–1000 m and below 4000 m are influenced by intermediate and bottom waters from the Southern Ocean.

Our time series agree well with the observation‐based ocean reanalyses (ORAs) EN4, IAP and ISHII for the upper layer from 1975 (best-sampled time period considered the most reliable, Fig. 2c) and to a lesser extent for the intermediate layer (Fig. 2d). Before 1975, our reconstruction and that of Bagnell and DeVries17 show the early-twentieth-century warming in the upper layer extending to 1960 whereas it stops earlier in EN4 in favour of the subsequent cooling (Fig. 2a, b). The substantial warming of the 700–2000 m layer seen in our reconstruction from the late 1950s (Fig. 2d) has been largely reported in the literature14,40,41,42 and is also evidenced in ORAs. Furthermore, the noticeable cooling-to-warming sequence between 1940 and 1990 is also seen in EN4 and IAP. For the 2000–4000 m layer, our reconstruction shows steep warming between 1945 and 1980, also seen in Gebbie et al.15 (their Fig. 3) and hinted by Bagnell and DeVries17. Below 4000 m, EN4 does not reproduce the 1945–1980 warming seen in our reconstructions, in Bagnell and DeVries17 and Gebbie et al.15 (their Fig. 3). However, EN4 shows some consistency with the recent cooling-to-warming reversal highlighted by our time series and also seen in decadal surveys43 and in Bagnell and DeVries17. The discrepancy between our results and EN4 is the largest in the deep ocean before 1960 when there is sparse observation coverage44. Our comparison to the independent 1873–76 Challenger temperatures shows a good agreement except in the upper ocean where Challenger temperatures also diverge from SST anomalies for this period (Fig. 2c, a). Summing up, our reconstruction of ΔOHC for the full depth ocean (Fig. 2b) shows warming from the 1930s that agrees well with Bagnell and DeVries unabated warming from 1946. This contrasts with the 1940–70 pronounced cooling found in EN4 full-depth ocean for which warming starts in 1970.

Our resulting warming between 1850 and 2018 is 0.304 °C ± 0.08 for the 0–700 m and is 0.075 °C ± 0.05 below 700 m, thus four times smaller than the upper layer. However, considering their large volumes, the layers below 700 m account for 62% of the full water column ΔOHC (6 ± 1.6 ZJ in the upper ocean and 9.9 ± 1.4 ZJ below). The heat gain partitioning is 33.6% for 700–2000 m (5.3 ± 1.0 ZJ), 23% for 2000–4000 m (3.7 ± 0.6 ZJ) and 5.4% for 4000 m–bottom (0.9 ± 0.3 ZJ). Those findings are compatible with the reconstruction of the Atlantic Ocean by Gebbie et al. (their Fig. 5)15 suggesting that 53% (19%) of the warming since 1850 occurred below 700 (2000) m, but not with the lower contributions of the deep ocean of Zanna et al.16 (23% and 4%, their Fig. 1; note that Zanna et al.16 neither considered the Nordic Seas as a source region nor the SSTs before 1854). The Bagnell and DeVries17 ΔOHC reconstruction for 1946–2017 at 25°N in the Atlantic Ocean shows a warming distribution of 43% for 0–700 m, 24% for 700–2000 m and 33% below, comparable to the 40, 30 and 30%, respectively, found for our reconstruction for the same period. Those reconstructions highlight the important role of the deep waters in sequestering heat.

### Origin of excess heat

To explain the ΔOHC evolution at 25°N, we first determine the surface source regions that feed the water masses of the section and quantify their contributions to warming for 2018 relative to 1850. Figure 3 shows the origin of ΔOHC at 25°N as the contributions from nine source regions (also qualified as uptake regions). The North Atlantic contributes to 93% (14.8 ± 1.9 ZJ) of the warming at 25°N, although its regions only supply 75% of the water masses at 25°N, the rest of the water mass volume being ventilated in the Southern Hemisphere (Fig. 3b). The tropical and subtropical North Atlantic (NA SubT, 5.0 ± 1.2 ZJ) warm the upper layer by 81%. Below, the main northern contributors are the Labrador and Irminger Seas (Lab-Irm, 7.6 ± 1.0 ZJ) and the Nordic Seas (Nordic, 2.6 ± 0.9 ZJ) respectively warming the intermediate layers by 82.3% and 6%. Although Lab-Irm contributes less to the volumes of the deep (15.8%) and bottom layers (8.9%), it warms these layers more (51.4%, 49.4%) than Nordic (45%, 37.7%). The Mediterranean Sea warms all layers by less than 4% (0.7 ± 0.4 ZJ), despite a large volume contribution (13%). In regard to the negligible contribution from the Arctic, note that we are considering only the western Eurasia Basin (Fig. 2 and Supplementary Note 2). That said, it is likely that some Arctic contribution is counted as Nordic and Lab-Irm because Arctic waters flow southward through Fram Strait in the shallow East Greenland Current towards Nordic and Lab-Irm before subducting. The southern hemisphere accounts for less than 7% of the warming (1.1 ± 0.4 ZJ). This contribution is from the Sub-Antarctic (0.8 ± 0.2 ZJ, warming the intermediate layer by 10.5%) and tropical and subtropical South Atlantic (SA SubT, 0.6 ± 0.3 ZJ, 10.2% of the upper layer warming). Interestingly, although all the layers show net warming, the north-eastern subpolar Atlantic (NEA SubP, −1.1 ± 0.3 ZJ) cools the upper (−0.2 ± 0.2 ZJ), intermediate (−0.7 ± 0.1 ZJ) and deep (−0.2 ± 0.3 ZJ) layers while the Antarctic (−0.4 ± 0.4 ZJ) cools the deep (−0.2 ± 0.3 ZJ) and abyssal (−0.2 ± 0.2 ZJ) layers. Overall, the most striking result is the prevalent warming in the North Atlantic deep water, surpassing that of the NA SubT in the upper ocean. Its surface origins are mostly from the Lab-Irm but also from the Nordic Seas whose substantial contribution is, to the best of our knowledge, identified here for the first time.

### Interdecadal changes in regional contributions and projections

Turning our attention to the regional climate fluctuations in the source regions and how they impact decadal heat content change at 25°N overtime, we show in Fig. 4 the SST anomalies (ΔSST) times series in the source regions for the largest contributors and the ΔOHC responses at 25°N. First, we analyse the ΔSST times series. The signatures of the main climate periods identified by numbers 1–6 in Fig. 4 are readily seen on the regional ΔSSTs albeit modified by the interplay with North Atlantic Oscillation (NAO)45,46. NEA SubP and Lab-Irm SSTs show cooling during NAO-positive phases (NAO+, e.g., 1900–22, 1972–95, also periods of enhanced convection) and, in opposition, Nordic SST experiences warming during those NAO+ periods and cooling during NAO− (1955–1971, Fig. 4a, b, f)47,48,49, consistent with Deser et al.48. NAO changing phases are thus seen enhancing or counteracting the main climate fluctuations in ΔSST as further discussed below (Fig. 4a, c, d). Because Green’s functions allow us to calculate the impact at 25°N of SST variability of each 5° × 5° patch, they are unique tools to identify how these superimposed signals propagate and when these signals reach 25°N. This is evidenced in Fig. 4b–f showing that ΔOHC time series at 25°N bears a strong resemblance to the corresponding uptake region ΔSST time series with a lag equivalent to the modal age of the transit time distribution (see also Supplementary Fig. 3). Those modal ages range from 0 to 5 years in the SA SubT and NA SubT, 10 years in the NEA SubP to 40–55 years for regions contributing below 700 m (Lab-Irm, Nordic, Antarctic, Sub-Ant, Med-Sea). The correspondence is not one to one however as the Green’s Function age spectrum, which characterises the cumulative ventilation, is far more complex than a single time scale50 (Supplementary Fig. 3) due for example to the multiplicity of pathways between the source regions and 25°N (rapid propagation within the deep western boundary current46,51, slower interior routes and recirculations, mixing). Still, the low-frequency variability of ΔSST being preserved during propagation, insights on how and when regional climate fluctuations impact ΔOHC decadal variability at 25°N can be drawn from Fig. 4 and quantified hand in hand with a detailed view of the source region contributions to the different depth layers (Fig. 5).

Figure 5 highlights NA SubT and Lab-Irm as the main contributors to the 25°N OHC variability. The NA SubT sets the upper ocean ΔOHC; its contributions cancel out over the 1850–1997 period after which NA SubT builds up the layer warming (4.3 ± 1.5 ZJ) augmented by NEA SubP (1.1 ± 0.3 ZJ). The overall NEA SubP contribution is, however, negative in response to ΔSST that remained mostly negative since 1850 (Fig. 4b). Lab-Irm sets the intermediate layer ΔOHC with clear signatures of both the NAO phases and the main climate fluctuations but overall shows a warming accumulation in response to the continuously positive ΔSST since 1850 (Fig. 4c). As the upper ocean cools (−5.7 ± 0.7 ZJ) between 1850 and 1923 (Fig. 5a), the intermediate layer at 25°N shows a heat gain coming from warming in Lab-Irm (2.6 ± 0.7 ZJ) moderated by cooling in Med-Sea (−0.8 ± 0.5 ZJ). Then, between 1923 and 1959 (Fig. 5b), the intermediate layer shows a modest heat loss (−1.4 ± 0.5 ZJ) from all its contributors which we attribute to the predominance of the late-nineteen-century cooling and a switch to NAO+. The high heat gain between 1959 and 1997 (Fig. 5c, d) builds up from Med-Sea (1.0 ± 0.4 ZJ) and Lab-Irm (5.4 ± 0.7 ZJ) from the lagged response to the early-twentieth-century warming delayed until 1975 in Lab-Irm by NAO+ (Fig. 4c, f). The reversal to an intense heat loss (−3.5 ± 0.6 ZJ) between 1997 and 2005 (Fig. 5e) is attributed to the superimposition of Lab-Irm deep winter convection (1950–1955)52 with the mid-twentieth-century cooling (Fig. 4c). Heat gain (2.2 ± 0.6 ZJ) at 25°N resumes between 2005 and 2018 (Fig. 5f) mainly from the interruption of the mid-twentieth-century cooling in Lab-Irm and the shutdown of deep convection under NAO−53 (1955–1971, Fig. 4a, c). Because of the lagged response of the deep ocean to surface conditions, the Green’s Function framework also provides a new forecasting tool for deep OHC change on time scales of the modal ages, assuming no change in the circulation which is constrained here by the five 1992–2016 hydrographic surveys (‘Methods’). From 2018, Fig. 4c forecasts a slight decrease in OHC at 25°N, echoing the 1965–1975 SST cooling in Lab-Irm. It is followed by modest changes as the 1975–1995 NAO+ counteracts the late-twentieth-century warming. The latter then drives a substantial OHC increase (4 ± 0.8 ZJ) between 2045 and 2060 interrupted by a slight reversal in response to the recent 2006–2018 SST cooling period. Although those cooling events have produced replenishments of convected water under NAO+52,54, the latter vintage was warmer than the vintage of the early 1990s suggesting that it has sequestered anthropogenic warming (Fig. 4c). Our results clearly forecast a continuity of the century-scale warming for waters coming from Lab-Irm, Med Sea and Sub-Ant (the latter plateauing around 2035, Fig. 4c, f and Supplementary Fig. 5h) and thus for the 700–2000 m layer.

The ΔOHC of the 2000–4000 m layer is mainly influenced by the contribution of Lab-Irm and Nordic, the latter displaying low-frequency intervals of ~70 years between two successive heat losses (Fig. 4d). Between 1850 and 1923 (Fig. 5a), ΔOHC shows a slight heat gain coming from Lab-Irm warming (1.0 ± 0.5 ZJ) tempered by cooling from Nordic (−0.6 ± 0.4 ZJ). Between 1923 and 1997 (Fig. 5b–d), heat gain originates mostly from Nordic (2.4 ± 1.0 ZJ) warmed during the NAO+ that interrupted the late-nineteenth-century cooling, and then by the subsequent early-twentieth-century warming (Fig. 4d), with Lab-Irm contributing less (1.1 ± 0.4 ZJ). The 1997–2005 period (Fig. 5e) shows a heat loss, previously described43, that comes also primarily from Nordic (−0.4 ± 0.4 ZJ) and is attributed to the lagged response to the 1950–196049 mid-century cooling reinforced by NAO- (Fig. 4d). It reverts to warming for 2005–2018 (Fig. 5d, 0.8 ± 0.4 ZJ). The abyssal layer shows a comparable ΔOHC pattern but for an earlier and stronger occurrence of the recent shift to a cooling (1987, Fig. 2 and Supplementary Fig. 6) from Nordic (−0.9 ± 0.4 ZJ between 1975 and 2005) while Antarctic contributes to modest warming from 1975 (0.2 ± 0.2 ZJ). Finally, Fig. 4b forecasts an acceleration of Nordic contribution to the deep and abyssal warming at 25°N in response to the late-twentieth-century warming since 1970. This would make them the dominant contribution to heat gain below 700 m. We estimate that Nordic will contribute to a warming of 16 ZJ (~0.3 °C) at 25°N over 2018–2065 so 4 times the warming from Lab-Irm.

Nordic and Lab-Irm show very different responses at 25°N due in part to the opposing influence of the NAO on these two regions of North Atlantic deep water formation. Thus, during 1850–2018, deep water warming was dominated by Lab-Irm, which experienced an interruption of mid-century cooling by the 1960–1970 NAO- while Nordic had an enhancement of cooling. Also, Lab-Irm showed warming SST during 1865–1890 while Nordic SST was cooling, an opposition likely due to NAO- conditions (Fig. 4a, c and refs. 55,56). The roles will be reversed in the next 5 decades because Lab-Irm warming has been mitigated by successive NAO+ during 1971–1995 and 2012–2018 while Nordic has experienced enhanced warming by these NAO+ and horizontal heat transport increase from the ocean25,57.

The predominance of the warming of the full water column by the layers below 700 m was noted for the 1850–2018 long time scales (Fig. 3). The analysis of the interdecadal ΔOHC variability shows that the intermediate and deep waters at 25°N responded in the last decades to the mid-twentieth-century cooling (Fig. 4). As a result, and in opposition to 1850–2018, the strong full-depth warming for 1975–2018 (14.2 ± 1.9 ZJ, Fig. 2 and Supplementary Fig. 7) is predominantly due to the rapid response of the upper ocean39 (9.3 ± 1.6 ZJ or 65%) to the late-twentieth-century warming and twenty-first-century acceleration while the contribution of the deeper waters is lower. Our study forecasts an important heat gain in the deep ocean of the Subtropical North Atlantic in the next 50 years as it will carry the impact of the late-twentieth-century warming as well as a modest but increasing warming from the Southern Ocean (Supplementary Fig. 5).

### Where does the 25°N excess heat go?

Having identified the source regions of the 25°N excess heat, we now determine how the inferred excess heat is redistributed towards the north and south of the section. Figure 6 shows the excess heat transport time series across 25°N relative to its 1975–1986 mean (ΔXHT, ‘Methods’). This analysis was limited to times when we had information on the circulation strength and climatologies concord. ΔXHT time series were estimated for each of the 1992–2015 surveys and are driven by the temperature change only (each ΔXHT time series was determined using the ΔT times series and the velocity field at the time of the survey, ‘Methods’). ΔXHT five-survey standard deviation however includes variability due to circulation changes between the revisits of the section (‘Methods’). For 2018, the five-survey net transport average is 19.0 ± 3.5 TW northward, liable at 86% to the AMOC (Fig. 6a). The upper (lower) limb of the AMOC carries excess heat northward (southward). Above 1000 m, in the AMOC upper limb, the northward ΔXHT amounts to 22.9 ± 7.5 TW. Below 1000 m, 3.9 ± 1.1 TW of excess heat are carried southward (Fig. 6c) mainly in the deep western boundary current where higher excess heat correlates with higher southward velocity.

The northward transport of ΔXHT across 25°N supplies heat to the north of the section at a rate that is compared in Fig. 6a to the rate of change of OHC between 25°N and the Bering Strait ($$\frac{\partial {{{{{{\rm{OHC}}}}}}}}{\partial t}{|}_{ > 25{{{{{\rm{N}}}}}}}$$), the latter integrating the oceanic response to all drivers. The AMOC strength variability is known to modulate the heat content of the North Atlantic58, with a weaker (stronger) AMOC carrying less (more) heat northwards. Accordingly, $$\frac{\partial {{{{{{\rm{OHC}}}}}}}}{\partial t}{|}_{ > 25{{{{{\rm{N}}}}}}}$$ increases by ~1 W m–2 abruptly in 1990 following an AMOC59 strengthening and drops back by ~1 W m–2 in 2009 as the AMOC returns to a weaker state59,60 (Fig. 6a, b). During this period the northward ΔXHT increased due to the continuous warming of the upper layer. The difference between the ΔXHT and the warming north of 25°N can be attributed to the impact of the AMOC strengthening resulting in a larger transport of warm water northward during 1990–2009. For 2012–2018, which was under a weak AMOC, the net northward ΔXHT accumulates excess heat north of the 25°N section at an average rate of 0.89 ± 0.19 W m–2, equivalent to the 0.82 W m−2 estimated for $$\frac{\partial {{{{{{\rm{OHC}}}}}}}}{\partial t}{|}_{ > 25{{{{{\rm{N}}}}}}}$$, revealing a substantial role of ΔXHT to the warming of the North Atlantic. Noteworthy, 24% of this ΔXHT comes from the southern hemisphere (SA SubT, Sub-Ant, Antarctic, Supplementary Fig. 8). Overall, the excess heat redistribution contributes to a North Atlantic warming similar to ocean global warming of 0.65 ± 0.11 W m−2 reported for 2006–2015 from observations9,61 (here we have 0.67 ± 0.19 W m−2 for 2006–2015).

The AMOC lower limb (Fig. 6b) is found to warm the deep world ocean at a rate of 0.011 ± 0.004 W m−2 (2011–2018). Below 2000m, the warming rate of 0.009 ± 0.003 W m−2, which is smaller than the average warming of the global ocean below 2000 m depth (0.06 ± 0.03 W m−2 for 1992–201113,61). This evidences a contribution of the northern hemisphere to long-term storage of heat in the deep world ocean with a temporary low rate, which is explained by the recent impact of the mid-twentieth-century cooling from the Nordic, Labrador and Irminger Seas.

## Discussion

As GHGs are warming the planet, how is the vast surface uptake of excess heat by the oceans redistributed in the ocean interior? To dredge into this question, we determined Green’s functions to relate sea surface temperature variability of the world ocean to full depth sub-surface temperature at 25°N in the Subtropical Atlantic since the beginning of the industrial era. Our new historical reconstructions of heat content at 25°N are broadly consistent with prior studies with uncertainties expected to decrease as SST reconstructions continue to improve. Our reconstruction shows a fairly coherent view of the excess heat uptake and redistribution in regard to regional climate fluctuation. In particular, we identify the response to the North Atlantic Oscillation as key to explain some of the differences between the variability of deep and intermediate layer heat contents captured at 25°N in decadal surveys. Over 1850–2018, the reconstruction for the waters below 700 m evidences crucial warming contributions from the Labrador (dominant) and Nordic Seas. Recently, those seas have cooled the deep subtropical North Atlantic in response to the mid-twenty-century cooling before reversing to warming. Our work suggests that the deep subtropical North Atlantic will continue in the future its overall warming as a delayed response to the warming of the Nordic Seas since 1970 and Lab-Irm since the 1990s, alongside the Antarctic Bottom Water warming trend since the 1990s (Fig. 4c, d and Supplementary Fig. 5i) and thus stresses the importance of deep waters for Earth energy imbalance and sea-level rise predictions.

The warming north of 25°N by the northward transport of excess heat is consistent with observations for the Mediterranean Arctic25 and with models22 that showed northward redistribution of excess heat in the Atlantic. Our study evidences a crucial role of excess heat transport for the heat balance north of 25°N and identifies the AMOC as a primary mechanism for redistributing the excess heat. Noteworthy, we obtained a 24% contribution from the southern hemisphere to the northward transport of excess heat that counteracts the hemispheric asymmetry of Atlantic air-sea excess heat uptake. We estimated that the AMOC carried a continuously increasing net northward transport of excess heat since 1997 relative to 1975–1986 before reaching a plateau ~19 TW of excess heat transport in 2012–2018 that remarkably equals the heat content change north of the section up to the Bering Strait. We speculate that some of the northward transport of excess heat will contribute to accelerate the warming of the Arctic Mediterranean Seas and melt of sea ice.

## Methods

### Data

The ocean interior observations are eight snapshots of the circulation spread over 145 years. They are the 1870s HMS Challenger expedition and the seven repeat hydrographic surveys performed between 1957 and 2015 along the 25°N World Ocean Circulation Experiment (WOCE) A05 section, although they did not all follow exactly the same track and did not all measure all the tracers of interest (Supplementary Table 1 and Fig. 1). The spatially sparse depth and temperature measurements from the 1870s are taken from Gebbie15. Temperature, salinity and pressure data were collected for the seven A05 hydrography surveys. The water samples were analysed for geochemical tracers—dissolved oxygen (O2), nitrate (NO3), phosphate (PO4), dichlorodifluoromethane (CFC-12), trichlorofluoromethane (CFC-11)—for 1992, 1998, 2004, 2010 and 2015. Sulfur hexafluoride (SF6) was analysed in 2010 and 2015. The background ΔC14 data were interpolated from the Global Ocean Data Analysis Project (Glodap) gridded data set62 onto the 25°N survey locations. For the determination of the Green’s functions (see below), we used the last 5 surveys that have nutrient and transient tracer (CFC-12, CFC-11, SF6 and ΔC14) data. For the Bayesian adjustment to observed temperatures (see below), we used all the surveys except the Challenger data because of the very coarse sampling of the latter (see Supplementary Fig. 1). However, we used the Challenger data as independent measurements for the comparison to our time series in the 1870s in Fig. 2.

The global surface boundary conditions cover the full world ocean and were obtained from different data sets at 1° latitude × 1° longitude spatial resolution. The O2, PO4 and NO3 surface concentrations were taken from the World Ocean Atlas 201363 mean annual cycle. The surface background ΔC14 was taken from Glodap. In high latitudes where surface background ΔC14 is missing in Glodap, it was computed from Glodap v264 alkalinity using the correlation between potential alkalinity and background ΔC14 following Rubin and Key65. The CFC-11, CFC-12 and SF6 ocean surface concentration histories are from a mixed layer model66 taking into account their increasing saturation overtime for 1936–2010 and extended to present using atmospheric data from the National Oceanographic and Atmospheric Administration (NOAA) Earth System Research Laboratory (ERSL) Halocarbons and other Atmospheric Trace Species (HATS) group. Sea surface salinity histories from 1900 to 2018 are from the UK MetOffice EN4 reanalysis67. Sea surface temperature (SST) time series are from the NOAA Extended Reconstructed Sea Surface Temperature version 5 (ERSST v568). It covers 1854 to present and was extended back in time to year 0 using the EQ–0015 global SST recovered from paleoclimate data69 to include the impact of the warm medieval period and the little ice age. We also used an ensemble of 1000 members from ERSST v4 whose spread represents the uncertainty on the SST.

We used the following gridded ocean temperature datasets for comparison to our reconstruction at 25°N: the MetOffice statistical ocean reanalysis EN467 (1900 to the present, monthly, surface to bottom), the objective analysis of temperature of Ishii et al.70 (1945 to 2012, monthly, top 2000 m), the objective analysis of temperature of the Institute of Atmospheric Physics Global Ocean Temperature26 (IAP, 1940–present, monthly, top 2000 m), and the autoregressive artificial neural network (ARANN, 1946–2019, biannual, surface to bottom) from Bagnell and DeVries17. For convenience, all the gridded products used in this paper are called reanalyses.

### Determination of the Green’s functions

We assume that tracer propagation in the ocean can be modelled by a Green’s Function that relates time-and-space varying surface boundary conditions to interior tracer distributions71. We use the maximum entropy principle72 (MEP), which has the ability to incorporate prior information, and observational constraints to estimate a Green’s Function G for each sampling point in the ocean interior. G is a probability density function depending on transit times and surface locations (when and where the last contact of the water with the atmosphere occurred). Our set-up of the MEP follows previous work33,73 and our notations were adapted from Holzer et al.33, which can be referred to for further details. G has three dimensions (s: surface patches, n: years and m: months) and was estimated for transit time in the range 0–2000 years, 12 months per year and 836 patches corresponding to a division of the surface ocean into 5° latitude × 5° longitude (see Supplementary Note 3 for details of the discretization). Given the measurement $${C}_{j}^{I}({r}_{0},{n}_{0},{m}_{0})$$ of a tracer j at location r0 and time (n0, m0) in the ocean interior (I) and the surface boundary condition $${C}_{j}^{{{{{{{\rm{Surf}}}}}}}}(s,n,m)$$ for this tracer at location and time (s, n, m), the Green’s Function $${{{{{\mathscr{G}}}}}}\left({{{{{\rm{s}}}}}},{{{{{\rm{m}}}}}},{{{{{\rm{n}}}}}}|{r}_{0},{n}_{0},{m}_{0}\right)$$ relates surface boundary conditions to interior data such that

$${{{{{{\mathscr{C}}}}}}}_{j}^{I}({r}_{0},{n}_{0}{,m}_{0})=\mathop{\sum }\limits _{s,m}{{{{{\mathscr{G}}}}}}\left({{{{{\rm{s}}}}}},{{{{{\rm{n}}}}}},{{{{{\rm{m}}}}}}|{r}_{0},{n}_{0}{,m}_{0}\right)* {C}_{j}^{{{{{{{\rm{Surf}}}}}}}}(s,n,m)$$
(1)

where * denotes the convolution product and $${{{{{{\mathscr{C}}}}}}}_{j}^{I}$$ is an estimate of $${C}_{j}^{I}$$. Given an a priori estimate $$\mu \left(s,n,m|{r}_{0},{n}_{0}{,m}_{0}\right)$$ of $${{{{{{\mathscr{G}}}}}}}$$ and following the MEP, $${{{{{{\mathscr{G}}}}}}}$$ is uniquely defined for the maximum of

$$S=-\mathop{\sum }\limits _{s,n,m}{{{{{\mathscr{G}}}}}}\,{{\log }}\left(\frac{{{{{{\mathscr{G}}}}}}}{\mu }\right)+\mathop{\sum }\limits_{j=1}^{J}{\lambda }_{j}\left({C}_{j}^{I}-{{{{{{\mathscr{C}}}}}}}_{j}^{I}\left({{{{{\mathscr{G}}}}}}\right)\right)$$
(2)

where J is the number of measured tracers and λj are Lagrange multipliers. $${{{{{\mathscr{G}}}}}}\left({{{{{\rm{s}}}}}},n,m|{r}_{0},{n}_{0}{,m}_{0}\right)$$ defines the probability that a mixing component at location s and a transit time (n, m) contributes to $${C}_{j}^{I}$$. The cost function S combines the maximum entropy regularisation term (first term on the right-hand side) and the constraints (i.e., the differences between the estimated $${{{{{{\mathscr{C}}}}}}}_{j}^{I}$$ and the measured tracer concentrations $${{C}}_{j}^{I}$$). It permits reconstructing the observations exactly and their time histories at their sampling points. The determination of the maximum of the cost function S follows Holzer et al.33.

We focus on the subtropical Atlantic Ocean and the five repeats of the 25°N hydrographic section where geochemical tracers were measured. We used interior observations of eight tracers and their surface boundary conditions to compute the Green’s functions. The eight tracers are: potential temperature θ, practical salinity S, preformed nitrate NO3*, preformed phosphate PO4*, chlorofluorocarbon CFC-11, CFC-12, sulfur hexafluoride SF6, and the prebomb ΔC14*. NO3* and PO4* were computed using Redfield ratio independent of the region (175:17:1 for O2:NO3:PO4). Transit time distributions71 (the time-dependant part of G) are mostly constrained by the time-evolving transient tracers CFCs, SF6 and ΔC14*. The latter covers millennial to centennial timescales74,75, whereas CFCs and SF6 cover shorter time scales. For example, the CFC-12 (SF6) atmospheric history started in the 1930s (1960s) so go back 90 (60) years only. These man-made-compounds have a fairly well-known and rapidly changing time history, providing a convincing constraint on transit time76,77 on those shorter time scales.

The tracer surface boundary conditions were derived from the surface data sets reported above. For some data sets, the seasonal cycles were not available in the distant past. In these cases, we added to the annual value a mean seasonal cycle derived from the years of the time series for which the seasonal cycle was available. NO3* and PO4* were taken as cyclo-stationary following Holzer et al.33 (mean and seasonal values are stationary and values are repeatedly cycled for each year).

The time dependency of the prior μ is given for each sampling point by the inverse Gaussian Transit Time Distribution of a 1-D advection-diffusion ocean transport model that matches the combination of the transient tracer data78. In our application of the Transit Time Distribution method, we adjusted the Peclet number (square ratio between the mean age and the width of the transit time distribution quantifying advection relative to mixing in the transport79). The location dependency of the prior µ was estimated by an Optimal Multi-Parameter80 approach that calculates the contributions from the water mass formation area in the nine regions defined in Fig. 3 to each sampling point using corresponding surface values of the tracers.

The reconstructed time-series for tracer $${{{{{{\mathscr{C}}}}}}}_{j}^{I}({r}_{0},n,m)$$ was computed as:

$${{{{{{\mathscr{C}}}}}}}_{j}^{I}\left({r}_{0},{n}_{k},m\right)=\mathop{\sum }\limits _{s,m}{{{{{\mathscr{G}}}}}}(s,n,m|{r}_{0},{n}_{k},m)* {C}_{j}^{{{{{{{\rm{Surf}}}}}}}}(s,n\ge {n}_{k},m)$$
(3)

where nk is a year lag varying between present (nk = 0) and 2000 years back in time. Note that although the resolution is monthly, the time series of temperature presented in Fig. 2 are annual averages. Note that we use the same $${{{{{\mathscr{G}}}}}}(s,n,{m|}{r}_{0},{n}_{k},m)$$ for all lags nk, which implies steady state.

The contributions of a given 5° × 5° patch sl to $${{{{{{\mathscr{C}}}}}}}_{j}^{I}({r}_{0},{n}_{k},m)$$ was obtained as $$\mathop{\sum}\limits_{m}{{{{{\mathscr{G}}}}}}(s,n,{m|}{r}_{0},{n}_{k},m)* {C}_{j}^{{{{{{{\rm{Surf}}}}}}}}({s}_{l},n\ge {n}_{k},m)$$. The contributions of the 9 regions (Figs. 3 and 5) were obtained by summing over all patches sl belonging to each of the regions.

Each set of Green’s functions and corresponding potential temperature time series are specific to the survey they were inferred from and to the Green’s functions time frame, 0 to the date of the survey. Nevertheless, 5 potential temperature time series inferred from the 5 surveys show much similarity (Supplementary Fig 2), giving confidence on the robustness of the methodology. Yet, the potential temperature θ time series of the depth layers reconstructed from one survey does not fully capture all the variability specific to the other 7 surveys (Supplementary Fig 2). Therefore, we further adjusted each of the 5 sets of G to the observations of the 7 surveys (1957 to 2015) to ensure that the reconstructed temperature time series be close in a least squares sense to all temperature observations, merging compatibly the information from all surveys. This was done by minimising the following cost function:

$${({{{{{{\mathscr{G}}}}}}}_{{{{{{{\rm{bayesian}}}}}}}}-{{{{{\mathscr{G}}}}}})}^{2}+\alpha \,\mathop{\sum }\limits _{I}\frac{{\left({\theta }^{I}\left({{{{{{\mathscr{G}}}}}}}_{{{{{{{\rm{bayesian}}}}}}}}\right)-{\theta }_{{{{{{{\rm{hydrographic}}}}}}}}^{I}\right)}^{2}}{{({\sigma }^{I})}^{2}}$$
(4)

where $${{{\mathscr{G}}}}_{{{\rm{bayesian}}}}$$ is the adjusted Green’s Function, $${\theta }^{I}\left({{{{{{\mathscr{G}}}}}}}_{{{{{{{\rm{bayesian}}}}}}}}\right)$$ is the potential temperature obtained by convoluting $${{{\mathscr{G}}}}_{{{\rm{bayesian}}}}$$ with the SSTs, $${\theta }_{{{{{{{\rm{hydrographic}}}}}}}}^{I}$$ are the temperature observations from the hydrographic sections, σI is the error associated with $${\theta }_{{{{{{{\rm{hydrographic}}}}}}}}^{I}$$ and α is a weighting factor selected such that after minimisation the two terms of the cost function be order 1.

The σI are reported in Fig. 2 and include errors due to seasonal variability and to the different tracks of different cruises. Both errors were estimated by simulating each cruise in the EN4 data set and computing the deviations from the annual mean and from a reference track (see Supplementary Fig. 1). Note that, given their very coarse sampling, Challenger data were not used in the Bayesian adjustment, but were kept as independent measurements for display in Fig. 2.

Heat content was obtained by summing the temperature data multiplied by ρ0CP (where ρ0 is the density of seawater, CP is seawater heat capacity, ρ0CP = 4.1 × 106 J m−3 K−1 was used throughout) and by the area A associated with each grid point.

### Uncertainties

The errors on our potential temperature θ time series were computed as follows. First, a set of Green’s functions (there is one Green’s function per sampling point) was estimated for each of the 5 hydrographic surveys. Then, each of these sets of Green’s functions was convoluted with the NOAA-ERSSTv5, and each of the 1000 members of the NOAA-ERSSTv4 SST ensemble (perturbations of NOAA-ERSSTv4 built so that the standard deviation of the 1000 members describe the error on the SSTs) leading to the 5005 different time series of temperature anomaly along the 25° N line. The errors are the standard deviations of these 5005 estimates. Therefore, these errors account for the standard deviations in the SST as described by the 1001 different SSTs, as well as uncertainties in tracer measurements and standard deviation due to changes in the circulation81 as described by the 5 different sets of Green’s functions derived from the 5 different hydrographic surveys (the Green’s functions carry information about the transport by the circulation of the admixture components from the time they left the surface to the time of sampling.).

The Green’s functions represent the circulation that has propagated the tracers measured during the five hydrographic surveys of 1992–2015. Changes in the circulation outside this sampling period are therefore not reflected in these Green’s functions and the circulation used for our reconstructions is biased towards this sampling period. For the same reason, the uncertainty due to the circulation can have a similar bias. Typically, we expect 10% to 15% changes in AMOC intensity over the last millennium82,83,84. Noteworthy, it has been suggested that a ±25% change in the circulation, applied to the little ice age relative to the 1990s, does not affect the qualitative patterns of ΔT propagation in the North Atlantic over the common era and causes only limited changes in the signal amplitudes and times of arrivals69 (their Fig. 3S).

### Transport calculations

The absolute geostrophic velocity field perpendicular to the hydrographic survey was estimated for each of the five repeated surveys following Atkinson et al.30. A reference velocity was determined to reach a balance in volume transport between the Ekman transport, the Gulf Stream and interior geostrophic transports. Velocities in the bottom triangle (area below the deepest common level of the two hydrographic profiles used to compute geostrophic velocity) were computed as in Atkinson et al.30. The Gulf Stream and Ekman transports were from Atkinson et al.30 except for the 2015 transports that were from Morarji85. Volume transports were computed by multiplying the velocities by the area associated with each grid point as for the computation of heat content, taking into account that the velocity grid is at mid-distance between two hydrographic stations. Heat transport time series across the section presented in Fig. 6 was computed by first interpolating the temperature estimates on the same vertical grid as the velocity, then converting the temperature to heat, then averaging heat at two adjacent hydrographic stations and multiplying it by the velocity and the associated area. This was done for each time step of the temperature time series and for each cruise using the velocity field derived from this cruise. The time series in Fig. 6 are the averages of the times series computed for the five repeated CTD surveys performed during 1992–2015. Their 1975–1986 mean is set at zero for reference.