Attribution of interannual-to-centennial sea-level changes in climate models

Attribution of interannual-to-centennial sea-level changes in climate models | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Attribution of interannual-to-centennial sea-level changes in climate models Ou Wang, Tong Lee, Thomas Frederikse, Ichiro Fukumori, Ian Fenty This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7087515/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract Dynamic sea level along the United States (U.S.) East Coast has risen in recent decades and is projected to continue rising throughout the 21st century, according to most climate models from the Coupled Model Intercomparison Project Phase 6 (CMIP6). However, the mechanisms by which ocean surface forcing drives this rise remain unclear. Understanding these processes is critical for improving sea-level projections. The adjoint sensitivity-based attribution method from the Estimating the Circulation and Climate of the Ocean (ECCO) project provides a means to establish causal relationships between sea level and ocean forcings. Here, we demonstrate that by convolving ocean forcings from a CMIP6 model with ECCO adjoint sensitivities of sea level to these forcings, we can reconstruct sea-level variations along the U.S. East Coast from 2000 to 2100 in the CMPI6 model. We identify subpolar North Atlantic surface heat flux as the key driver of the long-term trend, while wind stress dominates interannual-to-decadal variability. Earth and environmental sciences/Climate sciences/Climate change/Attribution Earth and environmental sciences/Climate sciences/Climate change/Projection and prediction Earth and environmental sciences/Climate sciences/Climate change/Climate and Earth system modelling Earth and environmental sciences/Climate sciences/Ocean sciences/Physical oceanography Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1. Introduction Human activity has warmed the Earth (IPCC, 2021), leading to substantial societal impacts due to sea-level rise (SLR) resulting from climate change (Fox-Kemper et al., 2021). However, regional sea-level changes can be significantly different from global mean sea level (GMSL) changes. Regional sea-level change includes contributions from the ocean's dynamic response to atmospheric, hydrological, and cryospheric forcings (hereafter referred to as ocean forcing )—known as sterodynamic sea-level change—as well as from vertical land motion and Earth’s gravitational and rotational adjustments (Sweet et al., 2022). This study focuses on sterodynamic sea-level change relative to the global mean, often referred to as dynamic sea-level change (Gregory et al., 2019). Sterodynamic effects cause large regional differences in local sea-level changes along the U.S. coastline (Harvey et al., 2021). However, distinct sectors can be identified within which sea-level variations are remarkably coherent. For instance, coastal sea-level variations in the Northeast Sector (Maine to Cape Hatteras, North Carolina) and the Southeast Sector (Cape Hatteras to Florida) are more coherent within each sector than they are between different sectors (e.g., Wang et al., 2024). The relatively lower coherence of sea-level variations across sectors reflects the diverse nature of their underlying forcing mechanisms (Calafat et al., 2018; Diabaté et al., 2021; Ezer, 2019; Frederikse et al., 2017; Little et al., 2021; Piecuch et al., 2016; Thompson, 1986; Volkov et al., 2019, 2022, 2023; Wang et al., 2022; Wang et al., 2024; Yin, 2023). The El Niño-Southern Oscillation (ENSO) and Pacific Decadal Oscillation (PDO) significantly influence sea-level variations along the entire West Coast (e.g., Bromirski et al., 2011; Verdy et al., 2014; Hamlington et al., 2022), while open ocean Rossby waves can considerably affect sea-level variations on the Southeast and Gulf Coasts (Dangendorf, et al., 2023). Despite progress in understanding these sea-level changes and their forcings—including wind vs. surface buoyancy (e.g., Cabanes et al. 2006; Köhl & Stammer, 2008; Piecuch & Ponte, 2012, 2013; Forget & Ponte, 2015; Stammer et al., 2013 and the references therein) and local vs. remote atmospheric impacts (e.g., Piecuch et al., 2016, 2019; Dangendorf et al., 2023)—many studies rely on correlation analyses, which cannot establish causality, or are based on simple models, which exclude important physical processes. Correlation-based analyses have related sea-level variations along the East Coast to local and remote forcings (Andres et al., 2013; Dangendorf et al., 2023), the Gulf Stream and the Florida Current (Ezer, 2019), the Atlantic Meridional Overturning Circulation (AMOC) (Little et al., 2019; Zhang et al., 2025), gyre-scale heat convergence (Volkov et al., 2019, 2023; McCarthy et al., 2015; Steinberg et al., 2024), climate modes (Dong et al., 2022; Kopp, 2013; McCarthy et al., 2015; Valle-Levinson et al., 2017), steric height in ocean interior (Frederikse et al., 2017), and others. These studies suggest that a common forcing—or multiple covarying forcings—may influence sea level and other related variables. Over the next three decades, regional SLR along the U.S. coastlines is projected to exceed GMSL rise, with the East and Gulf Coasts expected to experience greater increases than the West Coast (Sweet, et al., 2022). By 2080–2099, the subpolar North Atlantic is projected to experience one of the highest regional SLRs, with the multimodel mean sea level more than 20 cm higher than in 1995–2014 under various Shared Socioeconomic Pathways (SSPs) (Jevrejeva et al., 2024; Lyu et al., 2020). The influence of ocean forcing will likely continue to exhibit significant geographical variability. Earth's warming adds uncertainty to regional sea-level projections because ocean forcing is changing in ways which are difficult to predict (e.g., Widlansky et al., 2020). The efficacy of regional dynamic sea-level projections hinges critically on a comprehensive understanding of which, where, and how ocean forcing drives sea-level variations. Coupled climate models, such as those of the Coupled Model Intercomparison Project Phase 6 (CMIP6), are essential for understanding past and present climate and for projecting future changes under different SSPs. While these models provide projections of sea level and other climate variables, it is critical to identify which forcings—and from which regions—drive projected sea-level changes. This knowledge is key to improving projection accuracy. To achieve this, models must accurately capture the dominant forcing contributions, which are likely regionally dependent. One way to gain insight into these contributions is through forcing perturbation experiments, where a specific forcing in a given region is slightly modified, and the resulting model response is compared to the original run to isolate the impact of that forcing. However, such experiments are computationally expensive, making it impractical to isolate the effects of different forcing types, regions, and time periods. Here we describe an innovative proof-of-concept study that identifies the key forcing of regional sea-level change by leveraging the resources of the Estimating the Circulation and Climate of the Ocean (ECCO) system. ECCO produces global ocean and sea-ice state estimates by synthesizing satellite and in-situ observations with a state-of-the-art ocean circulation model, the Massachusetts Institute of Technology General Circulation Model (MITgcm). These estimates adhere to the fundamental laws of physics and thermodynamics, which relate the ocean’s time-evolving state to its forcing (Heimbach et al., 2019). A unique strength of ECCO is its adjoint model (Wunsch & Heimbach, 2007), which is not generally available for climate models. The same adjoint model used for state estimation in ECCO can also efficiently compute sensitivities of any modeled quantity of interest (QoI) to its different forcings as a function of lead time and space. In contrast to forward model sensitivities—which require a large number of perturbation experiments—the adjoint model can evaluate the OoI sensitivities in a single model integration, making it far more computationally efficient. The utility of adjoint sensitivity in attribution studies has been demonstrated in investigating the drivers of sea-level variations in the Mediterranean Sea, the Arctic Ocean, and along the U.S. East Coast (Fukumori et al., 2007, 2015, 2021; Wang et al., 2022, 2024). In these studies, the ECCO adjoint sensitivities are convolved with the ECCO forcing to reconstruct the QoI simulated by the fully nonlinear ECCO model. If the reconstructed QoI reproduces the OoI simulated by the fully nonlinear model, one can attribute the forcing contributions based on the linearity of the reconstruction (see Eq. ( 1 ) later in the paper). The adjoint-based method allows precise, quantitative attribution of sea-level variations or other QoIs to specific ocean forcings and establishes causal mechanisms that correlation-based analyses cannot achieve. The adjoint-based attribution method diagnoses the underlying causal mechanisms with a high degree of granularity that exceeds what is possible with traditional forward model sensitivity experiments. Note that the aforementioned attribution studies are based on the ECCO state estimation framework, with both adjoint sensitivities and forcings derived from the ECCO model. It would be valuable to conduct similar adjoint-based attribution studies on projected sea-level variations from coupled climate models to better understand future sea-level changes under different emission scenarios and potentially to improve projection accuracy. Such information is crucial for informing climate-related policies, including efforts to avoid reaching climate-change tipping points. However, at present, adjoint models are not available in climate models for computing these sensitivities, except in some exploratory studies (Stammer et al., 2018). To circumvent the lack of adjoint sensitivities in climate models, we hypothesize that, to first order, the physics of state-of-the-art ocean models used in ECCO and in coupled climate models of comparable resolutions are similar. Both are governed by the Navier-Stokes equations and represent the physics of the ocean. The sensitivities that reflect the ocean’s response to ocean surface forcings should therefore also be consistent between ECCO and these climate models. Successfully reconstructing the projected sea-level variations in climate models using this approach would enable attribution studies of future sea-level changes and provide insights into their underlying causal mechanisms. In this paper, we demonstrate that we can successfully reconstruct projected sea-level variations through 2100 at Nantucket, MA, and Charleston, SC, from a CMIP6 climate model, MPI-ESM1.2-HR (Müller et al., 2018), by convolving ECCO adjoint sensitivities with forcings from that CMIP6 model. We then analyze the different terms of this convolution to conduct attribution studies of projected coastal sea-level variations in the 21st century. Under scenario SSP5-8.5, MPI-ESM1.2-HR projects that dynamic sea-level changes at both locations from 2000 through 2100 are dominated by a linear trend of SLR: a 25 cm rise at Nantucket and 10 cm rise at Charleston. Heat flux is the dominant contributor to the long-term dynamic sea-level trend at both locations. Spatially, for both Nantucket and Charleston, the heat flux contributions to the linear trends are mainly from the subpolar North Atlantic. For interannual-to-decadal sea-level variations, however, wind stress is the primary contributor at both locations but exhibits markedly different spatial patterns. At Nantucket, wind stress contributions mainly originate from the coastal region upstream along the coastally trapped wave path, while at Charleston, offshore contributions dominate—reflecting the roles of coastally trapped waves and westward-propagating Rossby waves, respectively. 2. Results 2.1. Reconstructing climate model sea-level variations As described in Introduction, we hypothesize that, to first order, the governing physics of the ECCO ocean model is similar to that of the ocean model from a state-of-the-art coupled climate model of comparable resolution. In other words, we can convolve ECCO adjoint sensitivities with forcings from a coupled climate model to reconstruct projected sea-level variations. To demonstrate our working hypothesis, we convolve the ECCO adjoint sensitivities (see Supplementary Information Text S1 for a discussion of the adjoint sensitivities at various lead times) with forcing anomalies from MPI-ESM1.2-HR to reconstruct its projected sea-level changes at Nantucket, Massachusetts, and Charleston, South Carolina. For both locations, we reproduced the historical and projected dynamic sea-level changes from 1900 through 2100 (not shown), with the reconstruction explaining 88% of the variance of simulated sea level at Nantucket and 84% at Charleston. Here, we focus on the time period between 2000 and 2100 (Figs. 1 a and 1 c). The time series are monthly, with the seasonal cycle removed and 12-month low-pass filtering applied. The simulated sea-level variations (cyan) for the period from 2000 to 2014 are from a historical simulation, while those for the period from 2015 to 2100 are from an SSP5-8.5 run. The simulated sea-level variations represent forced changes and are shown relative to the sum of sea-level trend and acceleration from piControl (green), which is considered a bias and removed from historical and scenario runs (see Methods). From 2000 to 2100, sea-level changes at both locations are dominated by a trend: an increase of 25 cm at Nantucket and 10 cm at Charleston. In contrast, the sea-level changes due to model drift (trend plus acceleration; green) are much smaller: -1.2 cm for Nantucket and − 0.6 cm for Charleston. That the adjoint-based reconstruction reproduced the sea-level changes simulated by the climate model demonstrates that our working hypothesis is reasonable, that is, to first order, the sensitivities of U.S. East Coast sea level to surface forcings, as derived by the ECCO adjoint model, are consistent with those of the climate model MPI-ESM1.2-HR. Now that we successfully reconstructed the sea-level variations simulated by the climate model, we can decompose the forcing contributions to different forcing types. For both locations, the sea-level change from 2000 to 2100 is mainly due to heat flux forcing (cyan curves in Figs. 1 b and 1 d), with the reconstructed sea level using heat flux explaining approximately 80% of the variance of the total reconstruction. Freshwater flux has a secondary contribution to the sea-level trend at Nantucket, explaining 29% of the variance of the total reconstruction, while it has almost no contribution to that at Charleston. Wind stress (green) has minimal contributions to the long-term trend at both locations, but they are mainly responsible for the interannual and decadal sea-level changes. For Nantucket, the wind stress contribution is further separated into reconstructions due to along-bathymetry and cross-bathymetry wind stress (Fig. 1 b). The contribution from along-bathymetry wind stress (red) dominates that from cross-bathymetry wind stress (purple), reflecting the leading influence of coastally trapped waves on sea-level variations at Nantucket (Wang et al., 2022; see also Supplementary Information Figures S1 i–S1p for adjoint sensitivities of Nantucket sea level to along- and cross-bathymetry wind stress). This physical mechanism also motivates the choice to separate wind stress into along-bathymetry and cross-bathymetry components, rather than zonal and meridional components. The positive along-bathymetry direction is defined such that shallow water lies to the right. The positive cross-bathymetry direction is oriented 90° counterclockwise from the along-bathymetry direction and points toward increasing isobaths. For Charleston, we separate the wind stress contribution into zonal and meridional components (Fig. 1 d), as sea-level variations there are more affected by Rossby waves from the open ocean (Wang et al., 2024; see also Supplementary Information Figures S2i–S2p for adjoint sensitivities of Charleston sea level to zonal and meridional wind stress), which are less influenced by bathymetry. Having determined the relative importance of different forcing types to U.S. East Coast sea-level changes, we further investigate the spatial distribution of these contributions. Figure 2 illustrates where forcing influences sea-level variations at Nantucket (Figs. 2 a- 2 d) and Charleston (Figs. 2 e- 2 h) by showing the variance of the summation of the right-hand side of Eq. 1 (see Methods) over both space and lead time, explained by the summation over lead time only. Taking heat flux as an example, the values represent explained variance per unit area (km -2 ) of the total heat-flux-reconstructed sea level at Nantucket (Fig. 2 a) and Charleston (Fig. 2 e) by heat flux from different locations. The other panels present similar maps for the other forcings. These maps will be referred to as forcing influence maps (FIMs). For both locations, heat flux contributions originate mainly from the subpolar North Atlantic, while contributions from other regions are negligible. Frederikse et al. (2017) reported a strong decadal-scale correlation between steric height in the subpolar gyre and sea level along the U.S. Northeast Coast, suggesting a common forcing for both, or different forcings that co-vary. How does heat flux in the subpolar North Atlantic affect sea-level variations along the U.S. East Coast? Using forward forcing perturbation experiments, Wang et al. (2022) found that remote buoyancy forcing in the subpolar North Atlantic can affect sea level at Nantucket a few years later via advective—and likely also diffusive—processes. The influence of subpolar North Atlantic heat flux reaches Nantucket via the Labrador Current and the southward-flowing slope current. South of Cape Hatteras, however, there is no more southward-flowing slope current. The Florida Current flows northward very close to the coast. The mechanisms by which heat flux in the subpolar North Atlantic affects sea level at Charleston are further examined in Discussion. Freshwater flux in this study includes the net balance of evaporation, precipitation, and runoff. For Nantucket, the freshwater flux contributions are mostly positive but relatively small (Fig. 2 b). However, along the Greenland and Labrador coasts, several isolated locations exhibit large positive contributions, primarily from river runoffs and glacier/ice sheet meltwater. Note that MPI-ESM1.2-HR does not include a fully coupled dynamic ice-sheet model and, therefore, may not fully represent feedback mechanisms involving glacier meltwater in a warming climate. The Amazon River (river mouth located at ECCO model grid point 0.6 o N, 49.5 o W) and the outlet of Jakobshavn Glacier in Greenland (69 o N, 51.7 o W) account for the largest and second-largest contributions per square kilometre, respectively. For Charleston, freshwater flux has positive contributions from the pathways of the Florida, Loop, and Caribbean Currents. There are also pronounced contributions from various rivers. Because the total freshwater contribution to the sea-level change at Charleston is negligible (Fig. 1 d), we omit a detailed discussion of the spatial contributions. Wind stress contributions to sea-level variations at Nantucket and Charleston are shown in Figs. 2 c– 2 d and 2 g– 2 h, respectively. Because of the dominant influence of coastally trapped waves on sea-level variations at Nantucket, as discussed earlier, we separate the wind stress contributions into along-bathymetry (Fig. 2 c) and cross-bathymetry (Fig. 2 d) components. Contributions to both components are predominantly positive from the nearshore regions north of Nantucket along the U.S. and Canadian coasts, extending from the Gulf of Maine to the Labrador Shelf. The spatial patterns of these wind stress contributions are consistent with coastally trapped waves propagating counterclockwise from upstream coastal regions north of Nantucket and affecting sea-level variations at Nantucket. For Charleston, we separate the wind stress contributions into zonal and meridional components. Contributions due to zonal wind stress come mainly from a zonal band of positive values that extends from Charleston offshore into the ocean interior (Fig. 2 g), similar to wind stress contributions to interannual sea-level variations at Charleston during 1992–2015 (Wang et al., 2024). We attribute this zonal band to the effect of westward-propagating Rossby waves generated by open-ocean wind stress—the same mechanism identified by Wang et al. (2024). Since Rossby waves (except for barotropic ones) are less affected by bathymetry, separating wind stress into along-bathymetry and cross-bathymetry components, as done for Nantucket, is not meaningful. In addition to the zonal band, there are positive contributions due to zonal wind stress along the continental slope deeper than 2000 m off the Mid-Atlantic Bight, Gulf of Maine, and Grand Banks. Meridional wind stress exhibits a prominent band of positive contributions along the 2000-m isobath, extending from the southern part of Florida to the Gulf of Maine (Fig. 2 h). This band is flanked by two localized negative regions, both roughly confined to the latitudinal extent of the South Atlantic Bight. There are also relatively weaker positive contributions due to meridional wind stress, extending from the Scotian Shelf to the Labrador Shelf. 2.2. Attribution of sea-level trend We have shown sea-level changes at both locations are dominated by a trend (Fig. 1 ). Figure 3 shows the linear fit to sea-level reconstructed using all forcings (black), as well as reconstructions using individual forcings. Heat flux is the dominant contributor to the linear sea-level trend, explaining nearly 100% of the variance of the linear fit of the reconstruction using all forcings. Freshwater flux is a distant secondary contributor at Nantucket and has a negligible influence at Charleston. Wind stress contributions to the linear trend of sea-level changes are also small at both locations. Spatially, the FIMs for heat flux contributions to the linear fit of sea-level variations at both locations (not shown) are very similar to those for sea-level variations across all time scales combined (Figs. 2 a and 2 e), with the main contributions coming from the subpolar North Atlantic surface heat flux. 2.3. Attribution of interannual to decadal sea-level variability We further examine the interannual-to-decadal variability by applying a band-pass filter between 13 months and 50 years to the detrended monthly reconstructed sea-level time series. On these time scales, wind stress plays a major role for both Nantucket (Fig. 4 a) and Charleston (Fig. 4 c), explaining 87% and 69% of the variance of the total interannual-to-decadal reconstructed sea level for Nantucket and Charleston, respectively. Heat flux is the second largest contributor for both locations, explaining 23% and 19% of the variance, respectively. Freshwater flux is the least significant contributor, explaining 4% of the variance for both locations. For the same reasons specified in Section 2.1 , we separate the wind stress contribution to sea-level variations at Nantucket into components due to along-bathymetry and cross-bathymetry wind stress (Fig. 4 b). The contribution from along-bathymetry wind stress (red) clearly dominates that from cross-bathymetry wind stress (purple), explaining 81% and 28% of the variance of the total interannual-to-decadal sea-level reconstruction, respectively. For Charleston, we separate the wind stress contribution into zonal and meridional components (Fig. 4 d), with the contribution from zonal wind stress (red; explaining 63% of the variance) dominating that from meridional wind stress (purple; explaining 8%). Spatially, the contributions of wind stress to interannual-to-decadal sea-level variations at both locations—Figures 5 c and 5 d for the contributions of along-bathymetry and cross-bathymetry wind stress to sea-level variations at Nantucket, and Figs. 5 g and 5 h for the contributions of zonal and meridional wind stress at Charleston—resemble those of the total reconstructed sea-level variations (Fig. 2 ). This is expected but still worth confirming, as Figs. 1 b and 1 d show that wind stress has little contributions outside interannual-to-decadal time scales. For Nantucket, heat flux still has large remote contributions from the subpolar North Atlantic (Fig. 5 a), similar to those for the total reconstructed sea level (Fig. 2 a). Additionally, there are large local and regional contributions from the nearshore regions stretching from northeast of Nantucket to the southern edge of the Grand Banks (Fig. 5 a). These local and regional contributions are barely visible in the corresponding FIM for the total reconstructed sea-level variations. For Charleston, the largest contributions come from the U.S. Southeast Coast south of Charleston and from the Gulf of Mexico, following the paths of the Florida Current and the Loop Current. Wang et al. (2024) suggested that heat flux from the Caribbean Sea and Gulf of Mexico likely affects sea-level variations at Charleston via the Florida Current and its upstream precursors. The spatial contributions of freshwater flux to interannual-to-decadal sea-level variations are shown in Figs. 5 b and 5 d for Nantucket and Charleston, respectively. Because the freshwater flux contributions are small (as shown in Fig. 4 a for Nantucket and Fig. 4 c for Charleston), we omit a detailed discussion of the spatial patterns. However, it is worth noting that the spatial patterns of freshwater flux contributions resemble those of heat flux, with some additional contributions clearly associated with river runoff. 2.4. Forcing contributions as a function of lead time Similar to the FIMs for spatial distributions of forcing contributions, Fig. 6 shows forcing contributions as a function of lead time (weeks), with each curve representing the explained variance of sea level reconstructed with a specific forcing by the same forcing at different lead times. In other words, it shows the variance of the summation of the right-hand side of Eq. 1 over both space and lead time, explained by the summation over space only. The wind forcing contributions (green) reach their peak at a short lead time for both Nantucket (Fig. 6 a) and Charleston (Fig. 6 b), reflecting the effect of fast-propagating coastally trapped waves. Thereafter, the contributions decrease with increasing lead time, with those for Nantucket declining more rapidly than those for Charleston. For example, the contributions first drop below 0.1% at week 81 for Nantucket and at week 188 for Charleston. The longer decay time for Charleston reflects the greater influence of slow-propagating Rossby waves from the open ocean, in contrast to Nantucket, where sea-level variations are primarily influenced by fast-propagating coastally trapped waves. Compared to wind stress, the heat flux contributions extend over much longer time scales, as indicated by the long tails of the heat flux curves (cyan), with explained variance remaining at 0.1% at lead times of 600 weeks for Nantucket and 1050 weeks for Charleston. The longer tail of the heat flux contribution, compared to that of wind stress, reflects the slower oceanic processes associated with heat flux forcing in the subpolar North Atlantic. (Supplementary Information Figures S1 and S2). For sea-level variations at Charleston, heat flux also has a peak contribution at a short lead time of six weeks. This likely reflects the influence of heat flux from regions south of Charleston and the Gulf of Mexico via the Florida and Loop Currents, which have core speeds exceeding 1 m s -1 (Garcia et al., 2014; Volkov et al., 2020), spanning several thousand kilometres within a six-week period. Freshwater flux contributions (orange) also exhibit long tails, but we omit detailed discussion given their relatively minor influence. 3. Discussion 3.1. Heat flux trend in the subpolar North Atlantic drives sea-level rise at Nantucket and Charleston Why does heat flux have dominant contributions to projected SLR between 2000 and 2100 at both Charleston and Nantucket (Fig. 1 )? Wang et al. (2022) found that buoyancy forcing (mainly due to heat flux forcing) was a secondary contributor to sea-level changes at Nantucket between 1992 and 2015, although spatially, buoyancy forcing from the subpolar North Atlantic made the largest contribution among all buoyancy forcings globally. Wang et al. (2024) showed that buoyancy forcing from the subpolar North Atlantic contributed less to sea-level changes at Charleston between 1992 and 2015 than did buoyancy forcing from the Gulf of Mexico and the Caribbean Sea (see their Fig. 4 b). In contrast, here we find that heat flux in the subpolar North Atlantic is the key driver of sea-level trend (Figs. 2 a and 2 e). This results from the large heat flux trend in the subpolar North Atlantic (Fig. 7 ), which reaches 0.40 W m -2 per year in the area spanning 46°N–65°N and 62°W–10°W — one of the largest trends across the global ocean. In fact, when we repeat the convolution but with heat flux detrended only in the subpolar North Atlantic area, the resulting sea-level reconstruction shows no significant trend (not shown). It is also worth noting that even under scenario SSP1-2.6, the heat flux trend between 2000 and 2100 in this region remains one of the largest across the global ocean, with a pronounced rate of 0.17 W m -2 per year. This highlights the significant impact of remote heat flux forcing from the subpolar North Atlantic on SLR along the U.S. East Coast. 3.2. How heat flux in the subpolar North Atlantic affects sea level at Charleston Wang et al. (2022) suggested that heat flux in the subpolar North Atlantic affects sea level at Nantucket via advective (and likely also diffusive) processes by the Labrador Current and the slope current. Hsieh and Bryan (1996) found a similar advective process via coastal currents, which transfer perturbed sea level in the North Atlantic in a simple shallow-water model. For sea level at Charleston, however, Wang et al. (2024) showed that a similar advective mechanism cannot explain the equatorward propagation of positive sea-level anomalies across Cape Hatteras from the north because the mean current flows poleward between Nantucket and Charleston. Here, we further examine the physical mechanism by which heat flux from the subpolar North Atlantic affects sea-level changes at Charleston. We conduct the same forward perturbation experiment as in Wang et al. (2022) to analyse the temporal evolution of perturbed sea level and related variables. In this experiment, a downward heat flux perturbation with a maximum magnitude of 5 W m -2 is applied south of Greenland over a two-week period centred at 12Z on 9 December 1992. Details of the experimental configuration can be found in Section 6.1.1. of Wang et al. (2022). The results of the perturbation experiment suggest that heat flux contributions from the subpolar North Atlantic likely affect sea level at Charleston via Arrested Topographic Waves (Csanady, 1978, Eq. 3; Hughes et al., 2019; Wu, 2021; Wu and He, 2025). The theory of Arrested Topographic Waves can explain how offshore changes influence nearshore sea level at frequencies much lower than those associated with barotropic and first baroclinic coastally trapped waves. For such low-frequency variability, bottom friction plays an important role in allowing offshore changes to overcome the potential vorticity barrier—arising from strong gradients of f/H (where f is the Coriolis parameter and H is depth)—and to affect nearshore sea level. Given the low-frequency nature of the variations, temporal changes are negligible, and the governing equation reduces to a diffusion equation, in which nearshore sea level dissipates along the direction of propagation of coastally trapped waves rather than over time. Offshore sea level serves as the boundary condition for nearshore sea-level changes. The perturbed heat flux initially creates a positive sea-level anomaly south of Greenland, which then spreads southward and offshore, reaching the Grand Banks region in approximately 15 months (see Section 6.1.1. of Wang et al., 2022). Around the Grand Banks, part of the signal spreads offshore along the counterclockwise gyre circulation, while another part lingers near the Grand Banks, where closed contours of f/H—resulting from the local bathymetry—tend to retain it for an extended period. Some of the signal continues southward, affecting a large swath of the nearshore region—across Cape Hatteras and along the Florida coast—even though there is no southward mean coastal current south of Cape Hatteras. This nearshore signal persists over time and behaves like Arrested Topographic Waves. Figure 8 a shows perturbed dynamic sea level for December 1995, three years after the initial perturbation was applied, while Fig. 8 d shows the same for December 1996. The similarity in nearshore sea-level patterns one year apart, as well as those near the Grand Banks, suggests that temporal changes in sea level are of low frequency. The magnitude of the nearshore sea level gradually decreases along the direction of propagation of coastally trapped waves, as expected from the diffusion equation, where the direction of propagation of coastally trapped waves is analogous to time (Csanady, 1978). When perturbed anomalies first arrive in the nearshore region, nearshore sea level undergoes a rapid adjustment as barotropic coastally trapped waves quickly propagate away. The remaining sea-level change stays in the nearshore region, with the positive offshore sea-level anomalies over the Grand Banks and its nearby open ocean acting as the boundary condition for the nearshore changes. Because the open-ocean sea-level anomalies are low-frequency variations—a prerequisite for the presence of Arrested Topographic Waves on the shelf—long-term coherent anomalies can persist along a long swath of the coastal region, as shown by the perturbation experiment results. In contrast, if the open-ocean anomalies are transient, the nearshore anomalies will also be transient, likely propagating away as coastally trapped waves. To maintain physical consistency, sea-level changes in the nearshore and open ocean must connect smoothly. Because the water depth on the shelf is shallow, warming alone cannot raise nearshore sea level enough to avoid a cross-shelf discontinuity. Therefore, when the perturbed baroclinic signal from the open ocean reaches the coast, it converts to a barotropic signal, and some mass convergence or divergence must occur. Indeed, the perturbation experiment shows that perturbed dynamic manometric sea level—the mass-related sea-level change—is confined to the nearshore region (Figs. 8 b and 8 e; see Piecuch et al. (2021) for its definition), while perturbed steric height remains offshore (Figs. 8 c and 8 f). In summary, the results of the perturbation experiment are consistent with the theory of Arrested Topographic Waves. North of Cape Hatteras, the perturbed sea-level changes in the nearshore region are likely due to the combined effects of coastal currents and Arrested Topographic Waves. However, the effect of Arrested Topographic Waves dominates near Cape Hatteras and farther south, where no mean southward coastal current exists. We note that Csanady (1978) discussed open-ocean signals induced by wind or freshwater flux as open boundary conditions for Arrested Topographic Waves. However, as shown in the perturbation experiment presented here, such signals can also arise from changes in heat flux or ocean heat content (e.g., Steinberg et al., 2024). As the subpolar North Atlantic is projected to gain more heat through 2100 (Fig. 7 ), this forcing mechanism will lead to prolonged SLR along the U.S. East Coast. 3.3. Implications Heat flux from the subpolar North Atlantic is the primary driver of sea-level trends at Nantucket and Charleston under SSP5-8.5. This suggests that, to accurately project sea-level trends along the U.S. East Coast, coupled climate models must produce reliable heat flux in the subpolar North Atlantic. This dominant heat flux contribution persists across other scenarios in MPI-ESM1.2-HR, including the low-emission, strong-mitigation SSP1-2.6 (Table 1 ). In contrast, during the period 1900–1999, there were negative linear trends in sea-level change of -1.0 cm and − 1.7 cm at Nantucket and Charleston, respectively. The much larger projected SLR, even under SSP1-2.6, highlights serious threats to coastal communities in this century. Because of the dominant remote heat flux contribution, we emphasize that coastal communities along the U.S. East Coast should prioritize the “upstream” (i.e., opposite to the direction of coastally trapped wave propagation) remote forcing when addressing future sea-level changes, in addition to changes in local forcings. In the MPI-ESM1.2-HR historical and scenario runs used in this study, the heat flux trend in the subpolar North Atlantic is one of the largest across the global ocean between 2000 and 2100 (Fig. 7 and Section 3.1 ). Table 1 Sea-level rise based on linear fits of the total reconstructed sea level using all forcings, and of reconstructions using specific forcings, between 2000 and 2100 at Nantucket and Charleston under different SSP scenarios. The numbers in parentheses indicate the fraction of the variance of the linear fit of the total reconstruction that is explained by each individual forcing reconstruction. Place SSP scenario Sea-level Rise (cm) Total Heat flux Freshwater flux Wind stress Nantucket SSP1-2.6 11.5 8.8 (0.94) 1.1 (0.18) 1.6 (0.26) SSP2-4.5 25.8 18.7 (0.92) 3.8 (0.28) 3.2 (0.24) SSP3-7.0 24.6 19.9 (0.96) 5.1 (0.37) -0.4 (-0.03) SSP5-8.5 26.8 20.0 (0.97) 5.6 (0.38) -0.8 (-0.06) Charleston SSP1-2.6 6.0 6.4 (0.99) 0.2 (0.07) -0.7 (-0.24) SSP2-4.5 13.9 11.0 (0.95) 1.5 (0.21) 1.4 (0.19) SSP3-7.0 13.1 11.6 (0.99) 1.4 (0.20) 0.1 (0.02) SSP5-8.5 15.5 13.4 (0.98) 0.5 (0.06) 1.6 (0.19) Our study demonstrates that the sensitivities of sea-level changes along the U.S. East Coast derived from the ECCO adjoint model are, to first order, similar to those in the coupled climate model. This opens the door to applying the same adjoint-based methodology to attribute sea-level changes simulated by coupled climate models across different periods (historical versus projected), emission scenarios (low versus high), and models. Comparing results from such attribution studies can shed light on the driving forces behind projected coastal sea-level changes and potentially improve projections by coupled climate models. To keep this study focused, we highlight only the main contributions of different forcing types and regions to sea-level changes along the U.S. East Coast across various time scales. However, our broader results (e.g., certain features from the FIMs in Fig. 2 ) motivate further investigation into other regional forcing contributions, facilitate comparisons of regional sea-level projections across different emission scenarios, enhance understanding of the consistency or discrepancy among climate model projections, and provide valuable information for improving regional sea-level projections. 4. Methods 4.1. Adjoint attribution analysis with ECCO framework We employed the same adjoint-based attribution method that has been used to study sea-level and ocean bottom pressure (OBP) variations across the global ocean, including along the U.S. East Coast (Fukumori et al., 2007, 2015, 2021; Wang et al., 2022, 2024). The methodology is described in detail in those studies; here, we provide a brief overview. The model setup used to derive the adjoint sensitivities is a flux-forced configuration of ECCO Version 4 Release 3 with nominal 1° horizontal resolution, identical to that used in Wang et al. (2022, 2024). We first define a scalar objective function, J , as the dynamic sea level in a region of interest at target time t g . The ECCO adjoint model is then used to compute 𝜕 J /𝜕 F(s,t g - \(\:\text{τ}\) ) , the gradients of J with respect to weekly ocean forcings, F , at every location, s , and lead time (back in time), \(\:\text{τ}\) before target time t g . The ocean forcing vector F includes wind stress, heat flux, and freshwater flux at the ocean surface. In this study, J was defined as the monthly mean dynamic sea-level anomaly relative to the global mean at either Nantucket or Charleston in December 2015. These gradients of J with respect to ocean forcings, also referred to as adjoint sensitivities, are derived using the so-called tangent-linear assumption , which states that the ocean’s response to infinitesimal forcing perturbations can be described by linear dynamics. Another, often useful, assumption is the stationarity assumption , which states that the ocean’s response to infinitesimal forcing perturbations depends not on when the perturbation is applied but only on the lead time . Where the stationarity assumption holds, we write the adjoint sensitivities as 𝜕 J /𝜕 F(s,- \(\:\text{τ}\) ) to emphasize their independence from t g . Adjoint sensitivities reveal ocean physics. See the Supplementary Information for adjoint sensitivities of sea level to forcings at selected lead times. A convolution of the ocean forcing anomalies and adjoint sensitivities can be used to reconstruct sea-level anomalies at an arbitrary time t . To do so, one first forms the product of ocean forcing anomalies, F i '(s,t- \(\:\text{τ}\) ) , and the adjoint gradients for each forcing type i , location s , and lead time \(\:\text{τ}\) , ranging from \(\:\text{τ}\text{=0}\) back to a maximum earlier lead time, \(\:{\text{τ}}_{max}\) . The central idea regarding lead time is obvious but warrants explicit statement: sea-level anomalies at time t can only be caused by ocean forcing anomalies at or before time t . Next, one sums these products across lead time, space, and forcing type to obtain the objective function anomaly J’ at t : $$\:{J}^{{\prime\:}}\left(t\right)\approx\:{\sum\:}_{i}{\sum\:}_{s}\sum\:_{=0}^{={}_{max}}\frac{\partial\:J}{\partial\:{F}_{i}\left(s,-\right)}{F}_{i}^{{\prime\:}}\left(s,t-\right).$$ 1 To reconstruct a time series of sea-level anomaly, one simply repeats the above convolution recipe for all different times. To validate the adjoint convolution approach, we compare the reconstructed sea-level anomalies against those produced by the fully nonlinear ocean model. This comparison validates the veracity of the preceding approximations. After the adjoint convolution is validated, we quantify the relative contributions of different ocean forcings to the time variability of J by decomposing the reconstructed sea-level anomalies spatially and temporally, as presented in this paper. 4.2. Coupled climate model We used forcings and sea-level variations from MPI-ESM1.2-HR (Müller et al., 2018), a CMIP6 coupled climate model. The ocean model in MPI-ESM1.2-HR is the Max Planck Institute Ocean Model (MPIOM). It is a primitive equation model with a horizontal resolution of 0.4° and 40 vertical levels, compared to a nominal 1° horizontal resolution and 50 vertical levels in ECCO. Like ECCO, MPIOM has a dynamic-thermodynamic sea ice model (Jungclaus et al., 2013; Müller et al., 2018). CMIP6 models provide climate simulations covering the period from 1850 to 2100 and beyond. These simulations involve different models from major climate centres and represent climate change under different emission scenarios. The model output includes a wide range of atmospheric and oceanic states and fluxes for both historical and future climate conditions. CMIP6 encompasses a variety of experiments; however, our focus was on the pre-industrial control ( piControl ), historical , and scenario runs (Eyring et al., 2016; O’Neill et al., 2016). The historical simulations span 1850–2014, while the scenario runs extend from 2015 to 2100 and beyond. These runs are continuous, permitting potential concatenation of the historical and scenario runs. The piControl run was used to estimate and remove model drift the historical and scenario runs (see below). CMIP6 output is available via the Program for Climate Model Diagnosis and Intercomparison (PCMDI) portal ( https://pcmdi.llnl.gov/CMIP6/ ). For the scenario runs, we focused on the business-as-usual SSP scenario with high and unchecked greenhouse gas emissions ( SSP5-8.5 ), but discussed other scenarios when needed (Riahi et al., 2017). We first reconstructed sea surface height (CMIP6 variable zos ) simulated by MPI-ESM1.2-HR, which represents dynamic sea level and has a global mean of zero (Gregory et al., 2019). This aligns with the adjoint calculation, where the objective function is the dynamic sea-level anomaly at Nantucket and Charleston relative to the global mean. To ensure that zos has a zero global mean, we explicitly removed its global area-weighted mean from the dataset downloaded from the PCMDI data portal. For forcings, we used the following four variables from MPI-ESM1.2-HR: hfds , wfo , tauuo / tauu , and tauvo / tauv , representing heat flux, freshwater flux, and zonal and meridional wind stress at the ocean surface. Since ECCO and climate models use different grids—and the adjoint reconstruction would be conducted on the ECCO grid—we interpolated the gridded forcings from the climate model to the ECCO model grid using the nearest neighbor method. River runoff locations may differ between models, so we adjusted them by mapping CMIP6 runoffs to the nearest ECCO ocean grid cell, ensuring their inclusion in the adjoint reconstruction. The CMIP6 forcings are monthly means, which were interpolated to weekly means to match the temporal resolution of the adjoint sensitivities. Coupled climate models often exhibit drift. To distinguish model drift from forced trends, we calculated the trend in the control run, piControl. The trend was considered the drift and subtracted from sea surface height (zos) and forcings of the historical and scenario runs. We also estimated the sea surface height acceleration (i.e., the second derivative of sea surface height) of the piControl run and removed it from sea surface height of the historical and scenario runs, because a linear trend in the forcing is physically expected to produce acceleration in sea level. To reconstruct the bias-corrected sea surface height, we convolved the drift-removed forcings from the coupled model MPI-ESM1.2-HR with the ECCO adjoint sensitivities. Although evaluating the skill of MPI-ESM1.2-HR simulations is not the focus of this paper, it is worth noting that the model’s historical simulations compare reasonably well with observations, including 20th-century warming trends (Müller et al., 2018). Declarations Acknowledgments This research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration (80NM0018D0004). © 2025. All rights reserved. Data Availability Statement Output from the CMIP6 model MPI-ESM1.2-HR is accessible through the portal in the Program for Climate Model Diagnosis and Intercomparison (PCMDI) ( https://pcmdi.llnl.gov/CMIP6/ ). 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L., Schmid, C., Chomiak, L., Germineaud, C., Dong, S., & Goes, M. (2022). Interannual to decadal sea level variability in the subpolar North Atlantic: The role of propagating signals. Ocean Science, 18(6), 1741–1762. https://doi.org/10.5194/os-18-1741-2022 Volkov, D. L., Zhang, K., Johns, W. E., Willis, J. K., Hobbs, W., Goes, M., et al. (2023). Atlantic meridional overturning circulation increases flood risk along the United States southeast coast. Nature Communications, 14(1), 5095. https://doi.org/10.1038/s41467-023-40848-z Volkov, D. L., Lee, S.-K., Domingues, R., Zhang, H., & Goes, M. (2019). Interannual sea level variability along the southeastern seaboard of the United States in relation to the gyre-scale heat divergence in the North Atlantic. Geophysical Research Letters, 46, 7481–7490. https://doi.org/10.1029/2019GL083596 Wang, O. (2023) Repository for adjoint convolution analysis of sea level variations near Charleston and Nantucket [Dataset]. Zenodo. https://doi.org/10.5281/zenodo.10084712 Wang, O., T. Lee, C.G. Piecuch, I. Fukumori, I. Fenty, T. Frederikse, et al. (2022). Local and remote forcing of interannual sea-level variability at Nantucket Island. Journal of Geophysical Research: Oceans , 127, e2021JC018275. https://doi.org/10.1029/2021JC018275 Wang, O., Lee, T., Frederikse, T., Ponte, R. M., Fenty, I., Fukumori, I., & Hamlington, B. D. (2024). What forcing mechanisms affect the interannual sea level co-variability between the Northeast and Southeast Coasts of the United States? Journal of Geophysical Research: Oceans, 129, e2023JC019873. https://doi.org/10.1029/2023JC019873 Widlansky, M.J., Long, X. & Schloesser, F. (2020). Increase in sea level variability with ocean warming associated with the nonlinear thermal expansion of seawater. Commun., Earth Environ. , 1 , 9. https://doi.org/10.1038/s43247-020-0008-8 Wu, H. (2021). Beta-plane arrested topographic wave as a linkage of Open Ocean forcing and mean shelf circulation. Journal of Physical Oceanography, 51(3), 879–893. https://doi.org/10.1175/jpo-d-20-0195.1 Wu, T., & He, R. (2025). Gulf Stream Near Cape Hatteras Modulates Sea Level Variability Along the Southeastern Coast of North America, Volume 52, Issue 7, e2024GL112776. https://doi.org/10.1029/2024GL112776 Wunsch, C., & Heimbach, P. (2007). Practical global oceanic state estimation. Physica D: Nonlinear Phenomena, 230(1–2), 197–208. https://doi.org/10.1016/j.physd.2006.09.040 Yin, J., Schlesinger, M. & Stouffer, R (2009). Model projections of rapid sea-level rise on the northeast coast of the United States. Nature Geosci , 2 , 262–266. https://doi.org/10.1038/ngeo462 Zhang, L., Delworth, T. L., Koul, V., Ross, A., Stock, C., Yang, et al. (2025). Skillful multiyear prediction of flood frequency along the US Northeast Coast using a high-resolution modeling system. Sci. Adv., 11, eads4419. https://doi.org/10.1126/sciadv.ads4419 Additional Declarations There is NO Competing Interest. Supplementary Files SuppleinfoClimatemodelSLAattribution.docx Supplementary Information for Attribution of interannual-to-centennial sea level changes in climate models Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7087515","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":490732065,"identity":"82583205-30b9-4d46-a63f-9cd71b390b4e","order_by":0,"name":"Ou Wang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5UlEQVRIiWNgGAWjYBADOcYG5gbStBgzNjCSqCWxgYFYLfwSCWwSP3fUpjfPbmxgLqipk2fgX3xMAp8WyRkJbJK9Z47nNs452MA849hhwwaJZ2l4tRjcSGC7wdt2LLdxRmIDMw/bAcYGiTPGBoS03PzbdiydEazlX509UVpu87bVJIC18LYxJzbw9xg+wOuXnoftv2XbDhiC/HKYt+9wcpsEWyJeLfzsyYcN37bVyRvObj74mOdbnW0//+EDB/BpYYBEx2EGwxkMDGCVbBIJ+DVAQR2DPDxg+QnYMQpGwSgYBSMOAAB1RkzYcyK2bQAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0003-0386-6398","institution":"Jet Propulsion Laboratory, California Institute of Technology","correspondingAuthor":true,"prefix":"","firstName":"Ou","middleName":"","lastName":"Wang","suffix":""},{"id":490732066,"identity":"c4b1a7d1-9baf-4100-b692-02f1ba7f55ac","order_by":1,"name":"Tong Lee","email":"","orcid":"https://orcid.org/0000-0001-9817-2908","institution":"California Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Tong","middleName":"","lastName":"Lee","suffix":""},{"id":490732067,"identity":"417924fc-91b8-458c-937e-d2a77097e881","order_by":2,"name":"Thomas Frederikse","email":"","orcid":"https://orcid.org/0000-0002-5024-0163","institution":"Jet Propulsion Laboratory, California Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Thomas","middleName":"","lastName":"Frederikse","suffix":""},{"id":490732068,"identity":"c8957b3d-938f-4eb2-b5ef-c9da2d1dc95e","order_by":3,"name":"Ichiro Fukumori","email":"","orcid":"","institution":"Jet Propulsion Laboratory, California Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Ichiro","middleName":"","lastName":"Fukumori","suffix":""},{"id":490732069,"identity":"245f1545-aae1-4268-9616-dd8d4d078226","order_by":4,"name":"Ian Fenty","email":"","orcid":"https://orcid.org/0000-0001-6662-6346","institution":"Jet Propulsion Laboratory, California Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Ian","middleName":"","lastName":"Fenty","suffix":""}],"badges":[],"createdAt":"2025-07-09 22:40:30","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7087515/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7087515/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":88591441,"identity":"d00bb226-1122-4990-a4e6-1c0319d093db","added_by":"auto","created_at":"2025-08-08 05:44:11","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":254326,"visible":true,"origin":"","legend":"\u003cp\u003eNantucket: (a) Dynamic sea level from simulation (blue; SSP5-8.5, after removing the sum of the linear trend and acceleration from piControl), reconstruction (orange), and the removed piControl trend and acceleration. (b) Reconstructed sea level by heat flux (blue), freshwater flux (orange), and wind stress (green). The wind stress reconstruction is further separated into components due to \u003cem\u003ealong-bathymetry\u003c/em\u003e(red) and \u003cem\u003ecross-bathymetry\u003c/em\u003e (purple) wind stress. See the text for the definitions of along-bathymetry and cross-bathymetry. Curves in (b) are vertically shifted for clarity. Panels (c) and (d) are the same as (a) and (b), but for Charleston. In panel (d), the wind stress reconstruction is separated into reconstructions by \u003cem\u003ezonal\u003c/em\u003e(red) and \u003cem\u003emeridional\u003c/em\u003e (purple) wind stress. The numbers in panels (a) and (c) represent the fractional variance of simulated sea level explained by the total reconstruction, while the numbers in panels (b) and (d) indicate the fractional variance of the total reconstruction explained by the reconstructed sea level using each individual forcing.\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-7087515/v1/6643c175ebe0a989f30a44f1.png"},{"id":88591621,"identity":"fa0fd81b-d42f-46c3-8874-2b7ea8633fd4","added_by":"auto","created_at":"2025-08-08 05:52:11","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":125856,"visible":true,"origin":"","legend":"\u003cp\u003eForcing influence maps for sea-level anomalies at Nantucket due to (a) heat flux, (b) freshwater flux, (c) \u003cem\u003ealong-bathymetry\u003c/em\u003e and (d) \u003cem\u003ecross-bathymetry\u003c/em\u003e wind stress. See the text for the definitions of along-bathymetry and cross-bathymetry. Panels (e)-(h) are the same as panels (a)-(d), but for sea-level anomalies at Charleston. Furthermore, panels (g) and (h) are for \u003cem\u003ezonal\u003c/em\u003e and \u003cem\u003emeridional\u003c/em\u003e wind stress. The values represent fractions per unit area (km\u003csup\u003e−2\u003c/sup\u003e) of variance, explained by sea-level anomalies reconstructed using a specific forcing at each location, of reconstructed SLA by the same forcing from all locations. Nantucket and Charleston are denoted by x in panels (a)-(d) and (e)-(h), respectively. The gray curves are the 200-m, 700-m, and 2000-m isobaths.\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-7087515/v1/5330bc4547455fc72f5b9de6.png"},{"id":88591471,"identity":"96e822b2-d7a2-42c0-a7b0-bc06650c12aa","added_by":"auto","created_at":"2025-08-08 05:44:14","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":78504,"visible":true,"origin":"","legend":"\u003cp\u003eThe linear fit of sea-level variations at (a) Nantucket and (b) Charleston reconstructed using all forcings (black), heat flux (blue), freshwater flux (orange), and wind stress (green). The numbers in the legend indicate the variance of the linear fit of total reconstructed sea level explained by each individual forcing reconstruction.\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-7087515/v1/43e5b280bd5bd62fbff0c498.png"},{"id":88592149,"identity":"52e47810-1233-4f95-8414-bb63288a5c48","added_by":"auto","created_at":"2025-08-08 06:00:11","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":308830,"visible":true,"origin":"","legend":"\u003cp\u003eNantucket: (a) Interannual-to-decadal (13 months to 50 years) sea-level variations reconstructed using all forcings (black), heat flux (blue), freshwater flux (orange), and wind (green). (b) Wind stress reconstruction (green) separated into \u003cem\u003ealong-bathymetry\u003c/em\u003e (red) and \u003cem\u003ecross-bathymetry\u003c/em\u003e(purple) components. See text for definitions of along-bathymetry and cross-bathymetry. The numbers in the legend indicate the fraction of variance of the total interannual-to-decadal sea-level reconstruction explained by each individual forcing reconstruction. Panels (c) and (d) are the same as (a) and (b), respectively, but for Charleston. In panel (d), the wind stress reconstruction is separated into reconstructions by \u003cem\u003ezonal\u003c/em\u003e (red) and \u003cem\u003emeridional\u003c/em\u003e(purple) wind stress.\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-7087515/v1/a4e582f3465da5ee87f2aabb.png"},{"id":88591442,"identity":"4877533f-6fda-4d06-a2f6-87a633dd85c8","added_by":"auto","created_at":"2025-08-08 05:44:11","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":191959,"visible":true,"origin":"","legend":"\u003cp\u003eSame as Figure 2, but for the interannual-to-decadal (13 months to 50 years) sea-level variations.\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-7087515/v1/1e297b838be826c2c9386e91.png"},{"id":88591624,"identity":"6d308896-1c9a-4ce5-b1c7-1614900a71de","added_by":"auto","created_at":"2025-08-08 05:52:11","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":157549,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Fraction of variance of sea level at Nantucket, reconstructed using heat flux (cyan), freshwater flux (orange), and wind stress (green), explained by reconstructions with the same forcing at different lead times (in weeks). The y-axis uses a logarithmic scale for values (or absolute values, if negative) larger than 0.1, and a linear scale for values between -0.1 and 0.1. (b) Same as (a), but for Charleston.\u003c/p\u003e","description":"","filename":"image6.png","url":"https://assets-eu.researchsquare.com/files/rs-7087515/v1/cde40eff955d2aac83fae837.png"},{"id":88591627,"identity":"005c2c5a-55fc-427c-9df6-2cabe6965f6c","added_by":"auto","created_at":"2025-08-08 05:52:12","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":890351,"visible":true,"origin":"","legend":"\u003cp\u003eLinear trend of net downward heat flux (W m⁻² year⁻¹) across the ocean surface from 2000 to 2100 in the historical and SSP5-8.5 runs of MPI-ESM1.2-HR.\u003c/p\u003e","description":"","filename":"image7.png","url":"https://assets-eu.researchsquare.com/files/rs-7087515/v1/d45c4252c87d1a5d5667fb0e.png"},{"id":88591451,"identity":"c84c0dbd-36a1-452a-85db-da4ccdaa4931","added_by":"auto","created_at":"2025-08-08 05:44:12","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":476891,"visible":true,"origin":"","legend":"\u003cp\u003ePerturbed monthly-mean (a) dynamic sea level (m), (b) dynamic manometric sea level (m), and (c) steric height (m) for December 1995. Panels (d)–(f) are the same as panels (a)–(c) but for December 1996. Nantucket and Charleston are denoted by an x and a circle, respectively.\u003c/p\u003e","description":"","filename":"image8.png","url":"https://assets-eu.researchsquare.com/files/rs-7087515/v1/447339dd09d219a053040253.png"},{"id":88592151,"identity":"55f17dd7-be15-4eaf-817e-2d1a7a8fcd7c","added_by":"auto","created_at":"2025-08-08 06:00:18","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3242569,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7087515/v1/72e6f95c-162a-41cd-88a1-a1dae5e79d83.pdf"},{"id":88591446,"identity":"2330a33c-0184-4962-a075-cdb5ad0d80eb","added_by":"auto","created_at":"2025-08-08 05:44:11","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":3314701,"visible":true,"origin":"","legend":"Supplementary Information for Attribution of interannual-to-centennial sea level changes in climate models","description":"","filename":"SuppleinfoClimatemodelSLAattribution.docx","url":"https://assets-eu.researchsquare.com/files/rs-7087515/v1/201e788df6bbf3160b6cbef8.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Attribution of interannual-to-centennial sea-level changes in climate models","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eHuman activity has warmed the Earth (IPCC, 2021), leading to substantial societal impacts due to sea-level rise (SLR) resulting from climate change (Fox-Kemper et al., 2021). However, regional sea-level changes can be significantly different from global mean sea level (GMSL) changes. Regional sea-level change includes contributions from the ocean's dynamic response to atmospheric, hydrological, and cryospheric forcings (hereafter referred to as \u003cem\u003eocean forcing\u003c/em\u003e)\u0026mdash;known as sterodynamic sea-level change\u0026mdash;as well as from vertical land motion and Earth\u0026rsquo;s gravitational and rotational adjustments (Sweet et al., 2022). This study focuses on sterodynamic sea-level change relative to the global mean, often referred to as dynamic sea-level change (Gregory et al., 2019).\u003c/p\u003e\u003cp\u003eSterodynamic effects cause large regional differences in local sea-level changes along the U.S. coastline (Harvey et al., 2021). However, distinct sectors can be identified within which sea-level variations are remarkably coherent. For instance, coastal sea-level variations in the Northeast Sector (Maine to Cape Hatteras, North Carolina) and the Southeast Sector (Cape Hatteras to Florida) are more coherent within each sector than they are between different sectors (e.g., Wang et al., 2024). The relatively lower coherence of sea-level variations across sectors reflects the diverse nature of their underlying forcing mechanisms (Calafat et al., 2018; Diabat\u0026eacute; et al., 2021; Ezer, 2019; Frederikse et al., 2017; Little et al., 2021; Piecuch et al., 2016; Thompson, 1986; Volkov et al., 2019, 2022, 2023; Wang et al., 2022; Wang et al., 2024; Yin, 2023). The El Ni\u0026ntilde;o-Southern Oscillation (ENSO) and Pacific Decadal Oscillation (PDO) significantly influence sea-level variations along the entire West Coast (e.g., Bromirski et al., 2011; Verdy et al., 2014; Hamlington et al., 2022), while open ocean Rossby waves can considerably affect sea-level variations on the Southeast and Gulf Coasts (Dangendorf, et al., 2023). Despite progress in understanding these sea-level changes and their forcings\u0026mdash;including wind vs. surface buoyancy (e.g., Cabanes et al. 2006; K\u0026ouml;hl \u0026amp; Stammer, 2008; Piecuch \u0026amp; Ponte, 2012, 2013; Forget \u0026amp; Ponte, 2015; Stammer et al., 2013 and the references therein) and local vs. remote atmospheric impacts (e.g., Piecuch et al., 2016, 2019; Dangendorf et al., 2023)\u0026mdash;many studies rely on correlation analyses, which cannot establish causality, or are based on simple models, which exclude important physical processes. Correlation-based analyses have related sea-level variations along the East Coast to local and remote forcings (Andres et al., 2013; Dangendorf et al., 2023), the Gulf Stream and the Florida Current (Ezer, 2019), the Atlantic Meridional Overturning Circulation (AMOC) (Little et al., 2019; Zhang et al., 2025), gyre-scale heat convergence (Volkov et al., 2019, 2023; McCarthy et al., 2015; Steinberg et al., 2024), climate modes (Dong et al., 2022; Kopp, 2013; McCarthy et al., 2015; Valle-Levinson et al., 2017), steric height in ocean interior (Frederikse et al., 2017), and others. These studies suggest that a common forcing\u0026mdash;or multiple covarying forcings\u0026mdash;may influence sea level and other related variables.\u003c/p\u003e\u003cp\u003eOver the next three decades, regional SLR along the U.S. coastlines is projected to exceed GMSL rise, with the East and Gulf Coasts expected to experience greater increases than the West Coast (Sweet, et al., 2022). By 2080\u0026ndash;2099, the subpolar North Atlantic is projected to experience one of the highest regional SLRs, with the multimodel mean sea level more than 20 cm higher than in 1995\u0026ndash;2014 under various Shared Socioeconomic Pathways (SSPs) (Jevrejeva et al., 2024; Lyu et al., 2020). The influence of ocean forcing will likely continue to exhibit significant geographical variability. Earth's warming adds uncertainty to regional sea-level projections because ocean forcing is changing in ways which are difficult to predict (e.g., Widlansky et al., 2020). The efficacy of regional dynamic sea-level projections hinges critically on a comprehensive understanding of which, where, and how ocean forcing drives sea-level variations.\u003c/p\u003e\u003cp\u003eCoupled climate models, such as those of the Coupled Model Intercomparison Project Phase 6 (CMIP6), are essential for understanding past and present climate and for projecting future changes under different SSPs. While these models provide projections of sea level and other climate variables, it is critical to identify which forcings\u0026mdash;and from which regions\u0026mdash;drive projected sea-level changes. This knowledge is key to improving projection accuracy. To achieve this, models must accurately capture the dominant forcing contributions, which are likely regionally dependent. One way to gain insight into these contributions is through forcing perturbation experiments, where a specific forcing in a given region is slightly modified, and the resulting model response is compared to the original run to isolate the impact of that forcing. However, such experiments are computationally expensive, making it impractical to isolate the effects of different forcing types, regions, and time periods.\u003c/p\u003e\u003cp\u003eHere we describe an innovative proof-of-concept study that identifies the key forcing of regional sea-level change by leveraging the resources of the Estimating the Circulation and Climate of the Ocean (ECCO) system. ECCO produces global ocean and sea-ice state estimates by synthesizing satellite and in-situ observations with a state-of-the-art ocean circulation model, the Massachusetts Institute of Technology General Circulation Model (MITgcm). These estimates adhere to the fundamental laws of physics and thermodynamics, which relate the ocean\u0026rsquo;s time-evolving state to its forcing (Heimbach et al., 2019). A unique strength of ECCO is its adjoint model (Wunsch \u0026amp; Heimbach, 2007), which is not generally available for climate models. The same adjoint model used for state estimation in ECCO can also efficiently compute sensitivities of any modeled quantity of interest (QoI) to its different forcings as a function of lead time and space. In contrast to forward model sensitivities\u0026mdash;which require a large number of perturbation experiments\u0026mdash;the adjoint model can evaluate the OoI sensitivities in a single model integration, making it far more computationally efficient.\u003c/p\u003e\u003cp\u003eThe utility of adjoint sensitivity in attribution studies has been demonstrated in investigating the drivers of sea-level variations in the Mediterranean Sea, the Arctic Ocean, and along the U.S. East Coast (Fukumori et al., 2007, 2015, 2021; Wang et al., 2022, 2024). In these studies, the ECCO adjoint sensitivities are convolved with the ECCO forcing to reconstruct the QoI simulated by the fully nonlinear ECCO model. If the reconstructed QoI reproduces the OoI simulated by the fully nonlinear model, one can attribute the forcing contributions based on the linearity of the reconstruction (see Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) later in the paper). The adjoint-based method allows precise, quantitative attribution of sea-level variations or other QoIs to specific ocean forcings and establishes causal mechanisms that correlation-based analyses cannot achieve. The adjoint-based attribution method diagnoses the underlying causal mechanisms with a high degree of granularity that exceeds what is possible with traditional forward model sensitivity experiments.\u003c/p\u003e\u003cp\u003eNote that the aforementioned attribution studies are based on the ECCO state estimation framework, with both adjoint sensitivities and forcings derived from the ECCO model. It would be valuable to conduct similar adjoint-based attribution studies on projected sea-level variations from coupled climate models to better understand future sea-level changes under different emission scenarios and potentially to improve projection accuracy. Such information is crucial for informing climate-related policies, including efforts to avoid reaching climate-change tipping points. However, at present, adjoint models are not available in climate models for computing these sensitivities, except in some exploratory studies (Stammer et al., 2018).\u003c/p\u003e\u003cp\u003eTo circumvent the lack of adjoint sensitivities in climate models, we hypothesize that, to first order, the physics of state-of-the-art ocean models used in ECCO and in coupled climate models of comparable resolutions are similar. Both are governed by the Navier-Stokes equations and represent the physics of the ocean. The sensitivities that reflect the ocean\u0026rsquo;s response to ocean surface forcings should therefore also be consistent between ECCO and these climate models. Successfully reconstructing the projected sea-level variations in climate models using this approach would enable attribution studies of future sea-level changes and provide insights into their underlying causal mechanisms.\u003c/p\u003e\u003cp\u003eIn this paper, we demonstrate that we can successfully reconstruct projected sea-level variations through 2100 at Nantucket, MA, and Charleston, SC, from a CMIP6 climate model, MPI-ESM1.2-HR (M\u0026uuml;ller et al., 2018), by convolving ECCO adjoint sensitivities with forcings from that CMIP6 model. We then analyze the different terms of this convolution to conduct attribution studies of projected coastal sea-level variations in the 21st century. Under scenario SSP5-8.5, MPI-ESM1.2-HR projects that dynamic sea-level changes at both locations from 2000 through 2100 are dominated by a linear trend of SLR: a 25 cm rise at Nantucket and 10 cm rise at Charleston. Heat flux is the dominant contributor to the long-term dynamic sea-level trend at both locations. Spatially, for both Nantucket and Charleston, the heat flux contributions to the linear trends are mainly from the subpolar North Atlantic. For interannual-to-decadal sea-level variations, however, wind stress is the primary contributor at both locations but exhibits markedly different spatial patterns. At Nantucket, wind stress contributions mainly originate from the coastal region upstream along the coastally trapped wave path, while at Charleston, offshore contributions dominate\u0026mdash;reflecting the roles of coastally trapped waves and westward-propagating Rossby waves, respectively.\u003c/p\u003e"},{"header":"2. Results","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.1. Reconstructing climate model sea-level variations\u003c/h2\u003e\u003cp\u003eAs described in Introduction, we hypothesize that, to first order, the governing physics of the ECCO ocean model is similar to that of the ocean model from a state-of-the-art coupled climate model of comparable resolution. In other words, we can convolve ECCO adjoint sensitivities with forcings from a coupled climate model to reconstruct projected sea-level variations. To demonstrate our working hypothesis, we convolve the ECCO adjoint sensitivities (see Supplementary Information Text S1 for a discussion of the adjoint sensitivities at various lead times) with forcing anomalies from MPI-ESM1.2-HR to reconstruct its projected sea-level changes at Nantucket, Massachusetts, and Charleston, South Carolina. For both locations, we reproduced the historical and projected dynamic sea-level changes from 1900 through 2100 (not shown), with the reconstruction explaining 88% of the variance of simulated sea level at Nantucket and 84% at Charleston. Here, we focus on the time period between 2000 and 2100 (Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea and \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec). The time series are monthly, with the seasonal cycle removed and 12-month low-pass filtering applied. The simulated sea-level variations (cyan) for the period from 2000 to 2014 are from a historical simulation, while those for the period from 2015 to 2100 are from an SSP5-8.5 run. The simulated sea-level variations represent forced changes and are shown relative to the sum of sea-level trend and acceleration from piControl (green), which is considered a bias and removed from historical and scenario runs (see Methods). From 2000 to 2100, sea-level changes at both locations are dominated by a trend: an increase of 25 cm at Nantucket and 10 cm at Charleston. In contrast, the sea-level changes due to model drift (trend plus acceleration; green) are much smaller: -1.2 cm for Nantucket and \u0026minus;\u0026thinsp;0.6 cm for Charleston.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThat the adjoint-based reconstruction reproduced the sea-level changes simulated by the climate model demonstrates that our working hypothesis is reasonable, that is, to first order, the sensitivities of U.S. East Coast sea level to surface forcings, as derived by the ECCO adjoint model, are consistent with those of the climate model MPI-ESM1.2-HR. Now that we successfully reconstructed the sea-level variations simulated by the climate model, we can decompose the forcing contributions to different forcing types. For both locations, the sea-level change from 2000 to 2100 is mainly due to heat flux forcing (cyan curves in Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb and \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ed), with the reconstructed sea level using heat flux explaining approximately 80% of the variance of the total reconstruction. Freshwater flux has a secondary contribution to the sea-level trend at Nantucket, explaining 29% of the variance of the total reconstruction, while it has almost no contribution to that at Charleston. Wind stress (green) has minimal contributions to the long-term trend at both locations, but they are mainly responsible for the interannual and decadal sea-level changes. For Nantucket, the wind stress contribution is further separated into reconstructions due to along-bathymetry and cross-bathymetry wind stress (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb). The contribution from along-bathymetry wind stress (red) dominates that from cross-bathymetry wind stress (purple), reflecting the leading influence of coastally trapped waves on sea-level variations at Nantucket (Wang et al., 2022; see also Supplementary Information Figures \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003ei\u0026ndash;S1p for adjoint sensitivities of Nantucket sea level to along- and cross-bathymetry wind stress). This physical mechanism also motivates the choice to separate wind stress into along-bathymetry and cross-bathymetry components, rather than zonal and meridional components. The positive along-bathymetry direction is defined such that shallow water lies to the right. The positive cross-bathymetry direction is oriented 90\u0026deg; counterclockwise from the along-bathymetry direction and points toward increasing isobaths. For Charleston, we separate the wind stress contribution into zonal and meridional components (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ed), as sea-level variations there are more affected by Rossby waves from the open ocean (Wang et al., 2024; see also Supplementary Information Figures S2i\u0026ndash;S2p for adjoint sensitivities of Charleston sea level to zonal and meridional wind stress), which are less influenced by bathymetry.\u003c/p\u003e\u003cp\u003eHaving determined the relative importance of different forcing types to U.S. East Coast sea-level changes, we further investigate the spatial distribution of these contributions. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e illustrates where forcing influences sea-level variations at Nantucket (Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea-\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed) and Charleston (Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ee-\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eh) by showing the variance of the summation of the right-hand side of Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (see Methods) over both space and lead time, explained by the summation over lead time only. Taking heat flux as an example, the values represent explained variance per unit area (km\u003csup\u003e-2\u003c/sup\u003e) of the total heat-flux-reconstructed sea level at Nantucket (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea) and Charleston (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ee) by heat flux from different locations. The other panels present similar maps for the other forcings. These maps will be referred to as forcing influence maps (FIMs).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFor both locations, heat flux contributions originate mainly from the subpolar North Atlantic, while contributions from other regions are negligible. Frederikse et al. (2017) reported a strong decadal-scale correlation between steric height in the subpolar gyre and sea level along the U.S. Northeast Coast, suggesting a common forcing for both, or different forcings that co-vary. How does heat flux in the subpolar North Atlantic affect sea-level variations along the U.S. East Coast? Using forward forcing perturbation experiments, Wang et al. (2022) found that remote buoyancy forcing in the subpolar North Atlantic can affect sea level at Nantucket a few years later via advective\u0026mdash;and likely also diffusive\u0026mdash;processes. The influence of subpolar North Atlantic heat flux reaches Nantucket via the Labrador Current and the southward-flowing slope current. South of Cape Hatteras, however, there is no more southward-flowing slope current. The Florida Current flows northward very close to the coast. The mechanisms by which heat flux in the subpolar North Atlantic affects sea level at Charleston are further examined in Discussion.\u003c/p\u003e\u003cp\u003eFreshwater flux in this study includes the net balance of evaporation, precipitation, and runoff. For Nantucket, the freshwater flux contributions are mostly positive but relatively small (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb). However, along the Greenland and Labrador coasts, several isolated locations exhibit large positive contributions, primarily from river runoffs and glacier/ice sheet meltwater. Note that MPI-ESM1.2-HR does not include a fully coupled dynamic ice-sheet model and, therefore, may not fully represent feedback mechanisms involving glacier meltwater in a warming climate. The Amazon River (river mouth located at ECCO model grid point 0.6\u003csup\u003eo\u003c/sup\u003eN, 49.5\u003csup\u003eo\u003c/sup\u003eW) and the outlet of Jakobshavn Glacier in Greenland (69\u003csup\u003eo\u003c/sup\u003eN, 51.7\u003csup\u003eo\u003c/sup\u003eW) account for the largest and second-largest contributions per square kilometre, respectively. For Charleston, freshwater flux has positive contributions from the pathways of the Florida, Loop, and Caribbean Currents. There are also pronounced contributions from various rivers. Because the total freshwater contribution to the sea-level change at Charleston is negligible (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ed), we omit a detailed discussion of the spatial contributions.\u003c/p\u003e\u003cp\u003eWind stress contributions to sea-level variations at Nantucket and Charleston are shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec\u0026ndash;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eg\u0026ndash;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eh, respectively. Because of the dominant influence of coastally trapped waves on sea-level variations at Nantucket, as discussed earlier, we separate the wind stress contributions into along-bathymetry (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec) and cross-bathymetry (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed) components. Contributions to both components are predominantly positive from the nearshore regions north of Nantucket along the U.S. and Canadian coasts, extending from the Gulf of Maine to the Labrador Shelf. The spatial patterns of these wind stress contributions are consistent with coastally trapped waves propagating counterclockwise from upstream coastal regions north of Nantucket and affecting sea-level variations at Nantucket.\u003c/p\u003e\u003cp\u003eFor Charleston, we separate the wind stress contributions into zonal and meridional components. Contributions due to zonal wind stress come mainly from a zonal band of positive values that extends from Charleston offshore into the ocean interior (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eg), similar to wind stress contributions to interannual sea-level variations at Charleston during 1992\u0026ndash;2015 (Wang et al., 2024). We attribute this zonal band to the effect of westward-propagating Rossby waves generated by open-ocean wind stress\u0026mdash;the same mechanism identified by Wang et al. (2024). Since Rossby waves (except for barotropic ones) are less affected by bathymetry, separating wind stress into along-bathymetry and cross-bathymetry components, as done for Nantucket, is not meaningful. In addition to the zonal band, there are positive contributions due to zonal wind stress along the continental slope deeper than 2000 m off the Mid-Atlantic Bight, Gulf of Maine, and Grand Banks. Meridional wind stress exhibits a prominent band of positive contributions along the 2000-m isobath, extending from the southern part of Florida to the Gulf of Maine (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eh). This band is flanked by two localized negative regions, both roughly confined to the latitudinal extent of the South Atlantic Bight. There are also relatively weaker positive contributions due to meridional wind stress, extending from the Scotian Shelf to the Labrador Shelf.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.2. Attribution of sea-level trend\u003c/h2\u003e\u003cp\u003eWe have shown sea-level changes at both locations are dominated by a trend (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows the linear fit to sea-level reconstructed using all forcings (black), as well as reconstructions using individual forcings. Heat flux is the dominant contributor to the linear sea-level trend, explaining nearly 100% of the variance of the linear fit of the reconstruction using all forcings. Freshwater flux is a distant secondary contributor at Nantucket and has a negligible influence at Charleston. Wind stress contributions to the linear trend of sea-level changes are also small at both locations.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eSpatially, the FIMs for heat flux contributions to the linear fit of sea-level variations at both locations (not shown) are very similar to those for sea-level variations across all time scales combined (Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ee), with the main contributions coming from the subpolar North Atlantic surface heat flux.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e2.3. Attribution of interannual to decadal sea-level variability\u003c/h2\u003e\u003cp\u003eWe further examine the interannual-to-decadal variability by applying a band-pass filter between 13 months and 50 years to the detrended monthly reconstructed sea-level time series. On these time scales, wind stress plays a major role for both Nantucket (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea) and Charleston (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec), explaining 87% and 69% of the variance of the total interannual-to-decadal reconstructed sea level for Nantucket and Charleston, respectively. Heat flux is the second largest contributor for both locations, explaining 23% and 19% of the variance, respectively. Freshwater flux is the least significant contributor, explaining 4% of the variance for both locations.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFor the same reasons specified in Section \u003cspan refid=\"Sec3\" class=\"InternalRef\"\u003e2.1\u003c/span\u003e, we separate the wind stress contribution to sea-level variations at Nantucket into components due to along-bathymetry and cross-bathymetry wind stress (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb). The contribution from along-bathymetry wind stress (red) clearly dominates that from cross-bathymetry wind stress (purple), explaining 81% and 28% of the variance of the total interannual-to-decadal sea-level reconstruction, respectively. For Charleston, we separate the wind stress contribution into zonal and meridional components (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed), with the contribution from zonal wind stress (red; explaining 63% of the variance) dominating that from meridional wind stress (purple; explaining 8%).\u003c/p\u003e\u003cp\u003eSpatially, the contributions of wind stress to interannual-to-decadal sea-level variations at both locations\u0026mdash;Figures \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ec and \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ed for the contributions of along-bathymetry and cross-bathymetry wind stress to sea-level variations at Nantucket, and Figs.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eg and \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eh for the contributions of zonal and meridional wind stress at Charleston\u0026mdash;resemble those of the total reconstructed sea-level variations (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). This is expected but still worth confirming, as Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb and \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ed show that wind stress has little contributions outside interannual-to-decadal time scales.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFor Nantucket, heat flux still has large remote contributions from the subpolar North Atlantic (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea), similar to those for the total reconstructed sea level (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea). Additionally, there are large local and regional contributions from the nearshore regions stretching from northeast of Nantucket to the southern edge of the Grand Banks (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea). These local and regional contributions are barely visible in the corresponding FIM for the total reconstructed sea-level variations. For Charleston, the largest contributions come from the U.S. Southeast Coast south of Charleston and from the Gulf of Mexico, following the paths of the Florida Current and the Loop Current. Wang et al. (2024) suggested that heat flux from the Caribbean Sea and Gulf of Mexico likely affects sea-level variations at Charleston via the Florida Current and its upstream precursors. The spatial contributions of freshwater flux to interannual-to-decadal sea-level variations are shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb and \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ed for Nantucket and Charleston, respectively. Because the freshwater flux contributions are small (as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea for Nantucket and Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec for Charleston), we omit a detailed discussion of the spatial patterns. However, it is worth noting that the spatial patterns of freshwater flux contributions resemble those of heat flux, with some additional contributions clearly associated with river runoff.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\u003ch2\u003e2.4. Forcing contributions as a function of lead time\u003c/h2\u003e\u003cp\u003eSimilar to the FIMs for spatial distributions of forcing contributions, Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows forcing contributions as a function of lead time (weeks), with each curve representing the explained variance of sea level reconstructed with a specific forcing by the same forcing at different lead times. In other words, it shows the variance of the summation of the right-hand side of Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e over both space and lead time, explained by the summation over space only.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe wind forcing contributions (green) reach their peak at a short lead time for both Nantucket (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea) and Charleston (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eb), reflecting the effect of fast-propagating coastally trapped waves. Thereafter, the contributions decrease with increasing lead time, with those for Nantucket declining more rapidly than those for Charleston. For example, the contributions first drop below 0.1% at week 81 for Nantucket and at week 188 for Charleston. The longer decay time for Charleston reflects the greater influence of slow-propagating Rossby waves from the open ocean, in contrast to Nantucket, where sea-level variations are primarily influenced by fast-propagating coastally trapped waves.\u003c/p\u003e\u003cp\u003eCompared to wind stress, the heat flux contributions extend over much longer time scales, as indicated by the long tails of the heat flux curves (cyan), with explained variance remaining at 0.1% at lead times of 600 weeks for Nantucket and 1050 weeks for Charleston. The longer tail of the heat flux contribution, compared to that of wind stress, reflects the slower oceanic processes associated with heat flux forcing in the subpolar North Atlantic. (Supplementary Information Figures \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e and S2). For sea-level variations at Charleston, heat flux also has a peak contribution at a short lead time of six weeks. This likely reflects the influence of heat flux from regions south of Charleston and the Gulf of Mexico via the Florida and Loop Currents, which have core speeds exceeding 1 m s\u003csup\u003e-1\u003c/sup\u003e (Garcia et al., 2014; Volkov et al., 2020), spanning several thousand kilometres within a six-week period. Freshwater flux contributions (orange) also exhibit long tails, but we omit detailed discussion given their relatively minor influence.\u003c/p\u003e\u003c/div\u003e"},{"header":"3. Discussion","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003e3.1. Heat flux trend in the subpolar North Atlantic drives sea-level rise at Nantucket and Charleston\u003c/h2\u003e\u003cp\u003eWhy does heat flux have dominant contributions to projected SLR between 2000 and 2100 at both Charleston and Nantucket (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e)? Wang et al. (2022) found that buoyancy forcing (mainly due to heat flux forcing) was a secondary contributor to sea-level changes at Nantucket between 1992 and 2015, although spatially, buoyancy forcing from the subpolar North Atlantic made the largest contribution among all buoyancy forcings globally. Wang et al. (2024) showed that buoyancy forcing from the subpolar North Atlantic contributed less to sea-level changes at Charleston between 1992 and 2015 than did buoyancy forcing from the Gulf of Mexico and the Caribbean Sea (see their Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb). In contrast, here we find that heat flux in the subpolar North Atlantic is the key driver of sea-level trend (Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ee). This results from the large heat flux trend in the subpolar North Atlantic (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e), which reaches 0.40 W m\u003csup\u003e-2\u003c/sup\u003e per year in the area spanning 46\u0026deg;N\u0026ndash;65\u0026deg;N and 62\u0026deg;W\u0026ndash;10\u0026deg;W\u003cb\u003e\u0026mdash;\u003c/b\u003eone of the largest trends across the global ocean. In fact, when we repeat the convolution but with heat flux detrended only in the subpolar North Atlantic area, the resulting sea-level reconstruction shows no significant trend (not shown).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eIt is also worth noting that even under scenario SSP1-2.6, the heat flux trend between 2000 and 2100 in this region remains one of the largest across the global ocean, with a pronounced rate of 0.17 W m\u003csup\u003e-2\u003c/sup\u003e per year. This highlights the significant impact of remote heat flux forcing from the subpolar North Atlantic on SLR along the U.S. East Coast.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\u003ch2\u003e3.2. How heat flux in the subpolar North Atlantic affects sea level at Charleston\u003c/h2\u003e\u003cp\u003eWang et al. (2022) suggested that heat flux in the subpolar North Atlantic affects sea level at Nantucket via advective (and likely also diffusive) processes by the Labrador Current and the slope current. Hsieh and Bryan (1996) found a similar advective process via coastal currents, which transfer perturbed sea level in the North Atlantic in a simple shallow-water model. For sea level at Charleston, however, Wang et al. (2024) showed that a similar advective mechanism cannot explain the equatorward propagation of positive sea-level anomalies across Cape Hatteras from the north because the mean current flows poleward between Nantucket and Charleston.\u003c/p\u003e\u003cp\u003eHere, we further examine the physical mechanism by which heat flux from the subpolar North Atlantic affects sea-level changes at Charleston. We conduct the same forward perturbation experiment as in Wang et al. (2022) to analyse the temporal evolution of perturbed sea level and related variables. In this experiment, a downward heat flux perturbation with a maximum magnitude of 5 W m\u003csup\u003e-2\u003c/sup\u003e is applied south of Greenland over a two-week period centred at 12Z on 9 December 1992. Details of the experimental configuration can be found in Section 6.1.1. of Wang et al. (2022).\u003c/p\u003e\u003cp\u003eThe results of the perturbation experiment suggest that heat flux contributions from the subpolar North Atlantic likely affect sea level at Charleston via Arrested Topographic Waves (Csanady, 1978, Eq.\u0026nbsp;3; Hughes et al., 2019; Wu, 2021; Wu and He, 2025). The theory of Arrested Topographic Waves can explain how offshore changes influence nearshore sea level at frequencies much lower than those associated with barotropic and first baroclinic coastally trapped waves. For such low-frequency variability, bottom friction plays an important role in allowing offshore changes to overcome the potential vorticity barrier\u0026mdash;arising from strong gradients of f/H (where f is the Coriolis parameter and H is depth)\u0026mdash;and to affect nearshore sea level. Given the low-frequency nature of the variations, temporal changes are negligible, and the governing equation reduces to a diffusion equation, in which nearshore sea level dissipates along the direction of propagation of coastally trapped waves rather than over time. Offshore sea level serves as the boundary condition for nearshore sea-level changes.\u003c/p\u003e\u003cp\u003eThe perturbed heat flux initially creates a positive sea-level anomaly south of Greenland, which then spreads southward and offshore, reaching the Grand Banks region in approximately 15 months (see Section 6.1.1. of Wang et al., 2022). Around the Grand Banks, part of the signal spreads offshore along the counterclockwise gyre circulation, while another part lingers near the Grand Banks, where closed contours of f/H\u0026mdash;resulting from the local bathymetry\u0026mdash;tend to retain it for an extended period. Some of the signal continues southward, affecting a large swath of the nearshore region\u0026mdash;across Cape Hatteras and along the Florida coast\u0026mdash;even though there is no southward mean coastal current south of Cape Hatteras. This nearshore signal persists over time and behaves like Arrested Topographic Waves. Figure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ea shows perturbed dynamic sea level for December 1995, three years after the initial perturbation was applied, while Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ed shows the same for December 1996. The similarity in nearshore sea-level patterns one year apart, as well as those near the Grand Banks, suggests that temporal changes in sea level are of low frequency. The magnitude of the nearshore sea level gradually decreases along the direction of propagation of coastally trapped waves, as expected from the diffusion equation, where the direction of propagation of coastally trapped waves is analogous to time (Csanady, 1978).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eWhen perturbed anomalies first arrive in the nearshore region, nearshore sea level undergoes a rapid adjustment as barotropic coastally trapped waves quickly propagate away. The remaining sea-level change stays in the nearshore region, with the positive offshore sea-level anomalies over the Grand Banks and its nearby open ocean acting as the boundary condition for the nearshore changes. Because the open-ocean sea-level anomalies are low-frequency variations\u0026mdash;a prerequisite for the presence of Arrested Topographic Waves on the shelf\u0026mdash;long-term coherent anomalies can persist along a long swath of the coastal region, as shown by the perturbation experiment results. In contrast, if the open-ocean anomalies are transient, the nearshore anomalies will also be transient, likely propagating away as coastally trapped waves.\u003c/p\u003e\u003cp\u003eTo maintain physical consistency, sea-level changes in the nearshore and open ocean must connect smoothly. Because the water depth on the shelf is shallow, warming alone cannot raise nearshore sea level enough to avoid a cross-shelf discontinuity. Therefore, when the perturbed baroclinic signal from the open ocean reaches the coast, it converts to a barotropic signal, and some mass convergence or divergence must occur. Indeed, the perturbation experiment shows that perturbed dynamic manometric sea level\u0026mdash;the mass-related sea-level change\u0026mdash;is confined to the nearshore region (Figs.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eb and \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ee; see Piecuch et al. (2021) for its definition), while perturbed steric height remains offshore (Figs.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ec and \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ef).\u003c/p\u003e\u003cp\u003eIn summary, the results of the perturbation experiment are consistent with the theory of Arrested Topographic Waves. North of Cape Hatteras, the perturbed sea-level changes in the nearshore region are likely due to the combined effects of coastal currents and Arrested Topographic Waves. However, the effect of Arrested Topographic Waves dominates near Cape Hatteras and farther south, where no mean southward coastal current exists.\u003c/p\u003e\u003cp\u003eWe note that Csanady (1978) discussed open-ocean signals induced by wind or freshwater flux as open boundary conditions for Arrested Topographic Waves. However, as shown in the perturbation experiment presented here, such signals can also arise from changes in heat flux or ocean heat content (e.g., Steinberg et al., 2024). As the subpolar North Atlantic is projected to gain more heat through 2100 (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e), this forcing mechanism will lead to prolonged SLR along the U.S. East Coast.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\u003ch2\u003e3.3. Implications\u003c/h2\u003e\u003cp\u003eHeat flux from the subpolar North Atlantic is the primary driver of sea-level trends at Nantucket and Charleston under SSP5-8.5. This suggests that, to accurately project sea-level trends along the U.S. East Coast, coupled climate models must produce reliable heat flux in the subpolar North Atlantic.\u003c/p\u003e\u003cp\u003eThis dominant heat flux contribution persists across other scenarios in MPI-ESM1.2-HR, including the low-emission, strong-mitigation SSP1-2.6 (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). In contrast, during the period 1900\u0026ndash;1999, there were negative linear trends in sea-level change of -1.0 cm and \u0026minus;\u0026thinsp;1.7 cm at Nantucket and Charleston, respectively. The much larger projected SLR, even under SSP1-2.6, highlights serious threats to coastal communities in this century. Because of the dominant remote heat flux contribution, we emphasize that coastal communities along the U.S. East Coast should prioritize the \u0026ldquo;upstream\u0026rdquo; (i.e., opposite to the direction of coastally trapped wave propagation) \u003cem\u003eremote\u003c/em\u003e forcing when addressing future sea-level changes, in addition to changes in \u003cem\u003elocal\u003c/em\u003e forcings. In the MPI-ESM1.2-HR historical and scenario runs used in this study, the heat flux trend in the subpolar North Atlantic is one of the largest across the global ocean between 2000 and 2100 (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e and Section \u003cspan refid=\"Sec8\" class=\"InternalRef\"\u003e3.1\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eSea-level rise based on linear fits of the total reconstructed sea level using all forcings, and of reconstructions using specific forcings, between 2000 and 2100 at Nantucket and Charleston under different SSP scenarios. The numbers in parentheses indicate the fraction of the variance of the linear fit of the total reconstruction that is explained by each individual forcing reconstruction.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"7\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePlace\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSSP scenario\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"5\" nameend=\"c7\" namest=\"c3\"\u003e\u003cp\u003eSea-level Rise (cm)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eTotal\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eHeat flux\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eFreshwater flux\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eWind stress\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c7\" namest=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e\u003cp\u003eNantucket\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSSP1-2.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e11.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e8.8 (0.94)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.1 (0.18)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.6 (0.26)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c7\" namest=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSSP2-4.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e25.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e18.7 (0.92)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e3.8 (0.28)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e3.2 (0.24)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c7\" namest=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSSP3-7.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e24.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e19.9 (0.96)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e5.1 (0.37)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e-0.4 (-0.03)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c7\" namest=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSSP5-8.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e26.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e20.0 (0.97)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e5.6 (0.38)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e-0.8 (-0.06)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c7\" namest=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e\u003cp\u003eCharleston\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSSP1-2.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e6.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e6.4 (0.99)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.2 (0.07)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e-0.7 (-0.24)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c7\" namest=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSSP2-4.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e13.9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e11.0 (0.95)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.5 (0.21)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.4 (0.19)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c7\" namest=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSSP3-7.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e13.1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e11.6 (0.99)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.4 (0.20)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.1 (0.02)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c7\" namest=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSSP5-8.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e15.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e13.4 (0.98)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.5 (0.06)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.6 (0.19)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c7\" namest=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eOur study demonstrates that the sensitivities of sea-level changes along the U.S. East Coast derived from the ECCO adjoint model are, to first order, similar to those in the coupled climate model. This opens the door to applying the same adjoint-based methodology to attribute sea-level changes simulated by coupled climate models across different periods (historical versus projected), emission scenarios (low versus high), and models. Comparing results from such attribution studies can shed light on the driving forces behind projected coastal sea-level changes and potentially improve projections by coupled climate models.\u003c/p\u003e\u003cp\u003eTo keep this study focused, we highlight only the main contributions of different forcing types and regions to sea-level changes along the U.S. East Coast across various time scales. However, our broader results (e.g., certain features from the FIMs in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) motivate further investigation into other regional forcing contributions, facilitate comparisons of regional sea-level projections across different emission scenarios, enhance understanding of the consistency or discrepancy among climate model projections, and provide valuable information for improving regional sea-level projections.\u003c/p\u003e\u003c/div\u003e"},{"header":"4. Methods","content":"\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\u003ch2\u003e4.1. Adjoint attribution analysis with ECCO framework\u003c/h2\u003e\u003cp\u003eWe employed the same adjoint-based attribution method that has been used to study sea-level and ocean bottom pressure (OBP) variations across the global ocean, including along the U.S. East Coast (Fukumori et al., 2007, 2015, 2021; Wang et al., 2022, 2024). The methodology is described in detail in those studies; here, we provide a brief overview. The model setup used to derive the adjoint sensitivities is a flux-forced configuration of ECCO Version 4 Release 3 with nominal 1\u0026deg; horizontal resolution, identical to that used in Wang et al. (2022, 2024).\u003c/p\u003e\u003cp\u003eWe first define a scalar objective function, \u003cem\u003eJ\u003c/em\u003e, as the dynamic sea level in a region of interest at target time \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003eg\u003c/em\u003e\u003c/sub\u003e. The ECCO adjoint model is then used to compute \u0026#120597;\u003cem\u003eJ\u003c/em\u003e/\u0026#120597;\u003cem\u003eF(s,t\u003c/em\u003e\u003csub\u003e\u003cem\u003eg\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e-\u003c/em\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{\u0026tau;}\\)\u003c/span\u003e\u003c/span\u003e\u003cem\u003e)\u003c/em\u003e, the gradients of \u003cem\u003eJ\u003c/em\u003e with respect to weekly ocean forcings, \u003cem\u003eF\u003c/em\u003e, at every location, \u003cem\u003es\u003c/em\u003e, and lead time (back in time), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{\u0026tau;}\\)\u003c/span\u003e\u003c/span\u003e before target time \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003eg\u003c/em\u003e\u003c/sub\u003e. The ocean forcing vector \u003cem\u003eF\u003c/em\u003e includes wind stress, heat flux, and freshwater flux at the ocean surface. In this study, \u003cem\u003eJ\u003c/em\u003e was defined as the monthly mean dynamic sea-level anomaly relative to the global mean at either Nantucket or Charleston in December 2015.\u003c/p\u003e\u003cp\u003eThese gradients of \u003cem\u003eJ\u003c/em\u003e with respect to ocean forcings, also referred to as adjoint sensitivities, are derived using the so-called \u003cem\u003etangent-linear assumption\u003c/em\u003e, which states that the ocean\u0026rsquo;s response to infinitesimal forcing perturbations can be described by linear dynamics. Another, often useful, assumption is the \u003cem\u003estationarity assumption\u003c/em\u003e, which states that the ocean\u0026rsquo;s response to infinitesimal forcing perturbations depends not on \u003cem\u003ewhen\u003c/em\u003e the perturbation is applied but only on the \u003cem\u003elead time\u003c/em\u003e. Where the stationarity assumption holds, we write the adjoint sensitivities as \u0026#120597;\u003cem\u003eJ\u003c/em\u003e/\u0026#120597;\u003cem\u003eF(s,-\u003c/em\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{\u0026tau;}\\)\u003c/span\u003e\u003c/span\u003e\u003cem\u003e)\u003c/em\u003e to emphasize their independence from \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003eg\u003c/em\u003e\u003c/sub\u003e. Adjoint sensitivities reveal ocean physics. See the Supplementary Information for adjoint sensitivities of sea level to forcings at selected lead times.\u003c/p\u003e\u003cp\u003eA convolution of the ocean forcing anomalies and adjoint sensitivities can be used to reconstruct sea-level anomalies at an arbitrary time \u003cem\u003et\u003c/em\u003e. To do so, one first forms the product of ocean forcing anomalies, \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e'(s,t-\u003c/em\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{\u0026tau;}\\)\u003c/span\u003e\u003c/span\u003e\u003cem\u003e)\u003c/em\u003e, and the adjoint gradients for each forcing type \u003cem\u003ei\u003c/em\u003e, location \u003cem\u003es\u003c/em\u003e, and lead time \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{\u0026tau;}\\)\u003c/span\u003e\u003c/span\u003e, ranging from \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{\u0026tau;}\\text{=0}\\)\u003c/span\u003e\u003c/span\u003e back to a maximum earlier lead time, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{\u0026tau;}}_{max}\\)\u003c/span\u003e\u003c/span\u003e. The central idea regarding lead time is obvious but warrants explicit statement: sea-level anomalies at time \u003cem\u003et\u003c/em\u003e can only be caused by ocean forcing anomalies \u003cem\u003eat or before time t\u003c/em\u003e. Next, one sums these products across lead time, space, and forcing type to obtain the objective function anomaly \u003cem\u003eJ\u0026rsquo;\u003c/em\u003e at \u003cem\u003et\u003c/em\u003e:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{J}^{{\\prime\\:}}\\left(t\\right)\\approx\\:{\\sum\\:}_{i}{\\sum\\:}_{s}\\sum\\:_{=0}^{={}_{max}}\\frac{\\partial\\:J}{\\partial\\:{F}_{i}\\left(s,-\\right)}{F}_{i}^{{\\prime\\:}}\\left(s,t-\\right).$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eTo reconstruct a time series of sea-level anomaly, one simply repeats the above convolution recipe for all different times. To validate the adjoint convolution approach, we compare the reconstructed sea-level anomalies against those produced by the fully nonlinear ocean model. This comparison validates the veracity of the preceding approximations. After the adjoint convolution is validated, we quantify the relative contributions of different ocean forcings to the time variability of \u003cem\u003eJ\u003c/em\u003e by decomposing the reconstructed sea-level anomalies spatially and temporally, as presented in this paper.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\u003ch2\u003e4.2. Coupled climate model\u003c/h2\u003e\u003cp\u003eWe used forcings and sea-level variations from MPI-ESM1.2-HR (M\u0026uuml;ller et al., 2018), a CMIP6 coupled climate model. The ocean model in MPI-ESM1.2-HR is the Max Planck Institute Ocean Model (MPIOM). It is a primitive equation model with a horizontal resolution of 0.4\u0026deg; and 40 vertical levels, compared to a nominal 1\u0026deg; horizontal resolution and 50 vertical levels in ECCO. Like ECCO, MPIOM has a dynamic-thermodynamic sea ice model (Jungclaus et al., 2013; M\u0026uuml;ller et al., 2018).\u003c/p\u003e\u003cp\u003eCMIP6 models provide climate simulations covering the period from 1850 to 2100 and beyond. These simulations involve different models from major climate centres and represent climate change under different emission scenarios. The model output includes a wide range of atmospheric and oceanic states and fluxes for both historical and future climate conditions. CMIP6 encompasses a variety of experiments; however, our focus was on the pre-industrial control (\u003cem\u003epiControl\u003c/em\u003e), \u003cem\u003ehistorical\u003c/em\u003e, and \u003cem\u003escenario\u003c/em\u003e runs (Eyring et al., 2016; O\u0026rsquo;Neill et al., 2016). The historical simulations span 1850\u0026ndash;2014, while the scenario runs extend from 2015 to 2100 and beyond. These runs are continuous, permitting potential concatenation of the historical and scenario runs. The piControl run was used to estimate and remove model drift the historical and scenario runs (see below). CMIP6 output is available via the Program for Climate Model Diagnosis and Intercomparison (PCMDI) portal (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://pcmdi.llnl.gov/CMIP6/\u003c/span\u003e\u003cspan address=\"https://pcmdi.llnl.gov/CMIP6/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e). For the scenario runs, we focused on the business-as-usual SSP scenario with high and unchecked greenhouse gas emissions (\u003cem\u003eSSP5-8.5\u003c/em\u003e), but discussed other scenarios when needed (Riahi et al., 2017).\u003c/p\u003e\u003cp\u003eWe first reconstructed sea surface height (CMIP6 variable \u003cem\u003ezos\u003c/em\u003e) simulated by MPI-ESM1.2-HR, which represents dynamic sea level and has a global mean of zero (Gregory et al., 2019). This aligns with the adjoint calculation, where the objective function is the dynamic sea-level anomaly at Nantucket and Charleston relative to the global mean. To ensure that zos has a zero global mean, we explicitly removed its global area-weighted mean from the dataset downloaded from the PCMDI data portal. For forcings, we used the following four variables from MPI-ESM1.2-HR: \u003cem\u003ehfds\u003c/em\u003e, \u003cem\u003ewfo\u003c/em\u003e, \u003cem\u003etauuo\u003c/em\u003e/\u003cem\u003etauu\u003c/em\u003e, and \u003cem\u003etauvo\u003c/em\u003e/\u003cem\u003etauv\u003c/em\u003e, representing heat flux, freshwater flux, and zonal and meridional wind stress at the ocean surface. Since ECCO and climate models use different grids\u0026mdash;and the adjoint reconstruction would be conducted on the ECCO grid\u0026mdash;we interpolated the gridded forcings from the climate model to the ECCO model grid using the nearest neighbor method. River runoff locations may differ between models, so we adjusted them by mapping CMIP6 runoffs to the nearest ECCO \u003cem\u003eocean\u003c/em\u003e grid cell, ensuring their inclusion in the adjoint reconstruction. The CMIP6 forcings are monthly means, which were interpolated to weekly means to match the temporal resolution of the adjoint sensitivities.\u003c/p\u003e\u003cp\u003eCoupled climate models often exhibit drift. To distinguish model drift from forced trends, we calculated the trend in the control run, piControl. The trend was considered the drift and subtracted from sea surface height (zos) and forcings of the historical and scenario runs. We also estimated the sea surface height acceleration (i.e., the second derivative of sea surface height) of the piControl run and removed it from sea surface height of the historical and scenario runs, because a linear trend in the forcing is physically expected to produce acceleration in sea level. To reconstruct the bias-corrected sea surface height, we convolved the drift-removed forcings from the coupled model MPI-ESM1.2-HR with the ECCO adjoint sensitivities.\u003c/p\u003e\u003cp\u003eAlthough evaluating the skill of MPI-ESM1.2-HR simulations is not the focus of this paper, it is worth noting that the model\u0026rsquo;s historical simulations compare reasonably well with observations, including 20th-century warming trends (M\u0026uuml;ller et al., 2018).\u003c/p\u003e\u003c/div\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAcknowledgments\u003c/h2\u003e\u003cp\u003eThis research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration (80NM0018D0004). \u0026copy; 2025. All rights reserved.\u003c/p\u003e\u003ch2\u003eData Availability Statement\u003c/h2\u003e\u003cp\u003eOutput from the CMIP6 model MPI-ESM1.2-HR is accessible through the portal in the Program for Climate Model Diagnosis and Intercomparison (PCMDI) (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://pcmdi.llnl.gov/CMIP6/\u003c/span\u003e\u003cspan address=\"https://pcmdi.llnl.gov/CMIP6/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e). The adjoint sensitivity and adjoint-convolution script are available on Zenodo at \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://zenodo.org/records/10084712\u003c/span\u003e\u003cspan address=\"https://zenodo.org/records/10084712\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (Wang, 2023).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAndres, M., Gawarkiewicz, G. 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Adv., 11, eads4419. https://doi.org/10.1126/sciadv.ads4419\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-7087515/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7087515/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDynamic sea level along the United States (U.S.) East Coast has risen in recent decades and is projected to continue rising throughout the 21st century, according to most climate models from the Coupled Model Intercomparison Project Phase 6 (CMIP6). However, the mechanisms by which ocean surface forcing drives this rise remain unclear. Understanding these processes is critical for improving sea-level projections. The adjoint sensitivity-based attribution method from the Estimating the Circulation and Climate of the Ocean (ECCO) project provides a means to establish causal relationships between sea level and ocean forcings. Here, we demonstrate that by convolving ocean forcings from a CMIP6 model with ECCO adjoint sensitivities of sea level to these forcings, we can reconstruct sea-level variations along the U.S. East Coast from 2000 to 2100 in the CMPI6 model. We identify subpolar North Atlantic surface heat flux as the key driver of the long-term trend, while wind stress dominates interannual-to-decadal variability.\u003c/p\u003e","manuscriptTitle":"Attribution of interannual-to-centennial sea-level changes in climate models","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-08 05:44:05","doi":"10.21203/rs.3.rs-7087515/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"communications-earth-and-environment","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"commsenv","sideBox":"Learn more about [Communications Earth and Environment](https://www.nature.com/commsenv/)","snPcode":"","submissionUrl":"","title":"Communications Earth \u0026 Environment","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Communications Series","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"1dcb5f77-afa5-4d5e-9da8-a553e6396765","owner":[],"postedDate":"August 8th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":52107389,"name":"Earth and environmental sciences/Climate sciences/Climate change/Attribution"},{"id":52107390,"name":"Earth and environmental sciences/Climate sciences/Climate change/Projection and prediction"},{"id":52107391,"name":"Earth and environmental sciences/Climate sciences/Climate change/Climate and Earth system modelling"},{"id":52107392,"name":"Earth and environmental sciences/Climate sciences/Ocean sciences/Physical oceanography"}],"tags":[],"updatedAt":"2025-08-08T05:44:05+00:00","versionOfRecord":[],"versionCreatedAt":"2025-08-08 05:44:05","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7087515","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7087515","identity":"rs-7087515","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}