Introduction

Recent improvements in in-situ observations and satellite measurements have enabled the monitoring of the sea-level budget on both global and regional scales1,2,3,4,5. Assessments of the sea-level budget (i.e., comparing the observed sea-level changes with the sum of contributions) have recently been conducted, showing the closure of the global mean sea-level (GMSL) budget within data uncertainties2,6,7. However, because of various physical processes, such as regional ocean dynamic effects, changes in regional sea-level and their contributions to the sea-level rise (SLR) budget on regional scales still remains a challenging issue4,8,9,10.

Regionally, the SLR deviates significantly from the global mean, with rates several times faster than the GMSL rate in some regions while being near zero in other regions2,11,12. Unlike the processes of the GMSL budget, regional geocentric SLR should match the sum of three major contributors: (1) the steric effect due to density changes in the regional water column, (2) the manometric contribution due to changes in mass, sometimes referred to as the bottom pressure term13, and (3) the glacial isostatic adjustment (GIA) effect related to long-term solid earth response to the last deglaciation14. The manometric SLR comprises of ocean mass redistribution (OMR) changes driven by ocean circulation and gravitational, rotational, and deformational (GRD) effects due to contemporary land ice mass and terrestrial water storage changes, i.e., the contemporary-GRD10,12,13. The sum of the local steric sea-level (SSL) and circulation-driven OMR is sometimes referred to as sterodynamic sea-level10,13,15,16. Both the sterodynamic process and contemporary-GRD are known as the driving processes behind the observed regional SLR pattern, which substantially differs from the GMSL rise16.

The northwestern Pacific region is characterized by a distinct geographical feature, with a series of marginal seas including the Yellow and East China Seas (YECS), South China Sea (SCS), and East/Japan Sea (EJS), which separate the eastern Asian continent from the North Pacific Ocean (Fig. 1). Previous studies have reported that over the past decades, SLR rates higher than the GMSL rise have been observed in these marginal seas17,18,19,20,21. Most of these studies have focused on sea-level fluctuations in response to climate variability, such as the El Niño-Southern Oscillation20, North Pacific Gyre Oscillation18,21, and Pacific Decadal Oscillation20, on interannual to decadal timescales. However, relatively less attention has been paid to assessing the underlying processes contributing to SLR budgets on marginal seas, including extensive continental shelves. Regional processes superimpose on the global mean, and thus, SLR on the marginal seas is expected to be largely different from that on the deep open ocean15,22. Because SLR occurring over the regional scale is threatening to inundate many low-lying islands and coastlines worldwide, understanding and quantifying the underlying regional processes is of high importance for projections of future ocean conditions.

Fig. 1: Geographic map of northwestern Pacific and sea-level rise trends.
figure 1

a Bathymetry of the northwestern Pacific (NWP) marginal seas including Yellow and East China Sea (YECS), South China Sea (SCS), and East/Japan Sea (EJS). Each marginal sea is defined as the area enclosed by solid lines. The abbreviation of KTS, LS, SS, and TS denotes the Korea/Tsushima Straits, Luzon Straits, Soya Straits, and Tsugaru Straits, respectively. b Trend of satellite-altimetry SLR in the northwestern Pacific over 1993–2017.

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In this study, we assess the regional SLR budget on three marginal seas in the northwestern Pacific (YECS, SCS, and EJS) and examine whether the combined contributions from individual processes can explain the observed geocentric SLR on these marginal seas. To close the sea-level budget, individual contributors to regional SLR were first analyzed and their sum was compared with the altimeter-measured sea-level since 1993. The sterodynamic sea level can be estimated by combining the in situ-based global thermosteric sea-level (GMTS) with the dynamic sea-level from ocean reanalyses12,13,16. This proposed method was used here to quantify the sterodynamic contribution during the altimeter era. In addition, we considered an observation-based approach for the sterodynamic SLR that directly combines in situ-based regional SSL with circulation-driven OMR derived from the Gravity Recovery and Climate Experiment (GRACE). This process-based assessment of the sea-level budget provides a more complete understanding of the underlying processes that drive regional sea-level changes and whether these regional processes fully account for the observed SLR in the northwestern Pacific marginal seas.

Results

Regional SLR assessments and underlying processes

Over the altimeter era (1993–2017), the geocentric sea-level exhibited a faster SLR rate in three marginal seas than in the GMSL2 (3.1 ± 0.4 mm/yr), with a relatively slower rate in the North Pacific subtropical gyre (Fig. 1b). To identify the contribution of underlying processes to the regional SLR trend, we compare the observed SLR trends to the sum of estimates of individual contributors (Fig. 2). The main contributions to the regional SLR trend are the ongoing mass redistribution including land-ice mass (ICE) and land water storage (LWS) changes, i.e., contemporary-GRD, and the sterodynamic components, while GIA has little effect on the rate of SLR by ~ 0.1 mm/yr along the continental shelves.

Fig. 2: Sea-level rise trend from the individual contributor.
figure 2

Regional maps of the estimated individual contributor of SLR trend in the northwestern Pacific over 1993–2017: a ICE, b LWS, c GIA, d Sterodynamic effect, and e the sum of all components. The components of ICE and LWS are derived from the estimates from Frederikse et al.7 and GIA contribution is examined using the estimate of Caron et al.23. The sterodynamic contribution is estimated by the sum of observation-based GMTS and regional dynamic sea-level from ocean reanalysis products (Figure S1). See Data and Methods.

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The SLR of contemporary ICE and LWS is nearly spatially uniform in the marginal seas, and the land-ice mass changes, due to glaciers and ice sheets, dominate the rate of the regional SLR trend associated with the redistribution of the ongoing mass (Fig. 2a, b). The LWS also makes a positive contribution to the regional SLR trend, with a roughly uniform trend over the northwestern Pacific. GIA has a large effect on areas close to former ice-age burdens like North America, North Europe, and Antarctica14,23,24, whereas it has little impact on the SLR trend in the northwestern Pacific, with a maximum of 0.14 mm/yr in the YECS (Fig. 2c). In contrast, the spatial pattern revealed in the geocentric sea-level rise are primarily caused by sterodynamic contribution (Fig. 2d), which is estimated by the sum of observation-based global mean thermosteric sea-level (GMTS) and the regional dynamic sea-level from ocean reanalysis products (see Data and Methods). In the western Pacific, the most dominant feature of the sterodynamic sea-level trend is a strong north-south contrast, with positive trends in the tropical region and negative trends in the subtropical North Pacific. This spatial pattern may be related to a decrease in the wind stress curl over the north Pacific since the late 1990s, which causesd a weakening in the North Pacific subtropical gyre and Kuroshio intensity25,26,27. Climate-related surface wind forcing can drive changes in ocean circulation, spatially redistributing heat and water masses, resulting in the regional dynamic changes28,29,30,31,32.

Figure 3 presents the mean sea-level budget time series for the three marginal seas, for which the sum of individual processes accounts for the observed SLR trends. According to the altimetry-based SLR trends, the SCS is experiencing the fastest rate (4.15 ± 0.38 mm/yr) of SLR in the northwestern Pacific marginal seas, followed by the EJS (3.95 ± 0.46 mm/yr) and YECS (3.5 ± 0.48 mm/yr). Although there exists a disagreement between the sum of estimated contributors and geocentric SLR trends for the SCS (3.30 ± 0.34 mm/yr), the sum of contributors is comparable to the geocentric SLR trends for YECS (3.62 ± 0.42 mm/yr) and EJS (3.34 ± 0.36 mm/yr). Trends of individual components show that the land ice melt and sterodynamic components are the major contributors, while GIA has a slightly positive contribution (Table 1). The mass loss from land ice that causes a roughly uniform trend explains approximately 45.4% to 51.3% of the sum of the contributors in these marginal seas, representing one of the dominant contributions to regional SLR trends. The contribution of the LWS is small with a positive trend for these marginal seas. The sterodynamic processes also determine most of the temporal evolutions in regional SLR, with 1.63 ± 0.41 mm/yr, 1.38 ± 0.38 mm/yr, and 1.28 ± 0.35 mm/yr for the YECS, SCS, and EJS, which correspond to contributions of 45.1%, 42.0%, and 38.5%, respectively. Furthermore, interannual sea-level variations over these marginal seas are indeed driven by sterodynamic effects, which account for approximately 98% of the total variance of the regional SLR. The correlation coefficients between the total sea-level and sterodynamic component reach 0.95, 0.97, and 0.94 in the YECS, SCS, and EJS, respectively. These estimates reveal that sterodynamic effects play a critical role in driving the spatial and temporal variations in regional SLR in the northwestern Pacific16,33.

Fig. 3: Mean sea-level budget time series and trends over 1993–2017.
figure 3

a Time series of mean sea-level in the YECS from altimetry (blue), ICE (light-blue), LWS (green), sterodynamic (red), and GIA (purple). Shaded areas represent one standard deviation uncertainty among each time series. c same as a but for SCS. e same as a but for EJS. The trend budget of SLR for b YECS, d SCS, and f EJS, respectively. Error bar represents 95% confidence intervals estimated slope of uncertainty.

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Table 1 Trends (mm/yr) of satellite-altimetry, individual contributors, and the sum of all components over 1993–2017 and 2003–2016.
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Observation-based estimate of sterodynamic SLR

As described in the above subsection, the sterodynamic contribution was estimated by combining in situ-based global thermosteric signal with the regional dynamic sea-level from ocean models. Equally, the sterodynamic sea-level can be expressed by the sum of the SSL due to density changes in the local water column and sea-level induced by circulation-driven OMR. Recent advances in GRACE data processing and in situ-based profiles have enabled the estimate of manometric sea-level due to changes in ocean mass and reliable SSL, respectively. Here, we attempt to assess the observation-based sterodynamic contribution by combining in situ-based SSL with the GRACE-derived OMR due to changes in ocean processes from 2003 January to 2017 June. This approach based on the combined use of in situ-based profiles and GRACE observations allows a direct comparison with available observations of individual processes on regional scales, which provides a complete picture of the underlying regional sea-level dynamics. The circulation-driven OMR component can be estimated by subtracting the mass changes from the ICE and LWS fingerprints from the GIA-corrected GRACE data (see Data and Methods). It is noted that during the GRACE period, the two strongest earthquakes of the 2004 Sumatra-Andaman (Mw 9.1) and 2011 Tohoku (Mw 9.1) occurred near the northwestern Pacific marginal seas. The GRACE dataset includes these two strongest earthquake signals that affect the local trend changes of ocean mass in the SCS and EJS (see Figures S2-S3). Therefore, the signals of the 2004 Sumatra-Andaman and 2011 Tohoku earthquakes were corrected using empirical orthogonal function (EOF) analysis, which was reported by pervious study34. After applying the EOF-based correction, sharp decreases in sea-level in the SCS and EJS due to the earthquake signals were significantly improved, and thus the trend rates of regional SLR significantly changed during the GRACE period (Fig. 4).

Fig. 4: Comparison of GRACE-derived OMR.
figure 4

Time series of OMR for three different products from GSFC (blue), JPL (red), and CSR (yellow) before (dashed lines) and after (solid lines) EOF-based correction for the 2004 Sumatra-Andaman and 2011 Tohoku earthquakes in a SCS and b EJS from 2003 January to 2017 June. The ensemble mean is shown by black line.

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Comparing the altimetry sea-level with the sum of the observation-based sterodynamic, contemporary-GRD, and the GIA components shows reasonable agreement in spatial SLR trends during 2003–2016 (Fig. 5). As mentioned above, the contemporary-GRD changes (ICE and LWS, Fig. 5a, b) can explain a large portion (59.5–74.3%) of the regional SLR trends over these marginal seas (Table 1), and an increase in Greenland mass loss since the mid-2000s notably contributes to contemporary sea-level changes1,3. However, the sterodynamic processes are responsible for the spatial patterns of SLR trend (Fig. 5c). Recent studies have indicated that steric changes alone cannot account for regional sterodynamic sea-level changes because the ocean circulation-driven OMR can play an important role in the regional SLR over continental shelves and coastal regions16,22,33.

Fig. 5: Sea-level rise trend from the individual contributor and satellite-altimetry.
figure 5

Regional maps of the estimated individual contributor and satellite-altimetry of SLR trend in the northwestern Pacific over 2003–2016: a ICE, b LWS, c Sterodynamic effect, d the sum of all components, and e satellite-altimetry. The sterodynamic contribution is estimated by directly combining in situ-based SSL from IAP product with the GRACE-derived OMR from GSFC product. See Data and Methods. The GIA trend in Fig. 2c was used to calculate the sum of all components.

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To further examine the sterodynamic contributions, we decompose the sterodynamic sea-level into an in situ-based local SSL component and GRACE-derived OMR component (Fig. 6). Local SSL changes dominate the sterodynamic SLR in most regions during the GRACE period of 2003–2016, except along the shallow continental shelves, including the YECS. As mentioned above, negative trends over the subtropical North Pacific may be related to changes in the large-scale wind stress curl over the Pacific subtropical26. For the deep-water regions of the SCS and EJS, positive trends of the SSL appear as the heat penetrates deeper ocean depths (Fig. 6a). In contrast, the sterodynamic SLR along the continental shelves mainly arises from the circulation-driven OMR process rather than the local SSL changes (Fig. 6b). This result is consistent with previous studies that showed the importance of ocean-bottom pressure changes induced by mass redistribution on continental shelves and coastal areas22,33,35. Because the thermal expansion is relatively small on the continental shelves where the water depth decreases, a net mass is transferred onto the shallower regions from the deeper ocean (see Fig. 1 of Dangendorf et al.33). This was also noted by Chen et al.15, who focused on the dominance of mass contribution in the YECS based on the results of climate model projections during the 21st century (Coupled Model Intercomparison Project Phase 5 dataset).

Fig. 6: Observation-based SSL and OMR trend.
figure 6

Regional maps of SLR trend for a local SSL and b OMR components in the northwestern Pacific over 2003–2016. Data sources are based on IAP product for SSL and GSFC product for OMR, respectively. The other data sources for SSL and OMR components are also shown in Figs. S4 and S6.

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The time series of regional sea-level budgets and trends for the three marginal seas are shown in Fig. 7, which compares the altimetric SLR with estimates of the underlying processes. The temporal evolution of the geocentric SLR agrees well with the sum of all components, and the estimates are not distinguishable within the uncertainty except for the SCS, representing the closure of the regional SLR budget and the consistency of different datasets (Table 1). Similar to the estimate for the period of 1993–2017, the mass loss from land ice contributes more than 50% of the trend from the sum of the processes for all marginal seas and the sterodynamic process, i.e., SSL and OMR components, explains most of the temporal evolution of the regional SLR. The variability of observation-based sterodynamic sea-level was also compared with the reanalysis-based one, and the two time-series were highly correlated each other for all regions (Figure S5). This comparison gives a reliable sterodynamic contribution to regional sea-level changes that was cross-checked, suggesting an important role of ocean dynamics on regional sea levels. The contributions of the LWS and GIA were relatively small compared to those of the other processes. In particular, the sterodynamic processes for these marginal seas are attributed to geographical differences in the underlying dynamics. Along the continental shelves including the YECS, the sterodynamic sea-level is substantially induced by the circulation-driven OMR component. The rate of the circulation-driven OMR component is 1.23 ± 0.86 mm/yr in the YECS, which explains 31.8% of the total SLR rate, while the local SSL effect makes only a small contribution (6.2%, Table 1). On the other hand, the changes in local SSL for the SCS and EJS contribute to 29.5% (0.89 ± 0.69 mm/yr) and 17.7% (0.68 ± 0.29 mm/yr) of the sum of the individual components, respectively, with stronger SSL rise in the deep-water regions than the surrounding continental shelf regions. The contribution from the circulation-driven OMR is relatively smaller than that of the YECS, with a rate of 0.68 ± 0.69 mm/yr in the EJS and nearly zero in the SCS. Although the uncertainties that may arise from systematic errors of space observations are still large, these results confirm the steric-driven change in ocean bottom pressure between the deep ocean and shallow marginal seas, which play a role in driving SLR trend along the continental shelves15,22,33.

Fig. 7: Mean sea-level budget time series and trends over 2003-2016.
figure 7

a Time series of mean sea-level in the YECS from altimetry (blue), ICE (light-blue), LWS (green), in situ-based SSL (orange), GRACE-derived OMR (yellow), and GIA (purple). For SSL component, we used in situ-based products: IAP, EN4, and JMA and an ensemble mean of these datasets is used. For OMR component, we used the GRACE from different products: GSFC, JPL, and CSR and an ensemble mean of these products is used. Shaded areas represent one standard deviations uncertainty among each time series. c same as a but for SCS, and f EJS, respectively. The trend budget of SLR for b YECS, d SCS, and f EJS. Error bars represent 95% confidence intervals estimated slope of uncertainty.

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The sum of the contributors also explains the observed sea-level fluctuations on interannual time scales (i.e., de-trended variations), showing high correlation coefficients ( > 0.85) for all marginal seas (Table 1). However, the contributor to the explained variance of sea-level variability differs among the regions: for the SCS, local SSL explains a substantial fraction of detrended sea-level changes (80%), while the fluctuations for the YECS (95%) and EJS (83%) were dominated by the circulation-driven OMR process (Table 2). Heat advection associated with westward transport through the Luzon Strait drives the basin-mean heat content in the SCS, thereby leading to SSL variability as shown in Fig. 7b18,36,37,38. Meanwhile, the dominant variability of the circulation-driven OMR in the YECS and EJS is likely to be the result of mass exchange between the marginal sea and the rest of the ocean39. Previous studies have found a near-uniform barotropic fluctuation in the EJS, with monthly to interannual timescales40,41. This mass fluctuation may be related to a near-stationary balance between the inflow through the Korea/Tsushima Strait and the outflow through the Tsugaru and Soya Straits41. Although not focused on in this study, further investigations of sea-level fluctuations in the EJS in line with the mass flux through the straits are required in the future.

Table 2 Percentage of explained variance of the sum of all components for SSL and OMR over 2003–2016.
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Discussion and conclusion

Recent advances in observation have improved the understanding of the GMSL budget and underlying processes, however, the process-based assessment on regional scales is still challenging due to several physical processes with spatial and temporal variability. Because sea-level changes occurring over regional scales pose a threat to coastal communities with high population density, understanding and quantifying the underlying regional processes is of great importance. This study assessed the regional SLR budget in the northwestern Pacific marginal seas in terms of different individual processes. To provide a better understanding of the underlying processes, we examined whether the regional sea-level budget can be closed with a combination of observations and ocean reanalyses over 1993–2017, as well as with independent observations from in situ-based profiles including Argo floats and satellite gravity measurement since 2003.

By comparing the sum of the estimated reanalysis-based contributions with the altimetry SLR, it was found that the trend of the sum is comparable to the geocentric SLR trends for YECS and EJS. Trends of individual process show that the land ice and sterodynamic are the major contributors for all three marginal seas, while GIA has a small contribution. The mass loss from land ice explains a large fraction ( ~ 50%) of the observed SLR trends over the northwestern Pacific, which is consistent with previous estimates of the GMSL budget5,7. Unlike the land ice contribution, the spatial pattern of the SLR trend and its interannual variability after detrending are dominated by sterodynamic processes16,33. To examine the detailed sterodynamic processes, the sterodynamic sea-level was further decomposed into two processes, local SSL and circulation-driven OMR components, using completely independent datasets from in situ profiles and GRACE measurements since 2003. Along continental shelves including the YECS, the sterodynamic sea-levels are substantially induced by the circulation-driven OMR component, which accounts for approximately one third of the total SLR rate, while the steric effect makes only a small contribution. In contrast, the changes in the local SSL for the SCS and EJS differently contribute to the sum in spatial patterns, with a stronger SSL rise in the deep-water region than in the surrounding continental shelf area. These results highlight the circulation-driven change in ocean mass between the deep ocean and shallow marginal seas, which drives regional SLR trend and their interannual variability along the continental shelves15,22.

Our results show that the regional SLR budget in YECS and EJS can be reasonably close to independent observational datasets. However, a large gap exists in the SCS, indicating that the trend of the sum is much smaller than that in the altimetry SLR. One possible source of underestimation may be associated with local SSL estimates based on in situ and Argo measurements (Figures S6-S7). The comparison among the three SSL estimates shows a substantial spread around the ensemble mean for the SCS, which is approximately three times larger than those for the YECS and EJS. This indicates an inconsistency in different datasets, especially in the SCS, which may arise from insufficient sampling, instrumental biases, and mapping choices42,43,44. Despite systematic errors in space measurement and in situ uncertainties, this observation-based SLR budget demonstrates the utility of independent observational platforms for a process-based assessment by achieving the regional SLR budget closure. As efforts to improve and continue to lengthen both satellite measurements and in situ observations, our understanding of relevant processes will be enhanced with respect to monitoring and projecting regional sea-level changes that improve the basis for future vulnerability.

Data and methods

Sea level observation from satellite altimetry

To identify the spatial and temporal changes of sea-level rise (SLR) in the Northwestern Pacific marginal seas, we use the geocentric sea-level data derived from AVISO monthly 0.25 degree gridded sea surface height anomaly data from 1993 to 2017 (https://data.marine.copernicus.eu/product/SEALEVEL_GLO_PHY_L4_MY_008_047/description). The altimeter-derived regional geocentric sea-level (\({{SL}}_{ALT}\)) can be expressed by three main processes: (1) changes in local ocean density and ocean dynamics, which is called sterodynamic sea-level13 (\({{SL}}_{{SD}}\)), (2) changes in Earth’s Gravity, Rotation, and Deformation (GRD) caused by contemporary mass redistribution from land ice and land water storage changes (\({{SL}}_{{GRD}}\)), and (3) ongoing surface movement of glacial isostatic adjustment14,23,45 (\({{SL}}_{{GIA}}\)). The relation between these processes can be written using the following budget equation:\({{SL}}_{ALT}={{SL}}_{{SD}}+{{SL}}_{{GRD}}+{{SL}}_{{GIA}}+{{SL}}_{{RES}}\). \({{SL}}_{{RES}}\) is a residual given by the difference between the geocentric sea-level and the sum of all components, which includes uncertainties of data used. For the assessment of sea-level budget, here we compare the regional SLR (\({{SL}}_{{ALT}}\)) trends to the sum of estimates of individual contributor, i.e., \({{SL}}_{{SD}}\), \({{SL}}_{{GRD}}\), and \({{SL}}_{{GIA}}\). The uncertainty of the sum of contribution is calculated by quadratic sum of each component (\(\sqrt{\sum {{\sigma }_{i}}^{2}}\)). \({\sigma }_{i}\) is the uncertainty of each component. The 95% confidence level for the trend was calculated as follow: \(b\pm {t}_{(1-\frac{\alpha }{2},n-p)}* {SE}\left(b\right)\), where \(b\) is the trend estimate, \({SE}(b)\) is the standard error of the trend estimate, and \({t}_{(1-\frac{\alpha }{2},n-p)}\) is the percentile of the t-distribution with \(n-p\) degrees of freedom, \(n\) is the number of observation and \(p\) is the number of regression coefficients. Here \(p\) is 2 (trend estimate and intercept). Because each datasets have different resolution, the individual component of sea-level were regridded to a regular 1° grid by linear interpolation to facilitate comparison for spatial distribution (Figs. 2, 5). To assess the time series of regional sea-level budget, all individual datasets were averaged over all grid cells within each basin, as depicted in Fig. 1. Then, the ensemble mean of each process dataset was computed to estimate the sea-level budget.

Sterodynamic effect

Following the method described previously (e.g.,12,16), the regional sterodynamic sea-level (\({{SL}}_{{SD}}\)) is estimated by combining global mean thermosteric sea-level (GMTS) with dynamic sea-level (DSL) from ocean reanalysis: \({{SL}}_{{SD}}={GMTS}+{DSL}\).

We use GMTS estimates from three sources of in situ-based ocean subsurface temperature: Institute of Atmospheric Physics46 (IAP), Met Office Hadley Centre observations datasets EN.4.2.247 (EN4), and Japan Meteorological Agency48,49 (JMA). An ensemble mean of these products is taken to estimate the observation-based GMTS and uncertainty is derived from spread of the ensemble mean (i.e., standard deviation). For the estimate of regional SLR associated with ocean dynamics, we use two monthly products of ocean reanalysis over the 1993-2017 period, including the German contribution of the Estimating the Circulation and Climate of the Ocean project50 (GECCO3) at 1° spatial resolution and Estimating the Circulation and Climate of the Ocean version4 release 451,52,53 (ECCO v4r4) at 1/2° resolution. Because the ocean models used in these products do not conserve the ocean mass or heat, a time-varying global mean of each product is removed from their sea-surface height to calculate the regional DSL, thereby setting the global mean of DSL to zero11,12,16,54. The mean of these DSL products is finally added to the observation-based GMTS to estimate the sterodynamic effect. Figure S1 shows the spatial patterns of \({{SL}}_{{SD}}\) trends calculated using GECCO and ECCO products, respectively. The two products show a similar spatial pattern of the trends, which generally agrees with the pattern of \({{SL}}_{{ALT}}\).

\({{SL}}_{{SD}}\) can be also estimated by the sum of steric sea-level (SSL) due to density changes in local water column and part of manometric sea-level induced by ocean mass redistribution (OMR). Recent advances in Gravity Recovery and Climate Experiment (GRACE) data processing and Argo array floats enable the estimate of manometric sea-levels due to changes in ocean mass and reliable SSL over 0–2000 m, respectively. Here, we estimate the observation-based sterodynamic contribution by combining Argo-observed SSL with GRACE-derived OMR.

The local SSL is calculated by vertically integrating density anomalies at each grid point and each time step: \({SSL}={\int }^{0}_{H}\frac{\rho \left(P,S,T\right)-\rho (P,{S}_{0},{T}_{0})}{\rho \left(P,{S}_{0},{T}_{0}\right)}{dz}\), where T, S, and P are in-situ temperature, salinity, and pressure respectively, \({T}_{0}\), \({S}_{0}\) are reference temperature and salinity (0 °C, 35psu), and H is local depth. For the SSL component, we use three monthly in situ-based products (IAP, EN4, and JMA) at 1° by 1° grid over 2003 January to 2017 June. An ensemble mean of these datasets is used to estimate the local SSL trend in each marginal sea and the uncertainty is given by standard deviation.

Since 2002, the GRACE provides global measurements of ocean bottom pressure that enable the monitoring of mass contribution to SLR budget. Local changes in ocean mass derived from GRACE measurements are represented by the sum of ICE, LWS, and OMR components: \({Mass}={ICE}+{LWS}+{OMR}+{Res}\). From this relationship, we can estimate the OMR change by subtracting the ICE and LWS contributions from the water mass if assuming negligible residual component (Res) that includes earthquake34 and sedimentation signals55,56, and uncertainties in GRACE processing. We use monthly GRACE RL06 mass concentration (mascon) from the three products – the NASA Goddard Space Flight Center57 (GSFC), the Jet Propulsion Laboratory58 (JPL), and the Center for Space Research59 (CSR) from 2003 January to 2017 June because the GRACE mission ended in October 2017 due to battery failure60. The GRACE data includes a leakage near the coastline due to a mixture of land and ocean signals. To address this leakage problem in coastal areas, the unregularized least squares estimator was applied in GSFC products, a Coastline Resolution Improvement (CRI) filter was applied to JPL products, and the new hexagonal grid was defined in CSR products. All products applied GIA correction based on the ICE6G-D model from Peltier et al.24. For the mass changes from ICE and LWS, we use the estimate of Frederikse et al.7.

It should be noted that during the GRACE period, the two strongest earthquakes of the 2004 Sumatra and 2011 Tohoku occurred in the northwestern Pacific marginal seas. The GRACE mascon data includes the two strongest earthquake signals that affect the local changes in ocean mass trends. We applied an empirical orthogonal function (EOF) analysis to remove the signals during the earthquake periods, which was recently reported by Chao and Liau34. Figures S2–S3 present the EOF results for the GRACE data based on the three products (GSFC, CSR, JPL) during the two earthquake events. For all products, the first EOF modes indicate the strongest earthquake signals over the northwestern Pacific marginal seas, explaining more than 90% of the total variance. These signals were corrected by removing the recombined loading vector with the principal component from the GRACE mass data. The correction for the Sumatra earthquake was only applied to SCS and for the Tohoku earthquake only for the EJS (Fig. 4) because of the limited extent of the influence of the earthquake signal (Figures S2-S3). After the correction, we estimate observation-based OMR component by subtracting the ICE and LWS contributions from the GRACE mascon data. Several large earthquakes occurred near the SCS during the GRACE period; for example, the Indian Ocean in April 2012 (Mw 8.6) and Sumatra in September 2007 (Mw 8.5). However, both signals were not captured by EOF analysis and had a negligible effect on sea level change in the SCS. Therefore, we corrected only the two strongest earthquake signals, the 2004 Sumatra and 2011 Tohoku, to estimate observation-based OMR.

Because each dataset has a different spatial resolution, like GRACE JPL mascon showing gradual change along adjacent 3° mascon and CSR representing 1/4° degree, we present steric sea-level (SSL) and ocean mass redistribution (OMR) spatial trend from IAP and GSFC datasets in the manuscript (Figs. 5, 6). Each pattern from all GRACE products and SSL datasets are already given in the supplementary figures (Figure S4 and S6).

Contemporary mass redistribution and glacial isostatic adjustment

Contemporary mass redistribution, resulting from changes in melting ice (ICE, ice sheets and glaciers) and land water storage (LWS), cause gravitational, rotational, and deformation (GRD) effects, which is called contemporary-GRD fingerprints: \({{SL}}_{{GRD}}={ICE}+{LWS}\). ICE is the GRD effect resulting from the ice sheets of Greenland and Antarctica, and land glaciers. LWS is the water exchange between ocean and land, which contains groundwater depletion, dam retention, and natural variability. To assess the GRD effects from global mass redistribution, we use the yearly estimates at 1/2° spatial resolution from Frederikse et al.7, which provides reconstructed datasets, including effects of land glaciers, Greenland ice sheets, Antarctica ice sheets, and land water storage from anthropogenic and natural changes. These estimates are based on in-situ observation and models during the period of 1993–2003, while they are based on GRACE measurements after 2003 (for more details of dataset and its uncertainties, see Frederikse et al.7). To directly compare with the geocentric sea-level, relative sea-level components associated with the contemporary mass redistribution were transformed into the geocentric sea-levels by subtracting vertical land motion of each component61. The yearly estimates from Frederikse et al.7 were also converted to monthly interval estimates by using 3rd order interpolation method. Because high-frequencies shorter than annual are not involved in the interpolated datasets, we have also eliminated semi-annual and annual signals from all individual monthly datasets for a direct comparison.

Glacial isostatic adjustment (GIA) is the change due to ongoing movement in the solid earth caused by past glacier changes. To identify the GIA contribution to the regional SLR trends in the marginal seas, the geocentric GRD change associated with the GIA is examined using the estimate of Caron et al.23, which includes an estimate of the associated uncertainties. This estimate used the ensemble of 128,000 GIA model predictions informed by the Global Positioning System (GPS) and relative sea-level dataset. See Caron et al.23 for more details of the estimate.