The total sea-level signal is partitioned into steric and manometric sea level from the NEMO ORCA0083-N006 model run, details of which can be found in and . The model is applied to a high-resolution ORCA tripole grid (nominally 1/12∘) and is eddy-resolving; it incorporates a sea-ice model and is forced by the Drakkar Surface Forcing data set version 5.2 from 1958 to 2015 inclusive. This data set derives ocean model forcing variables from the ERA40 and ERA-Interim atmospheric data sets and includes freshwater fluxes (precipitation and snow). Freshwater runoff is added as seasonal cycles and does not exhibit inter-annual changes. Because of deficiencies in the freshwater forcing, a moderate relaxation of surface salinity to climatology is applied and a freshwater budget restoration is applied at time steps when a deficit is found (and only applied to areas with precipitation).

Steric sea level is calculated using the TEOS-10 equation of state applied to temperature and salinity modelled values at each model depth level. The total and steric sea-level anomaly are affected by the Boussinesq approximation in this model setup . This effect and the global ocean mean atmospheric pressure effect are removed by subtracting the global mean of each sea-level anomaly at each time step.

The manometric sea-level component is taken to be equal to the ocean bottom pressure anomaly, converted from pressure to millimetre change in height.

The ocean model has been shown to match observed variability well . We additionally check that the linear trend from the last decade of the model run, 2005-2015, with GRD added matches the altimetry observation of the absolute sea-level trend (Supplement Fig. S1). In this analysis, only coastal locations within 25 km of the low-resolution GSHHG coastline are considered.

We ensure that sea-level trend variance given by the NEMO model is appropriate for our aim by checking that the variance magnitude lies within the envelope of sea-level trend variance from historically forced model runs from the 6th Climate Model Intercomparison Program (CMIP6; ).

Model run data were obtained via JASMIN (UK data and storage facility, https://jasmin.ac.uk/users/access/, last access: 22 August 2021) and may also be obtained from the WCRP portal . Historical forcing (esm-hist) has been run in CMIP6 from 1850 to 2014 inclusive. Here we take the “zos” variable sea surface height monthly means from January 1958 until the end of the run in December 2014 (noting this is 1 year shorter than the high-resolution NEMO run). The “zos” variable is interpolated onto a regular lat–long 1/4∘ grid for each run and the global ocean mean is removed from each time step of each model. Appendix A lists the 43 CMIP6 model setups analysed in this study. In this analysis, only coastal locations within 25 km of the low-resolution GSHHG coastline are considered.

Major climate variability is represented by indices derived from various atmospheric and oceanic observables, such as air pressure at sea level, sea surface temperature, and surface wind speed or its gradient. Here, we determine the correlation of the principal component time series of rolling sea-level trends with the rolling trends of six major climate includes: the Pacific Decadal Oscillation (PDO; ), El Niño–Southern Oscillation (ENSO; Multivariate ENSO Index, ), North Atlantic Oscillation (NAO; ), Arctic Oscillation (AO; ), Southern Annular Mode (SAM; ), and Indian Ocean Dipole (IOD; ).

Additionally, the effect of the Atlantic Meridional Overturning Circulation (AMOC) is investigated. The AMOC index is calculated here from the NEMO model runs as an anomaly at each time step. The index is computed as the principal component of the low-pass-filtered (1-year running mean) and zonally integrated meridional transport (Sv), and then the rolling trend is calculated from this index.

It is acknowledged that these indices are not independent of each other. However, the EOF pattern and principal components of coastal sea-level change are orthogonal. Therefore, only one climate index is associated with each PC and not repeated in the reconstruction.

Absolute sea level is defined from the ESA SLCCI v2 multi-mission gridded product on a 1/4∘ grid with the most up-to-date corrections and processing available . The standard global mean trend GIA correction is applied at each grid point (-0.21 mm yr-1 for the ICE6G-VM_D GIA model, ). This global mean value represents the shift in geopotential surface of the geoid . Because we are interested in the spatial distribution of sea-level trends, the spatial redistribution of the geoid by GIA is also applied as a trend correction derived from the spherical harmonic coefficients provided by . Contemporary GRD variability driven my mass redistribution affects the sea surface. Satellite altimetry observes spatial changes to the geoid from a centre of mass and should be corrected for the global mean volume change due to solid-Earth deformation . We correct the gridded satellite altimetry for solid-Earth deformation associated with recent mass loading of the oceans following and using their published data .

Tide gauge observations are obtained from the Permanent Service for Mean Sea Level for revised local reference (RLR) stations only. The relative sea level is corrected for GIA only, and no account is made for contemporary GRD-induced or other VLM. Because we are primarily interested in the temporal variability of sea-level trends associated with climate variability, in the figures we remove the time mean trend; the linear trend correction does not affect the results. Non-linear solid-Earth deformation from GRD and other sources such as ground compaction and building load are not accounted for and will be present in the tide gauge trend variability. Monthly mean time series, omitting flagged data, are used to determine rolling trends, and periods for which less than 50 % of data are missing in each rolling decade are omitted.

The ocean models do not include any GRD changes. Observations by their nature include GRD effects. The solid-Earth deformation changes modify the basin shape and therefore global volume. For absolute sea level observed by satellite altimetry the global ocean mean solid-Earth deformation from contemporary mass redistribution and global mean glacial isostatic adjustment (GIA) effects are usually subtracted as a correction. Altimetry observes regional redistribution of the geoid when the anomalies are taken from a mean sea surface. Relative sea level observed by tide gauges includes solid-Earth deformation. To compare model data with observations, we add variability from a sea-level fingerprint method applied to comprehensive data sets of land and cryospheric mass loading. The data set has been used to estimate the GRD effect on global mean and basin mean sea-level trends with the time-varying vertical land movement used to correct tide gauge relative sea-level records . The GRD geoid fingerprints include the effect of mass changes in glaciers as well as the Greenland and Antarctic ice sheets, including uncharted glaciers and peripheral glaciers, and from natural terrestrial water storage (TWS), dam retention (or reservoir impoundment), and groundwater depletion. Here, we determine decadal rolling trends from the geoid variability of the sea-level fingerprint since 1958 and ignore the barystatic (global mean) component since we are interested in the spatial variability.

Over the 58-year NEMO model run, coastal sea-level rolling trends vary in time by a mean standard deviation of 3.6 mm yr-1, with some locations displaying a standard deviation in trends over 7.5 mm yr-1 (Fig. ), which is significantly larger then the mean trend over the modelled period of 2.2 mm yr-1.

The variance of total SSH in the NEMO model run generally sits within the spread of variance in the CMIP6 ensemble. There is increased variance in the CMIP6 ensemble mean compared with the NEMO model run in the Northern Hemisphere, particularly in the Beaufort Strait, Hudson Bay, and the North Sea into the Baltic Sea and to a lesser extent in the Mediterranean Sea and Black Sea (comparing Fig. a and b). It is well known that many coarse-resolution climate models do not reproduce sea level in semi-enclosed seas well because of resolution limits on fluxes with the ocean basins . In contrast, the NEMO model run displays a larger variance in sea-level trends around the coast of Greenland, in the tropical western Pacific and west coast of Australia, in the Caribbean Sea, and around Chesapeake Bay. However, most of these differences lie within the CMIP6 ensemble spread and are therefore not significant.

This analysis confirms there is high variability in decadal sea-level trend in the western tropical Pacific Ocean. On the eastern side where the coast faces the open ocean, the signal is dominated by steric changes, but through the Indonesian throughflow and in the marginal seas, the signal becomes manometric in nature (Fig. a, b). For most of the coastal locations, the variance in sea-level trend is dominated by manometric sea-level change; in 48.2 % of coastal locations defined from the NEMO grid the manometric sea-level change shows the largest contribution to variance, in 32.3 % of locations steric sea level is dominant, and in 17.5 % of locations the GRD effect is dominant.

Around the Greenland coast, in the vicinity of major ice mass loss that is variable in time, there is a large variability in decadal trends due to the GRD effect (Fig. c). The GRD signal driven by glacier and ice sheet mass loss also contributes more than one-quarter to the variability around southern Alaska, Hudson Bay, the Canadian Arctic, Iceland, and to a lesser extent around the Patagonian ice sheet. It is noted that this analysis relates to absolute sea-level equivalent, and VLM contributing to relative sea level is not considered. There is also a notable contribution from GRD in areas around the major river basins or other hydrology impacts (like groundwater abstraction or dam retention) where inter-annual variability in TWS is large, for example around the Amazon River basin, Niger River basin, and the Persian Gulf.

Even though in many of those regions the variability in the decadal trend around the global mean is small (around 1 mm yr-1), where the dominant contributions are GRD and/or local steric contributions from hydrology, future changes may exacerbate the trend. For example, in the Persian Gulf, decadal sea-level trends are dominantly affected by GRD changes over direct oceanographic changes in addition to global mean sea-level rise. It is noted here that there is a complex GRD signal from both hydrology and glacier mass loss. On the south-eastern African coast, as in much of the South Atlantic, where there are very few long-duration tide gauge measurements, the trend variability is small (less than 1 mm yr-1) in both the CMIP6 ensemble mean and NEMO model (Fig. a,b). Here, sea-level variability is strongly influenced by GRD effects from the variability of hydrology, with the Amazon, Niger, Congo, and Zambezi–Okavango basins driving more than 40 % of sea-level trend variability in places (Fig. c). Long-term anthropogenic or climate change impacts on the hydrology in these locations are likely to intensify the regional trend about the global mean.

We reconstruct decadal running sea-level trends from climate index trends by ocean basin for steric and manometric sea level separately and then combine the reconstructions. When compared with the NEMO model sea-level rolling trends at each coastal grid point (from which the regression coefficients were derived), the reconstruction displays statistically significant correlations (r>0.32 for a two-sided t test at the 95 % confidence interval with an auto-correlation of 0.5 in the rolling trends) along much of the global coastal locations (Fig. a). There is a notably poor correlation around south-eastern Africa, where the interaction of the Benguela and Agulhas currents as well as upwelling may interrupt far-field climate-driven sea-level variability. The proportion of sea-level trend variance reconstructed by climate variability through our approach is small around much of the global coast (orange, grey, pink in Fig. ). The reconstruction explains more than half of the decadal sea-level variance along the American continent's west coast, in the tropical Pacific Ocean, and in the Indonesian throughflow to the western Australian coast and west coast of Asia (blue in Fig. b). The primary mode explains more than half of the decadal trend variance in the semi-enclosed seas of the eastern Mediterranean, Black, and Baltic seas. Along the traditionally under-sampled West African coastline between 10∘ N and the Mediterranean outflow at the Strait of Gibraltar as well as between 5 and 30∘ S, the reconstruction explains between one-third and one-half of variability in decadal trends. The approach explains more than half of decadal trend variance over 25.8 % of the global, non-polar coastal ocean and with greater success in the Pacific Ocean where the ENSO variability is dominant (Table ). Table  presents the proportion of grid cells located in each basin where the reconstruction explains more than one-third, one-half, or two-thirds of the decadal sea-level trend variance (not area-averaged). The column “SSH” refers to a reconstruction using only total SSH EOFs, and the column “DSL + steric” refers to a reconstruction summed from the EOFs of all sea-level components. For each major basin, the approach can explain more than one-third of the decadal trend variance for 24.6 % to 73.1 % of coastal locations (Table ).

When considering the proportion of variance explained for a coastal location, the manometric sea-level signal becomes important. The first principal component modes from manometric and steric sea level are very similar to that from sea surface height and have the highest correlation with the same climate indices, except for the influence of AMOC in the Atlantic Ocean (Supplement Table S1 and Figs. S5 and S11). However, by adding the contribution from each component separately there is a marginal improvement in the overall variance explained by this approach (Table ). Splitting the variance into component parts allows the EOF analysis to determine more specific spatial patterns for each component part, whereas the total SSH is dominated by different physical processes in different areas (Fig. ).

Oscillations in observed tide gauge decadal trends are explained well by the climate index reconstruction in some regions, in particular across the tropical Pacific and the coast of the Americas as well as on the Atlantic west coast (examples are given in Fig. ). Where the majority of the signal is manometric, for example the west coast of Australia and the Gulf of Maine (Fig. c, e), coastally trapped waves propagate along the continental slope and shelf. Where the continental shelf is narrow, the reconstructed sea level is predominantly steric (Fig. b). In the tropical western Pacific, the dominant ENSO steric signal directly impacts tropical western Pacific tide gauge sites on the oceanward (eastern) coast, but the signal propagates through the Indonesian throughflow and around the island as a manometric signal, so by Cebu the signal is predominantly manometric (Fig. a). The tide gauge data do not have contemporary VLM removed (except GIA), nor the nodal tide or inverse barometer correction made. For visualisation we simply remove the mean trend for the whole period considered.

For locations with large-magnitude variability in the trend, i.e. with a standard deviation larger than the global mean trend of 3.5mmyr-1 (orange and yellow is Fig. a, b), typically more than half of that decadal signal can be attributed to climate forcing and reconstructed from climate indices. For 10 % of the coastal locations in this study, over two-thirds of the regional decadal sea-level trend about the global mean can be quantified by a linear relationship with climate index data (Table ).

The reconstructed sea-level variability due to primary climate modes can be compared against the spatially comprehensive satellite altimetry data, with the global mean trend removed (to emphasise regional patterns in sea-level change).

For a recent decade of observations, 2008–2018 inclusive, the reconstruction of the sea-level trend anomaly along the coast associated with climate indices (Fig. ) captures the dipole of the sea-level trend anomaly across the Pacific Ocean and at least one-third of the decadal trend anomaly in the Caribbean Sea and Black Sea, as well as the sign of the trend anomaly in southern Greenland, the Baltic Sea, and the north-western African coast. The reconstructed signal is not as strong as observed. In some regions, such as the Gulf of Mexico, the reconstructed trend associated with climate variability (Fig. b) displays the opposite sign to the observed trend (Fig. a); in these locations in this period, the observed-minus-reconstructed trends have a larger-magnitude trend from the global mean. The histogram of trend anomalies for this period are markedly more Gaussian when reconstructed with climate-index-related variability removed than the unaltered observations.

Notably in all basins, by removing the reconstructed variance by climate indices, the mean (median) coastal sea-level trend for 2008–2018 is increased by 0.7 (0.2) mm yr-1 globally (Table ). It is noted that we expect climate variability has affected the global mean sea level over the same period, which we do not account for here, but we may conclude that coastal sea levels have been suppressed by the phase of climate variability in 2008–2018 compared with the entire ocean mean.

Inter-annual sea-level variability can develop purely as a response to non-linear interactions in oceanic intrinsic variability and can evolve from seasonal forcing as strongly as from atmospheric forcing . Oceanic intrinsic variability exceeds the forced response to atmospheric forcing at some length scales over several years in high-resolution ensembles . Thus, sea-level variability is the aggregated response over integrating timescales of both atmospheric forcing and intrinsic variability in the system. It is acknowledged that the approach could be improved by comparing the PCs with phase-lagged trends in the climate indices and/or with other metrics describing the forcing.

Globally, the ENSO and PDO have been shown to dominate the decadal-scale variability of coastal sea level over other climate processes e.g.. Because the PDO or ENSO decadal variability dominates the power in sea-level variability, the EOF bases on a global data set are forced to be orthogonal to that mode. To investigate other drivers, we further mask the data into three oceanic basins: the Atlantic, Pacific, and Indian oceans. By focusing on each oceanic basin in turn, the dominant mode(s) from each region can be identified (Table ; Supplement Table S1 and Figs. S4 to S18). Since we aim to reconstruct decadal-scale sea-level trends, it is difficult to make direct comparisons with previous studies of climate variability and sea-level change. The dominant influence of ENSO and PDO indices with Pacific and Indian Ocean sea level agrees with other works e.g.. In the North Atlantic Ocean, our approach finds a stronger relationship between sea-level variability and AMOC, followed by the AO. Previous studies that include inter-annual variability find strong relationships with the NAO . Studies that separate the sea-level components have found that steric sea-level variability strongly relates to the Atlantic Multidecadal Oscillation (AMO) , and our approach results in a similar relationship between manometric sea-level change and the AO as in (Supplement Fig. S12).

Generally, climate models display lower sea-level variability than observed . In particular, the CMIP5 models were found to simulate sea-level variability comparable to observations but showed a bias in trends ; other authors found that the long-term memory, power-law character of sea level in CMIP5 models is too small, indicating the sea-level variability is too short-lived . Here, the use of a high-resolution model goes some way to minimise that influence, but we caution that the resulting reconstructed sea-level variability and its trend should be thought of as a minimum rise or fall in sea level expected with climate index evolution.

It is acknowledged that the EOF patterns and their PCs developed here are somewhat model-dependent and because of the linear approach taken may incorporate anthropogenic as well as internal forcing patterns. Because of the multicollinearity in the explanatory variables (climate mode indices) and auto-correlation in the variables, there are limitations on any type of regression analysis that attempts to associate climate variability with sea-level variability. The EOF analysis may split the variability from a given physical process into more than one mode, weakening the relationship with any single climate mode index. Therefore, the reconstructed climate-associated sea-level trends produced should be thought of as lower limits at each location of the trend variance about the mean trend. A multivariate approach with regularisation could be applied instead.