Decadal sea-level variability masks longer-term changes due to natural and anthropogenic drivers in short-duration records and increases uncertainty in trend and acceleration estimates. When making regional coastal management and adaptation decisions, it is important to understand the drivers of these changes to account for periods of reduced or enhanced sea-level change. The variance in decadal sea-level trends about the global mean is quantified and mapped around the global coastlines of the Atlantic, Pacific, and Indian oceans from historical CMIP6 runs and a high-resolution ocean model forced by reanalysis data. We reconstruct coastal, sea-level trends via linear relationships with climate mode and oceanographic indices. Using this approach, more than one-third of the variability in decadal sea-level trends can be explained by climate indices at 24.6 % to 73.1 % of grid cells located within 25 km of a coast in the Atlantic, Pacific, and Indian oceans. At 10.9 % of the world's coastline, climate variability explains over two-thirds of the decadal sea-level trend. By investigating the steric, manometric, and gravitational components of sea-level trend independently, it is apparent that much of the coastal ocean variability is dominated by the manometric signal, the consequence of the open-ocean steric signal propagating onto the continental shelf. Additionally, decadal variability in the gravitational, rotational, and solid-Earth deformation (GRD) signal should not be ignored in the total. There are locations such as the Persian Gulf and African west coast where decadal sea-level variability is historically small that are susceptible to future changes in hydrology and/or ice mass changes that drive intensified regional GRD sea-level change above the global mean. The magnitude of variance explainable by climate modes quantified in this study indicates an enhanced uncertainty in projections of short- to mid-term regional sea-level trend.

Sea-level variability at the coast is driven by a variety of global- to local-scale factors. Understanding the drivers of variability due to decadal-scale climate variability in historical and contemporary observations improves our understanding of sea-level change and enhances our ability to predict future, near-term sea-level change. By subtracting climate-driven sea level from observations, a more consistent global mean sea level can be obtained from altimetry

Regional sea level is projected to vary by 30 % from the global mean according to climate model evaluations

Decadal variability in global mean sea level is dominated by the El Niño–Southern Oscillation (ENSO) and Pacific Decadal Oscillation (PDO) and their evolution in time

The Pacific Ocean decadal sea-level variability is dominated by the ENSO and PDO processes

Although the spatial variability of regional, decadal-scale sea-level trends is dominated by the steric component

Here we use a 53-year run of a high-resolution ocean model to quantify and characterise decadal-scale sea-level trend variability at the local, coastal scale (with the global mean removed). A comparison is made with the CMIP6 historical run ensemble mean and spread. Climate model runs will not, in general, mimic the timing of internal atmosphere–ocean variability correctly but should capture much of its magnitude in the ensemble spread. Observed regional variability can be greater than coarse models suggest

Although ENSO variability dominates the spatial pattern of sea-level variability on decadal timescales, we wish to investigate if particular climate processes dominate sea-level trends, at the coast, over different regions, and for each component of sea-level change.

Climate and high-resolution ocean model runs are used to quantify the variability in decadal sea-level trends at the coast from each component part. A reconstruction of coastal, decadal sea-level trends using only standard climate mode indices is attempted that can be easily replicated by projecting climate mode indices onto PCs of decadal, coastal sea-level trends. Variability of the coastal, decadal trends in sea-level components (derived from the high-resolution ocean model sea-level components plus GRD) is characterised by an EOF analysis for each major ocean basin. The PCs of these sea-level component modes are correlated against climate mode indices to identify if a climate mode index covaries with any PC (of each sea-level component and in each ocean basin). For each sea-level PC in terms of diminishing variance explained (per component and basin), the climate index with maximum correlation is projected onto a PC by a linear regression until each climate index is used or the correlation is not statistically significant. Thus, the decadal sea-level variability that can be associated with climate variability is reconstructed by one climate index and regression coefficient for each EOF–PC mode, with the sum over reconstructed PCs giving the total sea-level variability.

Firstly, the magnitude of variance in regional sea level and its trend are determined from ocean models. These variances are calculated for total sea level and its component parts of manometric (model ocean bottom pressure) and steric contributions, plus the gravitation, rotation, and solid-Earth deformation response (GRD) contribution from the deviation from the global mean at each time step (refer to

We use output from a high-resolution (nominally

The observed absolute sea-level signal as observed by altimetry includes the GRD component that is spatially varying. The barystatic, global ocean mean volume change due to solid-Earth deformation is ignored in this study because we remove the global mean at each time step. We add only the spatial geoid signal to the sea surface height (SSH) from the models (with a global ocean mean of zero).

To quantify how much of the sea-level variability can be described by a relationship with climate indices, where the impact of sea-level change is highest – at the coast – we investigate reconstructing sea level from climate indices over a decadal timescale. We investigated both low-pass-filtered and rolling linear trends in time for each coastal grid cell time series and found the strongest relationship in the latter (not shown). We assume first-order auto-regressive (AR1) noise, appropriate for monthly sea-level time series

It is acknowledged that there are limitations in using EOF analysis and a linear regression to associate climate variability with sea-level variability. Of course, the EOF method identifies the largest variance for its leading mode, and each mode is orthogonal from that. Therefore, even when care is taken to deseason and detrend the coastal, sea-level component time series, variability from specific physical drivers may be distributed into several EOF–PC modes. However, by reducing the spatial dimensions using EOF analysis we limit computational effort and redundancy in the analysis because of spatial covariance and produce a small data set of EOF patterns and loadings with just one set of regression coefficients each.

To focus on where the impact of sea-level change is highest and because the EOF analysis determines orthogonal bases from the first PC with the largest variability, we only apply the analysis to coastal regions. We define coastal by distance to the nearest coastline, selecting those model grid centres less than 25 km of distance from one of the low-resolution coastlines in the global self-consistent, hierarchical, high-resolution geography (GSHHG) database

Our aim is to relate climate mode indices with the sea-level variability EOFs. A multivariate linear regression analysis could be used. Linear regression analysis only finds the analytical least-square error fit in the case of Gaussian data (no auto-correlation in the time series) and with independent explanatory variables. Some studies have reduced the impact of multicollinearity of the explanatory variables by low-pass and high-pass filtering correlated climate indices, giving new indices that represent short- and long-timescale processes

We take a simpler approach that does not have tunable parameters. For the reconstruction, we rank all leading EOFs and retain those that describe at least 5 % of the sea-level trend variability for each component of sea-level change. For each leading PC in turn, a linear regression is applied to the climate index with the highest correlation coefficient, provided the correlation is significant (by

Reconstructed trends are compared against the variability of running trends from the model, giving the variance explained by the climate index regression, calculated as the percentage ratio of trend variance at each grid cell, of the model-minus-reconstructed residual over the model rolling trends. The variance explained by these reconstructions of course varies by the adequacy of a simple linear model and the number of leading principal component modes used in the reconstruction.

To validate our method, an example period of satellite altimetry data from 2008–2018 is taken. We compare the reconstruction for the trend from 2008–2018 against observed sea level from satellite altimetry. The reconstruction for running trends centred on 1968–2011 is compared against tide gauge observations at arbitrary locations, demonstrating locations where the variance explained appears to be good. The decadal trend variability from tide gauge observations and the reduction in variability explained by all significant PCs are determined for manometric, GRD, and steric sea-level change combined and for each basin using the reconstructed sea-level rolling trend at the nearest model grid cell to each tide gauge location. The tide gauge relative sea level is corrected for glacial isostatic adjustment (GIA), but we do not correct for contemporary GRD-induced or other sources of contemporary vertical land movement (VLM) because of the limited number of tide gauges with co-located and benchmarked GNSS sites, instead removing the mean trend from tide gauge observed data. Rolling trends from observation data are treated identically as from model data: a seasonal signal is solved for within the regression design matrix (an annual and a semi-annual periodic) and the noise is assumed to have an AR(1) characteristic.

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

Steric sea level is calculated using the TEOS-10 equation of state

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 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,

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;

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

Tide gauge observations are obtained from the Permanent Service for Mean Sea Level

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

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

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.

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.

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.

Even though in many of those regions the variability in the decadal trend around the global mean is small (around 1 mm yr

Comparison of the variability in decadal sea-level trends between NEMO and an ensemble of CMIP6 model runs. The standard deviation of decadal trends (mm yr

Proportion of variance explained (%) by sea-level components of the rolling decadal trends in sea surface height from the NEMO model by steric sea level

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 (

Comparison of decadal rolling sea-level trends from the NEMO model plus GRD, and reconstruction using only climate indices: Pearson's correlation coefficient

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

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.

For locations with large-magnitude variability in the trend, i.e. with a standard deviation larger than the global mean trend of

Observed sea-level trends in tide gauge observed sea level (mm yr

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.

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

Comparison of 2008–2018 trend anomaly (mm yr

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

The proportion of coastal grid cells defined from the NEMO grid with more than one-quarter (25 %), one-third (33 %), one-half (50 %), two-thirds (67 %), and three-quarters (75 %) of decadal trend variance explained by the reconstruction. The values shown here are from assessment of the “coastal domain” and the NEMO model runs. “SSH” refers to the reconstruction using EOF and PC modes for the full SSH signal, and “DSL

Statistics of the global–coastal sea-level trend from 2008–2018 observed by satellite altimetry and when reduced by the reconstructed sea level expected from the climate index reconstruction for each basin (mm yr

Globally, the ENSO and PDO have been shown to dominate the decadal-scale variability of coastal sea level over other climate processes

The linear trend coefficient between the decadal trend in the climate index and the first PC time series in each basin and for each component of sea level.

Generally, climate models display lower sea-level variability than observed

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.

The current temporal duration of high-quality sea-level data with good spatial coverage conflates with the typical auto-correlated, integrated, long-memory timescale of variability in major atmosphere–ocean climate modes, as recently shown for steric sea-level variability, particularly in the Atlantic by

We present an analysis of the variance in local, short-term (decadal) sea-level trends about the global mean around the Atlantic, Pacific, and Indian Ocean coastlines. These data are an indicative lower bound of uncertainty in regional short-term trend deviations from global mean projections. The standard deviation of decadal trend exceeds the global mean of

For a recent decade of observations, from 2008–2018, the global–coastal mean sea level (here defined within 25 km of the coast and ignoring the Arctic and Antarctic coastlines) has been suppressed by climate variance by 0.7 mm yr

More than half of the decadal sea-level trend can be explained by a linear regression with major climate index trends at around 25 % of global coastal (within 25 km of the coast) locations, rising to 54 % of grid cells around the Pacific Ocean. The ENSO and PDO variability dominates here, and the open-ocean variability observed by many previous studies extends to and around the coast, most notably in the western tropical Pacific and along the coast of the Americas. Our approach has no lag or lead time introduced and explains less than one-third of the decadal variance in the low-latitude eastern Pacific Ocean and in the mid-latitudes of the western Pacific. In the Indian Ocean, our method is most successful in the eastern basin, where the propagation of ENSO-related sea-level disturbance dominates through the Indonesian throughflow and therefore dominates the first EOF mode, explaining more than 40 % of decadal variance along the western Australia coast but less than 20 % elsewhere. In the Atlantic Ocean our approach works well in the Baltic, Black, and eastern Mediterranean seas and along the west coast of North Africa (eastern tropical Atlantic Ocean), with more than 50 % variance explained in places, but is less informative on the north-eastern Atlantic margin. Notably, this region of North Africa and other regions where the variance explained is lower but still statistically significant, such as the Caribbean seas and Bay of Bengal, have a lack of good-quality and long-duration tide gauge data by which to evaluate the decadal-scale variability needed to make helpful forecasts of sea-level trends over the mid-term. The dominant influence of ENSO and PDO on sea-level change in the Pacific and Indian Ocean and the influence of AO on Atlantic Ocean manometric sea-level change match previous studies

The variability of GRD in the total sea-level trend should not be ignored over timescales of the order of 10 years (Fig.

The CMIP6 models used in this study are given in Table A1.

List of CMIP6 models used in this study.

The CMIP6 model run and NEMO model run outputs are available to download from their original sources (

The supplement related to this article is available online at:

All authors contributed to devising the study. RJB processed NEMO and CMIP6 model data, and SR undertook the remaining data processing, data analysis, and lead paper writing. All authors contributed to interpretation of the results and reviewing the paper.

The contact author has declared that none of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The authors are very grateful to the three anonymous reviewers for their comments and constructive criticisms of the discussion paper.
The authors were all supported by the European Research Council (ERC) under the European Union's
Horizon 2020 research and innovation programme under grant agreement no. 694188: the GlobalMass project (

This research has been supported by Horizon 2020 (GlobalMass (grant no. 694188)), the Leverhulme Trust (grant no. RF-2016-718), and a Royal Society Wolfson Research Merit Award.

This paper was edited by Ismael Hernández-Carrasco and reviewed by three anonymous referees.