The global acceleration of sea-level rise (SLR) during the 20th century is now established.
On the local scale, this is harder to establish as several drivers of SLR play a role, which can mask the acceleration.
Here, we study the rate of SLR along the coast of the Netherlands from the average of six tide gauge records covering the period 1890–2021.
To isolate the effects of the wind field variations and the nodal tide from the local sea-level trend, we use four generalised additive models (GAMs) which include different predictive variables.
From the sea-level trend estimates, we obtain the continuous evolution of the rate of SLR and its uncertainty over the observational period.
The standard error in the estimation of the rate of SLR is reduced when we account for nodal-tide effects and is reduced further when we also account for the wind effects, meaning these provide better estimates of the rate of SLR.
A part of the long-term SLR is due to wind forcing related to a strengthening and northward shift of the jet stream, but this SLR contribution decelerated over the observational period.
Additionally, we detect wind-forced sea-level variability on multidecadal timescales with an amplitude of around 1 cm.
Using a coherence analysis, we identify both the North Atlantic Oscillation and the Atlantic Multidecadal Variability as its drivers.
Crucially, accounting for the nodal-tide and wind effects changes the estimated rate of SLR, unmasking an SLR acceleration that started in the 1960s.
Our best-fitting GAM, which accounts for nodal and wind effects, yields a rate of SLR of about

Understanding the current and past rates of sea-level rise (SLR) is essential to make reliable sea-level projections and to adapt accordingly.
In the Netherlands, the current rate of SLR is used to estimate the volume of sand that must be supplied to maintain the coastline and avoid a retreat of dunes.
It also estimates how much salt and gas mining can be allowed under the Wadden Sea.
In addition, local sea-level measurements are important to evaluate sea-level projections

There is now high confidence in an acceleration of global SLR in the 20th century compared to the previous 3 millennia and in the period 2006–2018 compared to 1971–2018

Focusing on sea-level change along the coast of the Netherlands, the existence of an acceleration of SLR is still debated

The data availability along the Dutch coast is much better than for reconstructed global sea level

In this paper, we use a new time series approach which uses a generalised additive model (GAM), which allows us to estimate a nonlinear trend and the optimal multilinear regression model simultaneously.
The nodal tide and zonal and meridional wind are included in the GAM as predictive variables.
Both the zonal and meridional wind are used to reduce the uncertainty in the estimated rate of SLR.
Other authors did not always include the nodal tide as a predictive variable.
Using the GAM, we avoid making strong assumptions about the shape of the sea-level trend, like the piecewise linear shape assumed by

Annual-mean sea-level measurements are used as the average of the six reference tide gauges along the coast of the Netherlands: Delfzijl, Den Helder, Harlingen, IJmuiden, Hoek van Holland and Vlissingen (Fig.

We use the monthly mean zonal and meridional wind at 10 m and atmospheric pressure at sea level from two atmospheric reanalysis products. The first product, the ERA5 reanalysis, from the Copernicus Climate Change service Climate Data Store, is available from 1979–2022 with a backward extension to 1950

Four statistical models were developed and used to separate the influence of the different chosen predictive factors on SLR and to extract the resulting background sea-level trend.
All models are based on the generalised additive model (GAM,

The first model (Tr) estimates the sea-level trend only without using any predictive variables.
This setup makes no assumptions about the drivers of SLR.
We use this model as a reference to evaluate the improvements achieved by increasing the model complexity.
In the second model, the influence of the lunar nodal tide on sea level is added (TrNt).
A sinusoidal wave with unknown amplitude and phase and a fixed period of 18.613 years, the period of the nodal-tide potential, are included as predictive variables for the nodal tide in the GAM.
There has been some debate in the literature about the best way to estimate the influence of the nodal tide on the sea level in the North Sea.
Using linear regression to estimate the effect of the nodal tide along the Dutch coast shows an increased magnitude and a shift in the phase compared to the equilibrium tides

The third and fourth models combine trend, nodal tide and wind effects.
For the third model (TrNtW), wind effects are included by adding

Overview of the equations describing the four GAMs and summary of the statistical model performance. In the model equations,

Using our four GAMs including different predictive variables enables us to study the background sea-level trend, the influence of the nodal tide on sea level and the wind influence on sea level.
The wind influence on sea level can be obtained from the results of TrNtW and TrNtPd.
It is described by the third plus the fourth term (TrNtW) or the fifth term (TrNtPd) in the model equations given in Table

Using our four statistical models, we obtain the background sea-level trend (the first term in the equations in Table

To estimate our models from the data, we use a generic method for likelihood-based estimation of GAM

However, because the estimate of the rate of SLR is sensitive to low-frequency noise, we cannot assume that the noise spectrum is sufficiently closely approximated by the spectrum of the residuals, as

The GAM progressively better fits the data, measured by the deviance (Table

Comparison of the annual tide gauge data averaged over six tide gauges along the Dutch coast with three sea-level time series obtained from the generalised additive models (Tr, TrNt and TrNtW). Only TrNtW is plotted since it overlaps strongly with TrNtPd – their Pearson correlation coefficient is

Figure

After removing the trend from the data in Fig.

Comparison of the wind influence on sea level along the Dutch coast obtained from two different regressors: average zonal and meridional wind of the six tide gauge stations of Fig.

The rates of SLR obtained from differentiating the estimated smooth sea-level trend from each of the four models are shown in Fig.

In addition to reducing the uncertainty, the wind also influences the rate of SLR itself.
Both TrNtW and TrNtPd have lower rates in the first part of the 20th century compared to Tr and TrNt.
From the 1960s onward, the rates of SLR of TrNtW and TrNtPd increase rapidly.
The TrNtW model has the smallest standard error and estimates the largest rate of SLR over recent decades, which reached

The trend values are obtained by averaging the sea-level rate (Fig.

The

By estimating the trend, nodal tide and atmospheric processes underlying the wind influence on sea level simultaneously using the GAM, we can avoid a priori assumptions about the sea-level trend, like having a linear or quadratic shape.
Furthermore, the rate of SLR can be computed as a time-evolving variable over the whole observational period contrary to being calculated as a constant over an arbitrary period, as was done in

Over recent decades, our best-fitting model yields a rate of SLR of

When removing the wind influence from the sea-level observations, the underlying assumption is that this influence is only due to natural variability and that there is no structural change due to anthropogenic forcing.
However, as we find a wind-driven trend over the entire period of study 1836–2022 from both the wind and pressure difference model (Fig.

The four GAMs indicate a decrease in the rate of SLR from the beginning of the 20th century until about the 1960s, with a minimum in the 1940s for Tr and TrNt and in the 1960s for TrNtZw and TrNtPd, as can be seen in Fig.

From daily to interannual timescales, the wind influence on sea level in shallow seas is well understood through barotropic theory of the interplay between the Coriolis force, pressure gradient and surface wind stress (Eq. 3 from

We find a strong increase in the rate of SLR between the 1960s and 2000s (Fig.

In the appendices, we show and discuss our nodal-tide estimates (Appendix

In this study, we estimate the sea-level trend and the influence of the nodal tide and wind on sea level along the coast of the Netherlands. We analyse the average of the observations from six tide gauges and zonal and meridional wind and atmospheric pressure at sea level from two reanalysis data sets. Using four different GAMs, we estimate a smooth trend and (depending on the model) the effects of the nodal tide and wind. One model has no predictive variables; others have only nodal tide or additionally include zonal and meridional wind or pressure gradient as predictive variables. We find that using the local zonal and meridional wind as predictive variables best estimates the sea-level trend based on the reduction of the deviance and of the standard error. The deviance is reduced when more predictive variables are added to the GAM: by 11 % when adding the nodal tide and by another 33 % to 52 % when adding the wind forcing.

Estimating the wind influence based on different choices of predictive variables in TrNtW and TrNtPd shows the method’s robustness, as both models lead to similar conclusions.
We find a long-term sea-level rise due to wind forcing of 0.13 mm yr

After obtaining the sea-level trend using the four GAMs, we obtain the rate of SLR by differentiating the trend.
This results in new insight into the evolution of the rate of SLR along the coast of the Netherlands over the observational period (Fig.

The nodal effects on sea level are represented by the second term of the equations shown in Table

In this study, we have used the average of the six tide gauges along the Dutch coast (Fig.

The rates of SLR obtained per tide gauge station using the GAM TrNtW.

In Fig.

With Fig.

The NAO is a mode of atmospheric variability that influences, among others, the storm tracks and hence average wind over the North Atlantic and the North Sea.
The NAO is known to influence the sea level in the North Sea, especially in winter

Figure

The picture that emerges from the coherence analysis in Fig.

Naturally, there are limitations to this exploratory analysis.
We only investigated annual time series and neglected the seasonality of the effects, though we focus here on multidecadal timescales.
The time series are also relatively short compared to the multidecadal timescales of interest, which affects spectral estimation in particular.
Furthermore, all observed climate variables used here are subject to anthropogenically forced trends.
Removing these trends is necessarily imperfect; we have used cubic polynomial detrending for the wind influence estimates and the North Atlantic SSTs, and the AMV time series is only linearly detrended.
To investigate whether the findings are influenced by our choice of SST reanalysis dataset, we also performed the SST correlation analyses of Fig.

Correlation pattern of our multidecadal wind influence estimates, W of TrNtW

Time series analysis of the wind influence estimates, W of TrNtW (left) and Pd of TrNtPd (right), and indices of the North Atlantic Oscillation (NAO) and Atlantic Multidecadal Variability (AMV).

The code and data are deposited on Zenodo with the identifier

IK, DLB, AJ and CdV developed the model code and performed the simulations. All the authors contributed to the interpretation of the results. IK and DLB prepared the paper with contributions from all the authors.

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.

In this study, we used the GAM implementation, LOWESS filtering and third-order detrending tool from the statsmodels library (

Iris Keizer and Sybren Drijfhout were supported by the Netherlands Knowledge Programme on sea-level rise. Dewi Le Bars was supported by H2020 project RECEIPT (REmote Climate Effects and their Impact on European Sustainability, Policy and Trade (grant no. 820712)). Roderik van de Wal and André Jüling were supported by the Netherlands Polar Program to the Dutch Polar Climate and Cryosphere Change Consortium under file no. ALWPP.2019.003. This publication was supported by PROTECT. This project has received funding from the European Union's Horizon 2020 research and innovation programme (grant no. 869304), PROTECT contribution number 70.

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