We use the recent backward extension of the ERA5 climate reanalysis (Hersbach et al., 2023) to simulate time series of still water levels from 1950 to 2024. Hourly wind speed and atmospheric pressure (u10, v10, and msl) are downloaded from the Climate Data Store (CDS) by Copernicus Climate Change Service (C3S). In a preprocessing step, we adjust the format of the meteorological data to make it compatible with the hydrodynamic modelling software. Sea level rise is included in the simulations by using a spatially-varying dataset of annual mean sea levels (Muis et al., 2023b). The underlying sea level rise data was compiled using the probabilistic model of Le Bars (2018) and is defined at a spatial resolution of 1°×1°; the data for 1950–2016 is based on observations, and the data from 2016 onwards is based on projections from the mean ensemble Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change (IPCC, 2013). The detailed methodology behind the sea level rise dataset is provided in the supporting information for the previous publication where this dataset was utilized (Muis et al., 2023a), the same sea level rise dataset is used for the extension, in order to maintain continuity. After the model is initialized, the pressure and wind speed forcing from ERA5 is applied, and to harmonize the vertical reference of the water levels the yearly mean sea level pressure over 1986–2005 is subtracted via an additional correction in the form of a negative pressure field (Muis et al., 2023b).

We simulate tides and storm surges with GTSMv3.0 using the same configuration as described in previous work (Muis et al., 2020). The GTSMv3.0 is a depth-averaged hydrodynamic model with global coverage that dynamically simulates tides and storm surges. GTSMv3.0 is based on the unstructured Delft3D Flexible Mesh software (Kernkamp et al., 2011). We make use of a singularity container, which allows us to run Delft3D Flexible Mesh on any HPC cluster in a simple, portable, and reproducible way. GTSM has a spatially varying resolution, which goes up to 2.5 km at the global coast and 1.25 km at the European coast. The bathymetry is derived from various sources: General Bathymetric Chart of the Ocean (GEBCO) with a 30 arcsec resolution (Weatherall et al., 2015), European Marine Observation and Data Network (EMODnet) at 250 m resolution in Europe (EMODnet Bathymetry Consortium, 2018), and Bedmap2 for the bathymetry under and thickness of the permanent ice shelves in Antarctica (Fretwell et al., 2013). These datasets are internationally recognized, openly available, and provide full global coverage. However, it must be noted that the GEBCO dataset has a relatively low resolution and can carry significant uncertainty in data-scarce regions. This limitation is inherent to the global modelling based on open data. The model has no open boundaries. Tides are induced by including tide generating forces using a set of 60 frequencies (tidal constituents), defined in Delft3D Flexible Mesh software and selected to achieve optimal trade-off between accuracy and computational efficiency. Storm surges are generated by the transfer of momentum from the wind to the water, with an additional contribution by the changes in atmospheric pressure through the inverse barometer effect. We use the Charnock formulation (Charnock, 1955) with a drag coefficient of 0.041 to estimate the wind stress at the ocean surface. To minimize the data storage requirements, we use a set of 44 734 output locations (Muis et al., 2020) that include ∼18000 coastal points every ∼10–50 km along the coast and ocean points on a semiregular grid at a resolution that varies between 0.25 and 5°. The model runs are set up using an automatized workflow by creating separate yearly model simulations with a spin-up time of 15 d, and a timestep of 10 min. Using a parallel setup with 128 cores and 224 GB of RAM, each 1-year simulation takes approximately 1 d to complete. Subsequently the output from the yearly simulations can be combined to obtain the full dataset by removing the spin-up part of the simulation.

In the postprocessing step we compute storm surge levels as a difference between a total water level simulation and a tide-only simulation. For this we use a tide-only simulation that is already available from CDS and covers the same period (Muis et al., 2025a). In addition, the NetCDF4 file format is optimized, the data for the spin-up period is removed, unnecessary variables are dropped, and metadata is prescribed. Datasets with timeseries of hourly mean water levels and daily maximum water levels are derived directly from the 10 min timeseries of water levels.

The data analysis consists of two steps. First, we compute monthly and annual minima and maxima for water levels and surge heights. Then, we detrend the timeseries by removing the annual means from the still water level dataset to achieve a stationary dataset without sea level rise. Based on this detrended dataset, we compute percentiles and return values. To obtain the latter, we apply extreme value analysis (EVA) to estimate the exceedance probabilities. Following Wahl et al. (2017), we apply the Peak Over Threshold (POT) approach and we fit the Generalized Pareto Distribution (GPD) on the peaks that exceed the 99th percentile water level, then we derive estimates for various return periods, including confidence intervals. We use a 72 h window for the de-clustering of the events to ensure their independence. We use the Maximum Likelihood Estimation (MLE) to fit the GPD parameters, with the Monte Carlo method used to define confidence intervals. This analysis is realized using the pyextremes package (Bocharov, 2023). The analysis is done for the extended period (1950–2024), as well as the original period (1979–2018) to enable comparison between datasets of different duration.

To validate the dataset, we compare the modelled still water levels with high-frequency observations of sea levels from the tide gauge stations in the Global Extreme Sea Level Analysis (GESLA) dataset, version 3 (Haigh et al., 2023). The validation is performed for two periods: 1979–2020 (recent period, where GESLA data is available) and 1950–1978 (backward extension period). We only use the tide gauge stations where there is less than 25 % of data missing in either of the two periods, and remove duplicated stations, keeping the longest records among the duplicates. Additionally, the data records are filtered according to the data quality flag value to only use records where no data quality issues are indicated. This selection results in 107 stations that can be used for extreme value analysis, where each station has a matching location in the GTSM-ERA5-E dataset (within 10 km distance). The data coverage in the resulting observational dataset used for data validation is 96.2 % for 1950–1978, and 97.5 % for 1979–2020 (on average across stations).

Each observation record is resampled to hourly data. In order to match the vertical reference of the GTSM-ERA5 dataset, the mean water level in 1986–2005 is subtracted from each record, and daily, monthly and annual maxima are calculated. The model performance of GTSM-ERA5-E is evaluated by comparing observed and modelled values for daily, monthly and annual maxima. For each station, the model data is filtered to only include the periods where observation data is available, and resampled to daily, monthly and annual maxima timeseries. We use the mean bias (MB), the mean absolute error (MAE), and the mean absolute percentage error (MAPE) to compare the modelled and observed data. Next to that, we calculate the root mean square error (RMSE) and Pearson correlation coefficient across timeseries for each station. Mean and standard deviation of these parameters across stations provide an indication of the model performance as compared to observations. Comparing these metrics between the two validation periods (1950–1978 and 1979–2020) provides insight into the differences in performance between the original period and the backward extension.

A comparison between the modelled and observed values at 107 observation stations globally is shown in Table 1. The comparison is presented for the recent time period (1978–2020) and the backward extension time period (1950–1978). In general, there is a good agreement of the validation metrics between the two periods, indicated by very similar values for Pearson correlation of 0.6 for annual maxima (with standard deviation across stations being 0.24 and 0.27 for the recent period and backward extension period respectively). Also the RMSE shows very similar values for both periods. For both periods there is a similar degree of underestimating annual maxima, by 0.10–0.11 m on average (standard deviation across stations of 0.25–0.26 m). The only notable difference is in the MAPE of the monthly maxima, which is larger in the backward extension period (annual maxima MAPE does not show a similar difference). A closer look at individual stations' statistics reveals that large differences in monthly maxima MAPE are observed only for 5 stations (not limited to a specific region). These differences in performance can have various sources, including changes in tide gauge location or changes in record quality further back in time. Overall this validation demonstrates that the extended time period has the same level of agreement with observations as the recent time period, with nearly all performance metrics for the monthly and annual maxima timeseries showing very small differences. This suggests that the backward extension of the ERA5 dataset for the period 1950–1978 is well suited for use in the modelling of global water levels, with resulting data having comparable quality to the GTSM-ERA5 dataset that covers the period 1979–2018, at least in the regions covered by this validation.

Figure 2 shows the spatial distribution of the statistical metrics for the annual maxima from Table 1 across stations. This figure also shows the global coverage of filtered GESLA being limited to specific regions with long-term records, mainly clustered in Western Europe, North America and Japan. The general underestimation of extremes is consistent with findings from previous work (Muis et al., 2016, 2020; Dullaart et al., 2020) and can be attributed to the underestimation of extreme winds in ERA5 in combination with the model's resolution. Especially storm surges induced by tropical cyclones, which have steep pressure gradients within a relatively small area, will be impacted by the low model resolution and are likely to be underestimated. This underestimation is visible in Fig. 2 as the largest negative bias and RMSE shown at the East coast of the USA, where the annual maxima are dominated by tropical cyclone activity.

In addition to the impact of the dataset extension on water level statistics, Fig. 3 also demonstrates the GTSM-ERA5 water levels and storm surge height comparison to observations for several specific major storm events in the extension period (1950–1978) at three tide gauges with long-term records. This includes the storm surge caused by the extratropical storm in the North Sea in 1968, hurricane Carla (1961) that impacted the United States, and typhoon Marie (1954) that impacted Japan. The storm surge signal was obtained from the tide gauge records by removing the tidal component using hatyan software (Veenstra, 2026).

The storm surge caused by the North Sea storm in 1968 at the Esbjerg tide gauge is the fourth highest water level in 1950–2024 and it is well-captured in the GTSM-ERA5-E with good agreement both in terms of timing and magnitude of the maximum water levels. For the Galveston tide gauge, water levels during storm Carla are the second highest over the 1950–2024 record (second to Hurricane Ike in 2008); the magnitude and timing of the storm surge are well-represented by the GTSM-ERA5-E, with differences in the decay of the elevated water levels after the storm surge peak – in the observations the water levels stay elevated for a longer period. In the case of typhoon Marie and the Hosojima tide gauge (highest measured water level in 1950–2024), GTSM-ERA5-E captures the timing of the maximum water levels well, but underestimates the total water levels. When comparing the modelled and measurement-derived surge timeseries, the peak surge height is underestimated for the North Sea storm (-9 %) and typhoon Marie (-14 %), but is overestimated (+14 %) for Hurricane Carla.

The global water level statistics derived from the extended GTSM-ERA5-E dataset are compared to those derived from the original GTSM-ERA5 dataset to understand the impact and potential benefits of the longer timeseries. To quantify the difference in surges between the backward extension and the more recent period, we compare the surge height statistics by calculating the mean annual maxima values based the 30-year timeseries for 1950–1979 and 1995–2024. The difference is shown in Fig. 4, where it can be seen that in by far the most areas the difference is minor (within 0.1 m), indicating that the surge statistics are reasonably consistent between the extended and the original periods. There are, however, several areas where larger differences are visible. In general, there are negative differences in high-latitude regions, such as Antarctica and Northern Europe, and positive differences difference for most of the rest of the globe. It is not clear what drives these differences in surge statistics, and the extended GTSM-ERA5 dataset provides an opportunity for further research to explore these differences across the full 75-year period. It is possible that some of these differences are caused by climate variability (Lobeto and Menendez, 2024). In regions with limited historical weather records, the differences can also be influenced by varying ability of ERA5 backward extension to represent historical extreme storm events.

The availability of longer timeseries is potentially useful for a more robust estimation of extreme values. Figure 5 shows the 100-year return values based on the extended dataset (75 years) and the original dataset (40 years). Differences are generally within 0.2 m, although increases and decreases up to 0.5 m occur locally. The largest increases in the 100-year return values are seen in regions affected by tropical cyclones. This could be linked to the occurrence of tropical cyclones that have relatively low probabilities and that are most likely under-sampled when a shorter period is considered. This includes regions such as Mozambique, Philippines, Caribbean, and northern Australia. There are also regions where there is a decrease, such as Northern Europe and parts of the northern coast of the United States. It is known that even on relatively large timescales of several decades there can be significant variability in storm surge extremes (Lobeto and Menendez, 2024). Future research could investigate these trends in detail and quantify the influence of interannual variability as well as climate change.

For 85 % of all timeseries data output locations in the dataset, the width of the 5 %–95 % confidence intervals for extreme return values of total water levels decreases when using the full length of GTSM-ERA5-E dataset in the extreme value analysis. The width of the confidence interval corresponding to the 100-year return values is reduced by 13 % on average across all output points. Figure 6 shows the difference in confidence interval width for the 100-year return values, demonstrating that for most regions globally the confidence intervals become narrower. An increase in the width of the confidence intervals is observed at clusters of locations in tropical cyclone regions. This is expected, considering that the sample size is too small and robust estimates of return period for those regions require thousands of years of tropical cyclone activity (Lin and Emanuel, 2016; Bloemendaal et al., 2020).

Additional insight into the differences between GTSM-ERA5 and GTSM-ERA5-E is obtained by considering the extreme value analysis results for individual locations. Figure 7 shows return value plots for eight locations globally, including the best-estimate values and confidence intervals based on the extended and original datasets, as well as based on observations. It shows that the effect of using longer records differs from station to station. At some locations, such as Esbjerg, Bergen and Galveston, the best-estimate return values from GTSM-ERA5-E and original GTSM-ERA5 are very similar, but the confidence interval becomes narrower when using GTSM-ERA5-E due to the longer time series. At other locations, such as Fremantle, Hosojima, Cuxhaven and Montauk, higher extreme return values are obtained when using longer timeseries – at these locations the extension of the time series allows the inclusion of more severe storms that were not part of the original 1979–2018 dataset. For locations with low storm surge activity, such as Newlyn, the return values do not change a lot between the datasets. This overview highlights the range of possible changes in estimated extreme water levels that can result from using a dataset covering a longer period of time. While for most (seven out of the eight) locations shown here, the return periods based on GTSM-ERA5-E are still within the confidence bounds of those based on GTSM-ERA5, the difference for higher return periods can be considerable. Hence, the plots indicate that in both tropical and extra-tropical regions the length of 40 years of data (as in the previous version of GTSM-ERA5) may not always be sufficient to robustly estimate return periods. It must be noted that the quality of the extreme value analysis fits based on the peak-over-threshold method with fixed threshold selection varies from location to location. The chosen single-distribution fit is relatively stiff, and is only partially affected by the highest extremes in the data. In the examples illustrated in Fig. 7 this is particularly visible for locations affected by tropical cyclones, such as Montauk and Galveston.

The comparison between GTSM-ERA5-derived and observations-derived extreme values in Fig. 7 shows that for most stations there is a vertical bias. This offset can be seen both for the fitted extreme value distribution (blue and black solid lines) as well as the individual extremes (blue and black dots). These biases are expected in a global model, and can be resulting from inaccuracies in the tidal signal (due to low resolution of the model and complexity of some of the coastlines, as well low accuracy of bathymetric information in some regions) and underestimations of surge magnitudes (which can be a result of underestimations of wind speeds in ERA5, especially for tropical storms, as well as due to inaccurate bathymetric information in some regions). However, the observed frequency of the individual extremes matches with the GTSM-ERA5-E dataset, which can be seen by comparing the blue and black dots in Fig. 7. The extended dataset can help to better identify the return periods of specific events, compared to the original shorter dataset. For example, at the Esbjerg tide gauge, the most extreme event in the GTSM-ERA5 was initially given a return period of 40 years, while based on the longer record length it is assigned a return period of 70 years, both based on GTSM-ERA5-E and observations.