The radar altimetry data used to generate this Dataset across the 11 study areas (see Fig. 1) are from the European Space Agency (ESA) missions CryoSat-2 and Sentinel-3A/B. The data in high resolution Synthetic Aperture Radar (SAR) mode were considered and reprocessed.

Reprocessing was performed using the ESA-developed cloud service SARvatore (SAR Versatile Altimetric Toolkit for Ocean Research & Exploration), which processes SAR altimetry data. This service incorporates the SAMOSA+ model and retracker algorithm, specifically designed for the altimeter waveform interpretation and parameter estimation under challenging coastal conditions, to optimize data in coastal environments .

From a computational perspective, the reprocessing campaign leveraged EarthConsole^®'s P-PRO (Parallel Processing) environment, which dynamically allocates computing resources across a distributed cluster. This parallel architecture significantly reduced overall CPU time by executing multiple processing chains concurrently and by colocating Earth Observation input data with the computing infrastructure. Data transfer overheads were minimized and task execution was accelerated, enabling the efficient handling of large data volumes.

As a result, along-track significant wave height Hs and normalized radar cross-section σ0 were obtained along the altimeter track with a resolution of 300 m. In the retracking procedure, the measured reflected radar waveform is fitted with a theoretical model, and several parameters, including the significant wave height and σ0, are estimated. The “misfit” quantifies the discrepancy between the measured waveform and the fitted model waveform. Therefore, a larger “misfit” indicates a poorer agreement between the observations and the model used in the retracking procedure. The dataset contains the information on the ’misfit’ between the model and measured altimeter waveform, that was later used for quality control.

The altimeter data were reprocessed as part of the OCRE EO (Open Clouds for Research Environments Earth Observations) project to generate high-resolution marine and coastal products. The data are freely available online in the EarthConsole® Virtual Altimetry Laboratory for registered users (https://avl-repo.earthconsole.eu/sarvatore/CENTEC_OCRE, last access: 19 September 2026).

Within the WAPOSAL project framework, based on the results of the OCRE EO project discussed above, estimates of wave period and wave power density were computed from along-track altimeter data. Information on Hs and σ0 and a “misfit” was used. The samples with a “misfit” greater than 4 counts are eliminated.

We estimated the zero-crossing wave period Tz as follows. In , it was suggested that Tz is linearly related to a variable named X, which is a combination of significant wave height Hs and of the normalized radar cross section σ0, with X=(Hs2⋅σ0)0.25 , and σ0 expressed in natural units (non-dB).

Therefore, following , using collocated Tz in situ wave buoy data and altimeter Hs and σ0 data, we have re-evaluated for each collocated data set the coefficients (a and b) of the following equation using linear regression 1Tz=aX+b.

To perform linear regression and validate altimeter measurements, data from 82 wave buoys within the study areas were used. The buoy data from the Copernicus Marine Environment Monitoring Service (IN-SITU OCEAN TAC) database, available at the website of Copernicus Marine Service (https://marineinsitu.eu/dashboard/, last access: 19 September 2026)), were used to validate the Tz and Hs obtained from satellite altimetry data in the UK, the Baltic, Norway, the French Coast, Portugal, Northern Spain, and the Mediterranean Sea. Additionally, within the Mediterranean Sea, in situ buoy data for the Italian coast were obtained from the website of RON database (Italian National Wave Network) available at the website https://dati.isprambiente.it/dataset-2/ron/ (last access: 19 September 2026).

In other regions – such as the Azores, French Guiana, French Polynesia, Madeira, and the Canary Islands – where buoys were not installed, the selected ERA5 grid nodes with available time series for wave parameters were used for validation. The data were downloaded from the website of Copernicus Climate Data Store (https://cds.climate.copernicus.eu, last access: 19 September 2026). The number of selected grid points varied by region (6–12 points), depending on the size and spatial extent of the study area. The grid points were selected to provide representative coverage of the coastal zone. No spatial interpolation was applied; instead, ERA5 data from each selected grid point were used directly. Time series of significant wave height and wave period were extracted from the ERA5 dataset and then processed in the same manner as the wave buoy observations.

Validation studies of ERA5 significant wave height have demonstrated good agreement with buoy measurements . However, these studies also indicate that ERA5 tends to underestimate significant wave height during extreme wave conditions. They further show that the accuracy of ERA5 improves with increasing distance from the coast, while variations in water depth have only a minor influence on its performance . In addition, evaluated ERA5 peak and mean wave periods against buoy observations and found good agreement, supporting the reliability of ERA5 wave period data for wave climate studies.

Altimeter and buoy or ERA5 data were matched in space and time. The matching maximum time interval is fixed as 45 min and the maximum spatial distance as 40 km. Although these thresholds are consistent with those commonly used in previous validation studies , the resulting statistics may be sensitive to the choice of spatial and temporal windows. Data where the distance to the coast is less than 1 km were excluded. Altimeter data on σ0 and Hs within a 40 km radius of the buoy or ERA5 node location were cleaned of outliers and averaged. Only locations with more than 100 observations were retained for further analysis.

Using the triplets (σ0, Hs, Tz), the regression coefficients a and b were determined for each buoy location.

The regression coefficients a and b were estimated independently for each buoy location using collocated altimeter and in situ observations. This site-specific calibration accounts for regional differences in wave climate, spectral characteristics, and coastal effects, which can influence the relationship between the altimeter-derived parameter X and the mean zero-crossing period Tz. This approach produces mission-specific time series of satellite-derived parameters that are consistently matched to in situ observations at each buoy location. The temporal spacing between collocated pairs depends on buoy position, in situ sampling frequency, and each satellite mission's revisit characteristics.

The estimation of the linear regression coefficients (a,b) is performed separately for each location, motivated by the fact that the relationship between the altimeter-derived parameter X and the mean zero-crossing period Tz is not strictly universal but depends on local sea state characteristics and environmental conditions, including:

variations in wave climate (wind-sea vs. swell dominance),

As a result, a single global calibration may introduce systematic biases when applied across heterogeneous environments. Performing the regression at each buoy location allows the empirical relationship to better adapt to local conditions and improves the accuracy of the retrieved Tz.

The collocated altimeter and buoy dataset was randomly partitioned into two equal subsets: a training set and a validation set. The training set was used to estimate the regression coefficients a and b, while the validation set was employed to evaluate model performance in terms of bias, scatter index, and correlation coefficient. This procedure was repeated 1000 times to obtain a stable estimate, and the resulting ensemble was used to compute averaged estimates of both the regression coefficients and the statistical metrics. Since the number of available buoys is limited, we used data from all available wave buoys and ERA5 locations both in the training and validation datasets.

In Fig. , scatter plots of Hs and Tz in the validation dataset, which includes all buoy data and Sentinel-3A/B data, are shown.

For Hs, the altimeter's bias relative to buoy measurements is 0.03 m, with a Root Mean Square Error (RMSE) of 0.22 m and a correlation coefficient (CC) of 0.98. For Tz, the altimeter's bias relative to buoy measurements is -0.0001 s, with an RMSE of 0.55 s and a CC of 0.91. For CryoSat-2, similar results are obtained: for Hs, bias = 0.02 m, RMSE = 0.23 m, CC = 0.98; for Tz, bias = -0.0001 s, RMSE = 0.57 s, CC = 0.91.

The strong agreement between buoy and altimeter measurements at the selected locations demonstrates the reliability of the altimeter data across the full coverage area. Therefore, the results of the linear regression are robust. The values of a and b, obtained at locations near buoys, were interpolated to the coordinates of the altimeter antenna footprints, and Tz was calculated along track using Eq. (). More details about the interpolation procedure are provided in .

Wave power density is calculated from measurements of Hs and Tz along the track using the following equation: 2P=ρg2Hs2Te64π where ρ= 1025 kg m⁻³ is the density of seawater, g= 9.8 m s⁻² is the acceleration due to gravity, and Te is the energy wave period.

Equation () is derived in a deep water approximation, which is valid only when the water depth exceeds half the wavelength. For longer-period swell waves, the deep-water assumption may not be strictly valid in parts of the shelf, where intermediate-depth conditions can occur. This may lead to a moderate overestimation of wave power density when the deep-water formulation is used.

Moreover, the empirical relationship between Tz and the altimeter-derived parameter X is based on dimensional arguments assuming deep-water wave dispersion . In this study, we apply the method using coastal-optimized altimetry products derived with the SAMOSA+ retracker, which improves the reliability of wave parameters in the nearshore zone (down to distances of approximately 5 km from the coast). Nevertheless, this represents a limitation of the approach, and future work will address this limitation by implementing finite-depth formulations of wave power density alongside high-resolution bathymetry and numerical wave models, enabling a more accurate assessment near the coastline.

The energy wave period is related to the zero-crossing wave period obtained along track as follows : 3Te=1.18Tz

In this study we utilize constant wave period ratio Te/Tz=1.18. However, this ratio depends on the spectral shape . In this study, we implicitly assume a unimodal spectrum typical of wind-sea or mixed conditions. Under such assumptions, Te/Tz typically ranges between 1.05 and 1.20, leading to an uncertainty in wave power density on the order of 10 %–15 %, and up to 20 % for more complex spectral conditions (e.g., bimodal sea states). This limitation is inherent to the use of bulk parameters and should be considered when interpreting the results.

Each Sentinel-3 satellite has a 27 d repeat cycle, which allows us to estimate the along-track average wave power density. It is assumed that the location of the track is repeated; however, there is a small displacement in satellite movement. Let us call the planned location of the repeated altimeter track the “trajectory”. First, the tracks belonging to the same trajectory are grouped. In each group of tracks, one reference track is selected. The coordinates of the altimeter resolution elements for this track are used as the coordinates for the resulting average wave power density. The data from the other tracks in the group are resampled to the coordinates of the reference track, and the average wave power density is then calculated.

The along-track mean wave power density derived from Sentinel-3A/B data is presented in Fig.  for the 11 study regions. While these data can be further processed through interpolation, binning, or smoothing, the original along-track product preserves the intrinsic high spatial resolution of the measurements. This high-resolution information is particularly valuable in coastal zones, where wave conditions exhibit strong spatial variability and may not be adequately captured by gridded products.

Based on the obtained dataset, the time series for the selected locations can be studied. Around the selected location, the altimeter data are collected within the circle with the radius of 40 km, cleared of outliers and averaged. As an example, we present the time series for the location situated offshore of São Miguel Island in the Azores archipelago. The time series for this location, derived from 11 years of CryoSat-2 data and 7 years of Sentinel-3A/B data, are shown in Fig. . For comparison, the time series for the same location is also presented using ERA5 data. Wave power density derived from CryoSat-2 was compared with ERA5 reanalysis data, yielding a bias of 3.5 kW m⁻¹ and an RMSE of 9.9 kW m⁻¹. For Sentinel-3A/B, the corresponding bias was also 3.5 kW m⁻¹, while the RMSE was slightly lower, at 9.7 kW m⁻¹. These results indicate good agreement between the satellite-derived and ERA5 wave power density estimates.

Seasonal variability in CryoSat-2 and Sentinel-3A/B is similar; however, due to differences in temporal sampling between the two missions, some intense wave events may be captured by one mission while being missed by the other. For the 2016–2022 period, data from the two missions complement each other and provide a more complete time series.

Both altimeter and ERA5 datasets exhibit pronounced seasonal variability, with elevated WPD values during winter and reduced energy levels during summer months, reflecting the dominant influence of North Atlantic swell and winter storm activity in the region. The satellite-derived WPD closely follows the ERA5 observations.

Other potential uses of the present dataset include seasonal variability analysis for the selected locations, as well as correlation analysis with other geophysical parameters. The present dataset is a valuable source of information for validating numerical wave model results.