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Beyond engineering applications, long-term wave records also play a vital role in ecological and environmental studies. Wave dynamics influence sediment transport, coastal erosion and habitat stability, directly affecting marine ecosystems. Understanding wave conditions enables the assessment of potential impacts on coastal ecosystems and to develop strategies for their conservation and resilience.

Modelling

To generate the data Deltares has developed and extensively validated a wave model, covering the coastal waters of Northern Spain, Western France, Belgium, the United Kingdom, Ireland, the Faroe Islands, the Netherlands, Northwestern Germany, Denmark (except for Baltic Waters), Western Sweden and Southwestern Norway.

The model uses an unstructured (varying resolution) mesh, allowing for an accurate schematisation of bathymetry and better model performance. The model can be used to compute wind-sea and swell wave conditions for the entire shelf at any pre-described period in time. It has (among others) been used to generate the above named NWECS long-term wave dataset.

Applications

The model was developed to support the offshore renewables energy with the varying model resolution, coarser in deep waters and finer in shallow waters, allowing the accurate modelling of wave conditions from offshore to nearshore covering farms, construction and maintenance ship routes and cable routes. The current in-house database is therefore a source of high quality long term data in all waters covered by the model.

When carrying out detailed studies with additional high quality bathymetry data, the model can be, due to its unstructured mesh, easily locally refined and used to generate more data.

SWAN (Simulating WAves Nearshore)

The execution of the wave computations is performed using the SWAN (Simulating WAves Nearshore) wave model, which is a state-of-the-art spectral wave model. SWAN is widely used for nearshore wave modelling in the international coastal engineering community and has been successfully validated under a large variety of field cases and conditions, such as shallow basins and extreme conditions. The software is continually undergoing further development.

Model domain and bathymetry

SWAN requires the specification of three types of grids:

  1. Computational grid, which defines the 2D geographical locations of the computational points in the calculation grid.
  2. Directional grid, which defines the wave directional range and resolution.
  3. Spectral grid, which defines the range and resolution of the computations in the wave frequency space.

The NWECS model is build up on a single unstructured computational mesh with the resolution depending on local depth and bottom features: finer in shallow regions with steep depth gradients. The model domain is shown in Figure 1. The model spatial resolution varies from about 27 km in the North Atlantic (deep water) to about 1.5-2.0 km in the North Sea and German Bight area.

Figure 1: Map of the British Isles and parts of north-western Europe, including France, Belgium, the Netherlands, Germany, Denmark and Norway. The map shows the model domain of the NWECS model, constructed from an unstructured triangular grid. The resolution of the grid varies depending on local depth and bottom characteristics: coarser (approximately 27 km) in the deep waters of the North Atlantic Ocean and finer (approximately 1.5–2.0 km) in shallow areas such as the North Sea and the German Bight. Land masses are light beige, water is black with a blue triangular mesh overlay.

The defined directional grid covers the full 360° circle, with a directional resolution of 8°, the angular interval between the points in the grid. This resolution has been defined based on our experience from other studies, a further increase of the resolution generally leads to less accurate results due to the spectral nature of the model.

The spectral grid of the numerical model is logarithmic with a constant relative resolution and covers a frequency range from 0.03 Hz to 1.0 Hz, allowing for representation of wave periods ranging from 1 s to 33.33 s, which is considered to fully and correctly cover the relevant wave conditions in the region.

The NWECS model bathymetry has been derived from the dataset compiled by the European Marine Observation and Data Network (EMODnet, 2020). The EMODnet data are available on a grid with a resolution of 1/8 arcminute x 1/8 arcminute (approximately 160 meters in longitude and 230 meters in latitude). An overview of the build NWECS model bathymetry with reference to Mean Sea Level (MSL) is presented in Figure 2.

Figure 2: Bathymetric map of the Northwestern European Continental Shelf and surrounding waters, showing sea floor depth (in meters relative to mean sea level) with a color gradient. Shallow areas near the coastlines appear in red and yellow (0 to -500 m), while deeper regions farther offshore transition to green, blue, and dark blue (-500 to -1500 m). Countries such as the UK, Ireland, France, the Netherlands, Denmark, and Norway are visible, with notable shallow areas including the North Sea, Irish Sea, and parts of the English Channel.

Boundary and input conditions

The wave model is forced non-stationary using wind and wave data from the reanalysis dataset ERA5 in combination with in-house detailed water level model data. ERA5 is the fifth generation ECMWF (European Centre for Medium-Range Weather Forecasts) atmospheric reanalysis of the global climate covering the period from January 1940 to present. The model uses a timestep of 1 hour, which is equal to the timestep of the ERA5 data.

The strength of the ERA5 reanalysis dataset is that has been derived from the combination of one of the leading numerical weather prediction models (the model of the European Centre for Medium-range Weather Forecasts, ECMWF) with an advanced data assimilation system. The ERA5 model has a global coverage and a a resolution of 30 degrees x 30 degrees (approximately 21 km in longitude and 33 km in latitude) and the analysis (data assimilation) is carried out hourly. The ERA5 dataset currently covers the period from 1940 until now at an hourly interval and has unprecedented accuracy in terms global atmospheric and wave data.

The ERA5 wave data are applied at the model’s North Atlantic boundaries and the time- and spatially varying water levels from the Deltares in-house Dutch Coastal Shelf Model with Flexible Mesh (2D DCSM-FM 0.5nm) are applied in the whole model domain as background hydrodynamics in the wave simulations (the effect of currents on the wave conditions is found to be negligible).

Validation of the NWECS model

The NWECS model results have been extensively validated against wave observation data throughout the model domain and they show excellent correlations with those data in terms of significant wave heights (cf. Figure 3), but with some underestimation of the peak values due to a general underestimation of the ERA5 peak wind speeds, which can be corrected by means of available calibration factors.

Figure 3: Map of the Northwestern European Continental Shelf showing spatial correlation between modeled and observed significant wave heights (Hs) from 2020 to 2022. Colored circles represent observation locations, with color indicating correlation coefficient values ranging from 0.8 (red) to 1.0 (green). Most stations show high correlation (≥0.9), especially in the North Sea and along the coasts of the UK, France, and the Netherlands. The map includes a triangular mesh overlay representing the model grid and a color bar on the right for correlation scale.

Also the modelled peak wave periods show good correlations with the observation data (cf. Figure 4). It is noted that due to the discrete and scattered behaviour of this variable, the correlation values appear to be of lower quality. However, these scattered values are mostly linked to calm wave conditions (i.e. low wind speeds in combination with swell waves). Furthermore, when conditions with higher significant wave height values are considered, the correlations strongly increase.

Figure 4: Validation map showing the correlation between long-term modelled wave periods and observations across the Northwestern European Continental Shelf from 2020 to 2022. The map features green-to-red colored circles at observation locations, with color indicating the correlation coefficient between model output and measurements. Correlation values range from 0 (red) to 1.0 (green). A triangular mesh representing the model domain is faintly visible in the ocean areas, and land areas are shown in white. A vertical color bar on the right indicates the correlation scale.


Scatter plot comparing Oléron Large Hs and NWECS Hs with a color-coded density scale. The x-axis and y-axis both range from 0 to 15. Three lines are shown: a blue dashed line (y = 1.065x - 0.301), a red dotted line (y = 0.941x), and a solid black line (y = x). Point density is represented by colors from white (low) to dark red/black (high), with a color bar labeled 'nr. entries'. A gray box in the top-left displays statistics: ρ = 0.97, rmse = 0.33, bias = -0.18, σ = 0.27, N = 19935.

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