3.1. Spatial Distribution of the Coastal Wave Energy Resource
The new hindcast simulation performed in this study provides a refined description of wave power spatial distribution across the south Aquitaine shelf. This detailed information is of great interest for WEC future development.
shows the spatial distribution of the mean wave power in the studied domain, obtained from the average over the 44 years of the hindcast simulation. This plot reveals a remarkable difference in the wave energy resource between the north (y
> 160,000 m) of the domain and the southern part, with significantly higher energy in the north. The delimitation between both areas corresponds to the Capbreton canyon, which cuts the domain in two following the x
-direction around y
~160,000 m. North of the canyon, the mean wave energy flux ranged from 25 to 34 kW/m with an average of 27 kW/m. South of the canyon, the wave energy flux progressively decreased to values between 10 and 25 kW/m with an average around 20 kW/m. This decrease was mainly due to refraction of the wave field over the strong bathymetric gradients on each side of the canyon, which tended to focus energy in the north while creating a “shadow area” in the south. It can be noted here that the refined grid resolution over the specific bathymetric feature of the canyon seemed to be crucial to capture the related impact on the local wave resource, whereas this effect could be underestimated or even ignored by coarser regional simulations. Another contribution to the north–south coastal energy gradient may have arisen from the protective effect of the Spanish coast for wave systems propagating from the southern part of the Atlantic basin with west incident direction. However, these systems are not dominant in the studied region, suggesting a more limited impact on the obtained spatial distribution.
Upon examining the results further onshore in Figure 3
, the effect of wave–bottom interactions was found to further intensify, resulting in a very heterogeneous wave energy distribution. Along the coast, some areas clearly focused wave energy while others received significantly less energy, mostly due to local refraction by the bathymetry. For instance, due to refraction over the Capbreton submarine canyon, wave power was very weak (5–6 kW/m) in front of Capbreton (see the location of the Capbreton Marina, noted F in Figure 3
). Conversely, right in the south and in the north of Capbreton, energy was focused and power reached 25–27 kW/m in the Capbreton/Labenne area in the south (noted G in Figure 3
) and more than 30 kW/m in front of Hossegor/Seignosse zone (noted E in Figure 3
), with the latter being famous for its world-class surfing spots. Another hotspot of wave power was found in front of Vieux-Boucau approximately 20 km north of Capbreton (noted D in Figure 3
). In this place, a maximum mean wave power of 34 kW/m was obtained, which was the maximum over the whole studied domain. In the southern half of the domain (y
< 160,000 m), very localized spots with higher wave energy were obtained, here again due to refraction over the complex bathymetry in this mixed sandy/rocky region. Such wave energy “patches” were found, e.g., along Anglet shore close to the Adour estuary (noted H in Figure 3
), or in the Saint Jean de Luz nearshore area (noted I in Figure 3
), which is also known for a localized bathymetry focusing effect (e.g., the so-called Belharra giant wave).
To further quantify these strong local variations in wave energy, Figure 4
depicts the longshore profiles of wave energy resource following 20-m (top) and 10-m (bottom) isobaths. The key points mentioned above are clearly visible again on this plot, especially the remarkable drop in wave energy related to the Capbreton canyon. Furthermore, the wave energy maximum located off Vieux-Boucau can be seen at 10-m depth. Another interesting feature when comparing results at 20-m and 10-m depths was the shoreward increase wave energy at this point, resulting in the 34 kW/m maximum at 10-m water depth. This emphasizes again the interesting additional information provided at the local scale by the refined computational grid. Moreover, it suggests that shallow-water wave focusing may have generated local maxima in wave energy that exceeded the offshore resource, confirming that the maximum resource was not always to be found offshore.
3.2. Offshore and Nearshore Wave Parameter Distribution
In view of the results of the previous section, two hotspots are specifically studied in this section: (i) Point A in Figure 1
, which benefits from optimum incoming wave energy in the offshore part of the domain; (ii) the Hossegor/Seignosse area, which appears to be the main nearshore energy hotpot. Firstly, Figure 5
shows the distribution of the annual wave energy depending on the significant wave height Hm0 and the energy mean period Te. The wave energy was obtained by integrating the wave power over the time frames corresponding to the corresponding wave parameters. Figure 5
shows that most of the annual energy was provided by sea states with wave heights ranging from 2 to 5 m and wave periods from 10 to 15 s at point A. The distribution was a little bit different at the Hossegor/Seignosse hotspot with larger heights and period ranges involved, i.e., 2–10 m and 8–18 s, respectively, although most of the energy was still carried by waves with characteristics similar to point A. At both hotspots considered, coarsely, half of the annual energy was roughly provided by numerous sea states with moderate energy fluxes (Pw
< 50 kW/m), while the other half was generated by rarer events of larger intensities. Remarkably, the latter were more frequent in the Hossegor/Seignosse area than at the offshore location considered. Thus, the coastal propagation, especially the focusing on Hossegor/Seignosse, tended to shift the availability of the wave resource toward larger wave heights and periods, in addition to an overall broadening of range of wave parameters with significant energy flux compared to the offshore.
The annual energy distribution is also plotted in terms of significant wave height and peak direction in Figure 6
. At point A, the energy was provided by a directional window between 280° and 310°, with most of the energy being provided by a 10° angular sector between 290°and 300°. At Hossegor/Seignosse, the energy was provided by a directional window between 275° and 305°, while most of the energy was provided by a 10° angular sector between 285° and 295°. Here again, this new set of information about the local wave resource may be of interest for WEC design and sizing, as well as efficiency evaluation at a specific installation point in the coastal area.
3.3. Time Variability of the Coastal Wave Energy Resource
We now examine the time variability of the resource. By considering seasonal variations, Figure 7
firstly shows the distribution of wave power in winter and summer. In winter, the repartition of hotspots was similar to that obtained when considering the entire year. A maximum winter wave power of about 62 kW/m was obtained in two locations. Although the wave resource was of the same magnitude, the spatial extent of the hotspots was different. The hotspot off Vieux-Boucau in the north was much smaller than the hotspots off Capbreton/Hossegor. In the southern part of the domain, the wave power ranged from 20 to 40 kW/m outside very local focusing points.
In summer, the situation drastically changed, with very low values of wave energy. The effect of the submarine canyon on the distribution of the wave energy resource is still visible in the right panel of Figure 7
; however, there were no more areas with a strong focusing effect, and the discrepancies between the northern and southern part of the domain were also not as important as for the winter season. North of the submarine canyon, the wave power varied between 8 and 11 kW/m, while, in the south, the values were quite similar, ranging from 5 to 10 kW/m. Comparing these values to the mean values in winter, an energy decay of about 80% was observed in the north and an energy decay of roughly 75% was observed in the south.
The computation of the variability index introduced by Cornet [19
] was performed to generalize the analysis of the variability to the whole domain. The coefficient of variation (COV) was obtained by dividing the standard deviation of the monthly mean wave power by its mean value over 44 years. Therefore, a COV equal to 1 corresponds to the case where the standard deviation is equal to the mean value. Examining the COV map plotted in Figure 8
, we can observe that the temporal variability of the wave energy flux was rather uniform over the whole domain. However, it can be noted that the variability was slightly higher north of the Capbreton submarine canyon.
The same analysis was carried out for the seasonal variation index (SV) and the monthly variation index (MV). Here, considering the 44-year mean wave energy flux, the seasonal variability index was obtained by computing the difference between the mean values of the most energetic season (December–February) and the mean values of the least energetic one (June–August), normalized with respect to the annual mean. For the monthly variation index, the same computation was done using the most and least energetic months.
reveals the same pattern for the spatial distribution of the wave energy variability indexes as in Figure 8
, with an accentuated separation between the south and the north of the Capbreton submarine canyon. In the southern part of the domain, SV ranged between 1.1 and 1.3 and MV ranged between 1.3 and 1.7. In the northern part of the domain, SV ranged between 1.4 and 1.7 and MV ranged between 1.8 and 2. Here again, the variability appears to be higher in the northern part of the domain. Additionally, we can observe that the areas with the highest wave energy resource described in Section 3.2
of the present study were also the areas with the highest variability.
Given the rather long duration of the coastal wave hindcast produced for this study, we examined the temporal variability in the wave resource to identify if a long-term trend was present. In fact, a WEC device has a lifetime of some decades; therefore, its design must fit the local resource to perform optimally over the whole period of exploitation. As shown in previous paragraphs, the south Aquitaine coastal shelf can be divided into two areas with different wave energy levels, namely, north and south of Capbreton canyon. To assess the long-term variability of the resource in these two areas, two points were specifically studied, one in the north (located offshore of Capbreton at 23.9-m water depth, represented by green squares in Figure 10
) and the other one in the south (located offshore Bayonne breakwater at 26.4-m water depth, represented by red triangles in Figure 10
). In Figure 10
, extractions of the annual wave energy flux, inter-annual variability between two consecutive years, annual wave energy maximum, and the 98th
percentile of the annual wave energy on these two control points are plotted for the 44-year hindcast duration. Linear regressions are also plotted to assess the evolution of these parameters over the hindcast duration.
As expected, the levels of wave energy observed in Figure 10
a were different at the two considered points. At the Bayonne location, wave power ranged between 15 and 25 kW/m with an average value around 20 kW/m. At the Capbreton/Hossegor location, the wave power ranged between 20 and 47 kW/m with an average value around 30 kW/m. Between two consecutive years, the resource was shown to vary significantly. The figure also highlights the fact that, even if the two points present different seafloor characteristics (sandy seafloor with small bathymetric gradients in the north and rocky seafloor with sharp bathymetric gradients in the south), the wave power evolved in a similar way, meaning that the inter-annual variability depended highly on the forcing. The similitude in the behavior of the wave energy was confirmed by Figure 10
b, where the inter annual variability is plotted for the two locations. Although the evolution was almost identical, it appears that the inter annual variability was slightly higher at the Capbreton/Hossegor point. The relative variations in Capbreton/Hossegor ranged between −57% and +93%, while, in the Bayonne location, the variations ranged between −50% and +72%.
Looking for long-term trends in the plotted timeseries, Figure 10
shows that the strong inter-annual variability and the absence of repetition patterns in this variability do not allow making conjectures on long-term resource evolution. When computing linear regressions, it appears that the linear correlation coefficients are extremely low, indicating that a linear evolution of the wave energy resource is to be discarded. The slopes of these regressions, although close to 0, are not relevant given the absence of any linear behavior in the simulated timeseries. Higher-order regressions were also tested (2, 3, 4) with the same results, i.e., a very low regression coefficient.