**4. Discussion**

In the previous section, the main results from the IBI wave model sensitivity tests performed (i.e., IBI-CU and IBI-DA) are shown. All the IBI wave simulations are validated with observational data sources for significant wave height and period, and the two test runs are compared with the control run (IBI-CO), which is performed using the same model set-up that has been used in the IBI operations since 2018.

The main aim of these sensitivity tests is to assess the impacts that potential upgrades in the wave model set-up have on the IBI wave model solution. The scientific qualification performed (based on comparisons of the IBI test model solutions with the control run, and the available observations) should provide enough information to decide if some of the proposed set-up novelties may be included in a new operational IBI-MFC wave system release. To make a decision on the adequateness of the proposed set-up upgrades to be launched as part of the next IBI operational wave system release, it would be necessary to verify if the new model solution improves or degrades, with respect to the control (and at what level).

Overall, skill computed along the whole test year do not show substantial improvement with wave–current coupling implementation, in terms of significant wave height accuracy. Model coupling performance (IBI-CU) is a little better for the mean wave period, but in any case, for both parameters, Hs and *Tm02*, the improvement with wave–current coupling is small and does not exceed 0.2%. The scatter index *SI*2 for the significant wave height (Table 3) and the 3% RMSD for the mean wave period computed with hourly observations at mooring buoys (Table 2). However, as it is well known, and extensively described in the literature [43–48], there are very specific situations when this current forcing improves the wave simulation (mostly in shallower coastal waters and related to the same case, where local waves propagate in the opposite direction to prevailing surface currents) differences on mean period have been observed, reducing the quality of the ocean-coupling model. There are some special cases, marked by differences, mainly in the mean period, representing a decrease in the wave model skill when coupling is activated, that should be discussed.

For instance, even though current forcing increases values of wave height so metrics are slightly better for the coupled model (IBI-CU), we see how, in some regions, such as the Gulf of Cadiz and Strait of Gibraltar (CADIZ and GIBST region), a significant decrease in quality in the coupled simulation (and particularly in the period) is detected.

This is seen in the two coastal buoys located close to the strait of Gibraltar (buoys 6101404 and Tarifa-coast-buoy), where the difficulty of obtaining a good ocean current performance produces worse results: they are strongly influenced by an unrealistic ocean current overestimate, the *Tm02*, when *Hs* is low (less than 0.5 m). Figure 8 illustrates this pattern at buoy 6200085 (Cadiz deep buoy; see locations in the maps depicted in Figure 2) for a whole month, September 2018. This case is used because of the availability of surface current observations (the buoy location is covered by the Puertos del Estado HF Radar System) [49]. Skill metrics for mean period *Tm02* weaken in the coupled model (correlation decreased from 0.83 for control simulation to 0.74 for IBI-CU in September). The time series depicted in Figure 8, help in analyzing this decrease in the validation scores. Figure 8b shows how differences in the wave period between the coupled and control run mainly occur on some specific days (events depicted in the figure by the dark blue squares). It is important to note that these days, when overestimated values for *Tm02* in the IBI-CU solution are identified, show very low significant wave height values (Hs values being lower than 0.5 m; see Figure 8a). The IBI model surface currents can be validated with HF Radar observation for the day 3 September 2018. Comparison of daily averaged IBI model currents (Figure 8c) with the HF radar observed ones (Figure 8d) show how the unrealistic simulation of surface current at this location (P16 point indicates location of Buoy 6200085 used for the wave validation) spuriously introduces energy into the wave model, generating the increments of mean period in these cases, marked by low wave heights.

**Figure 8.** Monthly time series for *Hs* (**a**) and *Tm02* (**b**) for the simulations of coupled model IBI-CU, (red line) and no coupled, IBI-CO (blue line) at buoy 6200085 in Gulf of Cadiz, observed data in black dots. The square in dark blue square encloses the overestimated values for *Tm02* in IBI-CU solution. On the bottom, images of the validation tool NARVAL (North Atlantic Regional Validation; [50,51]): daily mean of current velocity and direction for the IBI model solution (**c**) and HF radar (**d**). Point P16 is the location of the buoy 6200085.

**Figure 9.** Difference of Significant Wave Height, Hs, (in meters) from IBI-DA and IBI-CO runs during a North-East Atlantic storm (on the 30 November 2018 at 12 UTC).

These results emphasize the importance, when coupling ocean current with waves, of having realistic high-quality model surface current fields. As shown in this example, the use of model currents inputs, locally affected by unrealistic model features, may spoil the wave model performance, especially in very low energetic situations outside of the main storm events. As such, ref. [52] shows a similar misfit induced by model currents in Southern Ocean.

The assimilation of the altimeter data showed a significant reduction in the bias and scatter index on significant wave height. On average, the scatter index of Hs is improved by roughly 8% in open ocean. We noticed that the assimilation is skilled to efficiently correct the wave model errors related to the uncertainties of the wind forcing in the North Atlantic, especially during storm events, as illustrated in Figure 9. This clearly brings better initial conditions for swell propagation to coastal areas, as revealed at Cadiz buoy. However, there is still room for improvement in the assimilation scheme, namely better estimates of the covariance model errors, by taking into account the variability of the sea state in the IBI domain. Moreover, the use of variable correlation length, depending on whether the sea state is wind sea or swell dominated, will induce a better spread of the assimilation correction on the model grid points.

Results from the new IBI wave systems (proposed to be the new IBI wave operational release, named here IBI-OP) can be seen in Table 5.


**Table 5.** Estimated Accuracy Numbers related to Significant Wave Height (year 2018) for the IBI wave model scenarios. On the right (column IBI-OP), the new IBI operational wave system. Observational source reference: HY-2A satellite-derived product.

The statistical comparison for the entire year 2018 of the four scenarios, defined in Table 1, and the HY-2A altimeter shows a good evolution for each model upgrade (Table 5). However, the most relevant improvement is due to the data assimilation implementation (IBI-DA), with a scatter index *SI*2 and error indicator *HH,* decreasing more than 1%. The impact of ocean current, although less significant, improves the model qualification, increasing the significant wave height and with better accuracy of mean period (Tables 2 and 3).
