4.1.4. Currents

Currents speed and direction at 2.5 m depth were validated from 2015 to 2019 using mooring data from CMEMS INS TAC as reported in Table 2 and represented in Figure 5a (red stars). Metrics are reported in Table 7. The main impact due to wave fields on currents statistics is evident when considering the velocity directions, where the coupling reduces the BIAS and RMSE by ~16% and ~10%, respectively, when compared to the control run H0. The improved skill can be mostly attributed to the use of modified stress, showing experiment H2 the lowest BIAS (36◦).

**Table 7.** Validation of 2.5 m depth currents speed and direction: averaged statistics using data as provided by the available moorings in the 2015–2019 period.


The velocity direction RMSE indicated that the H1, H2 and H3 experiments have comparable errors in the range of 107–111◦ and that H4 is the best implementation, with a reduced error of around 100◦. Conversely to the direction, no significant differences were found for the statistics of currents speed in the forced simulation.

Figure 9 shows the five years averaged currents speed and direction at the mooring locations, and it allows us to appreciate how the currents change when hydrodynamics is forced with waves. Each column in the plot represents a specific mooring: EUXRo01, EUXRo02 and EUXRo03, from left to right.

**Figure 9.** Currents speed and direction at 2.5 m deep for moorings (**first row**), H0 (**second row**) and H4 (**third row**). Columns represent the three different mooring locations available.

Additionally, currents speed and direction from observations (first row), from the H0 experiment (second row) and the H4 experiment (third row) is shown. From a qualitative point of view, we can see that in both forced and free-run experiments the model has a stronger western currents component than the observation, probably due to low resolution in space and time of atmospheric forcings, considering also that the observation is taken on a precise location/time.

The main wave direction in this area is aligned with that of the currents (from North-East towards South-West). H0 experiment has a prevalence of one-directional bin, while if waves are considered, the direction of the main current is described by 3–4 directional bins. This explains that the currents simulated by the H4 experiment have a wider dynamic.

Contrarily to H0, in which stronger currents are defined mainly by one direction, the forced experiment H4 has 3–4 directional bins with almost the same speeds and occurrence frequency. Despite this change in magnitude, statistics from Table 5 do not highlight improved skills in the HM simulation. Unfortunately, the very low number of available moorings in the Black Sea region prevents us from performing a more robust validation of the results, but the wider dynamics of H4, which is closer to the observation than H0, seemed to be promising.

#### 4.1.5. RMSE vs. Significant Wave Height

To evaluate a correspondence between the improved representation of the ocean physics in the Black Sea thanks to wave-currents forced model, we propose in Figure 10 the time series of daily averaged RMSE differences for temperature (herein, RMSEdif) between fully-forced H4 and free-run H0 experiments in the layer 5–20 m and the corresponding mean, at observation location, of Hs on 2019.

**Figure 10.** Timeseries of daily H4-H0 RMSE difference (RMSEdif) compared to Hs. The grey line represents RMSEdif and is associated with a green or red scatter point if the forced run is respectively better or worse than free-run. The cyan line represents the mean Hs at observation locations.

This plot helps to evaluate whether the positive or negative impact of the coupling is dependent on specific Hs values or the whole Hs spectrum. The figure shows that in general, the H4 has an error lower than H0 in most of the year. The range of variability for RMSEdif evolves seasonally, during Winter and Spring is confined to [ −0.5: +1 ◦C], with the lowest value between mid of February—beginning of April, while during Summer and Autumn the range extends to [ −2: +1.8 ◦C]. From March to May and from September to October, Hs rarely exceeds 1.5 m and it is always close or below 1.0 m: in this period, the fully-forced run H4 seems to have the best performances (e.g., lower error than H0). This investigation revealed that the forced experiment performs better than the free-run when the sea state has no large fluctuations, as in February–April or in November During Summer and January, in which the variability of the wavefield is high, the forced run still performs better in most of the cases, but there are several days in which the H0 is the best.

As a general indication, the forced model confirms its good performance, demonstrating that in the thermocline region the improvement can be of the order of about 0.5 ◦C on average. However, to better assess this conclusion, the analysis requires further dedicated investigation over a smaller time scale.

#### 4.1.6. Validation for the Wave Component

In this study, a three-year validation (2016–2018) of Hs was conducted using J2 satellite data. The dataset, filtered according to a quality check, consisted of 10,479, 9035 and 10,447 observations for 2016, 2017 and 2018, respectively. Figure 11 compares W0 experiment (a-panel) with W3 experiment (b-panel) considering the whole dataset (29,961 observations).

**Figure 11.** Significant wave height validation using Jason-2 satellite from 2016 to 2018. Scatter-plots (**<sup>a</sup>**,**b**) refer to W0 and W3 experiments, respectively.

The coupling with currents and ΔT (W3 experiment) induced a performance improvement in all the statistics: BIAS was reduced from −7 cm to −5.7 cm, RMSE from 28.3 cm to 27.8, the Scatter Index from 0.201 to 0.199, while Pearson's correlation increased from 0.92 to 0.93 and Slope from 0.93 to 0.95.

Table 8 summarises the statistics for all of the wave experiments. All three wave experiments when forced with hydrodynamic fields (W1, W2 and W3) improved model performance, albeit to different extents. The lowest and negligible impact was derived from only-currents (W1 experiment). This result could be a side-effect of the validation method here used. Again, the absence of observations, e.g., from buoy wave gauge in this case, strongly affected our capability to validate the experiments and we were obliged to use satellite data, which has two main disadvantages: it is not reliable near the coast, where currents are stronger and may impact the waves; it does not provide information about wave direction, which could be affected by refraction phenomena.

On the contrary, ΔT (W2 experiment), which acts mainly on Hs has been positively evaluated and confirmed what is demonstrated in the literature [29]. When both currents and ΔT were considered (W3 experiment), the lowest error was obtained, with a reduction of ≈−18% in BIAS, ≈−2% in RMSE. Even the precision of the simulation has been improved, with reduction of scatter index and increasing 1% in *ρ* in correlation.


**Table 8.** Significant wave height (m) validation statistics.
