4.1.2. SST

SST validation was conducted using L4 satellite data presents SST BIAS and RMSE for the H4 experiment over the period January 2015–December 2019. Figure 7a shows the geographic distribution of the BIAS and RMSE, Figure 7b displays basin averaged metrics on a monthly timescale. The H4–H0 RMSE difference between fully-forced H4 and free-run H0 is then shown in Figure 7c. The 2D map of computed BIAS shows colder modelled temperature than observations in the North-Western sub-basin (here the absolute minimum BIAS value of about −0.7 ◦C occurs in the Karkinyts'ka Gulf), in the middle of the Central sub-basin and Central-Western Turkish coasts. Warmer BIAS is shown along the Crimean coasts, in the South-Western and Eastern sub-basin (here the absolute maximum BIAS value of about +0.7 ◦C occurs off-shore of the area of Trebisonda and Ordu). The RMSE 2D map reveals that most of the basin has an error lower than 0.3 ◦C, while in the Karkinyts'ka Gulf and along the Eastern coasts the RMSE is greater than 0.5 ◦C. The RMSE only exceeds 0.7 ◦C off-shore of Trebisonda and Ordu and on the North-Eastern coast of the Black Sea. So, the Eastern basin exhibits warm waters and high error. The time series of metrics for all considered experiments shown in Figure 7b are characterised by similar BIAS values with interannual and seasonal variability—warm BIAS during summertime due to model overestimation of the measured temperature from satellite—and the lowest error provided by H2 and H4 but still very close to the reference control run H0. The H4-H0 RMSE difference map (Figure 7c) reveals that the wave coupling produces a large improvement in the South-Western area, while in the South-Eastern part the coupling does not reduce the temperature error. The coupling approach also reduces the SST RMSE in the Odessa and Karkinyts'ka gulfs. Table 6 summarises SST BIAS and RMSE averaged at basin scale from 2015 to 2019 for all five hydrodynamic experiments. No significant change is found for BIAS in any of the experiments, or for RMSE in H1 and H3, which have comparable performance to H0 (≈0.88 ◦C). Performance is only enhanced in H2 and H4 (≈0.85 ◦C).

As the first conclusion, the considered single- and fully-forced experiments do not significantly ameliorate the skills at basin scale with respect to free-run experiment, apart from some specific regions in the Western basin where the effect of the air-sea interaction combined with waves affects the enhanced mixing and stress determining a general improvement of the model performances. Considering that H4 is our best implementation, all the next validations are mainly showed comparing H0 to H4.

**Figure 7.** 2015–2019 validation of Sea Surface Temperature vs. Satellite observation. (**a**) BIAS (upper panel) and RMSE (bottom panel) for H4 numerical experiment; (**b**) 5-year BIAS (upper panel) and RMSE (lower panel) time series of SST; (**c**) 5-year SST-RMSE difference between H4 and H0 experiments.



## 4.1.3. Water Masses

In this section, we present the Hovmöller diagrams for temperature and salinity computed by averaging daily mean fields at the basin scale. The Hovmöller diagram for temperature (Figure 8a) as computed in the free-run experiment H0 well shows that the CIL (around 50–150 m layer) is reducing between 2016 and 2019. This tendency was highlighted in [45], which described time vs. depth basin averaged properties of the Black Sea using available observations from 2005 to 2018. Winter signals, which ventilate the CIL, were weak in 2016, 2018 and 2019, becoming stronger in 2017. This phenomenon is also described in [45], in which CIL is referred to as "perforation". Figure 8b shows instead the temperature difference between H4 and H0 as Hovmöller diagram, highlighting an important mechanism activated by the fully-forced experiment, between 50–100 m, which enhances the CIL reduction as shown in [45] The coupling clearly modified the mixing processes of the basin. During Wintertime, it shows cold and homogeneous temperature differences from the surface up to almost 100 m deep, while starting from Spring, the surface temperature is slightly higher in H4 with a colder temperature core in the subsurface. The

behaviour reaches the maximum at the beginning of Summer, giving a steeper seasonal thermocline for H4. This suggests that when the wave field has stronger activity, the vertical mixing is higher in the forced experiment (Winter), while if the wave activity reduces, the model has lower vertical mixing (Summer). We argued that the main reason for the mixing reduction in the fully-forced experiment might be derived from wave-dependent surface boundary conditions for the TKE. Indeed, while in H4 the amount of TKE at the surface is proportional to wave energy dissipation, in H0 the surface TKE is prescribed using a parameterization for an old wind-sea [17].

**Figure 8.** Time versus depth versus temperature (**<sup>a</sup>**,**b**)/salinity (**<sup>c</sup>**,**d**) diagram for H0 (**<sup>a</sup>**,**<sup>c</sup>**) and H4-H0 difference (**b**,**d**). The shaded grey area refers to the model spin-up time. The shaded area refers to the model spin-up time.

The salinity Hovmöller (Figure 8c) from the H0 model results reveals a quite stratified vertical structure. It also reveals increasing salinity in the simulated period, which is not shown in the [45] work, probably due to the closed boundary condition at the Bosphorus. Figure 8d shows the salinity difference between H4 and H0: the fully-forced experiment exhibits slightly fresher waters at the subsurface up to about 50 m and saltier ones up to 100 m. The signal of increased CIL ventilation phenomena in H4, highlighted in the temperature plot (warm water around 50–100 m) is also evident in the salinity diagram (freshwater around 50–100 m).

From Figure 8b,d it is possible to appreciate the difference in the seasonal cycle for salinity and temperature between H4 and H0.

The seasonality of the difference is more evident in 2018. During the first part of the year, warmer-fresher waters from the surface reach almost 40 m deep, while during the second part of the year becomes shallower, reaching the minimum in Autumn. This cycle is easier to observe evaluating temperature (warm core at surface, and cold-core below), while it is more hidden in salinity because the fresher core at the surface is embedded in a whole water column from 0 to 50 m with a negative BIAS. The fact that salinity is always negative in the uppermost 50 m, and saltier below is probably dependent on a higher stratification on average in H4.
