*3.3. Final Calibration*

According to the main wave direction, the five numerical domains were run. The second step of the calibration procedure was obtained by comparing the numerical output with the records at the DWSD buoy located at MEDA A. Unfortunately, during the working period of the Buoy-A, the ADCP-A did not record any data due to malfunction. A unique time series from the five datasets has been re-constituted.

Figure 14 shows the comparison between the ensemble of numerical runs as reconstituted by the five numerical domains and the Buoy-A and related to 1 year of data. This period, however, is not a consecutive time, but it was reconstituted considering the available period of measurements at ADCP-A. In other words, the fictitious 1-year ADCP-A time series was built by linking the following timeslots: 1 May 2016–30 November 2016, 1 December 2017–8 March 2018, 22 March 2017–27 April 2017. Obviously, for the numerical runs, the same temporal windows from the hindcast data were used.

**Figure 14.** Comparison of time series obtained with the ensemble numerical runs, buoy records at MEDA A and ECMWF data for the reference point E3.

The results related to 1 year are graphically represented with polar diagrams, assembled in Figure 15. The wave rose of Figure 15a shows that the 1-year predominant offshore waves are the ones coming from WNW to WSW. Depending on the system morphology, the wave rose measured at the ADCP-A (Figure 15b) undergoes a radical transformation, both in predominant direction and wave energy. The comparison between ADCP-A and wave climate obtained by using a single numerical domain (i.e., M220◦, in Figure 15c) shows some differences.

The loss of directional information is noticeable for all wave height classes, resulting in an unrealistic predominant wave direction (210◦–225◦ N): the occurrence frequency of these waves is about 48%.

The ensemble numerical runs (Figure 15d) and the energy flux from each wave class are consistent with the ADCP-A measurements and the relationship between one wave sector and another is well evidenced. As highlighted in Figure 14, the smaller sampling frequency (6-h) for the numerical model leads to lower peak values and to a reinforcement of the lowest wave height class (i.e., <0.25 m), which also occurs if the enhancement factor for the input dataset is applied. If a moving average filter (spanning 6 h) is applied to the 1-year ADCP-A measurements in order to have a time series with the same sampling frequency of the numerical ensemble, an excellent correlation can be found, with a bias of 0.009 m and an *RMSE* of 0.52 m. The main wave climate parameters and main statistics obtained for the various sources are reported in Table 9.

The results shown as the mean energy flux at MEDA A are not negligible, in contrast with the intricate morphology of the Bagnoli-Coroglio Bay.

A tentative wave energy flux density contour map is shown along the analyzed coastline in Figure 16. It is stressed that the mean wave power is able to provide its effect up to the outer surf zone. The explanation is straightforward: when the wave front is parallel to the bathymetry and, in particular, if a favourable funnel shape of the coast is recognizable, the main phenomenon governing the wave transformation is energetic refraction, and shoaling could be easily recognized as an energy-conserving, non-dissipative mechanism. This effect could in part explain the validity of the results even though a Boussinesq-type model was not used.

**Figure 15.** Wave rose referenced to different wave height classes (in legend) and related to the fictitious 1-year period for: (**a**) ECMWF grid point E3; (**b**) ADCP at MEDA A; (**c**) numerical model by using M220◦ only; (**d**) reconstituted time series by the five numerical domains.




**Table 9.** *Cont.*

**Figure 16.** Mean wave power flux per unit crest (expressed in kW/m) in the Bagnoli-Coroglio Bay.

#### **4. Additional Considerations and Future Perspectives**

Waves are a concentrated form of solar energy. This energy flows through the Earth's climate system, and its components respond. The response (change in energy flow) usually has impacts on other parts of the climate system. This is known as feedback. Such feedback can be positive (it leads to reinforce a small change) or negative (it acts as a stabilizing force, pushing the system back to its original state). In the context of climate assessment (also in the perspective of climate change detection), this has the opposite connotation: positive feedback destabilizes the system (which is usually bad), while negative feedback acts against the perturbation [140]. Whereas several climate factors have been classified as positive or negative feedback, storm waves and sea level rises are not univocally defined. In the study of environmental restoration projects, like the one in Bagnoli-Coroglio Bay, the identification of feedback is important in order to better understand the sensitivity of local environmental parameters to changes. The authors of [141], in analyzing the impact of sea level rises and storms along the U.S East Coast, stumbled across a variation in sea surface height associated with the Gulf Stream. As is typical of many applications, wave climate changes sit in context with internal variability and other local causes. The non-tidal condition for the Bagnoli-Coroglio area makes it possible to avoid the influence of internal modes of variability in the atmosphere. Therefore, the results of the present study may be assumed as the basis for building other models for "climate" purposes, like those for sea level rises, water circulation and heat exchange at the water surface.

A second point concerns the effectiveness of the numerical model calibration by means of a short (thus affordable and feasible) period of in situ buoy measurement. A heuristic explanation could be that the available dataset respects the hypothesis of the representativeness of the sample, i.e., it is adequate to the distribution of wave parameters. In this vein, it appears crucial that measurements cover the majority of the wave height range. The fact that measurements at MEDA A were carried out during an intense winter storm, in fact, has proven to be essential.

It is worth noting that, in the present study, a "true" triple collocation method (e.g., [39,41]) is not possible due to the short overlap of time series at MEDA-B and lack of simultaneous measurements from ADCP-A and DWSD-A.

However, the reliability of the DWSD buoy, its versatility and cost-effectiveness allows the implementation of a sustainable global array of wave sensors that will support the validation of satellite products and enhanced climatological studies, as well as providing an indispensable tool for the calibration and validation of numerical models in coastal areas.

#### **5. Conclusions**

Any eco-restoration actions require a high level of accuracy in the assessment of the nearshore wave patterns and in the definition of wave climate scenarios for the following decades. Due to this delicate issue, the accuracy and reliability of the techniques and instrumentation used to define the waves are crucial. The present study provides a non-conventional application of the multi-collocation method. In fact, essentially due to a brief overlap of sea state observations carried out by the ADCP and the DWDS buoy, a full triple collocation method is impossible to apply. However, the direct measurements available at two different locations allowed, by means of a two-step strategy, the calibration of a numerical model. In particular, during the second calibration phase, a nonparametric wave height enhancement factor was required in order to achieve the best optimization of the numerical model. The enhancement factor consists of an amplification of each value of the WAM dataset provided by ECMWF. To estimate such an amplification, it was proposed as the assumption of the average discrepancy observed between the WAM hindcast dataset at a point located offshore of the study area and the time series, obtained by the transposition of the available offshore wave buoy records. Then, the ECMWF time series was used as input for the numerical model. It was remarked that the second step used a highly representative sample consisting of measurements collected in a period experiencing a large range of significant wave height. Hence, the "need for speed" is by no means limited to rough calibration, and the path of the two-step method exposed here moves in this direction.

To summarize, two main outcomes can be considered from this study:

1. the procedure here proposed, in which every sea state is subject to five (one for each grid model orientation) numerical propagations by a simpler spectral wave model, allows researchers to reach a good level of accuracy, similarly to a more time-consuming Boussinesq-type wave model which, nowadays, represents a state-of-the-art modeling technique if a very detailed wave disturbance in an enclosed coastal area needs to be explored;

2. the effectiveness of numerical model calibration by means of a short period of direct measurement, opening up opportunities to use low-cost GPS buoys. To bridge the gap of abundant direct measurements in the sea from traditional wave buoy networks, the capability of GPS-buoy clusters to provide data for assimilation, calibration and validation of both climate and weather models could be optimally leveraged.

Specifically for the study area, the results shown were not negligible values of wave energy flux at the study site, also if a significant variability of punctual wave power could be envisaged. The evaluation of wave climate here presented would provide the opportunity for careful eco-engineering solutions against storm control and for restoration purposes. In this vein, it is worth noting a first application of the method to provide wave data for a source apportionment assessment of marine sediment contamination in the study area [142]. Reliable nearshore wave assessment, in fact, makes it possible to assess restoration practices from the perspective of projected medium/long term changes in sea state characteristics; for instance, those stemming from climate change (both at global and local levels). Future field campaigns will help to increase confidence in the technologies and in the approach presented in this work.

**Author Contributions:** D.V. and R.D. carried out the conceptualization; P.C., L.C. and L.M. conceived the investigation; P.C., U.M.G. and F.C. made the formal analysis; L.C. and P.C. performed the methodology for buoy data analysis; F.C. and P.C. performed the methodology for ADCP data analysis; P.C. and U.M.G. wrote the original draft; D.V. L.M., and R.D. performed the review; P.C. and F.C. performed the editing stages. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Italian Ministry for Education, University and Research (MIUR) through the ABBaCo project, grant number C62F16000170001.

**Acknowledgments:** The support of the University of Campania "Luigi Vanvitelli" through the VALERE program (VAnviteLli pEr la RicErca) is gratefully acknowledged. A special thanks is addressed to Augusto Passerelli (SZN), Enrico Di Lauro and Vincenzo Ferrante (University of Campania) for actively supporting the field campaign, the pre-treatment of data and the set-up of the numerical model.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **Appendix A**

This appendix contains logic details about the algorithm used to assemble the five numerical runs.


2. Original hindcast wave direction dataset from ECMWF grid point E3, θ*ECMWF* (expressed in degrees measured clockwise from true north).

Result

• Ensemble dataset, *SEN*, of 1-year numerical runs with *N* = *1460* data (8760 h /6 h = number of ERA-Interim data spanning 365 days at six-hour time slots).

M260◦, M280◦, i.e., SM180◦ , SM220◦ , SM240◦ , SM260◦ , SM280◦ , respectively;

