*1.1. Motivations and Perspective*

Many coastal engineering applications require robust estimates of the "design sea state" with a certain return period, and incorrect estimates can have dramatic effects on the flood risk analysis or on the structural design of maritime structures. Therefore, trustworthy and robust wave datasets are required [1,2]. In the last few decades, satellite observations and meteorological reanalysis have resulted in considerable improvements in weather and wave climate forecasting. Their use is gradually increasing, a day at a time. Moreover, in Italy, where there is a long history of wave measurement [3], datasets such as those provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) [4] have become widely used to improve/substitute the dataset provided by the Italian Wave Buoy Network. The reasons can be addressed as:


As result, nowadays, ECMWF, which covers the period from 1 January 1979 onward and continuously extends forward in near real time, is assumed as the only source for wave climate assessment [8–14]. Several papers have discussed how to validate hindcast data (e.g., [15–24]). For coastal engineers and marine scientists, it is important to take into account the tendency to underestimate significant wave height values during severe storm conditions performed by the ECMWF dataset, as evidenced in several studies [6,8,25–35]. Biased estimates of wave heights will affect [36,37] both long-term return level estimates for extreme wave analysis and the short/medium time wave climate in nearshore areas, resulting from the wave model being forced with a hindcast dataset.

The detailed validation of the ECMWF hindcast model and coastal propagation model are beyond the scope of the present paper. The goals of this study are to:


The latter are of particular importance for the study site, the Bagnoli-Coroglio Bay, because it represents one of the most polluted areas in the world but is nestled between two marine protected areas (the Gaiola and the Baia marine protected areas). This large bay at the north-western end of the Gulf of Naples (Tyrrhenian Sea) is included within the contaminated Sites of National Interest (SIN) for the high levels of environmental contamination by heavy industrial activities by the Ilva, Eternit, Cementir and Federconsorzi industrial factories and plants [50,51]. Due to the limited exchange of water, the accumulation of pollutants poses major concerns for human and environmental health [52]. In 2015, the Italian central government took over the planning competences over the area. By the end of 2015, the remediation of soil surfaces and the marine area has not yet been completed. In the former industrial area, most of the buildings have been demolished, while the surface and subsoil have been remediated by only 50%. In the southern portion of the area, which hosted the asbestos industry, only 30% of the remediation has been completed [53]. In the period of 2016–2018, researchers collected updated information to develop the next phase of the restoration project. This research phase was granted by the ABBaCo project ("Sperimentazioni pilota finalizzate a restauro Ambientale e Balneabilità del SIN Bagnoli-Coroglio") [54,55], in which the present study takes form.

In addition to wave data for both littoral drift/shoreline modeling, future wave climate assessment should include other detailed eco-hydraulic analyses in order to respond to the nascent requests of marine biologists and ecologists (e.g., the coupled turbulence-dissolved oxygen dynamics modeling and forecasting, [56]; projected changes in wave climate [57,58], nearshore velocity field and related dynamics of deep chlorophyll [59–63], habitat mapping purposes [64–68] and ecosystem-based coastal defence [69–73]). Therefore, results from a high-resolution coastal propagation model have been compared with the in situ measurements of an innovative economical GPS-based wave buoy and with an acoustic Doppler current profiler (ADCP) in order to calibrate the numerical model itself. The measurements have been carried out by placing the pair of instruments very close to each other. In particular, a wave buoy called the directional wave spectra drifter, (DWSD) designed and fabricated by the Lagrangian Drifter Laboratory (LDL) of the Scripps Institution of Oceanography (SIO) [74], is examined, exploring its significant potential use in a low-cost drifter for measuring waves in coastal areas.

#### *1.2. Approach and Challenges*

The triple collocation—DWSD buoy, ADCP and virtual numerical point—makes possible an implicit validation between instrumentations and between instrumentation and numerical model. Considering the recent depletion of the IWN, as well as in all of Europe, mainly due to the high costs of maintenance of the traditional wave buoy systems, the opportunity to develop cost-effective and sustainable technologies to monitor waves is of strong interest to researchers and engineers. In the last decade, global positioning system (GPS) technology has been introduced in wave buoys as a cheaper alternative to traditional instruments which mainly utilized accelerometers to measure the pitch, heave and roll of the buoy [75–80].

Technological advancements of the GPS receivers have helped the development of reliable GPS-tracked wave buoys, which are currently gradually complementing conventional sensor-based wave buoys, offering the same high-quality data as traditional, well-established, accelerometer-based buoys such as the Datawell directional wave-rider buoys [81–93]. GPS technology has also been largely adopted in the development of surface drifters that track the world ocean surface circulation [86–88], while other authors [89–91] have recently proposed that the GPS drifter is particularly suited for nearshore or surf-zone applications. The use of a GPS receiver, as opposed to an autonomous instrument package, results not only in considerable cost saving but it enables also the development of smaller buoys, which can be easily transported, deployed and handled from a small boat. This wave buoy has been developed, moving on from the experience acquired from the Global Drifter Program (GDP) [86–89]. Its small size (40-cm diameter) also has the advantage of coping with a higher wave frequency, extending the range of measurement [93].

The idea to have multiple lines of evidence agree has always fascinated climate scientists and ocean modelers, and a cluster of wave buoys goes right in that direction. Therefore, this work describes an experience of a calibration procedure in which multiple numerical simulations, called ensembles, are calibrated by means of the DSWD buoy.

The method presented in this work allows an enclosing calibration procedure to be a building block in a single two-step approach. The triple collocation technique (applied in a point outside the study area) has been used solely to provide a first "rough" calibration. Having this fast calibration (first step), then (second step) the tuning of wave parameters in the numerical model, is refined by an ensemble of five numerical domains running in different wave sectors, in which time series are compared with another DWSD buoy located within the study site. Finally, we demonstrate the method via direct comparison with the wave time series measured by an ADCP installed in the bay. The final dataset obtained from the calibrated model has been used to describe the local wave climate. Quali-quantitative considerations from the whole historical dataset are drawn. The results suggest that the numerical model's calibrations, based on short-term wave buoy measurements, can be easily applied in different areas where detailed wave data are not available.

The paper is organized as follows: the next section provides detailed information on the hindcast model and the instruments used at the study site, as well as a description of the numerical model and the underpinning assumptions that were used to carried out the calibration. In Section 3, the validation results of the DSWD buoy against the ADCP are reported. Moreover, the final dataset obtained from the calibrated model has been used to describe the local annual wave climate. Sources of uncertainty, relevant shortcomings and contradictions between the calibrated and uncalibrated numerical model are

also highlighted. Section 4 is devoted to an overall discussion, with remarks on the future perspective. Finally, some conclusions are drawn.

#### **2. Wave Data and Methodology**

#### *2.1. O*ff*shore Wave Dataset*

The present work has been based on two sources of offshore wave data: wave buoy records and hindcast data. The first have been supplied by pitch-roll type directional buoys operating offshore in Ponza (central Tyrrhenian Sea). The records are available from 1 July 1989 [94,95], as a part of the IWN. From 1989 to about 2002, the wave buoys collected 30 min of wave measurements every 3 h, but when in the presence of wave heights greater than 1.5 m, the measurements were continuous. From 2002 to 31 December 2014, the wave measurements were always continuous and the wave characteristic parameters refer to 30-min time intervals. In any case, the dataset comprises the spectrum zero-moment wave height (*Hm0*), the mean wave period (*Tm*) and the mean wave direction (θ).

A gross stochastic error detection phase has been applied. The data processing has firstly regarded the missing data problem. Missing values reduce the representativeness of the sample and they can severely disturb the conclusions drawn from the data. For Ponza buoys, about 10% missing data, covering about 20 years of observation, have been detected. In order to get a conservative estimation in case of a lack in the time series, missing data or values of wave height of less than 0.2 m for several hours have been considered as errors and removed. However, to test the sensitivity of the results, *Hm0* = 1 m and 2 m have also been used. This analysis has shown that the estimated wave energy flux does not differ substantially (i.e., less than 12%) if wave heights of 1 m or 2 m are used to fill the missing data. Therefore, by considering missing data, unrealistic calm conditions and spikes, of the approximately 126 thousand available data of the whole dataset, only 96,879 values were considered useful.

In addition to these buoy records, the dataset was compared/complemented with the ECMWF dataset [4], in which historical observational data spanning an extended period are implemented through a single consistent analysis in forecast models. The ECMWF dataset is composed of a coupled ocean atmosphere and a general circulation model, i.e., an atmospheric reanalysis coupled with a wave model integration where no wave parameters are assimilated, making the wave part a hindcast run.

The dataset used is termed ERA-Interim, continuously updated in real time. Significant wave height (*Hm0*), mean period (*Tm*) and mean direction (θ), ranging from January 1979 to December 2018, were extracted from the ERA-Interim archive, available for download online [46].

The ECMWF internal WAve Model (WAM) covers the Mediterranean Sea by a base model grid with a resolution of 0.75◦ × 0.75◦. ERA-Interim and WAM products are publicly available on the ECMWF Data Server. The WAM provides wave characteristics assimilated every 6 h. Here, 12 grid points (E1–E12) were considered. The geographical coordinates and distance from the seabed of all offshore points that are of interest to the present study are shown in Table 1. The position of point O, as representative of the "offshore" of Gulf of Naples, and of point W (offshore Pozzuoli's Gulf), are also reported. Geographical information is graphically represented in Figure 1.


**Table 1.** Geographical information of ECMWF grid points E1–E12, Ponza wave buoy and reference point O (offshore of the Gulf of Naples) and point W (offshore Pozzuoli's Gulf).

**Figure 1.** Map of mid-Tyrrhenian Sea, showing the location of the Ponza wave buoy, European Centre for Medium-Range Weather Forecasts (ECMWF) grid points E1–E12 and reference point O (offshore of the Gulf of Naples) and point W (offshore Pozzuoli's Gulf).
