3.1. Introduction & Outline of the research

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GULF OF NAPLES

Chapters 1 and 2 introduced the importance of disposing of reliable wave measures, able to fully describe a given sea state. In this framework, HF-radars has been stated to represent an interesting alternative for the sampling of both currents and waves data. As regard the latter, the employment of HF-radars is a relatively novel application, and the relative scientific liter- ature has not exhaustively addressed this topic yet. Such consideration motivated the research resumed in the present Chapter, which presents a case study on HF-radar wave measures in the Gulf of Naples (Italy). This study was carried on with Dr. Simona Saviano and Prof. Enrico Zambianchi from the Department of Science and Technology, Parthenope University of Naples (Italy); Dr. Marco Uttieri, from the Department of Integrative Marine Ecology, Stazione Zoo- logica Anton Dohrn, Naples (Italy); and Prof. Giovanni Besio, from the Department of Civil, Chemical and Environmental Engineering, University of Genoa (Italy).

3.1. Introduction & Outline of the research

Land-based remote sensing by HF-radars presently provides a challenging opportunity for simultaneously measuring surface currents and wave parameters (Paduan and Rosenfeld, 1996;

Rubio et al., 2017; Capodici et al., 2019). The main advantage of these instruments is that they can collect continuous real-time wave and current measurements over wide areas, thus their use is becoming common for several projects and applications.

HF-radars sample the backscatter echo coming from the rough surface of the sea produced by the resonant first-order Bragg waves. First-order echoes provide measurements of surface currents (Paduan and Graber, 1997; Gelpi and Norris, 2003), while second-order echos are weaker and noisier than the first-order ones (Gurgel et al., 2006), but provide information on wave parameters using methods of integral inversion (for an exhaustive review on the physics underlying the waves acquisition by HF-radars, interested readers are referred to Crombie, 1955; Barrick, 1977, 1979; Lipa and Nyden, 2005). However, the accuracy of HF-radar wave measurements has started to be tested only recently (Lopez et al., 2016), thus the analysis of the spectrum for wave applications still needs to be deepened (Gurgel and Schlick, 2005). As a matter of fact, the parametrization of coastal effects such as (but not limited to) wave refraction, damping, shoaling and breaking does not come with ease, leading to locally varying wave field which makes difficult an absolute comparison between HF-radars and other wave-sampling devices and models, as pointed out by Wyatt et al. (2003).

In this framework, a case study on HF-radar derived measurements of the wave field was

presented by Saviano et al. (2019) in the Gulf of Naples (henceforth GoN; location shown in

Figure 3.1).

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22 Figure 3.1: Location of the GoN in the western coastline of Italy (source: Google Earth)

A close-up of the area under investigation and the instruments employed in Saviano et al.

(2019) are presented in Figure 3.2. The comparison between wave measurements retrieved by the HF antennas and a buoy deployed outside the radar coverage area indicated good agreement between the two platforms, in particular with HF-radar installed in proximity of lower edge of the domain (therefore closer to the buoy, cfr. Figure 3.2). By contrast, the comparison between the buoy and the two HF antennas sited in the innermost sectors of the GoN returned lower numerical consistency, although similar patterns were pointed out. As a matter of fact, this result could has been expected, not only owing to the non-negligible physical distance between the buoy and the two innermost sites, but also due to the wider fetch (possibly leading to more intense sea states) and to bathymetric issues.

On the basis of the divergences pointed out, the work of Saviano et al. (2019) was extended, in order to compare HF-radar wave measurements in the GoN with the outputs of two wave models carried out exactly in the radars locations. First, the models were validated through the comparison with buoy data defined at the outer edge of the GoN and used as a benchmark.

Subsequently, the models were employed to propagate the wave parameters within the gulf, and assess the reliability of the HF-radar measures.

The data and the methodology employed are summarized in Section 3.2., which shortly

introduces as well the numerical models used for the study. Results are subsequently presented

in Section 3.3., while Discussions and Conclusions are drawn in Section 3.4.

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Figure 3.2: a) Map of the Gulf of Naples (Southeastern Tyrrhenian Sea,Western Mediterranean Sea) with the locations of the three HF-radar sites and the PC wave buoy. The red semi-circles represent the Range Cell (RC5) of acquisitions (see text). b) Regional model: WWIII computational domain (green); blue diamonds indicate the grid points used for comparison. c) Local model: SWAN computational domain (blue), green diamonds indicate the grid points used for comparison. The bathymetric and orographic contours are spaced every 100 m. Coastline data: NOAA National Geophysical Data Center, Coast- line extracted: WLC (World Coast Line), Date Retrieved: 01 April, 2015, http://www.ngdc.noaa.gov;

bathymetric and orographic data from Amante and Eakins (2009) [Access date: 08 September 2011]

3.2. Data & Methods

3.2.1. The SeaSonde HF-radars network

Waves measures inside the GoN were collected by a 25 MHz SeaSonde HF-radars system

(manufactured by CODAR Ocean Sensors Ltd), operated by the Department of Science and

Technology at the “Parthenope” University of Naples. The network, used for the simultaneous

measurement of surface current (Menna et al., 2008; Uttieri et al., 2011; Cianelli et al., 2012,

2015; Kalampokis et al., 2016; Ranalli et al., 2018) and wave fields (Falco et al., 2016; Saviano

et al., 2019) was set up in 2004 with two monostatic antennas, in Portici (referred to as PORT)

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24 and Massa Lubrense (Sorrento, SORR); in 2008 it was integrated with a third site in Castellam- mare di Stabia (CAST). The instruments are shown in Figure 3.3. The GoN network is the first and longest-running installation in Europe (Rubio et al., 2017), and is presently operational, although since 2013 the SORR site has been discontinued. The SeaSonde system recorded and averaged single spectrum characteristics every 10 minutes along 1 km equally spaced circular annuli (range cells, RCs) centered on the antenna using a CODAR proprietary software (for specific cylindrical handling of HF radar data see Sciascia et al., 2018). To estimate the di- rectional ocean wave spectrum, SeaSonde assumes that it is homogeneous over the radar RC (Lipa et al., 2018). For the present analysis, the results of the range cell located between 5 and 6 km from the coast (RC5) were taken as reference, as such distance was proved to be the best operational alternative (Saviano et al., 2019). For the selected RC, information on spatially averaged wave parameters (significant wave height, centroid period and direction, referred to as H

_s^HF

, T

_c^HF

and θ

^HF

respectively) were extracted from the second-order spectrum by applying a Pierson-Moskowitz model (Lipa and Nyden, 2005). Furthermore, the data were filtered to remove spikes and spurious data. In particular, only data relative to waves higher than half a meter were considered: actually, for sea states lower than this threshold, the radio signal emitted may not be reflected and recorded, thus resulting in poor data capture. This is due to the limits intrinsic to the radar system, e.g. when the second-order echo is too small compared to spectral noise, this leads to erroneous readings or data gaps (Wyatt and Green, 2009; Wyatt, 2011; Atan et al., 2016; Lopez et al., 2016).

Figure 3.3: HF-radars operating in the GoN. From left to right: CAST, PORT and SORR antennas (courtesy of Dr. Simona Saviano)

3.2.2. Wave buoy

A SEAWATCH Wavescan Buoy manufactured by Fugro OCEANOR (like that of Figure 3.4) operated from August 2009 to mid-December 2010, and from mid-March to November 2012.

The buoy was installed at the southwestern limit of the basin of interest (PC buoy in Figure

3.2). It was equipped with a directional wave sensor and collected information about significant

wave height (H

_s^{BU OY}

), mean period (T

_m^{BU OY}

), peak period (T

_p^{BU OY}

) and directions (θ

^{BU OY}

),

providing data every thirty minutes; more details can be found in Saviano et al. (2019). Data on

H

_s^{BU OY}

, T

_m^{BU OY}

and θ

^{BU OY}

were used for the calibration of the regional and local numerical

models.

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Figure 3.4: SEAWATCH Wavescan Buoy (www.fugro.com)

3.2.3. The wave models

The regional hindcast was developed by the Department of Civil, Chemical and Environ- mental Engineering of the University of Genoa (DICCA, dicca.unige.it/meteocean/hindcast), with the Wavewatch III numerical model (henceforth WWIII, see Tolman, 1989; Tolman et al., 2009). WWIII is a third generation wave model, developed at NOAA/NCEP, that solves the random phase spectral action density balance equation for wavenumber-direction spectra; the wave growth and propagation is described by:

DN Dt = S

σ (3.1)

where N (k, θ) ≡ F (k, θ)/σ is the wave action density spectrum, σ = 2πf is the relative fre- quency of the wave and k = 2π/L is the wavenumber; S represents the net effect of sources and sinks for the spectrum F (k, θ), with the latter parameter being related to the density spectrum S(f, θ), introduced in Section 2.1.2. (more details can be found in Tolman et al., 2009).

The hindcast was defined all over the Mediterranean Sea from 01/Jan/1979 to 31/Dic/2018, with an approximate 0.1

^◦

resolution both in longitude and latitude. The wave model was forced by a 10 m wind field obtained from the non-hydrostatic mesoscale model Weather Research and Forecast (WRF-ARW) version 3.3.1 (Skamarock et al., 2008), based on NCEP Climate Forecast System Reanalysis (CFSR), for the period from January 1979 to December 2010 and CFSv2 (Climate Forecast System version 2) for the period from January 2011 to December 2018. The output was hourly recorded at the nodes of the computational grid, providing the spectrum inte- grated quantities (H

_s^REG

, T

_m^REG

, θ

^REG_m

), the peak wave features (T

_p^REG

, θ

^REG_p

), along with the u

^REG_w

and v

^REG_w

wind velocity components (Mentaschi et al., 2013a, 2015; Cassola et al., 2016).

Despite the information provided by the hindcast is discretized (i.e. one dataset for every node of the computational grid), wave features can be continuously defined within the boundaries of the model through a time-spatial interpolation of the grid nodes outcomes. Nevertheless, the spatial resolution of the model may not allow to get the waves data at fine scales in the near-shore areas, as it actually happens for the CAST antenna (see Figure 3.2 b)).

In order to evaluate the wave features at the HF-radar RCs, the SWAN model (Simulating

WAves Nearshore, Booij et al., 2003) was nested within the frame of WWIII. SWAN resolves

the same Equation of WWIII (cfr. Equation 3.1), but it contains some additional formulations

primarily for shallow waters. A finer regular grid was developed, with a 0.0025

^◦

lon/lat reso-

lution (almost 200 m at these latitudes), using a bathymetry of the area provided by the Hydro-

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26 graphic Institute of the Italian Navy. Then, hindcast data were used to set the wave conditions at the grid boundaries and to define the wind forcing over the whole domain. At this stage, it is worth mentioning that, in SWAN, sea states are modeled through a JONSWAP spectrum (Hasselmann et al., 1973), whose shape (thus the deriving wave features) depends on the γ and the θ

_s

coefficients, standing for the peak enhancement parameter and the directional spreading, respectively (see Equation (2.3) and (2.5) in Section 2.1.2.). Therefore, in order to select the best SWAN setting, four different model sets were developed, by varying γ and θ

s

at a time over the ranges most frequently encountered in the scientific literature. The modelled wave features due to each of the tested sets were than evaluated against the buoy measurements, in order to retain the most efficient γ/θ

s

combination (i.e. the one leading to the modelled wave features closer to the buoy data). A summary of the simulations is reported in Table 3.1.

set 1 set 2 set 3 set 4

γ[−] 2.2 2.2 3.3 3.3

θ

_s

[

^◦

] 10 20 10 20

Table 3.1: SWAN settings tested for the model validation

3.2.4. Validation of the wave parameters

The comparison of wave measures coming from different sources took advantage of both graphical analysis and statistical indexes used for computing the correlation between the data, defined as follows:

• ρ = 1 N

P

N

i

S

_i

− ¯ S

O

_i

− ¯ O σ

_O^st

σ

_S^st

• N RM SE =

s P

N

i

(S

_i

− O

_i

)

²

P O

²_i

• slope = S/O

• N BIAS = S − ¯ ¯ O O ¯

• SI =

s P

N i

S

_i

− ¯ S − O

_i

− ¯ O

2

P

N i

O

²_i

• HH = s

P

N

i

(S

_i

− O

_i

)

²

P S

_i

O

_i

(7)

where S

i

and O

i

stands for “simulated” and “observed” data, respectively; σ

^st

stands for the data standard deviation, whereas the overstanding bar indicates the average. ρ represents the correlation index, spanning in the ±1 range, where +1 (-1) indicates perfect correlation (anti-correlation) among the two investigated series, while 0 means that there is no correlation.

N RM SE (Normalized Root Mean Square Error) is a measure of the distances between two datasets, and is one of the most employed indexes for evaluating the goodness of fit between the observed values of a variable and the correspondent values predicted by a model; then, substracting the average component of the error from the N RM SE, the scatter index (SI) is obtained. N RM SE and SI combine information on both the average and the scatter errors between two series, and should provide values as small as possible (ideally, if a perfect match exists, both the indexes should attain values equal to zero). N BIAS is a measure of the average component of the error, which should result in close-to-0 values for series in good agreement.

slope measures the best linear interpolate for the resulting scatter of two series; under the hy- pothesis that two datasets are correlated, it attains positive values that may be lower or higher than 1, depending if the data to be validated are generally smaller or higher than the benchmark, respectively. Then, the index proposed by Hanna and Heinold (1985), referred to as HH, was employed. HH allows to overcome drawbacks that may arise for simulations negatively biased, i.e. that underestimate the measured quantities (see Mentaschi et al., 2013b, that proved how in such a case N RM SE and SI are not completely reliable). Finally, when dealing with circular quantities such as the wave directions, the aforementioned indexes cannot be directly computed.

In this case, it should be performed an analysis on the differences between the simulated and the observed data, previously normalized in the [−π; π] space (meaning that, in the worst case, two waves may happen to be antiparallel). The directional indexes were therefore adjusted as follows:

• N RM SE

_θ

=

r P

N

i

[mod

−π,π

(θ

_S_i

− θ

_O_i

)]

²

/N 2π

• N BIAS

_θ

= P

N

i

mod

−π,π

(θ

_S_i

− θ

_O_i

) 2πN

where the modulus operator mod

−π,π

implies to subtract a 2π angle if ∆θ

_i

> π, on the other hand, if ∆θ

i

< π a 2π angle is added to the difference.

3.3. Results

3.3.1. Validation of numerical models against buoy measurements

As a first step before comparing HF-radar measurements with numerical model reanaly-

sis, a validation of WWIII and SWAN performances was carried out against buoy data (see

Section 3.2.2.). Hence, the hourly hindcast outcomes at the buoy location within the period

25/Aug/2009 - 23/Dec/2010 were computed and further compared against the data sampled by

the buoy.

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28 Comparisons between WWIII and buoy data are shown in Figure 3.5, highlighting a re- markable agreement between the sampled and the modelled data, especially with respect to the significant wave heights and the mean periods (T

m

). Correlation indexes (ρ, slope) show values close to 1, whereas the error indexes are characterized by close-to-zero values. Scatter plots prove how the main divergences affect the minority of the data, characterized by darker color for the respective values. On the contrary, a higher uncertainty characterizes the mean directions.

As for the local scale analysis (i.e. waves downscaled in the GoN with the high resolution model SWAN), results of the comparison for each trial set of SWAN are summarized in Table 3.2. Here it can be appreciated how, on average, the consistency between the whole series are even improved with respect to the regional scale. Moreover, the values of the error metrics suggest that the resulting wave features are poorly sensitive to the selection of the peakedness factor γ and the directional spreading θ

s

. This is further confirmed by inspecting the Taylor diagram: as Figure 3.6 shows, scatters relative to the different simulation almost overlap to each other. If an overview of the total statistics does not reveal a significant dependence on the peak enhancement parameter and the spectrum directional spreading, zooming to a particular wave height series shows how different choices for these parameters may actually affect the model outcomes. As a general trend, θ

_s

equal to 20

^◦

results in wave heights slightly higher than those related to θ

s

equal 10

^◦

: the modelled wave heights can be therefore either closer or farther with respect to the buoy ones, depending on the sea state under investigation (literally, if the sea states are overestimated or underestimated with respect to the sampled ones, see Figure 3.7). However, these differences are flattened in the overall simulations, which embed almost two years of hourly sampled sea states. In view of the above, for this study the following SWAN simulations were performed setting γ and θ

_s

equal to 2.2 and 20 respectively, according to values typically suggested for the Mediterranean Sea (see for example Terrile et al., 2012;

Perez et al., 2017).

0 2 4 6

H_s^BUOY [s]

0 2 4 6

HsREG [s]

= 0.89 NRMSE = 0.31 slope = 0.90 NBIAS = -0.03 SI = 0.31 HH = 0.32

0 2 4 6 8 10 12

T_m^BUOY [s]

0 2 4 6 8 10 12

TmREG [s]

Jul 2009 Jan 2010 Jul 2010 Jan 2011 Jul 2011 Jan 2012 Jul 2012 Jan 2013 -150

-100 -50 0 50 100 150

mBUOY-REG [°N]

NRMSE = 18.3^° NBIAS = -0.941^°

0 0.5 1 1.5 2 2.5 3 3.5 4

Hs [m]

Figure 3.5: Validation of WWIII model results vs PC buoy recording. Left: H

s

; Center: T

m

; Right: θ

m

.

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set 1 set 2 set 3 set 4 2.2-10 2.2-20 3.3-10 3.3-20

H

_s

NRMSE 0.25 0.25 0.24 0.25

NBIAS -0.038 -0.043 -0.032 -0.036

slope 0.92 0.91 0.92 0.91

SI 0.24 0.25 0.24 0.25

HH 0.26 0.27 0.26 0.26

ρ 0.93 0.93 0.93 0.93

Table 3.2: Comparison of the statistical indexes employed to validate SWAN

1 0.75 0.5 0.25

centered root mean square error 0.25

0.5 0.75 1

standard deviation

0.9

correlation coefficient 2.2 3.3 10 20

centered root mean square error 0.5

standard deviation

0.9 ^2.2

3.3 10 20

Figure 3.6: Taylor diagram of H

s

between PC buoy and SWAN for different γ and θ

s

tested in the model implementation (see Table 3.1)

Jan 25 Jan 26 Jan 27 Jan 28 Jan 29

2010 0

0.5 1 1.5 2 2.5

H s [m]

= 2.2

buoy SWAN

s 10

SWAN

s 20

Figure 3.7: Comparison of H

s

between PC buoy and SWAN simulations for a particular sea state. The

figure show the outcomes for set1 and set2

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30 3.3.2. Comparison between HF-radar measures and numerical simulations

Once the wave model were validated, first a comparison between hindcast data and HF-radar data for the period 01/Jan/2010 -30/Dec/2012 was carried out at PORT and SORR Results are presented in Figure 3.8. In this case, no analysis was available for CAST, as here the radar measures lie outside the hindcast domain, as shown in Figure 3.2 b).

a)

0 1 2 3 4 5

Hs REG [m]

0 1 2 3 4 5

HsHF [m]

0 2 4 6 8 10 12 14

T_m^REG [s]

0 2 4 6 8 10 12 14

TmHF [s]

= 0.64 NRMSE = 0.29 slope = 1.22 NBIAS = 0.24 SI = 0.17 HH = 0.26

Jan 2010 Jul 2010 Jan 2011 Jul 2011 Jan 2012 Jul 2012 Jan 2013 -150

-100 -50 0 50 100 150

mHF-REG [°N]

NRMSE = 17.2^° NBIAS = -3.7^°

0.5 1 1.5 2 2.5 3 3.5

Hs [m]

b)

0 1 2 3 4 5 6

H_s^REG [m]

0 1 2 3 4 5 6

HsHF [m]

0 2 4 6 8 10 12 14 16

Tm REG [s]

0 2 4 6 8 10 12 14 16

TmHF [s]

-100 -50 0 50 100 150

mHF-REG [°N]

NRMSE = 25.8^° NBIAS = 5.15^°

0.5 1 1.5 2 2.5 3 3.5

Hs [m]

Figure 3.8: Comparison of wave parameters (H

s

, T − m, θ

m

) between HF-radar and WWIII. Panel a):

PORT; panel b) SORR

In PORT, H

s

and T

m

are characterized by significant correlations values (0.73-0.64 for ρ and

0.87-1.22 for slope, respectively), while the error indexes attain limited values, e.g. N BIAS

is equal to -0.05 and 0.24 for H

_s

and T

_m

, respectively. As for SORR, the comparisons result

in poorer agreements, especially for the significant wave height, though still showing reason-

able correlations between the two datasets. In this case, the more dispersed scatters in SORR

particularly depend on the presence of outliers in HF-radar records. This can be particularly

appreciated in panel b) of Figure 3.8, showing a relevant number of scatters departing from the

main point cloud. The same consideration holds as far as θ

m

is concerned, with poorer agree-

ments between HF-radar and model data at SORR with respect to PORT (both N RM SE and

N BIAS show higher values in the former case). However, as for the mean wave directions, it

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should be mentioned how it is not trivial to accurately model them, especially when mild sea states are considered. Indeed, as the colorbar of Fig. 3.5 shows, on average the mayor diver- gences take place for low values of H

s

. Finally, it is worth to recall that the radar data were filtered to get rid of possible spikes (see Section 3.1.), thus the scatters of H

s

and T

m

are low limited.

Subsequently, radar data were validated against the results linked to the SWAN model. In

this case, the extension of the computational domain allowed a comparison also for the CAST

antenna. Figure 3.9 shows the H

_s

time series comparison between the HF stations and the

simulations performed with SWAN. At PORT, downscaling the wave field over a high reso-

lution grid leads to H

s

values generally higher than those computed with the regional model,

and this is in turn reflecting on a under-estimation of HF acquisitions. On the contrary, at

CAST and SORR for some sea storm event an overestimation of radar measures with respect

to SWAN is observed. The above mentioned considerations are further confirmed by the results

shown in Figure 3.10. Here, it can be appreciated how in PORT (panel b)), the correlation ρ

remains substantially unchanged with respect to the regional analysis, attaining values around

0.70 for both comparisons. This implies that sea states characterized by the same relative in-

tensities among the respective series occur simultaneously. Nevertheless, results happen to be

more around the main bisector, in particular for the most intense sea states, showing values of

H

_s

generally higher in the local model. This is in turn reflecting in the decreasing/increasing

values of slope/N BIAS (from 0.87 to 0.70 and from -0.05 to -0.22 for the regional and the

local model, respectively). The general increment of the sea state magnitudes leads to better

comparisons for the local model mean periods, with lower values of N BIAS (which moves

from 0.24 to 0.17) and slope (from 1.22 to 1.13). The wave incoming directions show also a

slightly increasing deviation with respect to those of the regional analysis, with the N BIAS

index decreasing from -3.70 to -5.26. As for SORR (Figure 3.10 c)), a direct comparison with

the regional counterparts underlines how the local numerical model leads to a higher consis-

tency with the HF-radar wave measurements for all the parameters under investigation, with the

error metrics (N RM SE, N BIAS, SI and HH) switching to lower values, while ρ increases

from 0.65 to 0.71 and slope attains a value closer to 1 (1.41 versus 1.52 of the regional analy-

sis). These considerations equally apply to θ

_m

. The period T

_m

seems to be consistently caught

by radars, with error (correlations) indexes close to 0 (1). Finally, in CAST (Figure 3.10 a)),

results show good consistencies for all the investigated parameters, even though a systematic

over-estimation in the radar data can be appreciated.

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32 a)

Jan 20100 Jul 2010 Jan 2011 Jul 2011 Jan 2012 Jul 2012 Jan 2013 2

4 6 8

Hs [m]

CAST SWAN

b)

4 6 8

H s [m]

PORT SWAN

c)

2 4 6 8

Hs [m]

SORR SWAN

Figure 3.9: Comparison of H

s

time series between HF-radar measures and SWAN. Panel a): CAST;

panel b) PORT; panel c) SORR.

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a)

0 1 2 3 4 5 6

H_s^LOC [m]

0 1 2 3 4 5 6

HsHF [m]

0 2 4 6 8 10 12 14

T_m^LOC [s]

0 2 4 6 8 10 12 14

TmHF [s]

-100 -50 0 50 100 150

mHF-LOC [°N]

NRMSE = 10.7^° NBIAS = 3.52^°

0.5 1 1.5 2 2.5 3 3.5

Hs [m]

b)

0 1 2 3 4 5

H_s^LOC [m]

0 1 2 3 4 5

HsHF [m]

0 2 4 6 8 10 12 14

Tm LOC [s]

0 2 4 6 8 10 12 14

TmHF [s]

-100 -50 0 50 100 150

mHF-LOC [°N]

NRMSE = 17.9^° NBIAS = -5.26^°

0.5 1 1.5 2 2.5 3 3.5

Hs [m]

c)

0 1 2 3 4 5 6

H_s^LOC [m]

0 1 2 3 4 5 6

HsHF [m]

0 2 4 6 8 10 12 14 16

T_m^LOC [s]

0 2 4 6 8 10 12 14 16

TmHF [s]

-100 -50 0 50 100 150

mHF-LOC [°N]

NRMSE = 23.3^° NBIAS = 5.05^°

0.5 1 1.5 2 2.5 3 3.5

Hs [m]

Figure 3.10: Comparison of wave parameters (H

_s

, T

_m

, θ

_m

) between HF radar and SWAN. Panel a):

CAST; panel b) PORT; panel c) SORR

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34 3.4. Discussion & Conclusions

The comparison between the modelled wave data and the buoy measures outside the GoN, proved that the numerical models employed for the subsequent analysis are able to provide reliable outcomes for H

s

and T

m

, while θ

m

require further deepening. In case of the SWAN simulations, different sets were tested, varying the parameters most likely affecting the local- scale analysis: the peakedness γ and the directional spreading θ

s

, which rule the shape of the modelled wave spectra along frequency and direction, respectively. The simulations linked to the trial sets showed that the results are not significantly affected by the parameters selection (see Table 3.1 and Fig. 3.6), resulting in sound comparisons in all cases. The reason is to be found in the investigated features: the mean parameters are in fact computed by integrating the 2D-spectrum in frequency and direction, and the shape of the spectrum is not affecting its underlying area as much as it may actually do for single points referred to specific characteristics (i.e. the peak parameters), especially if the outcomes are not computed in very shallow waters.

In view of the above, taken as granted the reliability of the numerical models, the respective outcomes were employed to validate the HF-radar measures within the Gulf of Naples.

The comparison between WWIII and HF-radar measurements returns a reasonable agree- ment at PORT, while in SORR the wave features of the two platforms show more significant deviations. When zooming into the local model SWAN, the correlations between the modelled and the measured data improve in SORR, while they are lowered in PORT. These discrepancies implies the need of a clarification. As a matter of fact, the wave features related to WWIII and SWAN were carried out through different approaches: in case of the regional model, a time- spatial regression from the data of the closest nodes in the computational grid; in case of the local model, a numerical propagation of waves over a fine-resoluted grid. Therefore, similarities in the models outcomes are to be expected because of the depths the referring RCs are defined over, high enough for the target waves not to be dramatically affected by the bathymetry of the area, the bottom depth being almost 100 m in both PORT and SORR. However, divergences can arise because of the local effects due to the orography of the area. In fact, it should be pointed out that no significant physical effects are to be expected when propagating sea waves in front of the Capri coastline, whose fetch is free of obstacles for a huge distance. On the other hand, the wave field in the shadow zone behind the island of Capri may be more difficult to resolve, because of the complex morphology of the coastline. Therefore, even though the models were validated against the PC buoy data and represent a reliable benchmark, some of the deviations for modeled low sea states in correspondence of high states sampled by the radars could be due to model uncertainties. The problems related to complex morphological features of the GoN were also pointed out by Inghilesi et al. (2016), using both WAM and SWAN models.

Furthermore, it is worth recalling that the performance of HF-radars are limited by numer-

ous sources of error (e.g. environmental noise, interpretation methods, basin structure, see Laws

et al., 2010). In particular, previous studies on the comparison of mean wave direction and peak

period showed that the detected discrepancies can be linked to lower sea states, where direc-

tional spectra can be contaminated by noise due to spurious features such as those associated

with antenna side lobes, or to the sensitivity of these parameters to non-sea signals (i.e. in-

terference or ships) in the radar backscatter (Wyatt et al., 2003; Lorente et al., 2018). Further

investigations will be needed to assess if the H

s

overestimation of the HF-radar measurements

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may be explained by the inversion method used, which is based on an ideal Pierson-Moskovitz (PM) spectrum. However, the PM model is sufficiently sound to describe unimodal energy spectra from fully developed seas, though future implementations of the proprietary software will be capable of handling bimodal distributions as well (Lipa et al., 2018). A promising im- provement is provided by the development of inversion methods using a neural network, which can lead to improved statistics based on network training (Hardman and Wyatt, 2019).

In conclusion, the results here introduced suggest that the HF-radar may provide a first in- sight on local wave parameters, though it is necessary to implement new algorithms to broaden the range of wave parameters observed by these instruments, leading to the possibility of in- tegrating HF-radar data into wave models (Caires and Wyatt, 2003; Siddons et al., 2009; Wa- ters et al., 2013). This can be a useful tool for optimizing the initial conditions of a model and therefore improving the accuracy of the model estimates. The implementation of simple data assimilation algorithms incorporating HF-radar wave data within the wave model (WWIII, SWAN and WAM) to assess their performance are proposed in literature (Caires and Wyatt, 2003; Siddons et al., 2009; Waters et al., 2013), and represent a promising scientific advance- ment for the next future. When direct wave measures are available (i.e. buoy or satellite data), they should be preferred to validate the co-located HF-radar ones; otherwise, numerical models properly validated were shown to provide reliable wave data, and can be consequently used as a reference for further investigations. Of course, similar studies need to be performed in many different locations, to extend the validity of the results presented.

Beyond the application introduced in this study, the hindcast data presented in Section 3.2.

were widely validated against buoys and satellite data over the whole Mediterranean Sea (Men-

taschi et al., 2015, 2013a), therefore the works introduced in the following Chapters will take

advantage of them.

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EXTREME WAVES ANALYSIS BASED ON ATMOSPHERIC PATTERNS CLASSIFICATION

Section 2.3. introduced the Extreme Values Theory, a tool widely used for the analysis of extreme data in most of the geophysical applications. EVT is a statistical discipline, therefore it has to account both for the uncertainty characterizing the models framed in it, and for the nat- ural uncertainty of the data it is applied to. In the latter case, as far as sea waves are concerned, Chapter 3 showed how to couple radar measures and models outcomes may help in developing continuous data when they lack reliable alternatives, reducing in turn the statistical uncertainty which naturally characterizes the EVA. For a given location, the availability of high-populated dataset (as those of the hindcast DICCA) also allows to study in detail the local severe sea states, e.g. by investigating particular subsets of the extreme waves. In this regard, this Chapter presents a methodology for classifying samples of significant wave height peaks in homoge- neous subsets, and for the computation of the overall extreme values distribution starting from the distributions fitted to each single subset. This research was carried on with Prof. Sebasti´an Solari, from Instituto de Mecnica de los Fluidos e Ingenieria Ambiental - Universidad de la Rep´ublica Oriental de Uruguay, Montevideo (Uruguay) and Prof. Giovanni Besio, from the Department of Civil, Chemical and Environmental Engineering, University of Genoa (Italy).

4.1. Introduction & Outline of the research

EVT allows to estimate extreme (un-observed) values, starting from available records or modelled data which are assumed to be independent and identically distributed. It is therefore crucial to identify homogeneous datasets complying with the above mentioned requirement be- fore performing the EVA of a given physical quantity. When dealing with directional variables, it is common to group the data according to different directional sectors (Cook and Miller, 1999;

Forristall, 2004), being such approach recommended as well in many regulations (API, 2002;

ISO, 2005; DNV, 2010, among others). However, the use of directional sectors involves certain

drawbacks. First, it cannot be employed for variables being not characterized by incoming di-

rections (such as storm surge or rainfall). Second, data showing the same direction may be due

to different forcing; in the frame of wave climate, an example is that of waves propagating in

shallow waters, affected by refraction and/or diffraction. Finally, the borders of the directional

sectors are often subjectively defined, without verifying if the data belonging to each subset are

homogeneous and independent with respect to those of the other sectors (see Folgueras et al.,

2019, where they tackled this issue and proposed a methodology to overcome it). An alterna-

tive approach to classify the extremes implies resorting to the atmospheric circulation conditions

they are driven by, associating each extreme event to a particular weather pattern (referred to

as WP). Such approach has been already deep-seated in atmospheric sciences for the analy-

sis of precipitations, snowfalls, temperature, air quality and winds (Yarnal et al., 2001; Huth

et al., 2008, among others). Nevertheless, there are few studies linking weather circulation pat-

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terns with the most likely induced sea states (e.g., wave climate and storm surge). Holt (1999) classified WPs leading to extreme storm surges in the Irish Sea and the North Sea. Guanche et al. (2013) simulated multivariate hourly sea state time series in a location in the northwester Spanish coast, starting from the simulation of weather pattern time series. Dangendorf et al.

(2013) linked the atmospheric pressure fields with the sea level in the German Bight (south- eastern North Sea). Pringle et al. (2014, 2015) investigated how extreme wave events may be tied to synoptic-scale circulation patterns in the east coast of South Africa. Camus et al. (2014) proposed a statistical downscaling of sea states based on weather types, then applied to a couple of locations in the Atlantic coast of Europe to hindcast the wave climate during the twentieth century plus modelling it under different climate change scenarios. The latter methodology was improved by Camus et al. (2016), and further used by Rueda et al. (2016) for analysing signifi- cant wave height maxima. Solari and Alonso (2017) used WP classification to perform EVA of significant wave heights in the south-east coast of South America.

Except for Rueda et al. (2016) and Solari and Alonso (2017), none of the previous works focused on exploiting WP classification methodologies for defining homogeneous datasets to be further employed for EVA. However, the two methodologies differ in several aspects. Rueda et al. (2016) dealt with daily maxima significant wave heights along with surface pressure fields and pressure gradients, averaging over different time periods and applying a regression-guided classification to define 100 WPs. They subsequently fit a GEV distribution, estimating an Ex- tremal Index from the daily maxima significant wave height of each WP, from which they re- built the overall distribution of annual maxima (referred to as AM H

_s

). Despite the proposed methodology is able to reproduce the AM H

s

distribution, with such a large number of WPs it may be difficult to detect the most relevant physical processes behind the occurrence of extreme wave conditions. Furthermore, even though a large number of WPs was considered, only a few happened to significantly affect the EVA, as most of the WPs resulted to be associated to mild wave conditions. Finally, to retain daily maxima does not ensure the data to be independent, thus implying the need to use the Extremal Index. Solari and Alonso (2017) introduced instead a “bottom-up” scheme: they first selected a series of independent extreme sea states; then, they identified a reduced number of WPs that allows to group the selected data into homogeneous populations. A small number of WPs makes it easier to link the different subsets of extremes with known climate forcing. Above all, to work with independent peaks allows to rely on the classic and well known extreme value theory, with no need to refer to additional indexes and/or more complex models that may be unfamiliar for many analysts.

The work presented in this Chapter review the methodology of Solari and Alonso (2017),

showing an application to several wave datasets along the Italian coastline. The objective of

this research is twofold: (i) to explore how the definition of homogeneous subsets, based on

WP, affects the estimation of H

s

extreme values according to the EVA; (ii) to characterize the

identified WPs in the framework of the Mediterranean Region (MR) cyclones climatology. The

data employed and the methodology developed are introduced in the next Section. Results are

then shown and discussed in Section 4.3., and conclusions are drawn in Section 4.4..

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38 4.2. Data & Methods

This work takes advantage of eight hindcast points located in the Italian seas, as shown in Figure 4.1. This choice allowed to test the reliability of the proposed methodology under different local wave climates. In fact, the selected points are differently located along the Ital- ian coastline, and, being exposed to different fetches, they are characterized by peculiar wave conditions. The same locations were taken into account by Sartini et al. (2015), where they performed an overall assessment of the different frequency of occurrence of the extreme waves affecting the Italian coasts. Table 4.1 reports the names, depths, and coordinates of the selected locations.

The points correspond to as many buoys belonging to the Italian Data Buoy Network (Rete Ondametrica Nazionale or ”RON”, Bencivenga et al., 2012), which collected directional wave parameters over different periods between 1989 and 2012. Unfortunately, most of the buoys are characterized by significant lacks of data due to malfunctions and maintenances of the devices;

such a widespread lack of data would imply a loss of reliability for the following analysis.

Therefore, it was decided to refer to the hindcast data of the Department of Civil, Chemical and Environmental Engineering of the University of Genoa (see Section 3.2. Mentaschi et al., 2013a, 2015), which, being densely defined over a large time period, helps to perform reliable long-term statistical computations (Coles and Pericchi, 2003).

The wind data used to drive the wave generation model were used here to feed the cluster analysis of the wave peaks, while the pressure data were used for the analysis of the climatology related to the identified WPs.

B7 44^oN

46^oN

9^oE 36^oN

B3 B8

B5 B6 B2

B1

B4

12ôE 15ôE 18ôE 38ôN

40^oN 42^oN

Figure 4.1: Study area and investigated locations with their respective codes

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CODE LON LAT DEPTH [m] NAME

B1 9.8278 43.9292 83.8 La Spezia

B2 8.1069 40.5486 99.7 Alghero

B3 12.9500 40.8667 242.0 Ponza

B4 12.5333 37.5181 90.8 Mazara del Vallo

B5 15.1467 37.4400 65.4 Catania

B6 17.2200 39.0236 611.7 Crotone

B7 17.3778 40.9750 80.0 Monopoli

B8 14.5367 42.4067 55.8 Ortona

Table 4.1: Lon/lat coordinates and depths of the hindcast locations employed in the study (reference system: WGS84)

4.2.1. Extreme events selection

For each location, wave height peaks were selected through a POT approach, and in partic- ular by using a time moving window. This approach is slightly different with respect to that explained in Section 2.3., thus it is following explained. First, the whole series of H

_s

is spanned through a time moving window of given width; second, when the maximum of the data within the window happens to fall in the middle of the window itself, it is retained as a peak; finally, in order to get rid of the peaks which are not related to severe sea states, a first H

_s

threshold is chosen and only peaks exceeding this threshold are retained for further analysis. Figure 4.2 shows a sketch of the POT methodology introduced.

Figure 4.2: Example of POT data selection through moving window approach. The red dashed line represents the threshold fixed, while the blue light box is the window spanning the dataset

In this study, for each location the width of the moving window was set equal to one day,

meaning that the inter-arrival time between two successive storms is at least equal to one day,

precisely. The threshold was fixed as the 95

^th

percentile of the resultants peaks. This ensured to

maintain a uniform approach for all the locations, efficiently capturing the different features of

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40 the local wave climates. In addition to the significant wave heights, the waves mean incoming directions corresponding to the peaks (θ

_m

) were retained and further used for analyzing the outcomes of the clustering algorithm. Finally, for each peak the mean sea level pressure field (MSLP) and surface wind fields for several time lags (0, 6, 12 24, 36, and 48 hours earlier with respect to the peak’s date) were carried out over the whole MR. Wind fields were used to classify the selected peaks due to their parent WP, as described in the following section; MSLP fields were used instead for the post-processing and climatological analysis of the results.

4.2.2. Extreme events classification: definition of weather patterns

The classification of extreme events is based on surface wind fields (¯ u

_w

) observed in the whole MR during the hours before and concomitant to the time of the peaks. In order to de- fine the spatial and temporal domains to be taken into account, the correlation maps between the wind velocities and the H

s

peaks for different time lags were analyzed. These correlations were evaluated over a sub-grid of the atmospheric hindcast, with nodes spaced of 0.5

^◦

both in longitude and latitude. To compute the correlation between H

_s

and ¯ u

_w

series is not straightfor- ward, as the former variable is scalar and the latter is directional. Hence, to tackle this issue, this study referred to the procedure suggested by Solari and Alonso (2017). Given a time lag ∆t, the wind is defined by its zonal and meridional components (u

_x

, u

_y

)

_(i,j,∆t)

; the correlation between H

_s

peak series and the time lagged surface wind speed at any given node, is then estimated as the maximum of the linear correlations obtained by projecting the wind speed series in all the possible directions:

ρ

_(i,j,∆t)

= max

0≤θ<2π

{ρ H

_s

; ¯ u

_{(i,j,∆t,θ)}

} (4.1) where ρ

_i,j,∆t

is the resulting correlation for node (i, j) at time lag ∆t, ρ refers to linear correlation function, u

(i,j,∆t,θ)

is the surface wind speed projected along direction θ according to Eq (4.2):

¯

u

_{(i,j,∆t,θ)}

= u

_x(i,j,∆t)

cos(θ) + u

_y(i,j,∆t)

sin(θ) (4.2) in this way not only a maximal correlation is obtained for every node, but also the direction corresponding to the maximum correlation, estimated as:

θ ˆ

_ρ(i,j,∆t)

= argmax

0≤θ<2π

{ρ H

s

; ¯ u

_{(i,j,∆t,θ)}

} (4.3)

The correlation maps computed with Eq. (4.1), allowed to evaluate the spatial domain and the time lags for which ¯ u

w

is significantly correlated to (i.e., directly affecting) the resulting wave peaks at a given location.

Once the spatial and time domain of the wind fields producing the peak wave conditions

were defined, the wind fields were used for clustering and classifying the extreme events. To

this end, the k-means algorithm was used, fed with the normalized wind fields. k-means is

aimed at partitioning a N-dimensional population into k sets (clusters) on the basis of a sample,

in order to minimize the intra-cluster variance (MacQueen et al., 1967).

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This technique is based on the Euclidean distances between the elements of different states.

Reference is made to a data matrix X

_n,V

, being n and V the number of modelled data and variables of the problem, respectively. Given V arrays of n data, X

n,V

is built up as follows:

X

_n,V

=







x

1,1

... x

1,V

. ..

x

_n,1

... x

_n,V





 (4.4)

First, the scalar variables have to be normalized column-wise to X

n,V

in a common space, to be able to work with scalars characterized by different magnitudes. After the scaling of the variables, given the m number of clusters, at the first iteration the centroids (say X

_m,V^∗,1

) are randomly selected among the rows of X

_n,V

. Then, each data (e.g. each i

^th

row of X

_i,V

, i ∈ [1, n]) is “assigned” to the closest centroid:

m

_i

= m/ min d

_i

= kx

_i

− x

^∗,1_m,V

k, i = 1, . . . , n − m

(4.5) Where m

i

stands for the cluster the i

^th

data belong to. Once the m groups have been defined, the new centroids (x

^∗,2_m,V

) are simply computed as the means of the respective clusters:

x

^∗,2_m,V

= X

xi∈m_j

x

_i

n

j

(4.6) Being n

i

the number of elements assigned to the j

^th

cluster. The algorithm ends when the locations of the centroids are not further changing between two successive iterations (see Camus et al., 2011, for more details and applications).

In this study, the normalization of the wind fields sought to reduce the influence of the intensity of the wind speed on the classification, so that only the spatial form of the field and its time evolution were taken into account. Note that the values of H

s

did not play any role in the classification of the peaks but the identification of the point in time of the wind fields.

4.2.3. Analysis of the WPs climatology

Once the wind fields, and therefore peak H

s

series, were grouped into k clusters, the MSLP corresponding to the events within each cluster were averaged and the position of the lowest pressure was recorded, for all the ∆t taken into account. This allowed to track the paths of the averaged low pressure systems corresponding to each cluster, defining in turn the respective WP.

At a second time, the dynamics of the systems were compared with those of the cyclones

typically detected in the Mediterranean Sea (Trigo et al., 1999; Lionello et al., 2016), while the

frequency of occurrence of the events of different clusters were compared with the outcomes of

Sartini et al. (2015). The number of clusters needed to group the series was defined for every

location by looking at the outcome of the cluster analysis: when an increase from k to k + 1

clusters did not further lead to a new clearly differentiated WP, the research was stopped and k

was used for the cluster analysis of that particular location.

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42 4.2.4. Extreme value analysis

The EVA were performed independently over the subsets of H

_s

peaks resulting from the cluster classification. The threshold was selected in order to maximize the p

value

of the upper tail Anderson-Darling test, maximizing in turn the probability to obtain a dataset of extremes best modelled by a GPD (Solari et al., 2017). Hence, when a subset of the peaks within a given WP is defined, the three parameters of the GPD are estimated through the L-moments method (cfr. Section 2.3.), and the return-period (T

_r

) quantiles of the variable under investigation are computed. In this work, to estimate the overall T

_r

-H

_s

curve and its confidence intervals from the GPDs fitted to each WP, a bootstrapping approach was implemented (see Algorithm 21).

Algorithm 21 shows a pseudocode summarizing the bootstrapping procedure. First, N

_boot

series of H

_s

, each N

_years

long, are generated for every WP. Second, the series generated for the differ- ent WPs (N

W P

per location) are combined in order to obtain one single N

years

long series for each of the N

_boot

simulations. Third, an empirical relation between T

_r

and H

_s

(i.e. an empir- ical cumulative distribution function or ECDF) is estimated from each one of the N

_boot

series.

Lastly, expected value and confidence intervals of H

s

are estimated from the N

boot

ECDFs for several return periods. The method assumes a Poisson-GPD model for each WP and that the realizations of different WP are independent from each other. This independence hypothesis was evaluated by estimating the correlation between the annual number of peaks associated to each WP.

In summary, for a given location the overall work-flow can be summarized as follows:

• selection of a series of H

_s

peaks through a POT approach

• selection of the wind field data to be employed in the clustering algorithm (i.e. ∆t and spatial domain)

• classification of the H

_s

peaks due to the k − means algorithm

• definition of a suitable number (k) of WPs

• averaging of the MSLP corresponding to the peaks of each WP, for each ∆t taken into account

• performing EVA over the single subsets

• computation of the overall long term distribution through a bootstrapping technique

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for j ← 1, N

_boot

do for i ← 1, N

_{W P}

do

{H

s

}

i,0

← random(GP D, ˆ θ

_(i,0)

, N

i

) θ ˆ

_i

← f it(GP D, {H

_s

}

_i,0

)

{N

_simu

}

_i

← f

_i

( ˆ λ

_i

, N

_years

)

{H

_s

}

_i

← random(GP D, ˆ θ

_i

, {N

_simu

}

_i

) end for

{H

_s

}

_j

← [{H

_s

}

_i

, i = 1 . . . N

_{W P}

] H

_s

← sort({H

_s

}

_j

)

end for

H

_s

= ˆ f (T

_r

) ← {f

_i

} C.I. ← {f

i

}

Comments:

N

_boot

is the number of bootstrapping repetitions N

W P

is the number of WP

θ ˆ

_(i,0)

are the parameters of the GPD estimated from the original sample N

_i

is the length of the original sample of H

_s

peaks within the WP λ ˆ

i

is the yearly number of events of the i

^th

WP

N

_years

is the number of years simulated; it must be larger that the maximum return period to be analized

N

simu

is the numer of events in N

years

obtained for the i

^th

WP H

_s

= f (T

_r

) is the empirical Hs-Tr curve

This methodology was applied to all the hindcast locations shown in Fig. 4.1. For the sake of clarity, just the results of the locations B4 (Mazara del Vallo) and B7 (Monopoli) will be shown and discussed. However, all the considerations introduced hold for all the locations investigated, whose results can be found at the end of the Chapter.

4.3. Results and discussions

Once the series of H

_s

peaks is selected, the first step of the proposed methodology requires

to define the domains of ¯ u

w