Wave Spectral Evolution on the Coastlines of Southern Italy

Wave spectral evolution on the coastlines of southern Italy

G. Benassai, E. Chianese & E. Sansone Institute of Meteorology and Oceanography, Parthenope University, Naples, Italy

Abstract

The objective of the present study is the transfer of given sea wave spectra on deep water and the simulation of the wave spectral saturation from deep to intermediate water. The deep water spectra recorded offshore the coastlines of Southern Italy were transferred to the Gulfs of Naples and Salerno, where they were compared with wave spectra recorded by the Institute of Meteorology and Oceanography and waves recorded by the Naples Hydrographic Service, respectively. The JONSWAP parameters were calculated from the measured spectral density and related with the nondimensional fetch, energy and peak frequency through a regression in log scale, obtaining a satisfactory agreement with the published results. The relationships between the spectral parameters and the nondimensional fetch gave the possibility to transfer the wind wave spectra from the measurement sites to the sites of interest, offshore the Gulf of Naples and Salerno. The spectral transfer was extended to intermediate depth through mathematical models which take into account the saturation process. Finally the waves and the spectra obtained inshore were compared with the local wave records on the coastline of Salerno. Keywords: wave spectra, field data, JONSWAP parameters, regressions.

1 Introduction

In the present application a method is proposed to obtain the wave spectral evolution in waters of different depth. The method is based on the transfer of the measured spectra on deep water and on the saturation of the spectra on finite depth.

Coastal Environment V, incorporating Oil Spill Studies, C. A. Brebbia, J. M. Saval Perez & L. Garcia Andion (Editors) © 2004 WIT Press, www.witpress.com, ISBN 1-85312-710-8 302 Coastal Environment V, incorporating Oil Spill Studies

The offshore wave spectra were transfered from the measurement station offshore Ponza to the sites of interest, located offshore the Gulf of Naples and offshore the Gulf of Salerno, respectively. The inshore wave spectra were obtained by the offshore ones with a mathematical model which takes into account the saturation process. The numerical results, in terms of offshore wave spectra, were compared with the ones recorded offshore the Gulf of Naples by a waverider buoy owned and run by Institute of Meteorology and Oceanography. The inshore results, in terms of significant wave heights, were compared with the ones recorded by a meteo-oceanographic station owned by Naples Hydrographic Service on the coastline of Salerno in 9 m depth.

Figure 1: Site location of the wave and wind records.

2 Field data set

Data used in the present study consisted in waves recorded simultaneously on deep water and intermediate depth during the period 2000÷2001 and wind data recorded on the coastlines of Naples and Salerno. With reference to the site location of fig. 1, the following data were examined: a) wave data recorded by a WAVEC buoy of the Wave Measurement Network station, located offshore Ponza at coordinates ϕ= 40°52’00”N, λ = 12°57’00”E, working since July 1989, and recorded simultaneously by a Datawell Waverider buoy of the Institute of Meteorology and Oceanography located offshore Punta Campanella, working since June 2001. b) wind data recorded by Institute of Meteorology and Oceanography at Licola (a site on the low coastline 20 km northwest of Naples), corrected for the land location of the sensor; c) wave and wind data recorded by the meteo-oceanographical station of Naples Hydrographic Service located on the coastline of Salerno at the mouth of river

Sele at coordinates ϕ= 40°29’06”N, λ = 14°55’30”E, working since August 2000. A first selection of the wave records was made on the basis of a threshold value Hs=1.50m for the Ponza wave records. Monthly time histories of Hs and wave directions recorded offshore Ponza and Naples, and of wind directions and velocities recorded at Licola and at the Sele river mouth have been examined for this study. Fig. 2 gives an example for the time history of September 2001. A first inspection of fig. 2 shows that Naples wave records have an approximate delay of three hours with respect to Ponza wave records. This accounts for the time needed by the group celerity of the Ponza deep water waves to reach Naples location. A second selection was based on the fulfilment of the following hypotheses of the JONSWAP wind-sea wave spectrum: - peak frequency characteristic of the wind sea, without swell components; - fetch-limited waves. The first hypothesis excluded the sea states with peak frequencies and wind velocities getting a nondimensional peak frequency ν = fp U/g < 0.10 (swell). The duration-limited wave conditions were detected using the equation reported by CERC (1977): ζ = K exp [ A(lnχ)2 - Blnχ + C]1/2 + Dlnχ (1) where K=6.5882, A=0.0161, B=0.3692, C=2.2024, D=0.8798, χ= gx/U2 and ζ = gt/U, being x the fetch length and t the wind duration. Eq. (1), given in fig. 3, shows the two domains in which the combination of χ and ζ represents duration limited and fetch limited sea conditions.

6 6 Hs (Ponza)(m) Hs (Naples)(m) 5 5 Hs (Sele)(m) 4 4

3 3

2 2

1 1

0 0 1 2 3 4 5 6 7 8 9 10111213141516171819202122232425262728293031 12 12 Vv (Licola)(m/s) 10 10 Vv (Sele)(m/s) 8 8 6 6 4 4 2 2 0 0 360 360 270 270 , Dw (Ponza)(°N) 2Dv (Licola)(°N) 180 180 90 90 0 0

Figure 2: Time history of Hs and Dw recorded offshore Ponza and Naples and of Dv and Vv recorded at Licola in September 2001.

Coastal Environment V, incorporating Oil Spill Studies, C. A. Brebbia, J. M. Saval Perez & L. Garcia Andion (Editors) © 2004 WIT Press, www.witpress.com, ISBN 1-85312-710-8 304 Coastal Environment V, incorporating Oil Spill Studies

The field data in the fetch-limited domain have been considered without further adjustment, while for the field data in the duration-limited domain an equivalent fetch (that is the fetch corresponding to stationary wave conditions) was calculated and considered in the following.

1E+007

1E+006 Duration-limited

1E+005

1E+004

1E+003 Fetch-limited

1E+002

1E+001 1E+003 1E+004 1E+005 1E+006 1E+007

Figure 3: Experimental values of nondimensional fetch χ versus nondimensional duration ζ.

3 Spectral parameters and empirical relationships between them

The measured wave spectra of the selected sea states were parametrized in the JONSWAP form. The parameter α was calculated by the procedure indicated in Hasselmann et al. [7]:

.2 00 f p α = .0 65 f −1 ()2π 4 − 52 ()dffSfg (2) ()p ∫ .1 35 f p while the peak enhancement parameter γ was calculated as the ratio between the maximum spectral energy and the maximum energy of the Pierson-Moskowitz spectrum with the same value of α: 4 -5 2 -1 γ = S(fp)(2π) fp exp(5/4)(αg ) (3) where α is obtained from eq. (2). The energy density for fetch limited sea depends on the following variables: 2 m0 =σ = variance of surface elevation (Hs=4σ = 4√m0); Ua = wind velocity recorded at a reference height a (usually a = 10m on m.w.l.); χ = fetch length; g = gravity acceleration; fp =spectral peak frequency. Dimensional analysis gave the following nondimensional groups of variables, respectively energy, peak frequency and nondimensional fetch, expressed by the following equations:

2 2 4 ε = σ g / Ua (4) ν = fp Ua/ g (5) 2 χ = g x/ Ua (6)

Therefore, for fetch limited conditions: ε = f1(χ) ; ν = f2 (χ) (7) where f1 and f2 are functions to be determined. Hasselmann et al. (1973) obtained the following regression lines: ε =7.13×10 –6 ν -3.33 (8) α = 0.033 ν 0. 67 (9) ν = 3.5χ - 0.33 (10) ε = 1.6×10 - 7χ (11) α = 0.076χ -0.22 (12)

These relationships are not valid for fully developed sea, as JONSWAP data were limited to χ < 1×104, so they are suitable for conditions of local wave generation.

Hasselmann et al. [7] didn’t find a satisfactory correlation of γ, ωa and ωb with the two parameters ν and χ, so they provided their mean values, respectively: γ=3.3, ωa=0.07, ωb=0.09. Mitsuyasu et al. [10] considered ωa and ωb fixed to their JONSWAP mean values of 0.07 and 0.09, but rather than choosing γ constant, they integrated the JONSWAP spectrum and obtained other empirical relationships (given in Benassai [3]).

Lewis and Allos [9] using the relationships of ωa and ωb with ν obtained by Hasselmann et al. [7] integrated the equation of JONSWAP spectrum similarly to Mitsuyasu et al. [10] and proposed other relationships; moreover Kahma [8], on the basis of data recorded by four Waverider buoys displaced along 70 km in the Bothnian Sea, among Finland and Sweden, obtained a dependence of ν with χ comparable to the JONSWAP one, but with growth rates for ε greater than JONSWAP of a factor about 2. These relationships have been also reported in Benassai [3]. In the present study the empirical relationships between the spectral parameters were calculated on the basis of the sea states recorded in years 2000 and 2001, enriched with the data considered in Benassai [2]. Spectral parameters so obtained were related with nondimensional parameters (eqs 4, 5 and 6) through a regression in log-scale. The following experimental relationships were obtained: ε = 2.71×10 – 6 ν -3.76 (13) α = 0.027ν 0.51 (14) ν = 2.6χ - 0.29 (15) ε = 4.1×10 - 8χ 1.16 (16) α = 0.044χ - 0.15 (17)

The obtained regression lines are close to the ones obtained by the quoted authors, as reported in Benassai [3].

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4 Offshore wave spectra obtained with the transfer method

The offshore wave spectra in the Gulf of Naples were obtained starting from the recorded spectra offshore Ponza using the obtained relationships between the spectral parameters and the fetch length. The transfer of the equilibrium parameter α was done with eq. (17), while the enhancement parameter γ was fixed to the recorded value at Ponza, as no strong correlation was found (in accordance with part of the literature) between γ and χ. The inspection of the fetches shows that the fetches of Ponza are almost always longer than the ones of Naples, except for the directions 260° N and 270°N. This circumstance is more evident for the fetches of Salerno if compared with the fetches of Ponza for the directions 220°N÷270°N, as reported in Benassai [3]. Fig. 4 gives an example of offshore spectral transfer, characterized by Ponza fetch predominance. The spectrum of Ponza presents a greater energy than the one of Naples, in agreement with the direct proportionality between the nondimensional energy ε and the nondimensional fetch χ (expressed by eq. 16). The comparison between transfered and recorded Hs offshore the Gulf of Naples has been given in table 1 for the sea states of September and November 2001, taking into account the time shift of three hours between the two locations.

Wave Spectrum, event 10 09 2001 h 00:00 20

14 Spectrum rec. at Ponza, Hm0 =3.21m 12 s) 2 10 Spectrum transf. to Salerno, Hm0 = 2.68 m

S(f) (m 8

6 Spectrum rec. at Naples, Hm0 =1.98m

0 0 0.1 0.2 0.3 0.4 0.5 0.6 Frequency (Hz)

Figure 4: Spectra offshore Ponza, transfered and recorded offshore Naples.

The inspection of Tab. 1 leads to the following considerations. The transfered Hs are quite close to the recorded ones, except for the sea states 05090118 and 10090109. The first sea state come from 320 °N, which is related with secondary fetch (Gulf of Naples) so the transfer method was implemented with the wind

Coastal Environment V, incorporating Oil Spill Studies, C. A. Brebbia, J. M. Saval Perez & L. Garcia Andion (Editors) © 2004 WIT Press, www.witpress.com, ISBN 1-85312-710-8 Coastal Environment V, incorporating Oil Spill Studies 307 direction 305 °N, recorded by Licola meteorological station. The numerical results, although better than before, give a 29% scatter with the field ones. The second sea state comes from 261 °N, associated with main fetches; the wave direction is in agreement with the Licola wind measurement (255 °N) but the local waves recorded by the Naples buoy probably come from south-western directions, which are sheltered by the Isle of Capri.

Table 1: Hmo offshore Ponza, transfered and recorded offshore Naples.

(Hm0)0 TR. NAPLES LICOLA LICOLA REC. NAPLES COMP. ev. dd/mm/yy h DDw(°N) (m) (Hm0)0(m) DDv(°N) V'v (m/s) Hm0(m) TR-REC(%) 05/09/01 6 248 3.88 2.04 300 6.77 2.36 -14 05/09/01 9 254 3.02 2.36 285 9.91 3.32 -29 05/09/01 12 246 3.57 3.33 295 10.45 2.90 15 1 05/09/01 15 310 3.08 3.21 285 8.63 3.06 5 05/09/01 18 321 2.45 2.00 305 8.77 2.80 -29 05/09/01 21 250 2.03 1.32 0 2.17 1.69 -22 06/09/01 0 288 1.6 0.90 90 0.83 1.52 -41 09/09/01 15 227 2.15 0.97 240 5.27 1.09 -11 09/09/01 18 291 2.69 1.69 250 4.63 1.62 4 09/09/01 21 269 3.11 1.89 285 3.67 1.98 -5 10/09/01 0 283 3.21 2.68 245 5.03 2.30 17 2 10/09/01 3 235 3.35 2.92 255 6.45 2.71 8 10/09/01 6 275 2.91 2.69 260 6.33 2.34 15 10/09/01 9 261 3.06 3.28 255 5.95 2.00 64 10/09/01 12 284 3.02 2.79 270 6.90 2.08 34 08/11/01 15 258 3 1.50 275 5.23 1.92 -22 08/11/01 18 290 3.4 2.43 265 6.17 2.20 10 08/11/01 21 280 3.18 2.67 260 6.72 2.94 -9 09/11/01 0 236 2.6 2.27 265 8.33 2.20 3 3 09/11/01 3 283 2.17 2.00 245 5.61 1.76 14 09/11/01 6 258 1.9 1.33 165 2.19 1.48 -10 09/11/01 9 251 1.6 1.58 190 5.33 1.59 0 09/11/01 12 247 1.9 1.88 280 6.00 2.05 -8

5 Inshore wave spectra obtained with the saturation method

The transfer of the wave spectra in shallow water conditions (9 m depth) was done with TMA model, which assumes a JONSWAP spectrum multiplied by a transfer function, which depends on depth and frequency. The model is based on the following equations:

S(f,h) = S(f) Ξk(σh) (18) −2 2 2 hk )( =Ξ h {}+ 21)( ()σχσσχσ hh senh[]2 ()σχσ hh (19) with σ=h σ / gh and χ(σh) obtained from the solution of: 2 h [ σχσσχ hh ]= 1)(tanh)( (20) Fig. 5 gives an example of spectrum transfered offshore Salerno from the measurement site and then transfered on the coastline with the TMA model.

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Wave spectrum, event 26 11 2000 h 21:00 40

Spectrum transf. to Salerno, Hm0= 4.66m 35

Spectrum rec. at Ponza, Hm0= 4.60m 30

25 s) 2 20 S(f) (m 15

Spectrum TMA inshore, Hm0= 3.04m 5

0 0 0.1 0.2 0.3 0.4 0.5 0.6 Frequenza (Hz)

Figure 5: Comparison between the offshore spectrum recorded at Ponza and transfered to Salerno and the inshore TMA spectrum.

The transfer of the significant wave height was done starting from the Phillips’ wave number spectrum: α )( = kkF − 3 (21) 2 which is valid at any depth (self-similarity hypothesis). The definition of m0 gives: ∞∞ α −3 0 = ∫∫)( = ψ p ),( dkhfkkdkkFm (22) 002 Bouws et al. (1985), neglecting the contribution of the function ψ and –2 considering the spectral components k>kp , obtained as a result m0=α/4 kp , which, on the basis of the definitions of m0 = 4 mH 0 and p = 2π Lk p ,becomes: −2 H 2 2πα  m0 =   (23) 16 4  Lp  Taking into account the empirical relationship obtained by Bouws et al. for α as a function of the wind velocity and the peak wave length Lp, the quantity 43 LH pmo )( is found constant if the wind velocity is unchanged. So the ratio between the significant wave heights Hm0 follows the ratio between the peak lengths at the proper depths. The results of the comparison between the simulated and recorded significant wave heights on 9m depth for the selected sea states of the storms of November and December 2000 are given in table 2.

Table 2: Hs transfered offshore and inshore vs Hs measured inshore.

(Hm ) TR. SALERNO REC. SELE REC.SELE REC.SELE TR. SELE SELE (Hm ) ev. dd/mm/yy h DDw(°N) 0 0 0

(m) (Hm0)0(m) DDv(°N) Vv (m/s) Hm0(m) Hm0(m) TR-REC (%) 07/11/00 3 209 2.8 2.70 180 4.60 1.92 1.98 3 07/11/00 6 212 2.6 2.54 225 4.00 2.09 1.86 -11 07/11/00 9 226 2.9 2.80 240 2.70 2.03 2.14 6 07/11/00 12 227 2.8 3.18 295 5.00 2.13 2.33 10 07/11/00 15 230 2.8 2.85 205 2.20 2.24 2.09 -7 07/11/00 18 231 2.6 2.77 200 2.20 1.98 2.22 12 07/11/00 21 227 2.7 3.07 205 4.70 2.68 2.25 -16 08/11/00 0 230 2.9 3.29 205 4.50 2.73 2.42 -11 1 08/11/00 3 231 2.6 2.95 240 3.40 3.15 2.17 -31 08/11/00 6 238 2.4 2.82 220 4.60 2.43 1.96 -19 08/11/00 9 238 2.2 2.59 225 2.40 2.28 2.07 -9 08/11/00 12 235 1.9 2.24 240 3.00 1.83 1.97 7 08/11/00 15 220 1.5 1.62 195 2.20 1.73 1.43 -17 08/11/00 18 226 2.2 2.50 210 2.60 1.66 2.14 29 08/11/00 21 235 2.3 2.71 210 3.30 1.68 2.17 29 09/11/00 0 230 1.8 2.05 245 3.70 1.43 1.64 15 26/11/00 15 265 2.4 1.68 247 12.72 1.83 1.39 -24 26/11/00 18 266 3.6 2.26 301 7.75 2.32 1.73 -25 2 26/11/00 21 276 4.6 4.66 278 18.14 2.59 3.04 17 27/11/00 0 275 4.2 4.25 313 10.89 2.79 2.78 0 16/12/00 0 279 2.9 2.15 235 10.67 1.71 1.72 1 16/12/00 3 277 3.5 3.45 282 11.17 1.68 2.40 43 16/12/00 6 270 2.4 2.17 281 10.61 1.86 1.50 -19 3 16/12/00 9 270 2.2 2.13 336 6.44 1.46 1.56 7 16/12/00 12 280 2.1 2.13 291 7.36 1.54 1.63 6 16/12/00 15 282 2 2.03 296 6.36 1.35 1.68 25 16/12/00 18 273 1.8 1.72 304 5.42 1.11 1.32 19 27/12/00 18 206 2.4 1.56 208 7.50 1.79 1.25 -30 27/12/00 21 206 3.2 2.52 216 9.19 1.44 1.85 28 28/12/00 0 213 2.9 1.94 224 7.03 1.72 1.49 -14 28/12/00 3 224 2.8 2.35 237 9.17 1.89 1.80 -5 28/12/00 6 229 2.7 2.70 227 9.28 1.95 2.07 6 28/12/00 9 244 2.9 2.91 238 7.31 2.08 2.33 12 4 28/12/00 12 262 3.1 3.85 232 7.69 2.22 2.95 33 28/12/00 15 260 3.6 4.48 247 9.33 2.36 3.28 39 28/12/00 18 260 3.2 3.98 253 10.00 2.39 2.92 22 28/12/00 21 263 3.2 3.98 264 9.69 2.29 2.92 27 29/12/00 0 270 3.1 3.44 265 8.44 1.82 2.39 31 29/12/00 3 261 2.4 2.98 279 6.28 1.37 2.29 16

The inspection of tab. 2 leads to the following considerations. The values of Hm0 obtained with the TMA model are almost always higher than the recorded ones when the waves come from W and NW, while they are generally lower when the waves come from S and SW. In fact, the hypotheses of the transfer method are better verified for the sea states that first arrive at Ponza and then at Salerno. The differences between the transfered and recorded values for the waves coming from W and NW can be partially explained because the model doesn’t account for wave refraction, which can be significant for oblique

Coastal Environment V, incorporating Oil Spill Studies, C. A. Brebbia, J. M. Saval Perez & L. Garcia Andion (Editors) © 2004 WIT Press, www.witpress.com, ISBN 1-85312-710-8 310 Coastal Environment V, incorporating Oil Spill Studies wave propagation, that is when the offshore wave direction differs more than 20° from the normal to the bathymetry (240°N). However, the scatter in Tab. 2 rarely (only in 4 cases) exceeds 30%, and it is generally limited in 15-20%.

6 Conclusions

The present study showed a simple method to obtain the offshore and inshore wave spectra starting from the offshore measured data which are available in limited locations. Local studies of wave conditions are possible on the basis of the available wave records offshore the Italian coasts. The numerical results are satisfactory except when the model hypotheses are not well verified. The scatter is generally limited in 20%, which can be acceptable for engineering applications.

References

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