Page 3 - hydro-maritime_2010

r
σ, θ) in space, x , and time, t. Where the term action density, N, refers to the ratio between spectral variance and angular
frequency, (N = E/σ). N temporal variation is taken into account through the first term in the left side of the balance
equation (eq. 1) [15]-[16] :
ur
∂ N +∇ ⋅ ⎡ r U ⋅ ∂ cN + ∂ c N = S tot
σ ⎤
ϑ
r
⎦
t ∂ x ⎣ ( g c + ) N + ∂ σ ∂ ϑ σ (1)
The second term of the cinematic part of the equation (left side) accounts for the energy propagation in the surface
r
r
r
r
r
)
direction, x , having group celerity c =∂ σ / k∂ derived by the linear dispersion equation σ = 2 g |k | tanh⋅ ⋅ ( | k | d ,
g
r
depending on wave number vector, k , and local depth, d. The third and fourth term represent the effect of angular
frequency translation and the refraction effect, respectively, both due to depth variation and sea currents, where c σ and c θ
are the celerity propagation in the spectral space (σ, θ). The right side of the equation includes the source term, S tot,
representing all physical processes generating, dissipating, or redistributing the wave energy.

2.4 Maximum run-up assessment
Once the offshore wave propagation motion has been assessed, the maximum beach run-up [17] , R, needs to be evaluated.
[3]
The latter is quantified by means of an empirical relationship . The relationship (2) has been set-up for sandy natural
beaches having slope, βf, ranging between 1.5° and 10.8° and average sand diameter, d, between 0.18 and 0.80 mm.
R = c L⋅ zwm (2)
[3]
R is assumed to be proportional to the vertical scale, L zwm, of the run-up Rayleigh distribution (eq. 3) through a
proportionality coefficient, c, assumed to be equal to 0.89:
5 . 0
⎧ 60.0 ( ⋅ H ⋅ L ) tan β tan β ≥ 1.0 (3)
⎪
L zwm = ⎨ orms 0 f f
⎪ 05.0 ( orms ⋅ L 0 ) ⋅ H 5 . 0 tan β f < 1.0
⎩
where:
ƒ H orms is the deep water root mean square height;
ƒ L 0 is the deep water wave length calculated using:
2
L 0=gT /2π (4)
where T is the average wave period.

2.5 Tides oscillation assessment
The sea level fluctuation due to astronomical and meteorological influences cannot be neglected. The factor of main
interest is the frequent recurrence of this phenomenon with the sea storm. The increase of the sea level has a direct effect
on shoreline withdrawal and an indirect effect on heights and distances of lapping waves, depending on the water depth
increase.
To quantify the maximum tide level aiming to retrieve the effect of tide oscillation on the shoreline position, records of
the close Porto Empedocle marigraph were used (37°17'11.20'' N, 13°31'37.30'' E). The station is part of the marigraph
national network (Rete Mareografica Nazionale) set-up by ISPRA. The marigraph recorded homogeneous data suitable
st
th
to be used within this case study during the decade ranging between the 1 of January 1998 and the 26 of October 2008.
3. STUDY AREA AND IN SITU MEASUREMENTS
3.1 Geological and geo-morphological characterization
The Marsala coastal zone is a geological plane having NW-SE principal direction; its altitude is slightly decreasing from
NE to SW (sea direction). The landscape is characterized by a constant and regular morphology, typical of the wide
coastal planes that were modelled and smoothed by Quaternary sea action. The beach is located in the south of Marsala
town and extends for approximately 3 km between Torre Tunna (northern headland: 37°45'32.26''N, 12°27'40.00''E) and
Torre Sibilliana (southern headland: 37°43'36.31''N, 12°28'11.23''E). Geological lithology close to the ground surface, is

Proc. of SPIE Vol. 7824 78241Z-3

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