191
1 INTRODUCTION
A concept of wave in physical oceanography is
understood to be “vertical movement of sea surface”.
Wind-generated surface waves are only one group of
waves among the other waves as: tidal waves, storm
surges, tsunami, infra-gravity waves, swell waves,
wind waves and capillary waves. Sea surface waves
generated by wind are the waves arose following
dynamical pressure of wind blowing above the sea
surface. They have period from 0.25 s to 30 s with
appropriate wavelength of 0.1 to 1500 m (in deep sea;
Munk, 1950).
Scientists are more interested in investigation of
dynamics and kinematic of waves; how they are
generated by wind, how they travel and transform
and how they disappear from sea surface. On other
side “Engineers” (naval architects, mariners,
hydraulics, builders and etc.) are most interested for
the project, which includes: ships, platforms, ports,
breakwaters, piers, beaches and etc. The real waves
on sea surface, in situations with storm and hurricane
wind, looks very chaotic while swell waves appeared
very regular.
At present, five methods are available to deal with
description of sea state under action of waves at
particular sea area or location (Goda, 2000):
significant wave representation method, highest wave
representation method, probability calculation
method, irregular wave test method, and spectral
calculation method. Numerical modelling methods of
wave generation and dissipation have been used too
(e.g. Bertotti and Cavaleri, 2009).
Intense investigations around the world of wind
generated sea surface waves during 60th and 70th
Measurements and Numerical Modelling of Surface
Waves in Front of the Port of Split
N. Leder & T. Duplančić Leder
University of Split, Split, C
roatia
G. Lončar
University of Zagreb, Zagreb, Croatia
ABSTRACT: Wind generated surface waves were measured at V2 station (φ=43°29.3’ N; λ=16° 27.9’ E) in the
Brački Kanal Channel area of the Middle Adriatic, in front of the port of Split. This was undertaken in the
time interval from November 2007 to June 2008, by using Datawell MKIII waverider with all its compo-nents.
For the analysis and description of extreme sea states maximum recorded wave height Hmax and sig-nificant
wave height H1/3 were presented as well as associated wave spectra. The measurement results show that much
larger waves appear in the open Adriatic compared to the Middle Adriatic channel area. Numerical modelling
of wave generation in the Brački Kanal Channel area and wider island area of the Middle Adriatic Sea was
performed by using Mike 21/SW numerical model. Wind field used for the forcing in numerical simulations
relies on the results of the prognostic atmospheric model Aladin-CRO. For verification of model results, results
of measurement at a waverider station V2 located in front of the port of Split were used. It was concluded that
measured and modelled significant wave heights were very well matched.
http://www.transnav.eu
the
International Journal
on Marine Navigation
and Sa
fety of Sea Transportation
Volume 14
Number 1
March 2020
DOI:
10.12716/1001.14.01.24
192
years of 20th century initiated an interest for this
phenomenon in the Adriatic Sea.
In eastern part of the Adriatic first knowledge
about sea surface waves are based on collected visual
observations from the ships (e.g. Zupan, 1961).
Statistical analyses of collected data from ships have
been done continuously over the time. One of the
statistical presentation of ships visual wave
observations covering the east Adriatic Sea is given by
Leder (2002) showing relative frequencies of wave
heights (H) for different seasons. First instrumental
wave measurements along the east Adriatic coast
started in 1967 based on short-term experiments
(Tabain, 1985), while contemporary long-term
instrumental waves measurements started in 70th
years of 20th century. These years locations are
founded where had to be deployed waveriders at the
open Adriatic Sea; southeast of lighthouse St. Andrija
near Dubrovnik (South Adriatic, Smirčić et al., 1998);
near Palagruža Island (Middle Adriatic, Smirčić and
Gačić, 1983) and in the area of gas fields IKA and
IVANA (North Adriatic, Leder et al., 1998).
Measurements of the wind-generated surface
waves along the eastern part of the Adriatic Sea in
coastal areas are rare: previous systematic
measurements have been carried out in the open sea
(Leder et al., 2010).
It should be emphasized that knowledge of the
elements of the wave climate is very important for
navigation on the waterway and berth in the port or
anchoring in front of the port.
The Port of Split, situated at exceptional
geographic position in the Mediterranean, with
extraordinary maritime characteristics for reception of
vessels, has earned the rank of one of the most
important centres for local and international maritime
traffic. As of 2017, the port ranks as the largest
passenger port in Croatia and the largest passenger
port in the Adriatic, (https://portsplit.hr/en/). In this
paper results of measurements and numerical
modelling of wind generated surface waves in front
of port of Split are presented and compared with
results of measurements of waves in the open
Adriatic Sea area.
2 MATERIAL AND METHODS
Wind generated surface waves were measured at V2
station (φ=43°29.3’ N; λ=16° 27.9’ E; Fig. 1) in the
Brački Kanal Channel area of the Middle Adriatic, in
front of the port of Split. Wave measurements were
part of the scientific and research program – „The
Adriatic Sea Monitoring Program“ (Andročec et al.,
2009) and were undertaken in the time interval from
November 2007 to June 2008, by using Datawell
MKIII waverider with all its components. For the
analysis and description of extreme sea states
maximum recorded wave height Hmax and
significant wave height (H
S or H1/3) will be presented
as well as associated wave spectra.
The process of formation and development of
surface waves may be considered as a function of
three basic variables, and this functional relation is
usually given as the simple analytical expression:
F = F[(ω,v),P,T
t] (2.1)
where:
(ω,v), wind direction and speed,
P, length of fetch over which the wind blows,
T
t, duration of wind of a particular direction.
From the aspect of surface wave generation at V2
station in Brački Kanal Channel, the following winds
are predominant (Fig. 1):
− Sirocco (or Scirocco), ESE-SE direction, fetch about
100 km;
− Bora, NE-ENE direction, fetch about 3.5 km;
− Libeccio, SW direction, fetch about 15 km;
− Maestrale, Pulenat, W – WSW direction, fetch
about 30 km.
Figure 1. Lenght of fetch for dominant winds at the station
V2 near port of Split.
For easier understanding, brief definitions of
parameters applied in the analysis and description of
a certain sea state are given below, using terminology
and symbols adopted in the worldwide literature of
oceanographers, shipbuilders and hydrotechnic
engineers (Smirčić, 1985):
H
1/3 or HS - significant wave height, representing
average height of 33% of waves in a particular record.
This unit has characteristics of visually observed
wave heights;
H
1/10, - average height of 1/10 of highest waves in a
particular record;
H
max - maximum recorded wave height in a record;
H
av - average wave height in a record;
T
1/3 or TS - significant (mean) wave period for a
particular recording interval;
T
av - average wave period for a particular recording
interval;
T
max - maximum wave period for a particular
recording interval;
L
sr - mean value of a wave length, representing mean
value of horizontal distances between adjacent wave
crests in a record. It is calculated from known values
of mean periods using the simple empirical relation:
L
sr = 1.56 Tav
2
(2.2)
where T
av is given in seconds and Lsr in metres, while
maximum error is about 10% if d/ L
sr = ½ where d =
sea depth.
Furthermore, the above mentioned magnitudes
can be determined using the method of spectral
analysis, whose major task is to obtain the
193
distribution of total wave energy by frequencies,
knowing the spectrum moments m
i (i=0, 1), using the
simple relations:
− significant wave height
H
1/3=4√ m0, m0 = ½ ∫ S (f) df (2.3)
where S(f) is wave energy, f is wave frequency (f=1/T),
and
− significant (mean) period
T
1/3=2π (m0/m1), m1=½ ∫ S(f) f df (2.4)
Numerical modelling of wave generation in the
local waters of the channel and island system of the
southern Adriatic Sea was undertaken using Mike
21/SW. Wind field used for the forcing in numerical
simulations relies on the results of the prognostic
atmospheric model Aladin-CRO. For verification of
model results, results of measurements at a waverider
station V2, located in front of the town of Split, were
used, covering the period from 1 November 2007 to
19 June 2008.
In the numerical model Mike 21/SW, full spectral
formulation based on the papers of Komen et al.
(1994) was used. For discretization of the spectral
frequency domain, logarithmic scale with the
minimum frequency of 0.08 Hz (wave period 12.5 s)
to the maximum frequency of 1.15 Hz (wave period
0.87 s) was used, through 28 discrete steps. The
mentioned range provides coverage of all relevant
spectral periods that may be expected in the analysed
area. The model includes the processes covered by the
wind wave generation, non-linear wave interaction,
refraction and shoalling, as well as whitecapping.
Dissipation coefficients were used with constant
values of 3.9 and 0.5 (Lončar et al., 2010). Reflection
and diffraction have not been treated using this
model. Time integration is carried out with fractional
steps, whereby for the propagation of wave action
multi-sequence Euler's explicit method was used. The
function of sources in the wave action conservation
equation is treated on the basis of 3rd generation
models, and their numerical integration is carried out
according to the DIA (Discrete Interaction
Approximation) method shown in the papers of
Komen et al. (1994) and Hercbach and Jannsen (1999).
Generation of wave dynamics requires data on the
wind (intensity and direction) in the spatial domain of
the numerical model at 10 m above the sea surface.
These data were obtained from the prognostic
numerical atmospheric model Aladin with a
horizontal resolution of 8 kilometres and a temporal
resolution of three hours (Courtier et al., 1991; Brzović
and Strelec-Mahović, 1999; Ivatek-Sahdan and Tudor,
2004).
Spatial domain of the numerical model which
includes the area of the Splitski kanal, Brački kanal,
Hvarski kanal, Korčulanski and Neretvanski kanal
Channels is shown in Figure 2. with bathymetry
based on the spatial continuous raster grid data of 7.5'
in the longitudinal and latitudinal directions and
model domain discretization with an unstructured
grid of triangle finite volumes.
Numerical distances between nodes, set in the
centres of finite volumes, are variable, ranging from
150 m to 500 m. The model domain does not have
active open boundaries and all land boundaries are
completely absorbent. The exclusion of open
boundaries is apparently inherent with the process in
the nature (see Fig. 2; links between the islands of
Šolta and Hvar, and of Hvar and Korčula), causing an
error in cases when waves coming from the west.
Given the intensity, frequency and duration of the
wind with prevalent W direction, it may be concluded
that the entered error very rarely has an impact on
model results, and namely only in the area close to the
links between the islands. Initial conditions (1
November 2007) were defined with a zero spectra, i.e.
the absence of the initial wave motion throughout the
model spatial domain is assumed.
Figure 2. Spatial domain of the numerical model of wave
generation.
3 RESULTS AND DISCUSSION
3.1 Results of wave measurements
Maximum and significant wave heights measured at
V2 station between 1 November 2007 and 20 June
2008 are shown in Figure 3.
Maximum wave height of 2.84 m was measured in
a half-hour record (06:11 – 06:41 hours) on 3
December 2007, during strong Sirocco (SE) wind.
Significant wave height during this record was 0.92
m. Maximum significant wave height of 1.35 m was
measured in a half-hour record (04:30 – 05:00 hours)
on 6 March 2008, during strong Bora (NE) wind.
For the overall interval of wave measurement
(1/11/2007 - 20/6/2008) average maximum wave height
was 0.42 m, while average significant wave height
was 0.22 m. So the following relation between
maximum wave height and significant wave height is
obtained:
194
H
max=1.91 H1/3 (3.1)
Table 1 gives monthly maximum data of wave
elements during the measurement period from
November 2007 to June 2008 associated with values of
the ratio between maximum and significant wave
height (H
max/H1/3) and prevailing wind direction. In
the periods marked (*) the measurement data are
missing. It can be seen that only for December 2007
and February 2008 (strong Sirocco in both situations)
ratios between H
max and H1/3 are significantly different
from relation (1), probably due to the rapid change of
the Scirocco and Bora winds (or Libeccio) that occurs
very often in the area of Brački kanal Channel.
In 99.4% cases significant wave height was lower
than 1 m, while in 99.9% it was lower than 2 m.
Density spectrum of energy and direction of
surface waves for episode on 3 December 2007, when
maximum wave height was recorded, is shown in
Figure 4. Maximum density spectrum of energy
S(f)=0.29 m
2
/Hz corresponds to wave period of 3.45 s,
or frequency of 0.29 Hz matching the significant wave
height H
1/3=0.69 m. The figure also shows the
dispersion spectrum of wave directions by
frequencies in a half-hour record, demonstrating that
the predominant wave direction was SE.
Figure 3. Maximum and significant wave heights measured
at V2 station from 1 November 2007 to 20 June 2008.
Figure 4. Density spectrum of energy and direction of
surface waves on 3 December 2007, station V2.
Rose of significant wave heights H1/3 is shown in
Figure 5. Waves from ESE and SE directions are the
most frequent, while the frequency of calm is also
significant (31.7%).
Table 1. Monthly maximum values of wave elements for the
period extending from November 2007 to June 2008 in the
sea area of waverider station V2 (*28 December 2007; 25-
31January 2008; 17-19 March 2008; 10-21 April 2008; 06-08
May 2008 are missing).
_______________________________________________
Month/Year Hmax H1/10 H1/3 Hmax/ H1/3 Prevailing
2007/2008 (m) (m) (m) wave
direction
_______________________________________________
November 1.91 1.14 0.92 2,08 ESE
December* 2.84 1.16 0.92 3,09 SE
January* 1.85 1.19 0.96 1,93 ENE
February 1.86 0.80 0.64 2,91 ESE
March* 2.51 1.69 1.35 1,96 NE
April* 2.48 1.50 1.19 2,08 NNE
May* 1.59 0.93 0.72 2,21 SE
June 2.07 1.27 1.01 2,05 NNE
_______________________________________________
Figure 5. Rose of significant wave heights H1/3 at station V2
from 01 November 2007 to 20 June 2008.
3.2 Results of numerical modelling
Wind speed time series and the wind rose, obtained
from the Aladin-CRO model, at the position of the
waverider V2 for the time interval from 1 November
2007 to 19 June 2008 is shown in Figure 6.
195
Figure 6. Wind rose (left) and wind speed time series (right) for the period 1/11/2007 - 19/6/2008, obtained from the results of
Aladin-CRO model at the waverider station V2.
Figure 7 shows a comparison of the measured and
modelled significant wave height time series for the
waverider station V2. Model verification was
performed by calculating the following statistical
parameters: root mean squared error RMSE=0.14 m,
mean absolute error MAE=0.10 m and relative
absolute error RAE=0.75 (e.g. Komen et al., 1994). It
can generally be concluded that the modelled
significant wave values are very well matched with
the measured values. In situations where a sudden
increase of significant wave heights occurred, because
of the strengthening of the wind, the model also
simulated an increase of significant wave heights, but
in some situations with extremely rapid changes (e.g.
23 January and 6 March 2008) the model significantly
underestimated the measured values of significant
wave height. It could be explained that numerical
model Mike 21/SW was forced by the Aladin –CRO
model which has a prognostic character and usually
does not forecast extreme wind speed and direction
changes.
Figure 7. Comparison of the measured (waverider) and
modelled (Mike 21/SW) significant wave height H
s time
series for the waverider station V2.
Considering that the resulting wind speed and
direction fields are derived from the Aladin –CRO
model which has a prognostic character (the results
are pre +12 h), they need to be critically analysed. By
comparison of the resulting wind directions obtained
by the Aladin-CRO model at the position of the
waverider station (Fig. 6) with registered directions of
waves on the waverider station V2 (Fig. 5), there can
be seen a significant difference in the frequency for
the wind and wave directions NE-ENE and ESE-SE. It
must be pointed out that waverider station V2 is
located about 1.4 km from the coast, where waves
generated by Sirocco and Bora are channeled in E-ESE
direction in relation to topographic configuration of
Brački Kanal Channel.
Therefore a set of time intervals (situations) of
interest for further analysis is obtained (Tab. 2). It
should be noted that from the overall interval of
monitoring (1/11/2007 - 19/6/2008) only time intervals
in which wind speeds exceeding 5 m/s continuously
appear and when the results of wind directions from
the Aladin-CRO model coincide with measured
directions of wave propagation at the waverider site
V2 were exempted and analysed. This analysis does
not include situations with wind speeds exceeding 5
m/s continuously and changes of wind direction.
The values of the ratio between measured and
modelled H
s, for situations enumerated in Table 2, are
given in Figure 8. The ratio has values around 1 for all
analysed situations except those with the Sirocco
(situations 11, 12 and 13 in May and June 2008) when
model significantly underestimated measured wave
values (Fig. 7).
This confirms the fact that the numerical model
interprets the state of the wave climate with a degree
of reliability that corresponds to the reliability of
prognostic data on wind speed from the Aladin
model.
Figure 8. Values of the ratio between measured and
modelled H
s for situations given in Table 2.
196
Table 2. Time intervals (situations) where wind speeds are continuously higher than 5 m/s and when the results of wind
directions from the Aladin-CRO model coincide with measured directions of wave propagation at the waverider site V2.
__________________________________________________________________________________________________
Bora - NE (>5 m/s) Sirocco - SE (>5 m/s) Libeccio - SW (>5 m/s)
__________________________________________________________________________________________________
1 09.11.07. 21h → 10.11.07. 00h 1 22.11.07. 12h → 25.11.07. 03h 1 30.10.07.15h→30.10.07.18h
2 12.11.07. 09h → 12.11.07. 15h 2 07.12.07. 18h → 08.12.07. 15h West Wind - W (>5 m/s)
3 13.12.07. 09h → 14.12.07. 00h 3 04.01.08. 12h → 06.01.07. 00h 1 31.05.08.12h→31.05.08.15h
4 14.12.07. 12h → 14.12.07. 21h 4 11.01.08. 15h → 13.01.08. 21h 2 01.06.08.09h→01.06.08.15h
5 01.01.08. 09h → 01.01.08. 18h 5 15.01.08. 12h → 18.01.08. 00h
6 23.01.08. 14h → 23.01.08. 21h 6 03.02.08. 09h → 05.02.08. 06h
7 07.02.08. 09h → 07.02.08. 24h 7 10.03.08. 09h → 11.03.08. 09h
8 15.02.08. 15h → 16.02.08. 00h 8 16.03.08. 09h → 16.03.08. 21h
9 16.02.08. 21h → 17.02.08. 00h 9 07.04.08. 03h → 07.04.08. 18h
10 05.03.08. 06h → 07.03.08. 09h 10 30.04.08. 21h → 01.05.08. 12h
11 17.05.08. 03h → 19.05.08. 06h
12 20.05.08. 00h → 21.05.08. 12h
13 16.06.08. 21h → 17.06.08. 21h
__________________________________________________________________________________________________
Figure 9 shows the field of significant wave
heights Hs in the period of wind transition from
Sirocco (23.3.2008., 18:30 hours) to Libeccio. At the
term 18:30 hours SE waves were modelled (Hs≈0.60
m) in the eastern part of the Brački kanal Chanell,
while in front of port of Split model shows S waves
with Hs≈0.90 m. At the term 23.3.2008., 21:30 hours
model reach maximum values of Hs≈0.80 m for SW
waves (generated by Libeccio) on the measurement
station V2.
Figure 9. Significant wave heights Hs fields for 23/3/2008
18:30 hours (above, Sirocco) and 21:30 hours (below,
Libeccio).
4 CONCLUSION
Wind generated surface waves were measured at V2
station in the Brački Kanal Channel area, in front of
the port of Split in the time interval from November
2007 to June 2008. These measurements represent the
first systematic wave research in front of one of the
most important Croatian ports.
Maximum wave height of 2.84 m was measured on
3 December 2007, during strong Sirocco (SE) wind.
Significant wave height during this record was 0.92
m. Maximum significant wave height of 1.35 m was
measured on 6 March 2008, during strong Bora (NE)
wind. Relation between maximum wave height and
significant wave height was H
max=1,91 H1/3, but in
extreme situations ratios between H
max and H1/3 were
significantly different from this relation, probably due
to the rapid change of the Scirocco and Bora winds (or
Libeccio) that occurs very often in the area of Brački
Kanal Channel.
Density spectrum of energy and direction of
surface waves on 3 December 2007, when maximum
wave height of 2.84 m was measured indicated wave
period of 3.45 s and predominat SE wave direction.
For the overall interval of wave measurements,
waves from ESE and SE directions were the most
frequent, while the frequency of calm was also
significant (31.7%). In 99.4% cases significant wave
height was lower than 1 m, while in 99.9% it was
lower than 2 m.
Instrumental measurements of wind generated
waves show that absolute maximum of wave
height in the Adriatic Sea H
max=10.8 m was measured
in the open North Adriatic and extreme expected
value of wave height in the Adriatic is about 14 m
(Leder et al., 1998). Maximum waves greater than 8 m
have been recorded in the open sea area of the Middle
and South Adriatic (Leder, 2004). So it can be
concluded that in the semi-enclosed area of the Brački
Kanal Channel, where dimensions of fetch are
considerably smaller, the occurrence of such large
waves is impossible. Generally, it can also be
concluded that length of fetch is the major limiting
factor in the sea state development in the Adriatic Sea.
Numerical modelling of wave generation in the
local waters of the Brački Kanal Channel was
undertaken using Mike 21/SW numerical model.
Wind field used for the forcing in numerical
simulations relies on the results of the prognostic
atmospheric model Aladin-CRO. Comparison of the
measured (waverider) and modelled (Mike 21/SW)
significant wave height Hs time series for the
waverider station V2 in front of the port of Split has
revealed that the modelled wave values are very well
matched with the measured values. In situations
where a sudden increase of significant wave heights
occurred, because of the strengthening of the wind,
the model also simulated an increase of significant
wave heights, but in some situations with extremely
rapid changes the model significantly underestimated
the measured values of significant wave height. It
could be explained that numerical model Mike 21/SW
197
was forced by the Aladin-CRO model which has a
prognostic character and usually does not forecast
extreme wind speed and direction changes.
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https://portsplit.hr/en/
