Content uploaded by Caroline Paugam
All content in this area was uploaded by Caroline Paugam on Jul 28, 2021
Content may be subject to copyright.
Wind tides and surface friction coeﬃcient in semi-enclosed shallow
Caroline Paugama, Damien Sousa,b, Vincent Reya, Samuel Meuléc, Vincent Faured, Olivier
Boutrone, Emilie Luna-Laurente, Emmanuelle Mignef
aUniversité de Toulon, Aix-Marseil le Université, CNRS/INSU, IRD, Mediterranean Institute of Oceanography5
(MIO), UM 110, Toulon, France
bUniversité de Pau et des Pays de l’Adour - E2S UPPA, SIAME - MIRA, Anglet, France
cAix Marseille Univ, CNRS, IRD, INRAE, Coll France, CEREGE, Aix-en-Provence, France
dGIPREB Syndicat Mixte, Berre l’étang, France
eTour-du-Valat, Arles, France10
fSociété Nationale de Protection de la Nature (S.N.P.N.), Réserve Naturelle Nationale de Camargue, La
Capelière, Arles, France
The present paper is speciﬁcally focused on enclosed or semi-enclosed basins where the wind is
the dominant driver of water surface tilting, leading to the so-called wind tide contributing to15
water levels rise. Wind-induced free surface tilting is studied using the 1-D steady form of the
depth-averaged shallow water (Saint-Venant) momentum equation which reﬂects the depth-averaged
local balance between surface slope and wind stress. Two contrasted ﬁeld sites, the Berre and
Vaccarès lagoons, have been monitored providing water level data along a reference axis. This study
highlighted the occurence of wind tides at the two ﬁeld sites. The bimodal wind exposure ensured20
the robustness of the observations, with non-linear but symmetric behaviors patterns observed in
winds from opposite directions. It is observed that the higher the wind speed, the steeper the slope
of the free surface in accordance with the well known basic trend. In addition, a signiﬁcant eﬀect of
depth is observed, with greater surface tilting in the shallower lagoon. The data analysis conﬁrmed
the robustness of such a simple approach in the present context. Using the additional assumption of25
constant, i.e. wind-independent, drag coeﬃcients (CD) allowed a good match with the observations
for moderate wind speeds for both sites. However, the depth eﬀect required the CDto be increased
in the shallower basin. Classical empirical wind-dependent CDparameterizations provide better
wind-tide predictions than the constant-CDapproach in very strong wind conditions but totally
failed in predicting surface tilting in the shallower site, suggesting that physical parameters other30
than wind speed should be taken into account for the CDparameterization in very shallow lagoons.
Keywords: wind tide, coastal lagoon, shallow water, wind stress, drag coeﬃcient
Preprint submitted to Elsevier May 19, 2021
Coastal lagoons are complex systems, with high ecological and socio-economical stakes. Un-
derstanding the dynamics of water level in coastal lagoons is of primary interest for neighbouring35
infrastructures, inhabited and cultivated areas. When widely connected to the open sea, the lagoon
water levels are inﬂuenced by large scale variations of oﬀshore level, such as astronomical tides or
surges driven by low pressure and/or wind systems. An important process is associated to the direct
eﬀect of wind on the lagoon surface. The wind stress applied on the lagoon water surface induces
a tilting of the whole water body, leading to the so-called wind tide. This eﬀect can be important40
in many coastal lagoons which are often shallow and partially-enclosed basins and therefore may
contribute to ﬂooding of low-lying areas. The present paper is speciﬁcally dedicated to improve our
physical understanding of wind tides in enclosed or semi-enclosed basins where the wind is generally
the dominant driver of water surface tilting.
A series of studies have been carried out to quantify, understand and model wind tides in the45
ﬁeld. Among them, we can cite Kenney (1979) in Lake Winnipeg in Canada , Hellström (1941);
Platzman (1963); Keulegan (1953); Gillies (1959) in Lake Erie in Canada and the United-States,
Farrer (1957); Kivisild (1954); Saville (1952) in Lake Okeechobee in the United-States, Harris (1957);
Platzman (1965); Hugues (1965) in Lake Michigan in the United-States, Nomitsu (1935); Hayami
et al. (1996) in Lake Biwa in Japan, Nomitsu (1935) in Lake Kariba in Zambia and Zimbabwe,50
De Lauro et al. (2018) in Venice lagoon in Italy or Metler et al. (1975) in Lake Balaton in Hungary.
In order to provide estimates of the observed wind tide in relation to wind and basin features, some
well-documented examples using in-situ and modelled data are summarized in table 1. A wide
range of values is observed between the diﬀerent sites, related to diﬀerences in basin dimensions,
wind speed and other local features. Berre and Vaccarès lagoons in France have been selected in55
the present research work to speciﬁcally characterize wind tides in shallow water basins. It can
be brought to attention that, for any motion at the basin scale such as the wind tide, most of
coastal lagoons can be considered as shallow, i.e. where the typical horizontal length scale (wind
tide wave length) is very large compared to the mean depth. The main dynamics can therefore be
represented by the classical shallow water depth-averaged equations. An additional issue related60
to the shallowness is to assess the depth eﬀect on the wind-wave development, which should in
turn aﬀect the sea state, the surface drag and therefore the wind tide amplitude. To address this
issue, the two sites (the Berre and Vaccarès lagoons) have similar wind exposure but diﬀerent
levels of shallowness, allowing us to test the validity of surface drag parameterization developed in
deep environments and to identify a potential depth-eﬀect on surface drag and wind tide. First65
estimations of wind tide in Berre and Vaccarès lagoons presented in table 1 have been inferred
from existing numerical modelling studies, non speciﬁcally devoted to wind tide and water tilting
processes (Leredde et al., 2002; Alekseenko, 2013; Boutron et al., 2015).
A ﬁrst theoretical prediction of wind-induced mean water level variations in shallow basin can
be obtained by using the 1-D steady form of the depth-averaged shallow water (Saint-Venant)70
momentum equation (equation 1) (Hellström, 1941). This equation reﬂects the depth-averaged
local balance between surface slope and wind stress.
Lake Erie, Canada,
390 65 18 26.5 4 1 In-situ
58 47 3 30 4.5 7.8 In-situ
494 190 85 28 1.7 0.3 In-situ
Lake Kariba, Zam-
(Ward Peter (1979))
220 40 31 4.5 0.06 0.03 In-situ
Lake Biwa, Japan
(Hayami et al.
64 23 40 20 0.3 0.5 In-situ
Venice lagoon, Italy
(De Lauro et al.
45 5 10.5 16 0.1 0.4 In-situ
Berre lagoon, France
(Leredde et al.
18.7 7 6.9 17 0.2 1.1 Modelled
Berre lagoon, France
(Alekseenko (2013)) 18.7 7 6.9 22 0.23 1.2 Modelled
et al. (2015))
7.2 5 1.8 7.6 0.1 1.4 Modelled
Table 1: Examples of studies on wind tides in enclosed and semi-enclosed basins
Where ζis the free surface elevation (m), xis the spatial component in the wind direction (m),
hthe average water depth (m), ρwthe water density (kg.m−3) and gthe acceleration of gravity
(m.s−2). The wind stress τ(N.m−2) is generally inferred from a quadratic drag law (equation 2).75
where CDis the dimensionless surface drag coeﬃcient, ρathe air density (kg.m−3) and Veis
the x-component of the wind 10 meters above sea level (m.s−1).
Equation 1 shows that wind tide, i.e. the wind-induced variation of mean water level, is expected
to increase with increasing basin length, increasing wind speed and decreasing water depth. A
common simpliﬁcation is to assume a spatially-uniform wind over the considered basin, leading to a80
constant stress for a uniform bathymetry. The water surface is consequently linear with a constant
slope S (equation 3).
Where Lis the basin length (m) in the wind direction i.e. the fetch and ∆ζthe surface tilting
Following this approach, which will be adopted in the following analysis, only two measurement85
points are required to characterize the surface tilting and to analyse its dependency on wind features
and basin parameters. The validity of such simple conceptual framework in real cases will be
discussed later on.
A key parameter in equation 1 is the surface drag coeﬃcient CDwhich integrates a wide range
of small-scale processes related to wave development, surface roughness and atmospheric boundary90
layer stability into a single bulk quantiﬁcation of the energy transfer from the wind to the water
mass. CDcan be inferred from macroscopic estimation of the momentum relating the wind and
the surface tilting (equation 1) or obtained by local measurements of the turbulent stress. A
typical order of magnitude for CDis 1.2.10−3(Pugh and Woodworth, 2014) but it is known to
be aﬀected by a number of processes and the deﬁnition of an universal parameterization remains95
an active challenge. The main trend is that CDincreases with surface roughness which increases
with wind speed due to wave development (Powell et al., 2003). Various empirical wind-dependent
formulations have been proposed for CD(Wu, 1969, 1980; Garratt, 1977; Babanin and Makin,
2008). A decrease in CDfor extreme wind speed (higher than 33 m.s−1) was found because the sea
surface roughness becomes saturated Powell et al. (2003). These formulations all assume that the100
drag coeﬃcient is constant in space, i.e. that the length scale for surface roughness development
is negligible compared to the basin scale. Moreover, the depth eﬀect is also neglected, which
presupposes that the surface roughness in not aﬀected by depth.
Most of the wind tide studies and CDparameterizations have been carried out in large scale
and/or deep basins. Despite their ubiquity and socio-ecological importance worldwide, smaller scale105
shallow lagoons remain sparsely documented. The question arises of the validity of the common CD
parameterization and related theoretical estimation of wind tide through equation 1 in the context
of shallow lagoons. In order to address this issue with generalizable observations, the present
study is based on the comparative analysis of long-term water level data in two semi-enclosed
basins geographically close and exposed to similar wind conditions but with diﬀerent morphological110
conﬁgurations. Field sites and methods are presented in Section 2. In-situ data are presented
and compared with existing formulations in Section 3, while the processes involved and the overall
validity of the theoretical framework are discussed in Section 4.
2. Field experiments
2.1. Field sites115
The Berre and Vaccarès lagoons (ﬁgure 1) are shallow coastal lagoons located in the eastern
part of the Gulf of Lion, on the Mediterranean coast of France. This region is characterized by
intense and frequent wind events. The dominant wind forcing is from N to NW with strong winds
associated with an anticyclonic regime and canalized through the Rhône and Aude valleys (Mistral
and Tramontane). The region is also exposed to wind from nearly opposite directions, coming from120
east/south-east, during low pressure and wet conditions. In both regimes, mean speed during wind
events ranges between 11 and 14 m/s, with maxima over 20 m/s (Ullmann, 2008). This bimodal and
strong wind exposure makes this area a well-suited environment for studying wind-driven processes.
In the present study, the Berre and Vaccarès lagoons have been monitored to understand the
eﬀect of morphology, depth and wind exposure on the mean water level dynamics. Both sites are125
exposed to the same synoptic wind patterns with local adaptations but show diﬀerences in terms
of size and depth : Vaccarès lagoon is shorter, wider and shallower than Berre lagoon, enabling us
to study the depth-eﬀect on the response to wind events. Main morphological characteristics of the
study sites are summarized in table 1 and depicted in ﬁgures 1.b and 1.c . Numerical studies have
been recently carried out to describe water mass circulation at both sites, mainly for water quality130
issues (Boutron et al., 2015; Alekseenko, 2013). These studies provides ﬁrst estimates of the surface
tilting for selected wind conditions using common wind stress parameterization but dedicated long-
term in-situ documentation was still required to properly assess the wind tide development over a
wide range of wind conditions.
Figure 1: Maps of ﬁeld sites in south-eastern France (1.a), Vaccarès (1.b) and Berre (1.c) lagoons, bed elevation in
NGF referential (oﬃcial levelling network in metropolitan France).
Berre lagoon is situated in an urbanized and industrial area and ﬂooding is a major problem.135
Moreover, the EDF hydroelectric plant at Saint-Chamas sporadically discharges large quantities of
fresh water and silt into Berre lagoon at high volumes, up to more than once the volume of the
lagoon per year. Berre lagoon can be classiﬁed as a choked coastal lagoon (Mahapatro et al., 2013)
with a restricted communication with the sea via the Caronte channel, a channel with a maximum
width of about 200 meters, 6 km long and with a bathymetry between 7 and 10 m., see ﬁgure 1.c140
and further details in Section 2.2.2.
Vaccarès lagoon is located in the national nature reserve of the Camargue and is therefore
preserved and not urbanized. The communication with the sea is more complex than in Berre
lagoon because Vaccarès lagoon communicates mainly with the Impériaux system and also with
Lion/Dame lagoons according to Boutron et al. (2015) (ﬁgure 1.b). Communication with the sea of145
the entire hydrosystem is controlled at Saintes-Marie-de-la-Mer (SMM) by 13 manual sluice gates
of relatively moderate size (1 to 1.2 m), see Section 2.2.2 for additional information.
2.2. Data and instrumentation
2.2.1. Wind data
Wind data for Berre lagoon were provided from March 2019 to August 2020 by three-hourly150
wind measurements at the Marignane meteorological station (Météo-France), see ﬁgure 1.c. These
observational data are obtained from the international surface observation messages (SYNOP) cir-
culating on the global telecommunication system (GTS) of the World Meteorological Organization
(WMO). Wind data for Vaccarès lagoon were provided from July 2019 to August 2020 by hourly
wind measurements at the Tour-du-Valat station (Météo-France), see ﬁgure 1.b. For both wind155
data sources, the average wind speed data are the average over the last 10 minutes before the
selected time with a sampling period of 1 minute. In addition, these meteorological stations also
provide gust velocity data deﬁned as extreme speed values over a period of 1 minute measured
over the previous 10 minutes. Due to the proximity and the absence of signiﬁcant local reliefs be-
tween measurement stations and measurement sites, the recovered wind data at Tour-du-Valat and160
Marignane stations are considered very representative of the wind forcing encountered at Vaccarès
and Berre lagoons, respectively. Finally, at Berre, the three-hourly wind measurements are directly
synchronized with our three-hourly water level measurements described below while at Vaccarès
the hourly wind data are further averaged over three hours to get the synchronicity.
Wind statistics during both measurement campaigns are depicted in ﬁgure 2. Two dominant165
wind regimes are observed: NW or NNW winds (mistral) and SE winds. Strong wind conditions
can be observed at both studied sites with wind speeds that can be higher than 20 m/s.
The mistral is generally more western and faster at Berre lagoon (Marignane station) than at
the Vaccarès lagoon (Tour-du-Valat station). This diﬀerence is explained by the location of the
Marignane station, about 60 km to the east of Tour-du-Valat station and therefore closer to the170
mouth of the Rhône valley through which the mistral is channeled (Jacq et al., 2005; Obermann-
Hellhund and Ahrens, 2018).
2.2.2. Water level data
Water level in Vaccarès lagoon was monitored at two distinct stations from July 2019 to August175
2020. The measurements were carried out by two pairs of piezometers (Keller DCX-22AA) deployed
in the north-west (VACC_NO station) and the south-east (VACC_SE station) parts of the lagoon
to provide long-term pressure and temperature measurements both in the air and in the water.
Station locations depicted in ﬁgure 1.b were determined based on prevailing wind conditions but
Figure 2: Wind roses for Vaccarès (Tour-du-Valat station, hourly data over 13 months) and Berre (Marignane station,
tree-hourly data over 17 months) lagoons. Wind roses show the the occurrence of wind directions as well as their
speeds for both sites : in Vaccarès lagoon main wind directions are NNW and SE up to 20 m/s, and in Berre lagoon,
NW winds over 20 m/s and SE up to 20 m/s.
constrained by the shallow bathymetry and private properties that prevented direct access to the180
shoreline. Sampling period at both station is 10 min.
Water level data in Berre lagoon are provided by HTM-NET network (https://htmnet.mio.osupytheas.fr),
a network of instruments providing long term air and water pressure and temperature measure-
ments along the French south-east Mediterranean coast (Rey et al., 2020). The data used for the
present study was recorded from March 2019 to August 2020 with a similar setup as for Vaccarès,185
i.e. two pairs of piezometers (Keller PAA-36Xiw CTD). The two Berre lagoon stations were located
at Saint-Chamas and Le Jaï harbours (see ﬁgure 1.c), i.e. roughly in the dominant wind axis, to
provide pressure and temperature data every 2 minutes.
For both sites, stations were repeatedly positioned using a RTK DGPS and the processing was
carried out using the Bernesse GNSS Software (Dach et al., 2015) with data from the permanent190
Geodesic Network (RGP) of IGN. The vertical positioning uncertainty is estimated at approximately
Measurement station information for Vaccarès and Berre lagoons is summarized in table 2.
Berre Le Jaï 877723.4 6262302.3 2 2019-03-22 2020-08-28
Saint-Chamas 863587.3 6274333.3 2 2019-03-22 2020-08-28
Vaccarès VACC_NO 824113.3 6274390.3 10 2019-07-09 2020-08-25
VACC_SE 830229.5 6270643.0 10 2019-07-09 2020-08-25
Table 2: Stations information in Berre and Vaccarès lagoons: names, locations and data acquisition parameters
Water level calculation
The pressure diﬀerence between air and water oﬀers the means to determine the water level195
variation, based on the assumption of hydrostatic pressure (equation 4):
with ∆P=Pwater −Pair the local pressure diﬀerence.
The sea water density is calculated using the UNESCO seawater equation of state (UNESCO,
1979), using measured temperature and constant salinity (37.5 PSU). Considering the natural
variability of lagoon salinity (15 to 45 PSU), this implies a water level computational bias lower200
than 0.2 cm, which corresponds to the precision of the pressure measurements (Rey et al., 2020).
Apart from the wind, the water levels at the two sites are aﬀected by diﬀerent forcings.
In Berre lagoon, water level variations of the Mediterranean sea are transmitted through the
Caronte channel. Large-scale sea level ﬂuctuations due to atmospheric pressure systems are slow205
enough to be fully and uniformly transmitted within the Berre lagoon. At a smaller time-scale, the
micro-tidal oscillations of the open sea level are observed to propagate within the lagoon. A typical
tidal range of 20 cm is attenuated through the canal and is approximately equal to 5 cm within
the lagoon. A tidal phase shift of 40 min is observed between the two stations and the result is
a water level variation of 0.4 cm between the stations at a given time. Seiching oscillations have210
been observed at the Berre lagoon: the seiching period along the NW-SE axis is approximately 100
minutes and has a maximum amplitude of 8 cm (Paugam et al., 2020). The EDF hydroelectric
power station released few liquid inﬂows during the study period, these discharges have a uniform
impact on water level throughout the lagoon.
In Vaccarès lagoon, no tidal signal is observed within the lagoon due to very restricted SMM215
ﬂoodgates system and intermittent communication between the lagoon hydrosystem and the open
sea. However, the lagoon water level can show signiﬁcant variations due to several processes.
Most importantly, the mean water level at Vaccarès is strongly controlled by evaporation and
precipitation. It is estimated on the basis of historical data that the average annual precipitation
is in the order of 600 mm/yr and the average annual evaporation 1500 mm/yr. The mean water220
level in the hydrosystem is also impacted by human interventions.
•The SMM ﬂoodgates system is used to control the salinity of the hydrosystem and to en-
hance biological exchanges. The degree of communication depends on the number of opened
valves (up to 13) and on the opening duration which are empirically deﬁned and not properly
monitored. Overall, the exchanged ﬂuxes being small and attenuated by the Imperial and225
Lion/Dame systems, the inﬂuence on the Vaccarès lagoon water level is slow and limited.
•Discharges of water from agricultural channels can also impact the lagoon level. No proper
monitoring is available, but the inﬂows involved are small compared to the lagoon volume.
Each of the factors listed here can aﬀect the Vaccarès lagoon water level, but the mass ﬂuxes
involved are low enough to drive a uniform action throughout the lagoon, i.e. they will not aﬀect230
the 3h-averaged free surface slope calculation described below.
Water level measurement uncertainties
Here are summarized the diﬀerent sources of errors regarding water level determination:
•Pressure transducer error: 0.2 cm;
•The use of a constant salinity for sea water density calculation: 0.2 cm;235
•Tidal time shift in Berre lagoon between the two stations: 0.4 cm;
•Vertical positioning: 2 cm.
Considering the measurement and calculation biases mentioned above, the maximum error is
approximately 2.8 cm in Berre lagoon and 2.4 cm in Vaccarès lagoon.
2.3. Data processing240
To study the free surface tilting, the 3h-averaged water levels ζat the south-east station (ζSE )
and the north-west station (ζNW ) are used for both sites. The 3hrs averaging time window was
chosen as a compromise to be small enough to resolve the typical time scale of well-established wind
events but long enough to remove the water level variations caused by seiching.
Wind tides are studied at both sites using the same method. The free surface tilting ∆ζis245
deﬁned as the diﬀerence between ζSE and ζN W :
∆ζ=ζSE −ζN W (5)
The sign convention is therefore that if the north-west water level is lower than the south-east
level, the free surface tilting will be positive which correspond to NW (mistral) wind events.
Assuming that both wind forcing and bathymetry are spatially uniform, the deformation of the
free surface is assimilated to a linear slope S, simply calculated in practice using the water level250
diﬀerence ∆ζbetween two distinct measurement points separated by a distance L(equation 7).
The slope of the free surface is dimensionless but, for the sake of simplicity, it will be expressed in
the following in cm (vertical) per km (horizontal). The distance Lis deﬁned along given reference
axes (ﬁgure 3). In Vaccarès lagoon, the reference axis directly corresponds to the straight line
between the 2 stations (ﬁgure 3.a), oriented at 123°True North: LV accar ès= 7.2km. In Berre255
lagoon, the reference axis follows the long axis of the basin oriented at 140°(ﬁgure 3.b). The
distance Lis therefore calculated between the orthogonally-projected locations of Saint-Chamas
and Le Jaï stations on the reference axis: LBerr e = 18.7km.
Following Keulegan (1953) and Gillies (1959), the eﬀective wind speed Ve, i.e. the projected
wind component on the reference axis, is computed as follows260
with V the raw wind speed and θthe angle between the wind direction and the reference axis.
Veis therefore positive in case of NW wind and negative for SE winds (ﬁgure 3).
The simplest approach used in the following analysis is to consider a constant CDvalue at each
site. It can be deduced combining equations 3 and 1 with the quadratic drag law of equation 2, a
simple linear dependence is obtained between Sand V2
Figure 3: Determination of the eﬀective wind speed Veby projecting the wind component along Vaccarès (3.a) and
Berre (3.b) lagoons reference axis
where the surface drag coeﬃcient CDcan be inferred from the αregression coeﬃcient as follows
As mentioned in section 2.2.2, the mean water depth his assumed to be spatially-uniform but
may vary with time under the inﬂuence of a range of forcings. The spatial-uniformity assumption
(i.e. assuming a ﬂat horizontal bed) induces error in the CDdetermination lower than 2% compared
to the calculations performed assuming a linear sloping bed with the typical slopes for the two270
sites. The bottom elevation is deﬁned as the averaged elevation along the transect throughout
the reference axis of the lagoon. The time-varying water depth his obtained, for each 3h-burst,
by subtracting the ﬁxed bed elevation from the spatially-averaged but time-varying free surface
elevation < ζ >=ζSE +ζN W
3.1. Field conditions
Figures 4 and 5 show the time-evolution of the 3-hour average water levels of the two stations
and associated wind speeds and wind directions at Marignane station and Tour-du-Valat station for
Berre and Vaccarès lagoons respectively. A NW wind event is detailed on these ﬁgures for the two
sites. Water level data from Carro station outside of Berre lagoon provided by HTM-NET network280
is also presented in ﬁgure 4, the station is located 1n ﬁgure 1.c. The span of the experiments ensured
to cover a wide range of conditions at both lagoons, with several strong wind events in both main
directions (NW and SE).
Fluctuations of the mean water level at the two sites shown in ﬁgures 4 and 5 suggest that
in Vaccarès, the mean water level follows a seasonal trend, with higher/lower levels during win-285
ter/summer seasons. These seasonal ﬂuctuations have been driven by the combination of various
mechanisms described previously, but are not directly related to the wind forcing. Mean water
level ﬂuctuations are also observed in Berre lagoon but, in contrast with Vaccarès, the Berre lagoon
water level is aﬀected by day to week-scale ﬂuctuations of the open sea level transmitted through
the Caronte channel. The semi-diurnal tidal oscillations are attenuated of about 75%. Longer290
water level ﬂuctuations at Carro related to synoptic meteorological wind-pressure systems are also
transmitted in the lagoon.
Recorded water level data near the lagoon boundaries reveal the expected wind tide dynamics:
northwestern/southeastern water levels are lower during NW/SE wind conditions. The magnitude
in water level diﬀerence between the stations increases with the wind speed.295
Figure 4: Water levels (NGF referential) and wind data in Berre lagoon and Carro station from October 2019 to
December 2019. Note that the complete dataset cover a longer period from March 2019 to August 2020. The right
plots represent a 5-days mistral event.
3.2. Wind tides analysis
Figure 6 depicts the dependency of the surface slopes on eﬀective wind speed for the two sites.
The wind speed ranges are not perfectly symmetric at Berre, with stronger wind events being
observed in NW wind conditions. The direct relationship between wind forcing and surface slope
osberved in ﬁgure 6 conﬁrms that the wind is a major driver of mean surface slope in both systems.300
In weak wind conditions, slopes of the free surface are very low. Increase of wind speed induces a
non-linear increase in the slope. For the same winds, the slope is higher in Vaccarès lagoon due
to the shallower depth. Maximum values recorded for the two sites are summarized in table 3.
Maximum observed slopes are 3.5 cm/km corresponding to a surge of 13 cm in Vaccarès lagoon
and 2.2 cm/km corresponding to a surge of 20 cm in Berre lagoon. The slope development appears305
symmetric in case of NW or SE wind events: for a 10 m/s eﬀective wind speed, the slope is
approximately 2 cm/km in Vaccarès lagoon and 0.5 cm/km in Berre lagoon.
Overall, the orders of magnitude of observed slopes are in good agreement with existing mod-
elling studies in the Berre (Leredde et al., 2002) and Vaccarès (Boutron et al., 2015) lagoons (table
1). The observed slope values are generally higher than most of the existing ﬁeld observations310
(table 1), in relation with the shallow depths in Berre and Vaccares lagoon. The only exception is
Figure 5: Water levels (NGF referential) and wind data in Vaccarès lagoon from October 2019 to January 2020.
Note that the complete dataset cover a longer period from July 2019 to August 2020. The right chart represents a
the extreme value measured at Lake Okeechobee (Farrer, 1957) which associated a very long and
shallow basin exposed to violent storm winds.
during S-E wind
Berre lagoon 2.4 20.4 0.8 14.4
Vaccarès lagoon 3.5 11.1 3.6 12.5
Table 3: Maximum surface slopes during NW and SE wind events and associated wind speeds
Figure 7 depicts the relationship between Sand V2
h. For both sites, the overall trend is well
linear, which conﬁrms the validity of the idealized approach assuming spatially uniform wind stress315
and depth. Coeﬃcients of determination are high for both sites: R2
Berre = 0.87 and R2
0.91. Using a linear regression, values of α(equation 7) are determined: αB erre = 2.45 ×10−2and
αV accarès= 3.12 ×10−2. Related surface drag coeﬃcients using equation 8 are CD= 2.01 ×10−3
and CD= 2.56 ×10−3for Berre and Vaccarès lagoons, respectively. The possible causes for such a
diﬀerence in surface drag coeﬃcients are discussed later in Section 4.320
Considering the quality of the linear regression, the idealized constant-CD, i.e. wind-independent,
approach provides rather robust orders of magnitude for wind tide prediction. The CDwind de-
pendency can be assessed by testing three well-known empirical wind-dependent CDformulations
against the present in-situ dataset.
First, Wu (1969) proposed equations 9 and 10 for low (1 m.s−1<V<15m.s−1) and strong325
wind (V > 15 m.s−1), respectively.
Figure 6: Measured surface slopes Sversus eﬀective wind speed Ve, the average is a solid line and the error margins
are dotted lines. Berre and Vaccarès lagoon data are in red and blue dots, respectively.
The second formulation has been proposed by Garratt (1977) from observational data:
CD= (0.75 + 0.067V)×10−3(11)
Thirdly, a study of wind trend and gustiness on sea drag made by Babanin and Makin (2008)
in Lake George, Australia, enabled them to propose formulation 12.
CD= 1.92 ×10−7V3+ 9.6×10−4(12)
Figure 8 and table 4 compare the predictive performances of the constant and three wind-330
dependent CDformulations against the in-situ data. Root mean squared error (RMSE) and index
of agreement (IA) (Willmott (1981)) are used to quantify the prediction errors in table 4
In Berre lagoon, slopes are correctly predicted using a constant CDfor wind speeds below
15 m.s−1but are underestimated for higher wind speeds observed in NW conditions, similarly
to the prediction from Garratt’s wind-dependent formulation (equation 11). Such extreme wind335
conditions are better described by the equation 12 CDformulation, but the latter shows a poorer
prediction of medium winds, resulting in an overall larger error (table 4). The bimodal formu-
Figure 7: Sversus V2
hin Berre (upper chart) and Vaccarès (bottom chart) lagoons. The in-situ data are points, the
linear regressions are lines. R2,αand nare the linear determination coeﬃcient, the linear slope and the number of
lation proposed by Wu (1969) shows intermediate performance. In Vaccarès, each of the three
wind-dependent formulations signiﬁcantly underestimate the wind tide, resulting in much poorer
predictions than the constant CDapproach (table 4). This result highlights the fragility of existing340
empirical wind-dependent formulations of surface drag coeﬃcient, in particular when applied to very
shallow lagoons. The depth-eﬀect is therefore expected to not only directly aﬀect the momentum
balance, but also a range of surface processes aﬀecting the drag.
CDformulation used Error Berre lagoon Vaccarès lagoon
Constant CDRMSE (m) 1.00 ×10−61.97 ×10−6
IA 0.9251 0.9505
Wu (1969) RMSE (m) 1.03 ×10−62.86 ×10−6
IA 0.9167 0.8357
Garratt (1977) RMSE (m) 1.05 ×10−62.99 ×10−6
IA 0.8992 0.8109
Babanin and Makin (2008) RMSE (m) 1.11 ×10−63.24 ×10−6
IA 0.8824 0.7545
Table 4: RMSE and IA of measured and predicted slopes using a constant value of CDand wind-dependent CD
values from the literature in the two studied sites.
Figure 8: Sversus Ve: in-situ data are represented by dots and empirical formulations by solid lines.
The present research work has provided a detailed ﬁeld database on wind-induced free surface345
tilting, the so-called wind tides, in two shallow semi-enclosed basins. The measurements ﬁrst
conﬁrmed the expected main trend: the higher the wind speed, the steeper the free surface slope.
In addition, a signiﬁcant eﬀect of depth is observed, with greater surface tilting in the shallower
lagoon. From these observations, the 1-D steady depth-averaged momentum balance was used
to estimate the surface friction coeﬃcient based on the assumptions of a ﬂat horizontal bed and a350
spatially-uniform wind stress. The data analysis conﬁrmed the robustness of such a simple approach
in the present context. However, the parameterization of the surface drag coeﬃcient remains a
tricky issue. The existing wind-dependent parameterizations provided satisfactory agreement at
the deeper site but showed systematic underestimations of the wind tide at the shallower site. A
simple constant CDprovided slightly better performance, but required to use diﬀerent values for355
diﬀerent depths. These observations suggested that additional physical parameters should be taken
into account for the drag coeﬃcient parameterization in very shallow lagoons. To provide further
insight on the wind tide physics, discussion points are organised in four main topics: the wave ﬁeld,
the sloping bathymetry, the wind unsteadiness and the currents.
4.1. Wave ﬁeld360
The sea state inﬂuence on surface drag has been widely studied, mainly in the context of open
ocean and moderate wind speed. Air-sea interactions are very complex at small scales because
multiple mechanisms aﬀect sea drag simultaneously (Babanin and Makin, 2008). The eﬀect of the
wave ﬁeld structure on surface drag can be accounted for through wave age (Janssen, 1989; Donelan,
1982; Donelan et al., 1993; Uz et al., 2002; Young and Verhagen, 1996; Smith et al., 1992; Babanin365
and Makin, 2008; Kudryavtsev et al., 2014; Stewart, 1974; Oost, 1998; Oost et al., 2002) or wave
steepness parameters (Hsu, 1974; Taylor and Yelland, 2001). Studies have shown that the drag
coeﬃcient value is higher in windy seas, with short and steep waves, than in fully developed seas
associated with longer waves (Young and Verhagen, 1996; Smith et al., 1992; Babanin and Makin,
2008; Kudryavtsev et al., 2014; Uz et al., 2002). This eﬀect should be accounted for in enclosed370
basins, where limited fetch conditions will aﬀect the wind stress: short basins are expected to show
higher wind stress and drag coeﬃcient.
The sea state is also strongly aﬀected by the depth. Similarly to short fetch, a ﬁnite depth will
increase surface drag compared to open ocean by inhibiting the development of long waves (Smith
et al., 1992; Kudryavtsev and Makin, 2004; Babanin and Makin, 2008). In deep water condition,375
the wave age is deﬁned as the ratio between the wind speed and the wave celerity. The celerity
(c) increases with the period (T) of the waves : c= 1.56 ×T. Waves are considered to reach their
maximum period (unlimited fetch) when their speed is approximately equal to the wind speed. By
contrast, waves in shallow water conditions are non-dispersive, i.e. the limit of speed of the waves is
c=√gh regardless of their frequency and therefore waves do not necessarily reach the wind speed.380
This results in a depth-control of the wave ﬁeld favoring shorter waves in shallow water.
Both shorter and shallower basins are therefore associated to shorter wave spectra, expected to
enhance the surface drag. This latter mechanism has been conﬁrmed in laboratory experiments,
where reduction of the short wind-wave spectra caused a decrease of the wind stress by as much as
20-30% at a given wind speed (Uz et al., 2002). Taken together, these observations are in line with385
our observation of a higher drag coeﬃcient for the shallower and shorter lagoon (Vaccarès lagoon).
4.2. Sloping bathymetry
By contrast to most studies performed in unidirectional wind conditions, our sites are exposed
to two opposite wind directions. Such conﬁguration allowed to question the role played by a sloping
bathymetry on the wind tide amplitude, in direct connection with the previous analysis of depth390
Figure 9 depicts CDboxplot diagrams for Vaccarès lagoon. The presented data is focused
on signiﬁcant wind events, with wind speed greater than 5 m.s−1, and separated into NW (left
panel) and SE (right panel) wind directions. For great depths, the surface drag coeﬃcients are
in the same range for both wind directions. By contrast, for low depths (less than 1.5 m), a395
measurable diﬀerence is observed, with CDin SE wind conditions being higher than in NW wind
conditions by about 30 %. While ﬁner data and/or a wave propagation model would be necessary
to provide a comprehensive description of the involved physics, the hypothesis can be raised that,
for a given average depth over the studied transect, the bottom slope may play a role in the
wave development. In SE wind conditions, the depth decreases along the fetch, forcing the wave400
to propagate in shallower conditions, therefore limiting the spectrum development toward lower
frequencies, constraining the propagation speed and ﬁnally resulting in higher surface drag. By
contrast, in NW wind conditions, the depth increases along the fetch, allowing the waves to get
longer and to propagate faster, resulting in a relatively lower surface drag than in the opposite wind
direction. This eﬀect can be assumed to be stronger at the lowest depths where the bottom slope405
induces stronger relative variation of depth along the transect. This explains that the diﬀerence
in CDin opposite wind direction is only observed for the lower recorded depths in ﬁgure 9. It
should be borne in mind that this bottom slope eﬀect on CDstrictly relates to a modiﬁcation of
the wave ﬁeld development while the direct bottom slope eﬀect on the momentum balance remains
very slight in the present context, as discussed in Section 2.3.410
Figure 9: Boxplot of CDversus the water column in Vaccarès lagoon in case of NW wind events (left chart) and
SE wind events (right chart). Red lines represent medians, blue polygons contain 25-75% of the data, dashed line
boundaries contain 10-90% of the data, and red crosses represent extreme points.
4.3. Wind unsteadiness
Wind gusts are generally expected to aﬀect the drag coeﬃcient : high drag coeﬃcients occurs
when conditions are strongly non-stationary (Drennan et al., 1999; Babanin and Makin, 2008).
Uz et al. (2002) and Kudryavtsev and Makin (2004) highlighted that when the wind forcing is
modulated in time, the wind stress tends to be higher under decreasing wind than under increasing415
wind at a given wind speed. These processes are mainly related to the delayed response of short
wind-wave spectra to varying wind forcing. In the present study, no eﬀect of wind gusts on the
wind tide were identiﬁed. Further experiments with local and high frequency wind and wave
measurements are required to better understand the surface drag response to wind unsteadiness.
The simpliﬁed depth-averaged momentum balance equation used for the present analysis ignores
the potential eﬀect of currents on wind tide development. In realistic conﬁgurations, the wind stress
at the water surface drives a complex three-dimensional balance between free surface slope related
to barotropic pressure gradients and a variety of horizontal and vertical circulations depending
on the basin morphology and boundary conditions (Csanady, 1973; Orlić et al., 1994), not to425
mention baroclinic eﬀects. In shallow water, the bottom stress can signiﬁcantly contribute to the
momentum balance, with an increasing eﬀect in shallowing depth or rough bed conditions (Tickner,
1957). Keeping our idealized 1D depth-averaged approach, a ﬁrst estimate can be provided by
introducing an additional term for bottom friction τb/ρwgh in equation 1. This term is usually
quadratic: τb=ρwCbU2where Cbis the bottom friction and Uthe current velocity. Typical orders430
of magnitude for Ucan be extracted from the numerical studies performed in Vaccarès (Millet
et al., 2010) and Berre lagoons (Alekseenko et al., 2013). In Vaccarès lagoon, a current of 0.08
m/s was predicted during a 8 m/s NW wind event while for Berre lagoon, a 20 m/s NW wind
event led to a mean current of 0.12 m/s. Considering a classical value for bottom friction of 0.002
for a smooth sandy bottom (Hsiao S. V. and Shemdin O. H., 1978), the bottom friction term435
is expected to contribute less than 3% of the free surface slope in Vaccarès/Berre lagoons. This
conﬁrms the validity of the initial assumption of a negligible eﬀect of current on wind tide in the
present context. A more comprehensive knowledge of the full 3D wind-induced circulation system
will be necessary to assess more precisely the role of bottom friction and circulation patterns on
the wind tide dynamics (De Marchis et al., 2012).440
Wind tides are responsible for water level variations and can lead to damaging ﬂooding in low-
lying areas. The wind eﬀect is greater in semi-enclosed or enclosed basins and further ampliﬁed
at shallow depth. The present study is based on a long-term survey of water levels in two shallow
coastal lagoons located in the eastern part of the Gulf of Lion, France: Berre lagoon and Vaccarès445
lagoon. The two ﬁeld sites were selected owing to their similar wind exposure but diﬀerent mor-
phology and bathymetry. A wide range of wind conditions have been encountered, reaching up to
20 m.s−1. The free surface tilting was studied using two stations deployed along the main axis of
the wind forcing.
The observations showed the expected trend: the higher the wind speed, the steeper the free sur-450
face slope. They also conﬁrmed that, in shallow lagoon, the 1-D steady depth-averaged momentum
balance provides a very satisfactory description of the involved physics. However, the parameter-
ization of the surface drag coeﬃcient CDremains an unresolved issue. Existing wind-dependent
parameterization of CDprovided drastic underestimations of the wind tides, up to a factor three for
our shallower site. These ﬁndings emphasize the need for a better understanding of the depth-eﬀect455
on wave development in ﬁnite depth and consequently on the surface drag coeﬃcient prediction.
By contrast, the role played by wind gustiness and water circulation on the wind tide amplitude
appeared to be negligible compared to wind and depth eﬀects.
Future research work is planned at both sites, with high-resolution high-frequency measure-
ments of water levels and currents with the aim of better understanding the wind tide dynamics.460
Particular attention will be paid on wave ﬁeld development and the related surface drag coeﬃcient
together with the 3D circulation patterns aiming to characterize more ﬁnely their contribution in
the momentum balance in shallow lagoons, in order ﬁnally to improve our ability to predict wind
HTM-NET observational network has received recurrent co-ﬁnancing since 2013 from CNRS/INSU
for the national program SOERE, from ILICO-DYNALIT and also from the Toulon Provence
Méditerranée (TPM) urban community.
Météo-France is thanked for providing the wind data at the Tour-du-Valat and Marignane
The support is aknowledged of the Departmental Council of the Bouches-du-Rhône (CD13) for
station siting permits, SHOM for their collaboration, Tathy Missamou and Jean-Luc Fuda from the
Mediterranean Institute of Oceanography (MIO) for the installation and the maintenance of the
stations, Didier Mallarino from the OSU Pythéas institute for the HTM-NET website maintenance
and Météo-France for meteorological data.475
The Tour-du-Valat foundation and the Camargue National Nature Reserve are acknowledged
for their help in installing and maintaining the Vaccarès lagoon stations.
Alekseenko, E., Jan. 2013. Modélisation numérique de l’hydrodynamique de l’Etang de Berre: Ap-
plication à la recolonisation d’herbiers aquatiques. thesis, Ecole centrale de Marseille, publication480
Title: http://www.theses.fr (in french).
Alekseenko, E., Roux, B., Sukhinov, A., Kotarba, R., Fougere, D., Apr. 2013. Coastal hydrody-
namics in a windy lagoon. Computers & Fluids 77, 24–35.
Babanin, A. V., Makin, V. K., 2008. Eﬀects of wind trend and gustiness on the sea
drag: Lake George study. Journal of Geophysical Research: Oceans 113 (C2), _eprint:
Boutron, O., Bertrand, O., Fiandrino, A., Höhener, P., Sandoz, A., Chérain, Y., Coulet, E., Chau-490
velon, P., Oct. 2015. An Unstructured Numerical Model to Study Wind-Driven Circulation Pat-
terns in a Managed Coastal Mediterranean Wetland: The Vaccarès Lagoon System. Water 7,
Csanady, G. T., Oct. 1973. Wind-Induced Barotropic Motions in Long Lakes. Journal of Physical
Oceanography 3 (4), 429–438.495
Dach, R., Lutz, S., Walser, P., Fridez, P., 2015. Bernese gnss software version 5.2. user manual,
De Lauro, E., De Martino, S., Falanga, M., Riente, M. A., Oct. 2018. Far-ﬁeld synoptic wind eﬀects
extraction from sea-level oscillations: The Venice lagoon case study. Estuarine, Coastal and Shelf
Science 210, 18–25.
De Marchis, M., Ciraolo, G., Nasello, C., Napoli, E., 2012. Wind- and tide-induced currents in the505
Stagnone lagoon(Sicily). Environ Fluid Mech 12, 81–100.
Donelan, M. A., 1982. The dependence of the aerodynamic drag coeﬃcient on wave parameters.
Proc. First Int. Conf. on Meteorol. and Air-Sea Interaction of the Coastal Zone, 381–387Publisher:
Amer. Meteor. Soc.
Donelan, M. A., Dobson, F. W., Smith, S. D., Anderson, R. J., Sep. 1993. On the Dependence
of Sea Surface Roughness on Wave Development. Journal of Physical Oceanography 23 (9),
Drennan, W. M., Graber, H. C., Donelan, M. A., Aug. 1999. Evidence for the Eﬀects of Swell and
Unsteady Winds on Marine Wind Stress. Journal of Physical Oceanography 29 (8), 1853–1864,
publisher: American Meteorological Society.
Farrer, L. A., Jan. 1957. Wind tides on lake Okeechobee. Coastal Engineering Proceedings 1 (6), 7,
Garratt, J. R., Jul. 1977. Review of Drag Coeﬃcients over Oceans and Continents. Monthly Weather
Review 105 (7), 915–929.525
Gillies, D. K., 1959. Winds and water levels on Lake Erie. Roy. Meteorol. Sot. Can. Branch Publ
9 (1), 12–94.
Harris, D. L., 1957. The Eﬀect of a Moving Pressure Disturbance on the Water Level in a Lake.530
In: Redﬁeld, A. C., Miller, A. R., Groves, G. W., Harris, D. L., Reid, R. O., Marks, W.,
Chase, J. (Eds.), Interaction of Sea and Atmosphere: A Group of Contributions. Meteorological
Monographs. American Meteorological Society, Boston, MA, pp. 46–57.
Hayami, Y., Fujiwara, T., Kumagai, M., 1996. Internal Surge in Lake Biwa Induced by Strong535
Winds of a Typhoon. Japanese Journal of Limnology (Rikusuigaku Zasshi) 57 (4-2), 425–444.
Hellström, B. M. ., 1941. Wind eﬀects on lakes and rivers. Vol. Handlingar 158 of
Hsiao S. V., Shemdin O. H., 1978. Bottom Dissipation in Finite-Depth Water Waves. Coastal
Hsu, S. A., Jan. 1974. A Dynamic Roughness Equation and Its Application to Wind Stress
Determination at the Air-Sea Interface. Journal of Physical Oceanography 4 (1), 116–120,
publisher: American Meteorological Society.
Hugues, L. A., 1965. The prediction of surges in the southern basin of lake Michigan. Monthly
Weather Review 93 (5), 292–296.
Jacq, V., Albert, P., Delorme, R., 2005. Le mistral, en 1925 et aujourd’hui : Le mistral - quelques
aspects des connaissances actuelles. La Météorologie 50, 30–38 (in french).550
Janssen, P. A. E. M., Jun. 1989. Wave-Induced Stress and the Drag of Air Flow over Sea Waves.
Journal of Physical Oceanography 19 (6), 745–754, publisher: American Meteorological Society.
Kenney, B. C., 1979. Lake surface ﬂuctuations and the mass ﬂow through the narrows of
Lake Winnipeg. Journal of Geophysical Research: Oceans 84 (C3), 1225–1235, _eprint:
Keulegan, G. H., 1953. Hydrodynamic Eﬀects of Gales on Lake Erie. In: Journal of Research of the560
National Bureau of Standards. Vol. 50. pp. 99–109.
Kivisild, H. R., 1954. Wind eﬀect on shallow bodies of water with special reference to lake Okee-
chobee: Kungliga Tekniska Högskolans handlingar.
Kudryavtsev, V., Chapron, B., Makin, V., 2014. Impact of wind waves on the air-sea ﬂuxes: A
coupled model. Journal of Geophysical Research: Oceans 119 (2), 1217–1236.565
Kudryavtsev, V. N., Makin, V. K., Apr. 2004. Impact of Swell on the Marine Atmospheric
Boundary Layer. Journal of Physical Oceanography 34 (4), 934–949, publisher: American
Leredde, Y., Dekeyser, I., Devenon, J.-L., 2002. T-S Data Assimilation to Optimise Turbulent
Viscosity: An Application to the Berre Lagoon Hydrodynamics. Journal of Coastal Research
18 (3), 555–567.
Mahapatro, D., Panigrahy, R., Panda, S., et al., 2013. Coastal lagoon: present status and future
challenges. International Journal of Marine Science 3.
Metler, W., Bogárdi, I., Duckstein, L., 1975. Eﬀect of wind waves and wind tides on
the optimum control of large lakes. Water Resources Research 11 (3), 397–404, _eprint:
Millet, B., Robert, C., Grillas, P., Coughlan, C., Banas, D., Jan. 2010. Numerical modelling of
vertical suspended solids concentrations and irradiance in a turbid shallow system (Vaccares, Se
France). Hydrobiologia 638 (1), 161–179.
Nomitsu, T., 1935. Surface ﬂuctuations of Lake Biwa caused by the Muroto Typhoon. Mem. Coll.
Sci. Kyoto Imp. Univ., A 18 (5), 221–238.
Obermann-Hellhund, A., Ahrens, B., 2018. Mistral and tramontane simulations with changing
resolution of orography. Atmospheric Science Letters 19 (9), e848.
Oost, W., Komen, G., Jacobs, C., Van Oort, C., Jun. 2002. New evidence for a relation between590
wind stress and wave age from measurements during ASGAMAGE. Boundary-Layer Meteorology
103 (3), 409–438.
Oost, W. A., Mar. 1998. The KNMI HEXMAX stress data – a reanalysis. Boundary-Layer Meteo-
rology 86 (3), 447–468.595
Orlić, M., Kuzmić, M., Pasarić, Z., Jan. 1994. Response of the Adriatic Sea to the bora and sirocco
forcing. Continental Shelf Research 14 (1), 91–116.
Paugam, C., Meulé, S., Sous, D., Faure, V., Rey, V., 2020. Évolutions du niveau d’eau en bassin600
semi-fermé forcées par le niveau de la mer et le vent : exemple de l’étang de Berre. Paralia, Le
Havre (in french).
Platzman, G. W., 1963. The Dynamical Prediction of Wind Tides on Lake Erie. In: Platzman,
G. W. (Ed.), The Dynamical Prediction of Wind Tides on Lake Erie. Meteorological Monographs.
American Meteorological Society, Boston, MA, pp. 1–44.605
Platzman, G. W., 1965. The prediction of surges in the southern basin of lake Michigan. Monthly
Weather Review 93 (5), 275–281.
Powell, M. D., Vickery, P. J., Reinhold, T. A., Mar. 2003. Reduced drag coeﬃcient for high wind
speeds in tropical cyclones. Nature 422 (6929), 279–283.610
Pugh, D. T., Woodworth, P., 2014. Sea-Level Science: Understanding Tides, Surges, Tsunamis and
Mean Sea-Level Changes, cambridge u. press Edition. Vol. 68.
Rey, V., Dufresne, C., Fuda, J.-L., Mallarino, D., Missamou, T., Paugam, C., Rougier, G., Taupier-615
Letage, I., 2020. On the use of long term observation of water level and temperature along
the shore for a better understanding of the dynamics: Example of Toulon area, France. Ocean
Dynamics 70, 913–933.
Saville, T., Jun. 1952. Wind set-up and waves in shallow water. United States, Beach Erosion Board,
Engineer Research and Development Center (U.S.)Accepted: 2016-03-16T15:42:15Z Publisher:620
United States, Beach Erosion Board.
Smith, S., Anderson, R., Oost, W., 1992. Sea surface wind stress and drag coeﬃcients: The hexos
results. Boundary-Layer Meteorol 60, 109–142.
Stewart, R. W., Mar. 1974. The air-sea momentum exchange. Boundary-Layer Meteorology 6 (1),
Taylor, P. K., Yelland, M. J., Feb. 2001. The Dependence of Sea Surface Roughness on the Height
and Steepness of the Waves. Journal of Physical Oceanography 31 (2), 572–590.630
Tickner, E. G., May 1957. Eﬀect of bottom roughness on wind tide in shallow water. This Digital
Resource was created from scans of the Print ResourceAccepted: 2016-03-16T15:42:52Z Publisher:
United States, Beach Erosion Board.635
Ullmann, A., May 2008. Surcotes dans le Golfe du Lion et conditions atmosphériques: variabilité
contemporaine et future (1900-2100). phdthesis, Université de Provence - Aix-Marseille I (in
UNESCO, 1979. Ninth report of the joint panel on oceanographyc tables and standards. Technical
papers in Marine Sciences 30.
Uz, B. M., Donelan, M. A., Hara, T., Bock, E. J., Feb. 2002. Laboratory Studies Of Wind Stress
Over Surface Waves. Boundary-Layer Meteorology 102 (2), 301–331.
Ward Peter, R. B., 1979. Seiches, tides, and wind set-up on Lake
Kariba. Limnology and Oceanography 24 (1), 151–157, _eprint:
Willmott, C. J., Jul. 1981. On the Validation of Models. Physical Geography 2 (2), 184–194, pub-650
lisher: Taylor & Francis _eprint: https://doi.org/10.1080/02723646.1981.10642213.
Wu, J., 1969. Wind stress and surface roughness at air-sea interface. Journal of Geophysical Research
74 (2), 444–455.
Wu, J., May 1980. Wind-Stress coeﬃcients over Sea surface near Neutral Conditions—A Revisit.655
Journal of Physical Oceanography 10 (5), 727–740.
Young, I. R., Verhagen, L. A., Dec. 1996. The growth of fetch limited waves in water of ﬁnite depth.
Part 1. Total energy and peak frequency. Coastal Engineering 29 (1), 47–78.660