Numerical study of the marine breeze around Mallorca Island

Applied Ocean Research 40 (2013) 26–34

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Numerical study of the marine breeze around Mallorca Island ´ * , A. Orfila S. Ponce de Leon IMEDEA (CSIC-UIB), Miquel Marqu´es 21, 07190 Esporles, Balearic Islands, Spain

a r t i c l e

i n f o

Article history: Received 11 September 2012 Received in revised form 27 November 2012 Accepted 16 December 2012 Keywords: Breezes Wind waves Mallorca Island WRF SWAN ENVISAT

a b s t r a c t A study of marine breezes and their impact on the wave field around Mallorca Island was carried out by numerical simulations with the spectral wave model SWAN and three different wind fields: WRF – Weather Research and Forecasting model, HIRLAM – High Resolution Limited Area model and ECMWF – European Center for Medium-range Weather Forecasts. The main characteristics of the modelled breeze circulation and its effects on the wave field are analyzed. The modified wave field under breeze conditions and the correlations with their variability and daily short life time period are studied and discussed by analyzing the spectral balance. The results show that the accuracy of a wave forecast will depend on the quality of the wind field and its ability to simulate the sea breeze induced waves. The study period covers the summers of 2009 and 2010. In addition, to assess the performance of SWAN forced with two different winds the numerically obtained significant wave heights (Hs) are collocated against the ENVISAT-ESA’s Environmental Satellite measurements (GLOBWAVE data) of Hs around the Mallorca Island.  c 2012 Elsevier Ltd. All rights reserved.

1. Introduction Many studies have shown the existence of sea breezes in the coastal regions of mid-latitudes [1–3]. Sea breeze is a wind that develops over land near coastal areas at specific times of a day. The mechanism of generation of these winds is the increase of the temperature differences between the land and sea which creates a pressure minimum over the land (sea) and, consequently, the cooler air from the sea (land) blows inland (outland). Wind velocities associated with the sea breezes may range from 5 up to 10 m/s or more. The study of the breezes is of great importance due to the influence of these winds on the local wave field. Sea breezes induce changes in the incident wave field late morning (or early afternoon), increasing wave height and reducing mean wave period and changing also the wave propagation direction depending on the sea breeze [4]. Additionally, in areas where the sea breeze prevails the effect of these winds on the coastal dynamics can be considerable [5]. In the Mediterranean Sea the major characteristics of sea breeze circulation systems were investigated by Papanastasiou et al. [6] who, applying the WRF model in the coastal zone of Greece, verified the ability of the atmospheric model to simulate adequately the wind field under breezes by calculating several statistical indices. In addition, they pointed out that the WRF simulations described satisfactorily circulation systems such as land and sea breezes.

* Corresponding author. Present address: Centre for Marine Technology and En´ gineering (CENTEC), Instituto Superior Tecnico (IST), Technical University of Lisbon (UTL), Av. Rovisco Pais, 1049-001 Lisbon, Portugal. Tel.: +351 915639891; fax: +351 218474015. ´ E-mail address: [email protected] (S. Ponce de Leon).

c 2012 Elsevier Ltd. All rights reserved. 0141-1187/$ - see front matter  http://dx.doi.org/10.1016/j.apor.2012.12.003

In the Central Mediterranean basin the importance of the sea breezes in Calabria was characterized by Federico et al. [7]. Their study shows that breezes dominate the local circulation and play an important role in the local climate. Marine breezes in the Balearic Islands were studied by [8] who described the sea breeze regime for the Mallorca Island. Later, [9] studied breeze circulation in Mallorca by a non-eulerian numerical model showing that the shape and topography of the Island determine the breeze’s convergence in the centre of the island. Moreover, they indicated how the wind associated with the breeze flow around the Bays of Palma and Alcudia (Fig. 1) and that at the east and west sides of the Island the breezes are weaker than in the bays. The objective of this work is to investigate the effect of the marine breeze on the wave field around Mallorca by performing numerical simulations. A sea state characterization under simulated breeze conditions is given. A quantification of the modelled wave field errors obtained from incomplete wind forcings (poor representation of breezes) is presented and discussed. The study period consists of typical sea breeze conditions corresponding to July and August 2009 and August 2010. The implications of the use of wrong wind field information (omission or poor representation of breezes) for a wave forecast in places where this phenomenon is of relative importance as in the case of Mallorca Island deserve attention for a correct wave forecast. The SWAN model [10,11] is applied for studying the effect of the marine breezes on the wave field around a small island. The wave spectra estimated from observations and simulations in the present study were mainly classified as wind sea (energy between about 0.1 and 4 Hz) that refers to young waves under growth or in equilibrium with local wind. Wind wave with a fetch up to an equilibrium state is

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3. Observations 3.1. Wave buoys

Fig. 1. Bathymetry grid for the SWAN nested grid and the location of the buoys (triangles) and the output SWAN point (cyan circle); B1 – Dragonera (west);B2 – Enderrrocat (Palma Bay); B3 – Alcudia Bay. ENVISAT tracks (blue circles) nearby Mallorca Island during July and August 2009.

of particular importance for the development and verification of wave models. Moreover, a wind-wave-related research seeks an ideal sea state with no swell presence. In this sense, Mallorca Island together with their local sea breezes where the fetch is around 30–40 km is an ideal natural laboratory. This study was performed using the available information around the island of Mallorca. In spite of the large amount of information provided by advanced instrumentation such as satellites, this information has limitations. In this particular study, satellite data near the coast were generally not available or suffered land contamination issues. The ENVISAT Hs measurements were selected because this mission covered the study period. The paper is structured as follows. Section 2 reviews the area of study: Mallorca Island in the Balearic Archipelago. Section 3 deals with the available observations in the area of study and Section 4 describes briefly the wave models and the numerical simulations setup. The marine breeze effect on the modelled wave field around Mallorca is given and discussed in Section 5. Finally, Section 6 concludes the work.

2. Study area Mallorca is the largest of the islands of the Balearic Archipelago, located near the eastern Mediterranean coast of Spain. The topography of the island is mainly characterized by the Tramuntana Mountains in the north-west side (1443 m of maximum height), and smaller mountains in the east and in the centre of the island reaching 500 m of height. Two large bays located to the NE and to the SW also form part of the suitable breeze scenario: Alcudia and Palma Bays (Fig. 1). The Island is roughly square shaped of 65 km oriented SW–NE. The topography of Mallorca determines the main features of the sea breeze such that around the Bay of Palma the wind blows from the south/south-west, where as at Alcudia Bay the breeze blows from the north east (Fig. 1). From April to November and almost day by day during summer, the sea breeze is present [9]. In July and August the weather conditions are often almost the same on a daily basis, being this area an excellent scenario for the study of the sea breeze in small islands and the associated mesoscale phenomena.

In situ measurements by moored buoys were available at two locations (B1 for 2009 and B2 for 2010, Fig. 1) during the study period. The buoys measured hourly significant wave heights (Hs), wave periods (zero crossing (Tm02) and peak period (Tp)) as well as atmospherical variables including wind speed at 3 m of height above the sea level, pressure, etc. Dragonera (B1) is a deep-water buoy (135 m) with a directional wave sensor located 20 km off the coast and operated by the Spanish Harbour Authority (accuracy in wave height <10 cm, direction 0.3◦ and period <2% of the nominal value). This location is less affected by the sheltering effect of Mallorca Island [12] than the other buoys around the island. The second one, Enderrocat (B2) is a shallow water buoy (28 m depth) with an accelerometer, which can measure wave heights between 0 and 5 m and periods of 3–8 seconds with an accuracy of ± 15%. This buoy is 6 km away the coast within the Bay of Palma and is operated by IMEDEA. Both locations are marked with triangles in Fig. 1. At B1, the performance of SWAN using WRF(1.5) was assessed for the summer of 2009 and at B2 by comparing the time series for August 2010 using HIRLAM(18). In addition, a SWAN output grid point (circle B3 in Fig. 1) was used for the analysis of the modelled breezes impact in the North of the Island (in Alcudia Bay). The SWAN spectra and source functions in the breezes summer period are analyzed in B2 (Fig. 1). At this point we want to remark that B2 is a more suitable location for the analysis of the modelled and observed breezes than B1 since this buoy is farther away from the coast and the sea breezes, if observed, are masked with other signals.

3.2. ENVISAT The ENVISAT RA2 altimeter is based on the heritage of the ERS-1 RA altimeter functioning at the main nominal frequency of 13.575 GHz (Ku Band), and also 3.2 GHz (S band) [13]. The altimeter provides point measurements at nadir of the satellite with a data sample frequency of 1 Hz and with a distance of approximately 6–7 km between each measurement along the altimeter track. The return signal to the altimeter covers a small footprint immediately below the satellite. The footprint of the radar is sea state (or wave height) dependent, but is about 19 km in diameter [14]. In order to calculate the significant wave height, the satellite altimeter measures the roughness of the sea. The Hs is derived from the slope of the leading edge of the return signal, which is related to the standard deviation of the height distribution of reflecting facets on the sea surface [14]. The performance of SWAN model using the WRF(1.5) and ECMWF(14) for two months of the summer of 2009 was assessed by spatial and temporal collocation of ENVISAT Hs from the GLOBWAVE data set [15] and wave model Hs following the method described in [16]. GLOBWAVE L2P database employed suitable quality control and calibration of the data streams from the various missions as described in [17]. Only calibrated Hs data flagged as “probably good measurement” were used in the present study. Because the area of the nested grid is small (this is discussed later in Section 4) mainly around Mallorca, there were no more than 60 points for the collocation for the two months July and August 2009. Also because of this, a similar analysis for the August month 2010 was discarded because only 26 satellite points were available for the collocation. Tracks of the ENVISAT around the island during the period of this analysis are shown in Fig. 1.

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Fig. 2. Coastal-ward wind direction measured (dt = 10 min) breezes at B2. Top panel – 30 days; middle panel – first five days of August; bottom panel – 1st of August 2010. The positive direction in the three panels is northward.

3.3. Time series In August 2010, wind records at B2 exhibited a clear wind variability associated with breeze summer conditions (Fig. 2, top). A five day period (1st–5th of August) shows a sinusoidal signal with a 24 hour period of the wind vectors (Fig. 2, middle panel). Land tends to heat and cool faster than the sea surface and consequently a thermal difference arises which generates the breezes across the coastline. The wind flows towards the coast from early in the morning around 8:00 until 20:00 hours whereas the sea is calm. Later, at night, the breeze circulation pattern reverses giving rise to an opposite flow directed from land to the sea. In summer, south-westerly winds (Garb´ı) usually occur in the Western Mediterranean. Garb´ı are moderate winds blowing when high-pressure systems come into Southern Europe and the Mediterranean. Garb´ı alternates with a strong wind from the north or north-west (Tramuntana). These weather conditions can be observed on 13th–14th and 27th–28th, August (Fig. 2, top panel). Coastal-ward wind direction data displayed for August 1st show the behaviour of the breezes during a day (Fig. 2, bottom panel). The positive direction in the three panels is northward. A spectral analysis of the measured wind speed at B2 was performed for a number of records of 4463 (1 month sampled at 10 min) (Fig. 3). The spectrum was estimated averaging 2 adjacent frequency bands, resulting in a frequency bandwidth of 0.0248 cycles per hour (cph). Periods of several hours can be seen in the power spectral density of wind speed in Fig. 3 corresponding to diurnal and semidiurnal fluctuations. A clear 24 hours signal associated with this daily process can be seen which is associated with the breezes. The spectral peaks at 0.042 and 0.083 cph (periods of 24 hours, and 12 hours) are indicated with arrows. The associated wave spectrum from the recorded signal shows similar variability at the 24 hours and 12 hours periods, although this last one may not be as significant as in the wind spectrum due to the lag between the wind and wave generation that causes the 12 hours spectral peak not to develop completely.

Fig. 3. Power spectral density of wind speed and waves buoy measured signal for B2 (August 2010). Arrows indicate spectral components of periods 24, 12 hours the low-frequency peaks are associated with diurnal and semidiurnal fluctuations.

Prediction). The ECMWF atmospheric model incorporates a 4D-VAR assimilation procedure [18]. Forecasts were provided every 6 hours with a horizontal resolution of 25 km until December 2009; from January 2010 it was increased up to 14 km. The vertical structure of the atmosphere is solved by a multi-level hybrid sigma coordinate system [19]. These winds have been interpolated in time to 1 hour to match with the input time step of the WAM [20,21] output wave boundary conditions for the SWAN nested grid. The HIRLAM is a hydrostatic, primitive-equation model which uses a 3D-VAR data assimilation scheme [22]. In the Western Mediterranean, HIRLAM forecasts are supplied by the Spanish Meteorological Agency (AEMET) providing wind fields every 3 hours at 18 km of grid size (low resolution) and 5 km (high resolution) twice a day with a 72 hours horizon [23]. In this configuration, HIRLAM takes the boundary conditions from the ECMWF atmospheric global model. The WRF [24,25] model is a next-generation mesoscale nonhydrostatic numerical weather prediction system designed to serve both operational forecasting and atmospheric research needs. Here, WRF simulations include three two-way nested domains with horizontal grid spacing (Δx = Δy) of 30 km, 6 km and 1.5 km. Domain 1 (coarser mesh) covers the western Europe and North Africa (32.6◦ N to 44.8◦ N, 5◦ W to 8.6◦ E) whereas the nested domains cover the western Mediterranean Sea (36.5◦ N to 42.2◦ N, 0.6◦ W to 5.9◦ E) and the Balearic Sea (38.6◦ N to 40.3◦ N, 1.6◦ W to 4.1◦ E). A total of 47 levels were used in the vertical, half of them in the lowest 1.5 km. The model coarse grid was spun-up and interpolated (using time-dependent boundary conditions) to the boundary of domain 1 from the NCEP reanalysis every 6 h. This configuration provides forecasts with a temporal resolution of 1 hour and 3 hours.

4. Numerical simulations 4.1. Atmospheric models (WRF, ECMWF, HIRLAM) In this study three different forcing wind fields are used: ECMWF (European Center for Medium Weather Forecast), the HIRLAM (High Resolution Limited Area Model) and the WRF (Weather Research and Forecasting) model from NCEP (National Centers for Environmental

4.2. The spectral wave models WAM and SWAN WAM(4.52) and SWAN(40.72) are phase-averaged or thirdgeneration spectral wave models that describe the evolution in time and space of the energy density wave spectrum F(σ ,θ ), as a function of the relative angular frequency σ (=2π f) and wave propagation direction θ [26]. A general form of the energy balance equation in

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where Γ is a steepness dependent coefficient, k is a wave number

Table 1 Physical processes activated for the study. Physical processes

WAM 4.52

SWAN 40.72

Wind input (Sin ) Whitecapping dissipation (Swcap ) Nonlinear interactions (Snl4 quadruplets) Nonlinear interactions (Snl3 triads) Bottom friction dissipation (Sds,b )

Janssen [27–28] Komen et al. [29]

Komen et al. [29] Komen et al. [29]

Hasselmann et al.[30]

Hasselmann et al. [30]

–

Eldeberky [31]

JONSWAP

JONSWAP

and σˆ and kˆ denote a mean frequency and a mean wave number, respectively. According to [28] the value of Γ was estimated by closing the energy balance of the waves in fully developed conditions. This implies that this value depends on the wind input formulation that is used. Since two expressions are used for the wind input in SWAN, also two values for Γ are used. The first expression is due to [29] and the second one is based on [28]. For more details about these formulations can be found in [26]. For continental shelf seas with sandy bottoms, the dominant mechanism appears to be bottom friction [35] which can be expressed as:

Cartesian coordinates can be expressed as,

∂ ∂F ∂ ∂ ∂ + (cθ F ) + (cσ F ) = Stot (cx F ) + (c y F ) + ∂t ∂x ∂y ∂θ ∂σ

(1)

where cx,y, σ ,θ are the wave propagation components in the (x, y, σ , θ ) spaces. Equations such as (1) are known as energy transport equations and their solution requires the specification of appropriate initial and boundary conditions, an appropriate propagation scheme to represent the transport of energy within the computational domain and the specification of the forcing term or source functions. In general, Stot is represented as the summation of a number of the physical processes that can be modelled numerically, describing the development and the dissipation of the modelled waves in time and space: Stot = Swind + Snl + Sds

(2)

where Swind represents the wind input, Snl is the non-linear wave– wave interactions and Sds is the wave energy dissipation. In this study we adopt the wind speed at 10 metres, according to the actual version of the WAM model, based on the quasi-linear model for the sea surface boundary layer from [27,28]. The physical processes (summarized in Table 1) taken into account in the SWAN simulations are wave generation by wind, nonlinear interactions between four spectral wave components, dissipation of wave energy by whitecappingand bottom friction dissipation [21]. Wind input (Swind ). The wave growth due to wind can be described as linear (A) and exponential growth (BE): Sin (σ , θ ) = A + BE (σ , θ )

(3)

in which A and B depend on wave frequency and direction, and wind speed and direction. In SWAN third generation model the linear growth is described by the expression of Cavaleri and MalanotteRizzoli [32]. Whereas the exponential growth by wind is described by [29] and by a second expression of [27,28] which is based on a quasi-linear wind-wave theory. The SWAN wind input adopted in the study was the exponential growth of [29] which is a function of the velocity friction (U* ) and phase celerity (Cph ):    ρa U∗ B = max 0, 0.25 cos (θ − θw ) − 1 σ (4) 28 ρw cph where ρ a and ρ w are density air and water, respectively. Dissipation of wave energy (Sds ). The wave energy dissipation term can be represented by the summation of three physical processes: whitecapping (Sds,w ), bottom friction (Sds,b ) and depth-induced breaking (Sds,br ). The whitecapping activated in the present study is based on [29] formulation. Whitecapping is controlled by the steepness of the waves. The whitecapping formulations are based on a pulse-based model [33], as adapted by the [34]: k Sds,w (σ , θ ) = − σˆ E (σ , θ ) kˆ

(5)

Sds,b = −C b

σ2 g2

2

sinh kd

E (σ , θ )

(6)

where Cb is a bottom friction coefficient. In this study, the empirical JONSWAP model was used with a constant friction coefficient equal to 0.067 m2 s−3 .

4.3. Wave models setup Taking in to account that WAM is adequate for deep water and large spatial scales (also due to being an explicit model), and that the SWAN model in addition accounts for the physical processes that take place in intermediate and shallow waters, two modules are assumed: one for the generation of the waves, where WAM is implemented and a second one based on SWAN for wave transformation. The SWAN model was chosen to forecast the wave in the target area because it employs an implicit solution technique which makes its very efficient in nearshore areas. The two-dimensional spectra computed by the WAM coarse mesh model are saved at grid points which are on the boundary of the SWAN nesting area. These spectra are then interpolated in space and time to the high resolution grid boundaries in such a way that the rescaled spectrum has the same mean frequency, mean wave direction and wave energy as found from a linear interpolation of these mean quantities to the fine mesh grid point. The WAM deep water wave model (coarse grid) required the integration and source functions time steps of 120 seconds. Sea breezes that can occur in short time scales and, having short duration, induce a highly dynamic effect that results in a wave field not having sufficiently time to develop to a fully developed sea state. Some numerical problems arise, when the SWAN model is applied in non-stationary mode with this rapid change of the breezes. In order to avoid this numerical problem the numerical simulations were performed with a small integration time step of 5 minutes to properly resolve (or simulate) the wave dynamic growth. A proper time step is crucial for SWAN being able to catch the effect of fast wind speed temporal changes on the wave field [36]. A coarse WAM wave model encompassing the Mediterranean basin was set to ensure the boundary wave conditions for a SWAN high resolution (dx = 1500 m) nested grid around Mallorca Island (Fig. 1). The WAM model mesh had of 173 × 65 grid points. The SWAN nested grid covering the shallow water around Mallorca Island had 181 × 101 grid points (grid resolution 1500 m). The grids geographical limits and other numerical parameters are compiled in Table 2. Different numerical simulations were performed using the different wind fields available for the wave forecast around the Balearic Islands (Table 2). The spectral energy balance equation was integrated in the range from 0.04177 up to 0.42 Hz for the WAM implementation (Table 3), while for the SWAN model the highest frequency was set up to 1 Hz.

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Table 2 Performed simulations with SWAN model using different wind fields around Mallorca Island.

Atmospheric model

dx = dy [◦ , km]

NCEPWRF(1.5) ECMWF(14)

0.0173◦ , 1.5 km 0.125◦ , 14 km 0.125◦ , 14 km 0.16◦ , 18 km 0.005◦ , 5 km

ECMWF(14)

HIRLAM(18) HIRLAM(5)

Wind input time step [hours]

Wave output time step [hours]

1

1

6

6

6

6

July and August 2009 July and August 2009 August 2010

3

3

August 2010

3

3

August 2010

Period of simulation

Table 3 Numerical parameters of the performed simulations. Parameters

Coarse grid

Nested grid

Third generation wave model versions Integration and source function time steps Spatial resolution (◦ ) (m) Number of points (NGX × NGY) Lowest–highest frequency (Hz) Frequencies Directions Propagation Type of model Latitudes, ◦ N Longitudes, ◦ E Longitudes, ◦ W

WAM 4.52

SWAN 40.72

120 seconds

5 minutes

0.25◦ (25000 m)

0.0125◦ (1500 m)

11245(173 × 65)

18281(181 × 101)

0.04177248–0.42

0.04177248–1

24 25 Spherical Deep water 30;46 37 6

34 36 Spherical Shallow water 39;40.25 1.75;4.0 –

Fig. 4. Time series comparison of the measured (buoy) and modelled (HIRLAM, dx = 18 km) wind speed [ms−1 ] at 10 m above the sea level (top) and SWAN computed (bottom) Hs (m) at B2 at August 2010.

5. Results and discussion 5.1. Validation against measurements: buoys and satellite A SWAN simulation was carried out using the HIRLAM(18) winds for the whole month of August 2010 (the four case in Table 2). A comparison between measured wind speed (U10) and significant wave height (Hs) at B2 against HIRLAM (U10) and the SWAN (Hs), respectively, is given in Fig. 4. The wind speed was corrected to 10 m according the neutral logarithmic profile described in [37]. Some differences associated with omission of the breezes are obtained from the comparisons between measurements (U10 and Hs) and models. The wind speeds reach maximum values during midday hours while the minimum values are observed during the late and early hours which are the typical behaviour associated with the local breeze. HIRLAM wind speed could not reproduce well the variation in each day owing to the spatial and temporal resolution. On average HIRLAM wind speed seems to change slightly earlier than the buoy observations. Consequently, some errors are obtained on the modelled wave parameter (Hs) clearly associated with the inconsistencies on the modelled HIRLAM wind speed (Fig. 4, top). These errors have a direct impact on the computed SWAN Hs along the analyzed period depicted in Fig. 4 (bottom). Additionally, B2 buoy is very near (6 km) of the shore and for land winds SWAN presented no sufficient accuracy. In SWAN model the output points should be at least 4 grid points from an upwind boundary to have reliable outcomes for this wind direction. This is possibly due to inaccuracies in source term-balance for short fetches [36]. In our case B2 is located at 4th grid point from the coast which is the real location of the buoy. The scatter index (SI)-defined as the standard deviation of the

Fig. 5. Time series (buoy-line) and NCEP-WRF-SWAN (dotted) of the wind speed [ms−1 ] at 10 m above the sea level (top) and the measured and hindcasted Hs [m] (bottom) at B1 during July and August 2009.

predicted data with respect to the best-fit line, divided by the mean observations and the best-fit line slope were calculated for August 2010. High scatter index for the Hs (0.4) and low best-fit slope (0.84) are obtained. The measured time series of wind and wave parameters versus hindcasted results are compared for the summer of 2009 at B1 (Fig. 5). As can be seen a good performance of the predicted wave Hs was obtained. High resolution NCEP-WRF data could reproduce the amplitude of the wind speed variation daily. However, some overestimations of the wind speed that induce enhanced Hs values are obtained. Slightly high scatter index for the Hs of 0.35 and reasonable good slope of 0.92 are obtained. Additionally, the performance of SWAN model was assessed by spatial collocation of the ENVISAT measured Hs against those obtained with SWAN (July and August 2009). From the analysis of the scatter plots obtained (Figs. 6 and 7) it can be seen that both atmospheric models produced similar statistical results for the Hs (WRF: slope = 0.82; si = 0.18; cc = 0.92; ECMWF: slope = 0.83; si = 0.16; cc = 0.93). It is necessary to point out that the statistical parameters resulted slightly better for the SWAN-ECMWF despite the fact that this wind field has coarser time and temporal resolutions. However,

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Fig. 8. Hourly modelled WRF breezes wind directions (top) and the SWAN mean wave propagation (bottom) directions for 26–29th of July 2009 for B2.

Fig. 6. Scatter plot after the collocation ENVISAT–NCEP-WRF(1.5 km)-SWAN for the Hs (m) for July and August 2009.

Fig. 9. Hourly WRF breezes wind directions and the SWAN mean wave propagation directions for 26th–29th of July 2009 at B3.

Fig. 7. Scatter plot after the collocation ENVISAT–ECMWF(14)-SWAN for the Hs (m) for July and August 2009.

due to the fact that WRF(1.5) is available at higher spatial and temporal resolutions we decided to perform the analysis below by forcing the SWAN model with WRF. In addition, [38] and [39] have shown that WRF model is suitable for forecasting the generation of wind waves in the Mediterranean. Therefore, here the high resolution WRF wind fields were used to study the effect of the sea breezes around Mallorca. 5.2. Influence of the marine breeze on the hindcasted wave field A four days period (26–29th of July 2009) was chosen for the analysis of the impact of the modelled breezes (WRF) on the SWAN

computed wave field. The wind and wave propagation direction vectors are shown at B2 and B3 (Figs. 8 and 9, respectively). As seen in Fig. 8, the fluctuation of the wind vectors (breezes) at B2 is in accordance with the previous measured wind during the summer of 2010 (Fig. 2). The effect of the breezes on the wave field does not have an immediate response and appears to be delayed. However, in Alcudia Bay (B3) the predicted wave direction seems to be less affected (Fig. 9, bottom panel) due to the fact that for the 28th and 29th the sea breeze had a shorter duration and was less intense than on the case of the 26th and 27th of July 2009 (Fig. 9, top panel). In order to analyze spatially the performance of the models in simulating the classical breezes of Mallorca as described in [9] (sea breezes with wind speeds of 5–7 m/s blowing from the sea towards to the land in both Bays of Palma and Alcudia as represented in Fig. 1), a spatial evolution analysis of the hourly WRF atmospheric model winds during 26th of July 2009 is given starting from 11 UTC (Fig. 10). During the first hours of 26th (from the 00 UTC up to 8 UTC) a gentle land breeze was observed in Palma Bay with wind speeds of about 5.5 m/s (not shown). The highest U10 values were observed to the NW of the Island, keeping almost stationary during the next five hours. The sea breezes started around 10–11 UTC when the wind turned from the sea to the land, and developed until approximately 20 UTC (Fig.

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Fig. 12. WRF sea breezes around Mallorca for 26th of July at 15 UTC (left) and 19 UTC (right) UTC, respectively.

Fig. 10. Hourly WRF wind fields (wind speed [ms−1 ]) for 26th of July 2009 around Mallorca Island.

Fig. 13. SWAN Hs [m] field around Mallorca for 26th of July at 15 UTC (left) and 19 UTC (right) UTC, respectively.

Fig. 11. Hourly SWAN-WRF(1.5 km) Hs [m] maps for 26th of July, 2009 (arrows – the wave propagation directions).

10). Hourly evolution of the breezes for 26th of July represented by WRF model and their associated predicted wave field are depicted in Figs. 10 and 11, respectively. At 12 UTC the sea breeze wind speed was around 9.2 m/s (from the NE) in Alcudia, whereas in Palma Bay around 6 m/s (from the S–SW). These breeze conditions induced a sea state in Alcudia with a Hs of 0.65 m propagating from the NE (Fig. 11). At Palma Bay the calm persisted. Sea breezes can be distinguished around the Island at 13 UTC; a similar situation can be observed at 12 UTC with a wind speed maximum to NW of Mallorca, nearby Cabrera island and also in Alcudia Bay (Fig. 10). At 15 UTC the sea breezes develop and the wind speed reaches the maximum value of about 7–9 m/s in both bays. From the WRF winds it was observed that the sea breeze at Alcudia seems to be stronger (9 m/s) than in Palma Bay (Fig. 10). From the Hs wave field of 26th of July at 15 UTC (Fig. 11), it can be seen that the maxima values are directly correlated with the breezes to the SE and NW of Mallorca (Fig. 10). However, low values of the Hs were predicted inside of Palma Bay (0.4 m) (Fig. 11). Modelled breezes using WRF high resolution (dx = dy = 1.5 km) wind appear to show that sea breeze variability is not always reflected in the hindcasted wave field for wind speeds lower than 7.5 m/s (Figs. 12 and 13). When the breezes develop to the east side of the Palma Bay (U10 about 7–8 m/s), low Hs values (around 50 cm) are predicted in Palma Bay (e.g. at 15 UTC, July 26th 2009) (Fig. 13). At Alcudia Bay a higher Hs of around 0.9 m can be seen to be the result of the

Fig. 14. Hourly SWAN-WRF winds wave 1d variance densities (VaDen in [m2 Hz−1 ]) spectra for 26th of July 2009 at B2 as a function of the frequencies (Freq. [Hz]).

breezes (U10 higher than 7.5 m/s). Besides, additional wave energy contribution can be observed propagating from the east boundary. 5.3. Influence of the sea breeze on the hindcasted wave spectra In order to further investigate the implications of the modelled WRF breezes on the hindcasted wave spectrum, the hourly evolution of the 1D spectra estimated with the SWAN model for 26th of July 2009 at B2 is shown in Fig. 14. The higher frequencies in the wave spectrum are considered (higher than 0.2 Hz and up to 1 Hz) for the analysis. In summer, the Balearic Sea is mainly dominated by wind sea generated by the local wind. Two peaked spectra of relatively low

S. Ponce de Le´ on, A. Orfila / Applied Ocean Research 40 (2013) 26–34

Fig. 15. SWAN source functions [m2 ] during the sea breezes of 26th of July 2009 at B2 (Swind – dashed line; Swcap – dashdot; Sfric – circle; Ssurf – plus; Snl3 – triangle; Snl 4 – squares; Freq = frequencies [Hz]).

energy can be observed at 11 and 12 UTC (Fig. 14), one of the peaks distributed at the high frequency part at 0.7 Hz (associated with the sea breeze) and the other peak at 0.2 Hz. It seems that at 11 UTC the see breeze circulation in Palma Bay is not yet fully developed as shown in [9] using radiosonde ascent data. At 13 UTC the energy excess starts to redistribute towards lower frequencies. At 14 UTC, the absolute spectral peak is distributed in the low frequency part at 0.4 Hz; however the wave energy level is still low. From 14 UTC and until the end of the selected period of the analysis (26th of July at 22 UTC) a clear one peaked spectrum is established.

5.4. The source terms To facilitate the analysis from the physical point of view the source terms (SF) of Section 4.2 are represented at location B2 for the 26th of July 2009 (Fig. 15). The evolution of SF for the same dates as shown in Fig. 14 allows to infer that the high frequency secondary peak represents the beginning of the sea breeze at Palma Bay. The wave growth by the energy input of the wind (Swin ) at 11 UTC has a relative importance in the spectral balance in agreement with the beginning of the breeze, whereas bottom friction dissipation (Sfric ) seems to play a noticeable role in the spectral low frequencies part (left first panel). As can be seen, at 11 and 12 UTC of 26th of July, the source term balance is dominated by the Sfric (at low frequencies) and by the Snl4 (at high frequencies). Later, when the sea breeze is strong (at 12 UTC and 13 UTC), Swind and Sfric play a similar minor role in the spectral domain. At 14 UTC, the nonlinear interactions Snl start to play a major role in the redistribution of the wave energy towards the low frequencies (Fig. 15), inducing a single peak spectral shape. At the same time Swind is the strongest process and Sfric has a minor role in low frequencies. At 15 UTC, when the breezes are developed, a single peak wave spectrum centred at 0.4 Hz is observed as the result of the role of the Snl and Swind in the spectral balance. Snl becomes strong enough with time from 16 UTC up to 21 UTC, while whitecapping dissipation (Swcap ) is less important than Swind . Later, at 17 UTC, the breeze is weak (6.6 m/s in Palma Bay), despite Swind still having a wave energy redistribution role at high frequencies, as well as Snl and Swcap . Finally, at 21 UTC, the Swind is weak enough and all the other physical processes determine the shape of the wave spectrum.

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Fig. 16. Computed SWAN one-dimensional wave spectra at B2 using the ECMWF(14) (solid line) and WRF(1.5) (dashed dot) during the breezes time of four days (26–29th of July 2009).

5.5. Sensitivity of a wave forecast to the wind input under breezes conditions Depending of the wind field chosen in a wave forecast under breezes situation, the effect on the forecasted wave field will be different obviously because the wind energy input will have implicit breezes information (or not) which will influence the different physical processes involved in the spectral energy balance. Considering that breezes can be observed from May up to November in Mallorca (more than 6 months [9], this mismatch in the low spatial and temporal resolutions could be led to significant deviations from the real wave height values. To assess the influence of the marine breezes on the hindcasted wave field a comparison of the SWAN estimated wave spectra was done using the ECMWF(14) (solid line) and WRF(1.5) (dashed line) winds that are the forecast data used for the operational purposes. The importance of the correct representation of the breezes to obtain a realistic wave spectra forecast under this local condition is shown in Fig. 16. SWAN one dimensional spectra obtained using both wind fields (ECMWF and WRF) are rarely coincident. It seems that occasionally the ECMWF wind reproduces the breeze conditions at high frequencies as can be seen at the spectra dated 26th July at 06 and 12 UTC (Fig. 16). From Fig. 16 it can be seen that the accuracy of the simulated wave height varies when using NCEP-WRF-SWAN and ECMWF-SWAN. The main reason of this is the temporal resolution of the wind data which on the case of NCEP-WRF is 1 hour and on the case of ECMWF is 6 hours, the hourly wind data allow for better representation of the breezes. Also, NCEP-WRF winds have a higher spatial resolution (1.5 km). 6. Conclusions A spectral wave model (SWAN) was applied to assess the impact of the sea breezes on the hindcasted wave field in the Balearic Islands. A modification of the hindcasted wave propagation direction was observed for wind speeds (breezes) higher than 7.5 m/s and consequently may affect the coastal wave forecast in the summer period. The main characteristics of the sea breeze circulation and its effects on the wave field were analyzed around Mallorca using the WRF winds. The attention was focused on the two opposite bays located to the north (Alcudia) and south (Palma). From the analysis, it seems that

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the WRF sea breezes in Alcudia Bay are more intense with a longer daily duration than in Palma Bay with the consequent modification of the waves (also described in [9]), which allows to infer that the WRF wind fields seem to satisfactorily represent the local land-sea breezes around the Mallorca Island as was described by [9]. This fact reveals that WRF winds could be useful for a correct predictability of the presence and impact of the sea breeze leading to a more realistic sea state prediction for operational wave forecasts around Mallorca Island. Contrarily, ECMWF wind fields do not represent with sufficient accuracy of the breezes as was shown in this study, seemingly due to the coarser resolutions in time (6 hourly) and in space (12 km). The fact that B1 and B2 locations are near shore (location B1 (Dragonera) is located at 20 km offshore and B2 (Enderrocat) is at only 6 km offshore) allows concluding that some interference from land is present in the comparison performed between ENVISAT altimeter Hs against Hs SWAN. Previous work pointed out that if buoys are too close to shore, altimeter overpasses will generally occur seaward of the buoy location, thus sampling higher wave conditions [40]. Furthermore, the collocation between the Hs from ENVISAT and from SWAN is affected because the satellite altimeter data are far from where the breezes occur, near the shore. Looking at Fig. 10 it can be seen that only a few ENVISAT track points are in the breeze zones (nearshore) and from the NCEP-WRF-SWAN Hs maps (Fig. 13) we can see that the direct effect of the breeze on the wave field is at those breeze zones where satellite data is not available (Fig. 1). The results of the present work show that for obtaining an accurate forecast of breeze generated wave conditions some problems still remain. Despite NCEP-WRF having high quality and temporal and spatial resolutions for the wave forecasts around small islands, it seems that some problems exist related with the local orography. In the future, to improve the wave forecast we are planning to introduce data assimilation from remote sensing sources. Acknowledgements The authors are thankful to Gerbrant Van Vledder (Delft University of Technology) for his comments on our manuscript. We also thank Guillermo Vizoso for bringing the breeze phenomena in Mallorca initially into our attention. We thank Lionel Renault who supplied the WRF wind field for July–August 2009. The authors would like to thank the Port Authority of Spain for providing the buoy data at Dragonera, to ECMWF for the wind fields and to AEMET for the HIRLAM wind. We thank the anonymous reviewers for their comments and suggestions that helped to improve the manuscript. A. Orfila would like to thank financial support from MICINN through project CTM201016915/MAR. References [1] Pav´ıa E, Reyes S. Variaciones espaciales y estacionales del viento superficial en la Bah´ıa de Todos Santos, B.C. (in Spanish). Ciencias Marinas. 1983;9(1):151–167. [2] Delgado OE, Ocampo-Torres FJ, Larios Castillo S. Breezes during some months of spring and summer in the northwest of the Gulf of California. Ciencias Marinas. 1994;20(3):421–440. [3] Fosberg MA, Schroeder MS. Marine air penetration in Central California. Journal of Applied Meteorology. 1996;5:573–589. [4] Masselink G, Pattiaratchi CB. The effect of sea breeze on beach morphology, surf zone hydrodynamics and sediment resuspension. Marine Geology. 1998;146:115–135. [5] Sonu CJ, James WR. A Markov model for beach profile changes. Journal of Geophysical Research. 1973;78:1462–1471. [6] Papanastasiou DK, Melas D, Lissaridis I. Study of wind field under sea breeze conditions; an application of WRF model. Atmospheric Research. 2010;98:102– 117. [7] Federico S, Pasqueloni L, De Leo L, Belleci C. A study of the breeze circulation during summer and fall 2008 in Calabria, Italy. Atmospheric Research. 2010;97(1– 2):1–13. [8] Jansa´ JM, Jaume E. The sea-breeze regime in the Mallorca Island (in Spanish). Revista de Geofisica. 1946;19:304–328.

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